*3.3. Overall Utility Based Metrics*

Overall utility based metrics again do not consider fairness among objectives, but rather strive to get the best overall utility from a final solution. Here, no guarantees are made towards any single objective, and one objective could be much worse than any other objective with the selected solution. However, the solution is guaranteed to yield the highest overall utility across the society.

## 3.3.1. Utilitarian Social Welfare

The utilitarian social welfare metric is one of the most simple notions of social welfare, which ranks solutions based on the sum of individual normalized cost values of objectives. The metrics are defined in Equation (10).

$$f\_{ll}(\mathbb{C}) = \sum\_{i=1}^{n} q\_{t\_i, \mathbb{C}}^{\prime} \tag{10}$$

From Equation (10), we see that the utilitarian social welfare metric prefers a solution *C* over solution *C* if and only if ∑*n i*=1 *q ti*,*C* < ∑*n i*=1 *q ti*,*C* .

#### 3.3.2. Nash Product

The Nash product social welfare metric combines the features of the utilitarian and the egalitarian social welfare metrics. This notion of social welfare seeks to achieve the best combined cost value across the society of objectives while working to reduced inequality among objectives. Its definition is found in Equation (11).

$$f\_N(\mathbb{C}) = \prod\_{i=1}^n q'\_{t\_i, \mathbb{C}} \tag{11}$$

The Nash product social welfare metric ranks solutions based on the product of individual normalized cost values of objectives. Hence, the Nash product social welfare metric prefers a solution *C* over a solution *C* if and only if ∏*n i*=1 *q ti*,*C* < ∏*n i*=1 *q ti*,*C* .

The Nash product metric maximizes society wellbeing by minimizing the combined product of the normalized cost values in a particular solution. Adherence to fairness comes from the fact that the contribution from high normalized cost values contributes proportionally The Nash product social welfare metric is meaningful for cost value vectors without zero value elements. If zero elements are present, only the zero element considered as the Nash product will yield zero regardless of the other values. To account for this fact, we modified the Nash product social welfare metric according to Equation (11), where we added the same non-zero value to all vector elements. This way, we never end up in a zero product situation.

$$f\_N(\mathbb{C}) = \prod\_{i=1}^n (q\_{t\_i; \mathbb{C}}^\prime + r) \quad [r \in Z^+] \tag{12}$$


*3.1.2 Relationship between the cohesion increment and the strength-stress ratio and plant span*

According to the 29 underground plants in **Table 2**, the cohesion increment Δ*Cb* of the surrounding rock is fitted to the plant span *B* and the strength-stress ratio *Kσ* by least squares surface fitting, and the equation is as follows:

$$(\Delta \text{C}\_{\text{b}}) = 0.01481(2K\_{\sigma}{}^{-2} + 0.405)B \tag{5}$$

#### **Table 2.**

*Relevant data of the powerhouse and calculation of the cohesion incrementally reinforced by the anchor bar.*

In **Figure 6**, the cohesion increment provided by the anchor is approximately linearly related to plant span *B*, which increases with an increase in plant span. In addition, the cohesion increment Δ*Cb* and strength-stress ratio still show 2 times nonlinearity.

### **3.2 Incremental cohesion of the surrounding rock for anchor cable reinforcement**

The anchor cable support parameters for 12 large and medium-sized hydropower plants are shown in **Table 3**, and the cohesion increment in the surrounding rock is calculated by Eq. (3), where *η* = 3.5.


**3. Geometric relations**

each point in one image, in homogeneous coordinates, to a ray in Euclidean threedimensional space. Secondly, SfM has to estimate the projection matrices *P* for the

*Visual representation from [2]. It depicts the challenge of converting a set of 4 pictures into a 3D sketch featuring the line segments and camera axis. The 4 cameras are represented as three axis reference frame in red.*

where **x** is a 2D point on the image, and **X** its projection in 3D space. **K** is intrisic to each camera, while **P** is extrinsic and embeds the 3D translation and rotation of

A common space can be built to host the cameras and spatial lines. For this new common space the camera that took the first processed picture takes the place of the origin, and for the rest of cameras **P** can be estimated from the lines matched between the captured images. Alternatively, camera poses can also be retrieved from a feature-point based SfM pipeline and these cameras be employed for the estimation of spatial lines. For instance, the feature-point descriptor SIFT [5] can be used to match points in images with a low ratio of outliers. These feature point relations are obtained both in the foreground and background. A set of relations between points or lines in two images allows to estimate the homography constraints between both views by applying the 5-point algorithm [12] using the points

the camera's image plane. The estimated translation is valid up to scale.

or the segment endpoints. A purge of outliers can be performed employing RANSAC [13] for robust estimation. Therefore, a set of stereo 3D projections is obtained combining the available images pairwisely, and each stereo system featuring both camera poses and a point cloud. The objective is to obtain an unique 3D point cloud sketch, embedding all cameras and point matches. Hence, camera poses are sequentially stacked, relative to each other, in the new spatial reference frame. And the 3D estimations for the feature points in the new 3D space can be computed as the center of gravity for their position relative to the common camera in both stereo systems. Finally a sparse bundle adjustment [14] is used to minimize the pixel distance of the back-projected 3D point and the original observation of this point on each image in homogeneous coordinates. These reprojection errors on the planes of the cameras are minimized employing the Levenberg-Marquardt algorithm. The resulting keypoint-based 3D reconstruction contains the optimized 3D

Several straight segment matching methods are based on texture descriptors [15, 16], coloring [17] or in keypoint-line projective invariants [18, 19]. Under these conditions, matching results will be influenced by the level of texture in the images.

In the case that a low number of detected segments can be distinguished by

**x** ¼ **PX**, (1)

cameras, representing a map from 3D to 2D:

*Applications of Pattern Recognition*

**Figure 1.**

**46**

estimations for the cameras and the point cloud.

A *3D abstraction method* estimates the position of 3D line segments Γ = {Γ1, Γ2, Γ3, ..., Γ*N*}, from an unordered sequence of images, taking from cameras with planes ϒ = {ϒ1 ,ϒ2 ,ϒ3 ,...,ϒ*M*}. Straight lines are detected in the original images, put in correspondence among them, forward projected into space, and rewritten in homogeneous coordinates.

The 3D line based sketch {ϒ,Γ} is built from the knowledge of correspondences among line projections *l* on camera planes, and the intrinsics of all the cameras. The following paragraphs explain the linear triangulation of these observations, as performed from scale-space images. This allows to discriminate and weight down lines that have been detected on two or more scales with a different slope. The practical consequence is that prior to any 3D extrapolation of the observed lines, matching inliers with inconsistent endpoint location among scales on both images can be avoided, as these lines might introduce uncertainty in the estimation for the pose of the camera.

The camera poses **P** are estimated from the endpoint correspondences of *l*. The Essential matrix **E** is computed from the camera pairs, by using the Five-Point Algorithm [12], and RANSAC [13] for hypotheses generation. Having **E** and *l*, the relative camera rotation and translation among the first pair of cameras *Pj* ¼ ½ � **R**j**t** are estimated using cheirality check and discarding the triangulated endpoints that are not in front of the cameras. The left camera is chosen to have the pose *P*1 ¼ ½ � **I**j0 , and the newly added cameras are stacked from this position in the unique reference frame.

The forward projection of lines in 3-space is described in the page 196 of Hartley and Zisserman's book [20]. The 3D forward projection **Γi** of a line, bundled in the same reference frame, can be obtained using the *DLT* method on the set of stereo 3D camera back-projections. This is performed in homogeneous coordinates because it allows to consider line endpoints in the infinite. Therefore, from now on, when a 2D point is mentioned it will be supposed homogeneous coordinates. There exists a 3 � 3 matrix **E**, known as the essential matrix, such that if *u* and *u*0 are a pair of matched points, then *u*0 **E***u* ¼ 0. If a sufficient number of matched points are known, the matrix **E** may be computed as the solution of an overdetermined set of linear equations. For the present problem, the internal calibration of the cameras is known, therefore it is possible to determine from **E** the relative placement of the cameras and hence the relative locations of the 3D points corresponding to the matched points. A linear triangulation method is projective-invariant because only camera and line distances are minimized.

The above described DLT method for lines starts with the segments on the pair of cameras ϒ*a*, ϒ*b* with the highest inlier ratio. Based on this first triangulation, the other cameras are appended to the 3D abstraction: The next camera ϒ*c* is chosen according to the higher inlier ratio of line matching with ϒ*a* and ϒ*b*. Analogously, the following camera ϒ*n* is picked among the ones with the higher inlier ratio of line matching with previously selected cameras. The detection of 2D lines *l* in the original images carry an uncertainty for the position of these observations. This uncertainty implies that no 3D point *X* will satisfy that their projections on cameras ϒ1 and ϒ2 are *x***1** ¼ *P*1 *X*, *x***2** ¼ *P*2 *X* respectively. Moreover, the image points do not satisfy the epipolar constraint *x***2***Fx***1** ¼ 0. Therefore, a method that only minimizes the distances on the image from the estimations to the observations is required: A projective-invariant triangulation method. A linear triangulation [20] method does not depend on the projective frame in which *X* is defined.

The forward projection from a normalized 2D line observed on the camera image plane *m*, denoted by *l m i* , is the plane *PmTl m i* , so the condition for a point *Xa* to be in this plane is:

$$\left(I\_i^m\right)^T \mathbf{P}\_m \mathbf{X}\_a = \mathbf{0}.\tag{2}$$

*xm p***3***T m Xj*,*E* � � � *p***1***T*

*ym p*3*T*

*xm p*2*T*

where *xm*, *ym*

coordinates.

represented as *l* = {*l*

� � and *xn*, *yn*

*Build 3D Abstractions with Wireframes DOI: http://dx.doi.org/10.5772/intechopen.96141*

equation of the form *AX j*,*E* ¼ 0. Solving:

mapping to a 3D line **Γ***j* via *Pm*, is the plane *Pm***Γ***j*.

1 1, *l* 1 2, ..., *l* 1 *N*, ..., *l M*

estimations for each 3D line [21].

camera plane ϒ *j* are the spatial points T *j*

intersections by forward projecting T *j*

**49**

routine with the endpoints of *l*. The correspondences in T *j*

*m X j*,*E* � � � *p*2*T*

*m X j*,*E*

*A* ¼

The result of the linear triangulation process is **Γi** and *uj*

� � � *ym p*1*TX j*,*E*

� � are the coordinates of *xm*

*xmp*3*T*

*ymp*3*T*

*xnp*3*T*

*ynp*3*T*

*m* � *pm*

*m* � *p*2*T m*

*n* � *p*1*T n*

*n* � *p*2*T n*

The solution for the 4 equations of the over-determined problem (four equations for four homogeneous variables) is only valid up to scale. The set of points in space

Every 3D segment Γ*i* is estimated as the center of gravity of the estimations for the same line for each par of images. The set of line projections observed in ϒ is

projections from *l* of the same 3D line Γ*i*. The Line Features are noted as *L* = {*L*1, *L*2, ..., *LN*}. The 3D lines Γ are obtained by forward projecting the endpoints of *l* from pairs of camera planes of ϒ, by using linear triangulation, analogously to Direct Linear Transformation (*DLT*) [20]. The cameras ϒ are sequentially bundled in the same reference frame. The new ones are stacked according to the *L*-to-Γ correspondences, computed in the previous stereo pair of cameras. The merged estimations for 3D lines {Γ*i*} are computed as the center of gravity of the spatial lines. The 3D sketch {ϒ,Γ} generated by linear triangulation is used as input for an optimization algorithm. The least-squares optimization named Sparse Bundle Adjustment (SBA) [14] is based on the Levenberg–Marquardt algorithm, and uses as input the estimated camera extrinsics ϒ and the set Γ, now containing unique

The 3D estimations for lines and cameras are drawn in the same spatial sketch, altogether with the cameras. Next, these spatial line segments Γ are fit to different different planes P. Γ is therefore segmented into different groups according to the planes P, and so is done with their projections *L*. The group of Line Features fitted to the plane P*t* is noted as *Ft*. The intersections of the coplanar lines *Ft* on the

the original images, now known which line segments are coplanar. The intersections of these coplanar lines on the images are described similarly as a feature point. Following this analogy, the descriptor for this feature point will be the pair of two coplanar lines drawing it. We have the correspondences of the straight lines accross images, so we can extrapolate these correspondences to their intersection for the cases where they are coplanar. Secondly, known the correspondences between these intersections, they can be triangulated analogously as it was performed in the first

linear triangulation algorithm, in order to create initial estimates for the 3D

1*T*

is the *r*-th row of *Pm*. It can be decomposed similarly for *Pn*, and compose the

*m Xj*,*E*

*m X j*,*E*

� � ¼ 0, (4)

� � ¼ 0, (5)

*j*,*E* and *xn*

*N* }. A Line Feature is defined as a subgroup of

*t* . Therefore, the algorithm can go back to

*t* . The set of estimations for the 3D points

*t* are then fed into the

� � ¼ 0 (6)

*:* (7)

, represented in cartesian

*j*,*E* respectively. *prT*

*m*

Each point *Xa* returns a linear equation in the entries of *Pm*. Denoting by *xi m*,*E* and *xi m*,*F* the forward projection of the endpoints of *l i m*, named *Xi E* and *Xi F*, under *Pm*, then any other 3D point on the line *Xi* ð Þ¼ *μ Xi E* þ *μXi F* projects to a point:

$$\mathbf{x}\_{i}^{m}(\mu) = \mathbf{P}\_{m}(\mathbf{X}\_{i,E} + \mu \mathbf{X}\_{i,F}) = \mathbf{x}\_{i,E}^{m} + \mu \mathbf{x}\_{i,F}^{m},\tag{3}$$

which is on the line segment *l m i* .

In the described method, an unique reference frame is built. The world reference system is fixed onto the first camera, hence its camera matrix, *PE*, is computed with *RE* ¼ *I* and *TE* ¼ **0**. The extrinsics for the partner camera *Pm* on the baseline is obtained from the essential matrix by using RANSAC. Before the subsequent DLT triangulations with a new camera, its extrinsics are estimated also by RANSAC from the 2D-3D results of the already computed DLT. From here, new cameras will be added incrementally, just one per DLT iteration, in order to avoid DLTs between two uninitialized camera projection matrices.

For DLT it is required a set of observed line correspondences, *l m j* to *l n j*, matched among images. The projection on the image plane of camera *m* of an endpoint *Xi*,*E* of the spatial line **Γ***j* is denoted as *xm j*,*E* ¼ *PmX j*,*E*. This point on the *m*-th camera plane is matched to its counterpart on the *n*-th camera *xn j*,*E* ¼ *PnX j*,*E*. Both equations can be combined into *AX j*,*E* ¼ 0, where **A** is the matrix of equation coefficients. It is built from the matrix rows *Ar* contributed from each correspondence, whose resemble the movement of each line between both views. *Xj*,*E* contains the unknowns for the endpoint position.

By using the cross product on the *m*-th camera: *l m j* � *PmX j*,*E* ¼ 0, *Build 3D Abstractions with Wireframes DOI: http://dx.doi.org/10.5772/intechopen.96141*

of matched points, then *u*0

*Applications of Pattern Recognition*

ϒ1 and ϒ2 are *x***1** ¼ *P*1

image plane *m*, denoted by *l*

be in this plane is:

*xi*

**48**

*m*,*E* and *xi*

a point:

camera and line distances are minimized.

*X*, *x***2** ¼ *P*2

does not depend on the projective frame in which *X* is defined.

*m*

under *Pm*, then any other 3D point on the line *Xi*

*xm*

two uninitialized camera projection matrices.

of the spatial line **Γ***j* is denoted as *xm*

unknowns for the endpoint position.

which is on the line segment *l*

**E***u* ¼ 0. If a sufficient number of matched points are

*X* respectively. Moreover, the image points do not

*i* , so the condition for a point *Xa* to

*PmXa* ¼ 0*:* (2)

*E* þ *μXi*

*m*, named *Xi*

*E* and *Xi F*,

*F* projects to

*i*,*F*, (3)

*m j* to *l n*

*j*,*E* ¼ *PnX j*,*E*. Both equa-

*j*, matched

*i*

ð Þ¼ *μ Xi*

*i*,*E* þ *μxm*

*j*,*E* ¼ *PmX j*,*E*. This point on the *m*-th camera

*j* � *PmX j*,*E*

¼ 0,

*m*

known, the matrix **E** may be computed as the solution of an overdetermined set of linear equations. For the present problem, the internal calibration of the cameras is known, therefore it is possible to determine from **E** the relative placement of the cameras and hence the relative locations of the 3D points corresponding to the matched points. A linear triangulation method is projective-invariant because only

The above described DLT method for lines starts with the segments on the pair of cameras ϒ*a*, ϒ*b* with the highest inlier ratio. Based on this first triangulation, the other cameras are appended to the 3D abstraction: The next camera ϒ*c* is chosen according to the higher inlier ratio of line matching with ϒ*a* and ϒ*b*. Analogously, the following camera ϒ*n* is picked among the ones with the higher inlier ratio of line matching with previously selected cameras. The detection of 2D lines *l* in the original images carry an uncertainty for the position of these observations. This uncertainty implies that no 3D point *X* will satisfy that their projections on cameras

satisfy the epipolar constraint *x***2***Fx***1** ¼ 0. Therefore, a method that only minimizes the distances on the image from the estimations to the observations is required: A projective-invariant triangulation method. A linear triangulation [20] method

The forward projection from a normalized 2D line observed on the camera

Each point *Xa* returns a linear equation in the entries of *Pm*. Denoting by

*i* ð Þ¼ *μ Pm*ð Þ¼ *Xi*,*E* þ *μXi*,*F xm*

In the described method, an unique reference frame is built. The world reference system is fixed onto the first camera, hence its camera matrix, *PE*, is computed with *RE* ¼ *I* and *TE* ¼ **0**. The extrinsics for the partner camera *Pm* on the baseline is obtained from the essential matrix by using RANSAC. Before the subsequent DLT triangulations with a new camera, its extrinsics are estimated also by RANSAC from the 2D-3D results of the already computed DLT. From here, new cameras will be added incrementally, just one per DLT iteration, in order to avoid DLTs between

*m*

*i* , is the plane *PmTl*

*l m i T*

*m*,*F* the forward projection of the endpoints of *l*

*m i* .

For DLT it is required a set of observed line correspondences, *l*

plane is matched to its counterpart on the *n*-th camera *xn*

By using the cross product on the *m*-th camera: *l*

among images. The projection on the image plane of camera *m* of an endpoint *Xi*,*E*

tions can be combined into *AX j*,*E* ¼ 0, where **A** is the matrix of equation coefficients. It is built from the matrix rows *Ar* contributed from each correspondence, whose resemble the movement of each line between both views. *Xj*,*E* contains the

$$
\lambda \pi\_m \left( p\_m^{3T} \mathbf{X}\_{j,E} \right) - \left( p\_m^{1T} \mathbf{X}\_{j,E} \right) = 0,\tag{4}
$$

$$\mathcal{y}\_m(\mathbf{p}\_m^{\text{3T}}\mathbf{X}\_{\cdot j,E}) - \left(\mathbf{p}\_m^{\text{2T}}\mathbf{X}\_{\cdot j,E}\right) = \mathbf{0},\tag{5}$$

$$\times\_m \left( \mathbf{p}\_m^{2T} \mathbf{X}\_{j,E} \right) - \jmath\_m \left( \mathbf{p}^{1T} \mathbf{X}\_{j,E} \right) = \mathbf{0} \tag{6}$$

where *xm*, *ym* � � and *xn*, *yn* � � are the coordinates of *xm j*,*E* and *xn j*,*E* respectively. *prT m* is the *r*-th row of *Pm*. It can be decomposed similarly for *Pn*, and compose the equation of the form *AX j*,*E* ¼ 0. Solving:

$$\mathbf{A} = \begin{bmatrix} \boldsymbol{\kappa}\_{m} \mathbf{p}\_{m}^{3T} - \mathbf{p}\_{m} \mathbf{}^{1T} \\\\ \boldsymbol{\chi}\_{m} \mathbf{p}\_{m}^{3T} - \mathbf{p}\_{m}^{2T} \\\\ \boldsymbol{\kappa}\_{n} \mathbf{p}\_{n}^{3T} - \mathbf{p}\_{n}^{1T} \\\\ \boldsymbol{\chi}\_{n} \mathbf{p}\_{n}^{3T} - \mathbf{p}\_{n}^{2T} \end{bmatrix}. \tag{7}$$

The solution for the 4 equations of the over-determined problem (four equations for four homogeneous variables) is only valid up to scale. The set of points in space mapping to a 3D line **Γ***j* via *Pm*, is the plane *Pm***Γ***j*.

The result of the linear triangulation process is **Γi** and *uj* , represented in cartesian coordinates.

Every 3D segment Γ*i* is estimated as the center of gravity of the estimations for the same line for each par of images. The set of line projections observed in ϒ is represented as *l* = {*l* 1 1, *l* 1 2, ..., *l* 1 *N*, ..., *l M N* }. A Line Feature is defined as a subgroup of projections from *l* of the same 3D line Γ*i*. The Line Features are noted as *L* = {*L*1, *L*2, ..., *LN*}. The 3D lines Γ are obtained by forward projecting the endpoints of *l* from pairs of camera planes of ϒ, by using linear triangulation, analogously to Direct Linear Transformation (*DLT*) [20]. The cameras ϒ are sequentially bundled in the same reference frame. The new ones are stacked according to the *L*-to-Γ correspondences, computed in the previous stereo pair of cameras. The merged estimations for 3D lines {Γ*i*} are computed as the center of gravity of the spatial lines.

The 3D sketch {ϒ,Γ} generated by linear triangulation is used as input for an optimization algorithm. The least-squares optimization named Sparse Bundle Adjustment (SBA) [14] is based on the Levenberg–Marquardt algorithm, and uses as input the estimated camera extrinsics ϒ and the set Γ, now containing unique estimations for each 3D line [21].

The 3D estimations for lines and cameras are drawn in the same spatial sketch, altogether with the cameras. Next, these spatial line segments Γ are fit to different different planes P. Γ is therefore segmented into different groups according to the planes P, and so is done with their projections *L*. The group of Line Features fitted to the plane P*t* is noted as *Ft*. The intersections of the coplanar lines *Ft* on the camera plane ϒ *j* are the spatial points T *j t* . Therefore, the algorithm can go back to the original images, now known which line segments are coplanar. The intersections of these coplanar lines on the images are described similarly as a feature point. Following this analogy, the descriptor for this feature point will be the pair of two coplanar lines drawing it. We have the correspondences of the straight lines accross images, so we can extrapolate these correspondences to their intersection for the cases where they are coplanar. Secondly, known the correspondences between these intersections, they can be triangulated analogously as it was performed in the first routine with the endpoints of *l*. The correspondences in T *j t* are then fed into the linear triangulation algorithm, in order to create initial estimates for the 3D intersections by forward projecting T *j t* . The set of estimations for the 3D points

resembling the intersections is a sparse cloud, and it is denoted as R. Finally, and same as with the endpoints, the 3D intersections R enter the least-squares optimization. The SBA returns the new optimized estimations for ϒ, and the optimal 3D intersections R. The spatial line and camera pose estimations are corrected by forward projecting them from the newly estimated camera planes ϒ. This returns the final sketch {ϒ,Γ}. The high level diagram on **Figure 2** shows the process described in this section.

adequate to improve the 3D sketch. Some of the reasons for this are that recurrent segment mismatches, fragmentation or the inaccurate placement of counterparts may prevent the convergence of the optimization. It is possible to perform a linebased Bundle Adjustment by converting the primitives into Plücker coordinates [20, 21] within the cost function of the optimisation process. This allows a reduction

in the number of parameters and the computational cost.

*Build 3D Abstractions with Wireframes DOI: http://dx.doi.org/10.5772/intechopen.96141*

ments correctly projected into space.

Truth mesh.

**51**

**3.2 How to compare the results with Ground Truth meshes**

In order to prove the validity of a 3D abstraction method, it has to be

benchmarked against a Ground Truth dataset for SfM, which includes both intrinsic and extrinsic parameters for the cameras. These are built with synthetic images from 3D models [22], or with real pictures [23] teamed with 3D model data including the pose of the cameras and the measurements from 3D scanning or Lidar. Both synthetic and real Ground-Truth datasets include a 3D model. The resulting point cloud is aligned with the Ground Truth mesh. The normal distance between the surface of the mesh and the points is computed. In order to assess how the generated sketch fits the Ground Truth model, the Mean Square Error of the distance between both spatial shapes is computed, because it acts as the natural loss function of a Gaussian distribution. In the case of 3D line sketch, in order to compare the sketch with the Ground truth mesh, the 3D straight segments must be discretized into points. To measure the difference in proportions between the generated 3D sketch and the Ground Truth mesh, the normal distance between the surface of the mesh and the discretized points on the lines is computed. Using the obtained error in the distances, discretized points on the lines are coloured to account how far they are from the surface of the mesh. There are several variables that condition the resulting 3D sketch number of images: Firstly, the number of images showing common elements of the scene is one of them. Secondly, the number of segments that can be matched between images. Thirdly, the transformation between both images might condition the matching inlier ratio, and hence, the number of seg-

For 3D line sketching methods, the length of the final 3D lines will depend on the fragmentation of the detected lines, and its number is closely related to the number of line correspondences between the images. Therefore, results of 3D reconstructions will unavoidably depend on the performance of the method for stages before the spatial projection. Quantitative measurements for 3D abstraction are performed on Ground Truth datasets. The proportions of the generated sketch is measured based on the distance between the segments and the Ground

Employing a feature-point based abstraction method is profitable for datasets with a sufficient number of pictures featuring textured surfaces, so a dense 3D point cloud can be created. For these 3D abstractions, cameras are located accurately due to the precision of the point rotation and translation invariants. This is the case of the results obtained by abstraction methods working altogether with SIFT pipelines [1, 22], but requiring dozens of high definition pictures with textured surfaces for

There are real world applications of Computer Vision that does not always permit to obtain high definition pictures, in textured environments, without blurring and digital noise. For these applications it can be advantageous to estimate the camera extrinsics independently of any feature point 3D reconstruction [2].

**Figure 3** shows a quantitative comparison of the methods [2] and [1] with just 6 and 8 images chosen from the dataset. **Figure 4** increases the number of images to 10

SIFT to be able to accurately estimate the camera extrinsics.

and 12. The test cases are labeled as *S*6, comprising image numbers


*Article* **Active Transportation and Obesity Indicators in Adults from Latin America: ELANS Multi-Country Study**

**Juan Guzmán Habinger 1, Javiera Lobos Chávez 2, Sandra Mahecha Matsudo 3,4, Irina Kovalskys 5, Georgina Gómez 6, Attilio Rigotti 7, Lilia Yadira Cortés Sanabria 8, Martha Cecilia Yépez García 9, Rossina G. Pareja 10, Marianella Herrera-Cuenca 11, Ioná Zalcman Zimberg 12, Viviana Guajardo 13, Michael Pratt 14, Cristian Cofre Bolados 15,16, Claudio Farías Valenzuela 15, Adilson Marques 17,18, Miguel Peralta 17,18, Ana Carolina B. Leme 19, Mauro Fisberg 20,21, André Oliveira Werneck 22, Danilo Rodrigues da Silva 23, Gerson Ferrari 15,\* and on behalf of the ELANS Study Group** †

Received: 2 September 2020; Accepted: 21 September 2020; Published: 24 September 2020

**Abstract:** Purpose: The aim of this study was to determine the association between active transportation and obesity indicators in adults from eight Latin American countries. Methods: Data from the ELANS study, an observational multi-country study (n: 8336; 18–65 years), were used. Active transportation (walking and cycling) and leisure time physical activity was assessed using the International Physical Activity Questionnaire (long version). The obesity indicators considered were: body mass index, and waist and neck circumference. Results: In the total sample, the average time dedicated to active transportation was 24.3 min/day, with the highest amount of active transportation being Costa Rica (33.5 min/day), and the lowest being Venezuela (15.7 min/day). The countries with the highest proportion of active transportation were Ecuador (71.9%), and the lowest was Venezuela (40.5%). Results from linear regression analyses suggest that active transportation was significantly and independently associated with a lower body mass index (β: −0.033; 95% CI: −0.064; −0.002), but not with waist circumference (β: −0.037; 95% CI: −1.126; 0.390 and neck circumference (β: −0.007; 95% CI: −0.269; 0.130). Conclusions: Active transportation is significantly associated with a lower body mass index. Governments should incentivize this type of transportation as it could help to reduce the obesity pandemic in Latin America.

**Keywords:** physical activity; active transportation; Latin America; obesity; body mass index; waist circumference

#### **1. Introduction**

Approximately 39% of the world's adults are overweight or obese [1]. In Latin America, a prevalence of up to 60% of overweight and obesity has been reported [2], which is a considerable burden for public health. There has been a consistent association between overweight and obesity and cardiovascular diseases, diabetes, and some types of cancer [3]. Overweight and obesity and related comorbidities are a global epidemic that may be mitigated by the adoption of healthier lifestyles, including being physically active [4–6].

Many studies have shown that physical activity has extensive health benefits such as reducing body weight, premature mortality, and cardiovascular disease risk [5,7]. The benefits of physical activity has been extensively represented by leisure time, such as physical exercise, but evidence shows that these benefits can also be obtained through walking or cycling, as "active travel" or "active transportation" [8,9]. Active transportation has been demonstrated to be an excellent strategy for increasing physical activity level, because it is a daily behavior, an opportunity to create a healthy habit and relatively cheap alternative [10,11]. Besides, it can be integrated into everyday life particularly for those not involved or interested in engaging in leisure time physical activity [12]. Strong evidence demonstrates that physical activity related to active transportation is a crucial population-based approach, which aims to reverse the health outcomes [8,9].

Over the past two decades, the Latin American region has experienced substantial economic development due to high levels of urbanization (80%) and a unique structural, cultural and social environment, and is actually by far the most unequal region in the world [13,14]. Latin American countries are characterized by high population density patterns, the unregulated expansion of urban environments, air pollution, high crime rates, high income inequality, high levels of poverty, and population aging, which might inhibit physical activity [14–16]. Governments and nongovernmental organizations have been adopting several policies such as building public park facilities, cycling infrastructure and

intervention strategies for improving active transportation (e.g., bike-sharing programs) to promote active transportation in Latin America [17–19].

Studies from Europe and the United States show that countries in which active transportation increases show decreasing obesity rates. In fact, many studies provided a contribution to the literature and filled several gaps of the association between active transportation and lower obesity indicators (body mass index) in high-income [20–22]. However, there is limited evidence on the association of active transportation and obesity indicators from Latin America representative samples [23]. In addition, Latin America has a high prevalence of physical inactivity and overweight/obesity [2,24]. Therefore, there is an urgent need to look for different strategies aiming to increase the active transportation levels and decrease obesity in the Latin American region. The aim of this study was to investigate the extent of the association between active transportation and obesity indicators in adults from eight Latin American countries.

#### **2. Materials and Methods**

#### *2.1. Study Design and Sample*

The Latin American Study of Nutrition and Health (Estudio Latinoamericano de Nutrición y Salud—ELANS) is a household-based cross-sectional survey that includes data collected from eight Latin American countries: Argentina, Brazil, Chile, Colombia, Costa Rica, Ecuador, Peru, and Venezuela. The study was based on a complex, multistage sample design, stratified by conglomerates, with all regions of each country represented, and random selection of main cities within each region according to the probability proportional to size method [25,26].

The sampling size required for necessary precision was calculated with a 95% confidence level and a maximum error of 3.5% and a survey design effect of 1.75. The sample was stratified by age, sex, and socioeconomic level. Socioeconomic levels were balanced based on national indexes used in each country [26]. Households within each secondary sampling unit were selected through systematic randomization. Considering quotas for age, sex and socioeconomic level, the selection of the participant belonging to the domicile was made using 50% of the sample's next birthday, and 50% of the sample's last birthday. Of the total sample of 9218 participants aged between 15 and 65 years, we included 8336 participants aged between 18 and 65 in this study. We excluded adolescents (15 to 17 years old) from the analyses because the ELANS study did not consider the age range of adolescents (10–19 years old) [27]. Additionally, adolescents may have restricted independent mobility that may yield different environment–physical activity associations than those observed in adults [28]. In addition, physical activity guidelines for adolescents differ from adults [29]. The rationale and design of the study is reported in more detail elsewhere [25].

All the study sites are academic-based (universities and other research institutions) and each site adhered to a common study protocol for fieldwork implementation, interviewer training, data collection and management, and the quality of control procedures. Data collection for ELANS took place from September 2014 to February 2015. The ELANS protocol was approved by the Western Institutional Review Board (#20140605) and registered at ClinicalTrials.gov (#NCT02226627). All participants of the ELANS study provided written consent.

#### *2.2. Exclusion Criteria*

During enrolment for the study, participants were excluded if they had a major physical/mental impairment that impacted on food intake and physical activity levels, were pregnant/lactating, and were ≤15 years old or ≥65 years old. For this study, we excluded participants <18 years of age from the total sample, and subjects without at least one anthropometric variable.

#### *2.3. Active Transportation, Leisure Time and Total Physical Activity*

The ELANS study employed the self-reported International Physical Activity Questionnaire-Long Form (IPAQ-LF), which was a validated measure design for Latin America [30]. IPAQ was developed to assess the physical activity levels of inhabitants from dissimilar countries [30,31]. We used a Spanish version [32] and it was adapted for all eight participating ELANS countries [14].

The ELANS study only summarized scores for active transportation and leisure time physical activity. The IPAQ-LF collected data on the reported frequency and duration (bouts at least 10 min continuously) of active transportation (walking and cycling) and leisure time physical activity (walking, moderate and vigorous physical activity) over the last seven days. Three outcomes for each domain were calculated: (1) engaging at least 10 min in active transportation and leisure time physical activity (yes, no); (2) how many days of physical activity in active transportation and leisure time physical activity; (3) how much time spent completing physical activity in active transportation and leisure time physical activity. Questions were asked separately for active transportation (walking and cycling), and leisure time physical activity (walking, moderate-intensity, and vigorous-intensity activities). Time spent in each domain was expressed as min/day.

#### *2.4. Obesity Indicators*

In each country, the obesity indicators (body weight, height, waist and neck circumferences) were evaluated in light clothing and without shoes using standard procedures and equipment. Data were collected by trained ELANS data collectors during a visit. Body weight (kg) and height (cm) were measured using a calibrated electronic scale Seca 213® (Hamburg, Germany). The measurements were taken during the end inhalation with the participant's head in the Frankfort plane [33]. The body mass index was calculated as the body weight divided by the square of body height (kg/m2). Participants were classified as underweight: <18.5; normal weight: 18.5–24.9; overweight: 25–29.9; or obese: ≥30 kg/m2 [34].

A nonstretchable tape with an accuracy of 0.1 cm was used to evaluate circumferences. Waist circumference was measured according to World Health Organization recommendations, i.e., with the participants standing, after regular expiration, to the nearest cm, midway between the lowest rib and the iliac crest on the horizontal plane with the subject in a standing position [34]. We used the "substantially increased risk of metabolic complications" cutoff defined by World Health Organization, >102 cm for men and >88 cm for women [34]. Neck circumference was measured in a plane as horizontal as possible, immediately below the laryngeal prominence, while standing erect with eyes facing forward [35] and was categorized as abnormal if the circumference was >39 cm for men and >35 cm for women [36]. All measurements were performed under strictly standardized conditions. Two measurements of the obesity indicators were performed, and the mean used for the analyses.

#### *2.5. Sociodemographic Variables*

Sociodemographics items collected by all countries included age, sex and socioeconomic level. Socioeconomic data were categorized into "low", "medium", and "high" based on the country specific indices [26]. Age was dichotomized into "18–34", "35–49", and "50–65" years. Ethnicity was classified as white, mixed (parents with dissimilar ethnicities) and other (Black, Asian, Indigenous, and Gypsy).

#### *2.6. Statistical Analyses*

Data were weighted considering sociodemographic variables, sex, age and socioeconomic level of the Latin American population to enable comparability for totals across countries. This was completed to have a representative sample of the adult population of each country. Descriptive statistics of mean, percentage and the associated 95% confidence interval (95% CI) were used to describe the sociodemographic obesity indicators (Table 1) and active transportation (Table 2). A Chi-square test was carried out to evaluate if there was a significant association between active transportation with the control variables mentioned before. For descriptive and categorical analysis, the self-reported time spent on active transportation was stratified into the following two categories: nonactive transportation (including those who reported nonwalking or cycling as part of their transportation) and active transportation (including those who reported ≥10 min of walking and/or cycling for transportation). A Pearson correlation was used to assess the association of active transportation with obesity indicators.

**Table 1.** Sociodemographic and obesity indicators of the population according to active transportation categories.

Figures as percentages if not stated otherwise. Chi-square tests were used for distributions. \*\* *p* ≤ 0.01; \*\*\* *p* ≤ 0.001. M: men; W: women.

**Table 2.** Correlation between active transportation and obesity indicators per country.

For the calculation of the CI, an asymptotic method (wald) was used based on a normal distribution. In addition, linear regression models (β; 95% CI) per country were used to verify the relationship of active transportation (10 min/day of active transportation as the independent variable) with body mass index, waist circumference and neck circumference (dependent variables). Our first model (model 1) was adjusted for sex, age, socioeconomic level, and ethnicity. The second model was additionally adjusted for sex, age, socioeconomic level, ethnicity, and leisure time physical activity. We also adjusted for leisure time physical activity (min/day) to examine whether the associations with time spent in active transportation were independent of time spent leisure time physical activity. All analyses were made using R-studio version 1.2.5033 [37,38]. The significance level was set at *p* < 0.05.

#### **3. Results**

The average response of the surveys was 99.4%, with a range between 98.5% and 99.8%, corresponding to Peru and Ecuador, respectively. The average time dedicated to active transportation was 24.3 min/day in the total sample (those who reported nonwalking or cycling as part of their transportation). Considering the full sample, the country with the highest amount of active transportation was Costa Rica (33.5 min/day), and the lowest was Venezuela (15.7 min/day). When the nonactive transportation group (those who reported nonwalking or cycling as part of their transportation) was excluded, the average was 41.6 min/day. Costa Rica still had the highest amount of active transportation (50.3 min/day), while Venezuela had the shortest time (35.6 min/day). The average time spent on leisure time physical activity was 16.6 min/day (95% CI: 15.3; 17.9) for the group that did not engage in active transportation. Meanwhile, for the group that does at least 10 min of active transportation, it was 35.2 min/day (95% CI: 33.3; 37.1) (*p* < 0.001).

Table 1 shows a descriptive analysis of the sample, dividing the sample into those who did not complete active transportation from those who did. There was a significant association between country and active transportation (*p* < 0.001). The country with the highest proportion of active transportation was Ecuador (71.9%), and the lowest was Venezuela (40.6%). There were no statistically significant differences in the proportion of active transportation between men and women, age groups, or socioeconomic level. On the other hand, the white ethnic group had a lower proportion of active transportation than the other groups (*p* < 0.001). When comparing the proportion of active transportation by body mass index, it was observed that the prevalence of active transportation was lower among overweight and obese participants than those with normal body mass index (56.1% and 51.4% vs. 57.3%) (*p* < 0.001). The same difference is observed for waist and neck circumference, where a lower proportion of active transportation was observed among those with increased indicators compared to those with a normal waist and neck circumference (56.5% vs. 52.6% and 56.3% vs. 53.0%, respectively) (*p* < 0.001).

The correlation between the active transportation and obesity indicator (body mass index, waist and neck circumference) by country is shown in Table 2. Body mass index and waist circumference were weakly and negatively associated with all countries (except Ecuador); however, the highest correlation value was Argentina and Venezuela. Furthermore, there was a weak and negative association between active transportation and neck circumference in the full sample—Peru and Venezuela (*p* < 0.05). The highest correlation value was Venezuela. Active transportation was not associated with neck circumference in Argentina, Brazil, Chile, Colombia, Costa Rica, and Ecuador.

We also conducted two different specifications for every regression model to investigate the association between active transportation and obesity indicators as continuous variables (Table 3). The first model, adjusted for sex, age, socioeconomic level, and ethnicity, showed that active transportation was significantly associated with a lower body mass index and waist circumference, but not with neck circumference. In the second model, including leisure time physical activity, active transportation was significantly associated only with a lower body mass index. An increase of 10 min regarding active transportation per day resulted in a −0.033 Kg/m2 change in the body mass index. No statistical association was found between active transportation with waist and neck circumference.

**Table**

#### **4. Discussion**

This is the first multi-country study with a representative sample of Latin Americans to determine the extent of association between active transportation and obesity indicators in adults. In general, we demonstrated that a greater amount of time on active transportation was associated with a lower body mass index. This association was independent of age, sex, socioeconomic level, ethnicity and leisure time physical activity. These are novel results that reflect what has been reported in some countries and multinational studies [21,39].

Our findings are compatible with other studies that reported a lower body mass index associated with active transportation [40,41]. Flint et al. [42] studied the association of active commuting and body mass index in a cross-sectional study of more than 15,000 people in the United Kingdom. Active commuting was associated with a lower body mass index—0.97 Kg/m2 and 0.87 Kg/m2 in men and women, respectively. Later, the same author [21] showed similar results in a cross-sectional study of more than 264,000 middle-aged adults. They found a lower body mass index—1.0 Kg/m2 and 0.67 Kg/m2 in men and women, respectively. Laverty et al. [39] carried out a multinational study of six middle-income countries, with more than 40,000 participants. They found that ≥150 min/week of active transportation was associated with a lower body mass index of 0.54 Kg/m2. Wojan et al. [43] searched for this association in the United States in a study of 12,405 adults. They found that active commuting produced an average treatment effect of −1.83 Kg/m2.

Different from previous studies [39,41], we did not find an association between active transportation and waist circumference. This was observed when the analysis was adjusted for leisure time physical activity (model 2), indicating a potential co-existence of physical activity in these different contexts and reinforcing a stronger association of leisure time physical activity with waist circumference compared to transport physical activity. Concerning neck circumference, although studies have found associations with moderate to vigorous physical activity [44], their relationship with active transportation in adults has not been describe before. Here, we observed that active transportation was associated with a lower neck circumference in Costa Rica and Peru only, which can be related to the higher prevalence of active transportation in these countries. However, further studies are needed in order to explore specific amounts and intensities of transport physical activity associated with obesity indicators.

We found that the mean time spent in active transportation was 24.3 min/day. Latin America has low levels of active transportation compared to European countries, such as Germany or Sweden [45–47]. Only about one-fifth of the time for transportation is spent in active transportation in Latin America [13]. This is especially important considering that 27% to 47% of people in Latin America do not achieve the physical activity recommendations for health [47]. In a previous study, we showed that the prevalence of physical inactivity (<150 min/week) was 40.6% (95% CI: 38.8, 42.5); ranging from 26.9% (Chile) to 47% (Costa Rica and Venezuela). Physical inactivity was greater in Argentina (43.7%; 95% CI: 38.1, 49.5), Brazil (43.5%; 95% CI: 39.4, 47.7), Costa Rica (48.0%; 95% CI: 42.1, 53.9) and Venezuela (47.1%; 95% CI: 42.1, 52.3) [47]. In this context, promoting public policies aimed to encourage this type of transport, as it can help more people achieve the physical activity recommendation for health [43]. This could help to significantly decrease the disease burden associated with physical inactivity [5,48]. Other countries have estimated that moderate increases in active transportation lead to savings in national public health services. For example, in the United Kingdom, it was found that an increase of 1 km in walking and 3 km in cycling per day would save £17 billion for the national health system in 20 years [49].

Moreover, those who change their mode of commuting gain weight if they shift from cycling or walking to car travel, but lose weight when shifting from cars to active commuting [50]. Martin et al. [40] showed that changing from private transport to active commuting decreased body mass index by 0.32 Kg/m2. Conversely, shifting from active commuting to private transport increased body mass index by 0.34 Kg/m2. As established before, urban factors impact on the choice of transport modality [13,23]. One of the strategies to increase active transportation in the population is to invest in creating neighborhoods and cities that favor this type of transport [18,23]. This could be a key to reducing the obesity pandemic that exists in Latin America and the world. Several countries in this region have

invested in infrastructure to encourage the use of active transportation—as is the case of some cities, such as Bogotá in Colombia, which invested in creating exclusive bike paths [18]. Our results are consistent with the findings reported in high-income countries. Therefore, they are generalizable to some extent for other middle-income countries.

The strengths of this study include the large sample from eight Latin American countries and standardized objective anthropometric indicators (body mass index, waist circumference and neck circumference). Given that a representative sample of these countries was studied, these results can be extrapolated to the rest of the adult population of these eight Latin American countries. Waist circumference is a well-established indicator of central obesity, a key factor in cardiovascular disease risk and metabolic syndrome [51]. While neck circumference is an indicator, which is still under study [36,52,53], its relationship with active transportation had not been previously reported in adults.

Within the limitations, we found that part of the sample (418 participants, 5.01%) was not classified by ethnicity. When using a subjective active transport measurement (IPAQ), there may be reporting bias [54]. From the four domains of physical activity, only the active transportation and leisure time physical activity sections were included. This decision was made for two reasons: (i) due to the greater relevance of these domains for targeted physical activity programming and policy efforts [30] and (ii) the weak validity of occupational and home-based physical activity questions [55]. The cross-sectional design of this study limits generalizability and limits conclusions regarding of causality. There is a possibility of reverse causality and residual confusion; it could be that obese people less actively travel.

#### **5. Conclusions**

This study supports that active transportation is significantly associated with a lower body mass index. Incentive active transportation could help to reduce the obesity pandemic and help more people to meet physical activity recommendations in Latin America. These findings are consistent with existing evidence from other regions of the world. For these reasons, the generation of public policies aiming to promote active transportation in Latin America should be prioritized.

**Author Contributions:** Conceptualization, J.G.H., J.L.C. and G.F.; Formal analysis, J.G.H., and J.L.C.; Investigation I.K., G.G., A.R., L.Y.C.S., M.C.Y.G., R.G.P., M.H.-C., I.Z.Z., V.G., M.P. (Michael Pratt) and M.F.; Funding acquisition, M.F. and I.K.; Writing—original draft: J.G.H.; Writing—review and editing: C.C.B., C.F.V., A.M., M.P. (Miguel Peralta), S.M.M., A.C.B.L., A.O.W., D.R.d.S. and G.F.; Statistical analysis, J.L.C. All authors have read and agreed to the published version of the manuscript.

**Funding:** Fieldwork and data analysis compromised in ELANS protocol was supported by a scientific grant from the Coca Cola Company, and by a grant and/or support from Instituto Pensi/Hospital Infantil Sabara, International Life Science Institute of Argentina, Universidad de Costa Rica, Pontificia Universidad Católica de Chile, Pontificia Universidad Javeriana, Universidad Central de Venezuela (CENDES-UCV)/Fundación Bengoa, Universidad San Francisco de Quito, and Instituto de Investigación Nutricional de Peru. André Werneck is supported by the São Paulo Research Foundation (FAPESP) with a PhD scholarship (FAPESP process: 2019/24124-7). This paper presents independent research. The views expressed in this publication are those of the authors and not necessarily those of the acknowledged institutions. The funding sponsors had no role in study design; the collection, analyses, or interpretation of data; writing of the manuscript; or in the decision to publish the results.

**Acknowledgments:** The authors would like to thank the staff and participants from each of the participating sites who made substantial contributions to ELANS. The following are members of ELANS Study Group: Chairs: Mauro Fisberg and Irina Kovalskys; Co-chair: Georgina Gómez Salas; Core Group Members: Attilio Rigotti, Lilia Yadira Cortés Sanabria, Georgina Gómez Salas, Martha Cecilia Yépez García, Rossina Gabriella Pareja Torres and Marianella Herrera-Cuenca; Steering committee: Berthold Koletzko, Luis A. Moreno and Michael Pratt; Accelerometry analysis: Priscila Bezerra Gonçalves, and Claudia Alberico; Physical activity advisor: Gerson Ferrari. Nutrition Advisors: Regina Mara Fisberg and Agatha Nogueira Previdelli. Project Managers: Viviana Guajardo, and Ioná Zalcman Zimberg.

**Conflicts of Interest:** M.F. has received fees and consultancy payments from biotechnology, pharmaceutical and food and beverage companies. He has also received fees, payments for consulting and financing research studies without any restrictions, from government sources and nonprofit entities. The rest of the authors also have no conflict of interest to declare. None of the entities mentioned had or have any role in the design or preparation of this manuscript.

#### **References**

© 2020 by the authors. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (http://creativecommons.org/licenses/by/4.0/).

International Journal of *Environmental Research and Public Health*


**15. Conclusion**

In conclusion, this study may be considered as a pilot study in the field of new, changing architecture due to pandemic crisis. Pandemics change everything; they change the politics, economics, and sociology of every culture they touch [1]. This research study was conducted parallel with the COVID-19 pandemic, which makes it a peculiar one and creates a great necessity to innovative architecture rather than the traditional concepts to overcome the challenges imposed by COVID-19 or future pandemics. Architects, concerned engineers, and other professionals need to consider the concepts concerning social distancing, not social isolation; less concentration per place; more space (inner and outer); new materials, signage, and written clear instructions; biophilic elements and features; and new techniques for circulation within buildings and outside them as well as the entry and exit of buildings, in addition to updating rules, regulations, design, environments, and sustainability manuals and standards to include measures to combat pandemics.

The authors believe that the initial three-setup hypotheses at the beginning of this chapter are satisfied through establishing the guidelines from the data collected and reviewed; also, proposals to update Building Rules and Regulations and Sustainable Building Standards and Criteria are highlighted for the prevention and control of the spread of pandemics within buildings and surrounding environments at the Kingdome of Bahrain and elsewhere in the world.

The study concludes that no single profession can address all the challenges of this pandemic; it is a professional multidisciplinary team challenge. Thus, architecture and other related building courses need to be modified to cope with the existing and potential future challenges and to use online learning as one of the many tools in the toolbox to enrich architectural education for healthy buildings and environments [93].

The established eight main categories of guidelines and recommendations integrate and complement each other to combat COVID-19 and other similar pandemics. It was experienced during pandemics that the spaces people inhabit can either protect them or make them sick. COVID-19 has also shown how the outbreaks of disease are spatial problems. Therefore, architecture can be well suited to design spaces that reduce the public's exposure to contamination globally. With the right building materials, airflow, and spatial strategies, spaces can be designed to support infection control.

Finally, the proposed guidelines in this chapter are intended to provide concerned university students, design professionals, employers, building owners, and public officials globally with tools (i.e., professional vaccine) for reducing and eliminating risk when designing new building projects, modifying existing buildings, conducting maintenance works and interior design projects, and reoccupying buildings during and after the pandemic.


**4.4 Alternatives including subxiphoid approach**

A subxiphoid approach (**Figure 7**) is usually less painful than VATS. The reason is that being in midline, less respiratory muscles are incised. It is also the preferred approach for patients who had recent sternotomy and subsequently presents with a

**63**

*Pericardial Diseases: Surgery for Pericardial Effusion DOI: http://dx.doi.org/10.5772/intechopen.81927*

are at high risk with general anesthesia.

*Healed scar from the subxiphoid incision (arrow).*

**5. Summary**

**Figure 7.**

postsurgery.

pericardial effusion. In this group of patients, rather than to redo sternotomy, only the inferior portion of the scar needs to be reopened for access to the pericardial cavity. The sternum and wires used to oppose the bone during the initial sternotomy do not require any further manipulation from this approach. This type of effusion, if related to bleeding postsurgery, usually does not recur frequently or long term; hence, this approach is simple and effective. A subxiphoid incision can be also used to create a pericardial-peritoneum window. This method, when paired with a pleuroperitoneal shunt, has been described to have comparable results to other methods [13]. The proposed shunt pumps fluid actively into the peritoneum cavity, and this can possibly reduce accumulation rates by preventing omentum from occluding the pathway from the pericardium to the peritoneum. Authors have been successful with this with only local anesthesia; hence, this alternative is useful for patients who

Surgical approach to pericardial effusion involves many a thought process. Different patients require different approaches for the best results. Decisionmaking should be made with the patient's best interest and wishes. It is rewarding indeed when patients get symptomatic relief and are able to return to their function *Pericardial Diseases: Surgery for Pericardial Effusion DOI: http://dx.doi.org/10.5772/intechopen.81927*

*Inflammatory Heart Diseases*

**Figure 6.**

mentioned earlier; it is easier to convert to sternotomy if required. However, most surgeons would avoid sternotomy if possible, as it brings about more pain with a bigger scar as well as higher risk of infection to both the superficial tissue and sternum. The greater the surgical trauma, the longer healing requires before adjuvant

Another variation of technique involves the consideration between general anesthesia and local anesthesia. General anesthesia remains the most common way of anesthesia for patients; it involves intubation and protection of airway under muscle paralysis, sedation and amnesia. But for patients who have hemodynamic compromise from pending cardiac tamponade due to a significant acute pericardial effusion, general anesthesia remains very high risk. In fact this group of patients is frequently the American Society of Anesthesiologists (ASA) class V, the highest-risk class. Many a surgeon have been demoralized after losing patients on the operating table, after this group of patients collapse upon giving the slightly amount of medication that could lower the vascular tone and reduce the blood pressures. Local anesthesia has been advocated to be safer in these patients, but often not practical as few patients could tolerate the pain of an anterior thoracotomy incision even with the best local infiltration. Mentioned later below, a subxiphoid incision could be more tolerable with this, and some surgeons have been successful with it. A new method in the middle ground could be non-intubated general anesthesia. This has been successful in reported VATS surgery [12]. Without muscle paralysis and using a laryngeal mask airway to continue spontaneous-assisted ventilation, this resulting loss of vascular tone could be reduced and perhaps reduce the risk of anesthesia. But the surgeon must also realize and cope with the increased muscle tone and continued ventilation of the lungs. Exposure

treatment like chemotherapy or radiotherapy could be initiated.

needs to be ensured as the lung cannot be isolated in this setting.

A subxiphoid approach (**Figure 7**) is usually less painful than VATS. The reason is that being in midline, less respiratory muscles are incised. It is also the preferred approach for patients who had recent sternotomy and subsequently presents with a

**4.4 Alternatives including subxiphoid approach**

**4.3 Variation in anesthesia methods**

*Healed scar from the left anterior thoracotomy incision (arrow).*

**62**

pericardial effusion. In this group of patients, rather than to redo sternotomy, only the inferior portion of the scar needs to be reopened for access to the pericardial cavity. The sternum and wires used to oppose the bone during the initial sternotomy do not require any further manipulation from this approach. This type of effusion, if related to bleeding postsurgery, usually does not recur frequently or long term; hence, this approach is simple and effective. A subxiphoid incision can be also used to create a pericardial-peritoneum window. This method, when paired with a pleuroperitoneal shunt, has been described to have comparable results to other methods [13]. The proposed shunt pumps fluid actively into the peritoneum cavity, and this can possibly reduce accumulation rates by preventing omentum from occluding the pathway from the pericardium to the peritoneum. Authors have been successful with this with only local anesthesia; hence, this alternative is useful for patients who are at high risk with general anesthesia.


This article presents a mathematical approach to the issue of the influence of selected parameters on the thermal performance of a solar collector. Based on the results of the computational experiment for hot (Madrid), moderate (Budapest) and cold (Helsinki) climatic zones, three new deterministic mathematical models (Equations (3)–(5) were developed. These equations can be used to determine the influence of five factors: volume of heat storage tanks, solar collector total area, maximum efficiency, and heat loss coefficient of solar collector, and daily consumption of DHW on the annual useful energy output. Based on these models, the degree and nature of the influence of the examined factors were estimated. It should be noted that the analysis presented in this article is the most This article presents a mathematical approach to the issue of the influence of selected parameters on the thermal performance of a solar collector. Based on the results of the computational experiment for hot (Madrid), moderate (Budapest) and cold (Helsinki) climatic zones, three new deterministic mathematical models (Equations (3)–(5) were developed. These equations can be used to determine the influence of five factors: volume of heat storage tanks, solar collector total area, maximum efficiency, and heat loss coefficient of solar collector, and daily consumption of DHW on the annual useful energy output. Based on these models, the degree and nature of the influence of the examined factors were estimated. It should be noted that the analysis presented in this article is the most appropriate for medium-sized SDHW systems.

appropriate for medium-sized SDHW systems. The change of the examined factors from the lower to the upper level showed significant fluctuations in their impact both for individual factors and for the weather zones (Table 5). The useful energy output *QSC* of thermal solar collectors to a large extent depends on the weather conditions and, above all, the intensity of solar radiation. The *QSC* value is 29.5% lower for Budapest and 41% lower for Helsinki compared to the most suit-The change of the examined factors from the lower to the upper level showed significant fluctuations in their impact both for individual factors and for the weather zones (Table 5). The useful energy output *QSC* of thermal solar collectors to a large extent depends on the weather conditions and, above all, the intensity of solar radiation. The *QSC* value is 29.5% lower for Budapest and 41% lower for Helsinki compared to the most suitable solar conversion zone in which Madrid is located.

able solar conversion zone in which Madrid is located. The results of the optimization procedure according to the energy criterion showed that the maximum annual useful energy output, which is possible to supply from solar collectors, is 1303 kWh/m2 for Madrid weather conditions, 918.5 kWh/m2 for Budapest, The results of the optimization procedure according to the energy criterion showed that the maximum annual useful energy output, which is possible to supply from solar collectors, is 1303 kWh/m2 for Madrid weather conditions, 918.5 kWh/m2 for Budapest, and 768 kWh/m2 for Helsinki conditions.

and 768 kWh/m2 for Helsinki conditions. The above results can be obtained at the optimum collector inclination β for a particular location, i.e., 36 degrees for Madrid, 39.5 degrees for Budapest, and 47.5 degrees for Helsinki. These values were not calculated based on the latitude that designers usually estimate it at. The novelty is the determination of the β value using the method described The above results can be obtained at the optimum collector inclination β for a particular location, i.e., 36 degrees for Madrid, 39.5 degrees for Budapest, and 47.5 degrees for Helsinki. These values were not calculated based on the latitude that designers usually estimate it at. The novelty is the determination of the β value using the method described in this article.

in this article. It is planned to develop similar models for selected main cities in Europe. The obtained dependencies will allow to write a simple application that can be used for a relatively precise determination of the annual useful energy output of thermal collectors. It is also planned to carry out a similar mathematical experiment using Solar Fraction as the It is planned to develop similar models for selected main cities in Europe. The obtained dependencies will allow to write a simple application that can be used for a relatively precise determination of the annual useful energy output of thermal collectors. It is also planned to carry out a similar mathematical experiment using Solar Fraction as the objective function.

**Author Contributions:** Conceptualization, M.Z. and W.J.; methodology, M.Z. and W.J.; energy simulations, M.Z.; mathematical modelling, W.J.; validation, M.Z.; formal analysis, W.J. and M.Z.; investigation, M.Z. and W.J.; writing—original draft preparation, M.Z. and W.J.; writing—review and editing, M.Z. and W.J.; project administration, M.Z.; funding acquisition, M.Z. and W.J. All authors have read and agreed to the published version of the manuscript.

**Funding:** This work was supported by the Bialystok University of Technology and financed by the Ministry of Science and Higher Education of the Republic of Poland [grant numbers WZ/WB-IIS/9/2019, WZ/WB-IIL/5/2019].

**Institutional Review Board Statement:** Not applicable.

**Informed Consent Statement:** Not applicable.

**Data Availability Statement:** Not applicable.

**Conflicts of Interest:** The authors declare no conflict of interest.

#### **References**

## *Article* **Designing for the Environment: An Example of Multi-Criteria Analysis Used for Solar Hot Water System Selection**

**Agnieszka Zelazna ˙ and Justyna Goł˛ebiowska \***

Faculty of Environmental Engineering, Lublin University of Technology, 40B Nadbystrzycka Str., 20-618 Lublin, Poland<EMAIL_ADDRESS>
**\*** Correspondence<EMAIL_ADDRESS>Tel.: +48-8153-844-06

**Abstract:** In the European Union, the building sector accounts for more than 40% of final energy consumption, contributing to the deterioration of the quality of the environment. Among the various solutions that aim to reduce the negative environmental impact caused by the operation of buildings, solar hot water systems (SHW) are popular. The choice of a SHW system is associated with the comfort of use and the access to low-cost energy. The design guidelines include the technical parameters for system operation such as materials, dimensions, sizing and operation temperatures. However, the legitimacy of choosing a particular solution and the available technical parameters are key issues. In the presented study, a multi-criteria analysis was proposed as a basis for the proper selection of system parameters, e.g., collector type, solar tank volume. A model of the SHW system was used to calculate the possible solutions, ensuring the same comfort of usage for several design options. The analyzed model was then used for the calculation of three various indicators: Simple Payback Time (SPBT), Primary Energy consumption (PE) and IMPACT 2002+. The application of a multi-criteria analysis based on a Life Cycle Assessment allowed for beneficial solutions to be found from the point of view of economics, non-renewable resources and environmental protection.

**Keywords:** solar thermal energy; SHW system; multi-criteria analysis; SPBT; EPBT; primary energy; IMPACT 2002+; LCA; sustainable design

#### **1. Introduction**

At present, energy seems to be an essential element for living in a modern society. The change in our lifestyle observed in recent decades resulted in a significant increase in energy consumption, especially in the case of the electricity, but also in other forms such as heat, required to meet the rising housing needs [1–3]. The growing interest in new renewable technologies in recent years is caused by several issues, such as the depletion of fossil resources, necessity to reduce air pollution, response to the problem of global climate change and the social expectations in the field of raising living standards and the comfortable use of buildings [4,5].

Among the renewable energy sources, solar energy is one of the most popular options because of several advantages. The energy supplied from the Sun to our planet exceeds the human demand for energy per year by about 8000 times. In theory, this means that the electromagnetic radiation from the Sun is able to cover the global demand for energy without the additional use of other energy sources. This energy is almost unlimited and does not cause environmental pollution, unlike conventional energy sources. The current level of radiation energy conversion technology does not allow the Sun's energy potential to be utilized in its entirety, which is why there is an aim to improve the devices that convert solar radiation into heat or electricity. An important disadvantage of using solar energy potential is that its absorption requires a large amount of space and favorable conditions [6]. The amount of solar radiation reaching the Earth's surface decreases with many factors, such as increasing cloudiness, as well as air contamination [7,8].

**Citation:** Zelazna, A.; Goł˛ebiowska, J. ˙ Designing for the Environment: An Example of Multi-Criteria Analysis Used for Solar Hot Water System Selection. *Energies* **2022**, *15*, 65. https://doi.org/10.3390/en15010065

Academic Editor: Jan Danielewicz

Received: 24 November 2021 Accepted: 20 December 2021 Published: 22 December 2021

**Publisher's Note:** MDPI stays neutral with regard to jurisdictional claims in published maps and institutional affiliations.

**Copyright:** © 2021 by the authors. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (https:// creativecommons.org/licenses/by/ 4.0/).

In the scientific literature of the last several years, an increasing interest in the subject of Life Cycle Assessment of solar systems can be observed; this applies to both technological processes and specific devices or materials. Various Life Cycle Impact Assessment (LCIA) methods are used. These include: Global Warming Potential (GWP), Cumulative Energy Demand (CED) and Eco-indicator 99. Some studies deal with the Life Cycle Assessment of solar energy installations and devices, including domestic hot water preparation systems and solar collectors themselves.

Over time, there have been significant advancements achieved by various research groups in the field of solar–thermal systems LCA [9–13]. Some of these include the LCA analysis of flat solar collectors [14] from raw material extraction, through production to obtaining a finished commercial product. The environmental load resulting from the transport of materials to the production plant was also taken into account. This research was based on the energy and ecological characteristics of the input products. The highest value of environmental load was connected with the following impact categories: primary energy consumption and acidification. The energy payback period, understood as the time needed to recover the energy expenditure incurred for the production of the collector, excluding the other elements and energy required for operation, was shorter than 1 year [14].

Another study [15] presented the Life Cycle Impact Assessment carried out for a solar heating installation located in Greece. The production stages of individual elements of the installation and their impact on the environment were considered. The system boundaries include the production of raw materials (steel, glass, copper, and aluminum), operation of the installation and final disposal. The installation consisted of a flat solar collector with a copper absorber (4 m2 ) and a domestic hot water tank with a capacity of 200 dm3 . An electric heater was an additional heat source. Studies showed that the system provided 1702 kWh per year, with solar energy accounting for 58.8% of this value. An LCIA analysis was carried out using the Eco-indicator 99 method, which showed that the largest environmental impact came from the solar hot water tank. Moreover, the greatest environmental burden was connected with the following impact categories: soil acidification, smog production and impact on global warming.

An environmental analysis was also used for the assessment of the selective surface for flat-plate solar collectors, which was carried out using the following methods: CED, GHG (Greenhouse Gas Protocol method based on the set of characterization factors by Intergovernmental Panel for Climate Change IPCC GWP 100a) and Eco-indicator 99. The authors compared the conventional method of selective surface production with the latest production method—roll to roll (R2R).

Research showed that the annual energy demand for the production of 200,000 m2 of selective surface is equal 7.91 TJ. Additional research based on CED allowed the energy payback time for R2R production to be determined, which was only 3–4 days. Among the analyzed factors, copper has the greatest impact on the environment, as it also requires the highest amount of energy in the production of selective surfaces. The results of the analysis clearly showed that the production of the selective surface for flat-plate solar collectors with the conventional method was much more harmful to the environment than the production by means of the roll-to-roll method [16].

A study in Munich (temperate climate conditions) presented an analysis of the life cycle of two hot water preparation systems with glazed solar collectors and unglazed polypropylene collectors. The Eco-indicator 99 method was used to assess the entire life cycle. The main components of both systems were solar panels and a 300 dm3 buffer tank. The glazed panel consisted of an outer aluminum frame, two layers of mineral wool, a copper absorber and a copper alloy absorber piping system. The whole construction was hermetically closed with 4 mm thick transparent glass. In contrast, the plastic collector considered in this study was a polypropylene strip 7 mm thick, 313 mm wide and of variable length, which allowed the panel to be modular. The duration of the operation of both installations was 10 years. For glazed solar collectors, the calculated index was 49.7 points, while for plastic collectors it was 18.7 points. The largest share here was the

use of fossil fuels: 52% and 68%, respectively. On the other hand, the GWP calculated over a period of 100 years was 1670.92 kg CO2eq for a glazed solar collector and 105.06 kg CO2eq for a plastic collector. The economic payback time, in comparison to the natural gas boiler, is in the range 9–11 years/8–13 years for the system with unglazed/glazed panels, respectively [17].

To conclude, it should be emphasized that the analyses carried out so far concern the production of materials, the entire life cycle of the installation or case studies [18–21]; however, attention is rarely paid to proper design parameters. In the literature, few research works address the topic of the life cycle of installations that operate under the temperate climatic conditions, such as the Polish climate, and relate to a long-term perspective. The present study significantly supplements the current state of knowledge due to the implementation of the selected design criteria into the analyzed model of life cycle.

#### **2. Materials and Methods**

In the current study, an attempt to conduct a holistic, multi-criteria analysis of a solar thermal system was presented in order to set the designer's guidelines and frames for correct system selection. A typical installation of solar hot water system (SHW), supported by an electric heater in the winter period was chosen as the subject of the analysis. The scheme of the typical solar installation is presented in Figure 1. The analysis included 6 variants of installations located in Central Europe (Poland, Łód´z: 51.759247◦ N, 19.455982◦ E), with orientation towards the south (azimuth 0◦ ) and inclination of 40◦ . The daily domestic hot water demand was assumed at constant level of 180 L. The characteristics of the technical parameters for different variants of installations are shown in Table 1. The aim of the modeling was to estimate the influence of selected design parameters (type of collector, piping and water tank capacity) on the economical, energetic and environmental aspects of SHW operation.

**Figure 1.** Scheme of the simulated installation.

**Table 1.** Technical parameters of the analyzed system variants.

The base scenario for comparison with the design options included an electric heater, while the annual electricity consumption equaled 2727 kWh. Modeling of solar energy gains was performed by using GetSolar software (Hottgenroth Software GmbH & Co. KG, Germany), a popular tool using f-chart-based estimation of energy gains from SHW systems in a chosen location (Łód´z, Poland), characterized by the total annual solar radiation of 3710.8 MJ/m2 and the average annual total insolation of 1560.4 h.

The main inputs to the analysis include: solar irradiance on collector plane and ambient temperature data (from WetSyn weather data synthesis program integrated with GetSolar software), type of solar system (single, combined, etc.), collector parameters (including optical efficiency and collector area), heat losses, water tank volume, inclination and azimuth, mass flow of solar fluid, pipes length and pipes diameter. The more detailed description of the f-chart model can be found in [22].

A detailed inventory, based on cost of materials and energy consumption estimated for every variant of system, was then used for the detailed Life Cycle Assessment. Modeling of the life cycle was based on the use of SimaPro v. <IP_ADDRESS> software (PRE Consultans, Amersfoort, The Netherlands) and Ecoinvent v. 3 database (Ecoinvent Assoiation, Zurich, Switzerland), which was used for the description of unit processes. Life Cycle Impact Assessment was performed by means of the the IMPACT 2002+ and CED v. 3 methods.

The IMPACT 2002+ method allows for the assessment of environmental stress connected with the life cycle of the solar system. The indicator (expressed in points: Pt) links all types of inventory results throughout the fourteen midpoint categories into four main damage categories: Human Health, Ecosystem Quality, Climate Change and Resources. The higher the indicator calculated by using this method, the greater the environmental impact of the system [23]. The functional unit was 1 kWh of energy generated by the system.

Cumulative Energy Demand (CED) method was used to estimate the total primary energy consumption (expressed in MJ) of the solar system throughout its entire lifetime, including the direct and indirect energy streams associated with the particular phases of life cycle [24].

For the validation of final results in CED, Monte Carlo statistical simulations (lognormal distribution) were implemented in order to compare the possible error between the achieved results.

In the multi-criteria analysis, the economic and environmental issues were discussed according to the following scheme. Firstly, Simple Payback Time (SPBT) was calculated for every variant of installation according to the definition, expressing the total cost of investment and operation divided by yearly savings [11].

In the next step, Energy Payback Time (EPBT) was calculated as a basis for technological foundations of the functioning of the system. EPBT was based on the CED results: in this case, statistical processing of data was a basis for the determination of the confidence interval. In the third part of evaluation, IMPACT 2002+ was calculated as an environmental criterion. The results obtained during the mentioned stages were then evaluated to indicate the most advantageous option with the use of the Weighted Sum Method.

#### **3. Results**

In the following subsection, the results of the economic, energetic and environmental evaluation of the analyzed SHW systems are presented with special attention paid to the financial and energetic payback times, as well as to the environmental damage categories affected by the production and operation of the systems. All of the detailed calculations are finally used to evaluate the selected installation options based on the ratings awarded in the multi-criteria analysis.

#### *3.1. Solar Hot Water Systems: Economic Evaluation*

The economic evaluation of the SHW system in variants I–VIII was based on the on-line price catalogues and average market cost of installation, with the use of direct contact with the owners and investors. The data on the operation of the installation and service costs were obtained from the users of the installation in the form of an interview confirmed by billing documentation.

The pump operation cost was based on the measured energy consumption in a 3-year operation period of heat-pipe collector installation [11] and the price of energy in Poland in 2018 (0.5055 PLN/kWh recalculated to 0.1113 Euro/kWh) according to the Energy Regulatory Office [25].

According to the data presented in Table 2, the Simple Payback Time in the basic option (investment cost covered by the owner only) exceeds 11 years in all of the variants, assuming a constant price of electricity. However, while considering the popular support programs such as Prosument 2, the payback time may be shorter. In this case, financing the investment by taking up credit is a clear approach, which may worsen the presented results. In the case of the support programs financed by the local authorities, where the discount may reach 70%, SPBT decreases by almost threefold to 4.1 years in the most effective options of installation.

**Table 2.** Results of economic evaluation for the analyzed system variants.

\*—own investment, \*\*—Prosument 2 program, 30% discount, 10 years credit, **\*\*\***—local programs with 70% discount.

#### *3.2. Solar Hot Water Systems: Energy Balance*

Energy balance of the SHW system was considered with the use of the CED method, as well as the calculation of the energy generated by the solar system. It is worth underlining that the predicted energy consumption in the 20-year operation period was included in the calculation, according to Figure 2.

**Figure 2.** Energy balance of one-year operation of system according to the applied model.

The obtained EPBT results (Table 3) are higher than in some literature studies [17]. This may be caused by both the differences in solar irradiation, as well as the type of system and source of energy used for pumping. In all the considered cases, the EPBT indicator was significantly shorter than the predicted lifespan, assumed as 20 years.

**Table 3.** Results of energetic and economic evaluation.

The results of LCIA conducted using CED indicator were subjected to a sensitivity analysis by means of the Monte Carlo statistical method (Figure 3). All system inputs and outputs were successively changed in the frames of standard deviation in 1000 trials, which allowed the scale of possible error to be shown in the calculations. The confidence level was assumed as 95%. In all the variants, the scale of possible error was similar, and the statistical distribution was positively skewed with a higher mean than the median in all analyzed cases.

#### *3.3. Solar Hot Water Systems: Environmental Impact Indicators*

The impact on the environment, considered as ecosystems, resources, human health and climate change, was assessed with the IMPACT2002+ method. The results of the impact assessment stage, recalculated to the functional unit (1 kWh of energy generated by the system) are presented in Figure 4. The share analysis on the level of processes shows that the electricity used for pumping is the most influential process in the SHW system life cycle. Other important elements include solar collectors and water tanks due to the high consumption of materials.

**Figure 3.** Results of CED calculation with the statistical error based on the Monte Carlo analysis.

**Figure 4.** Results of IMPACT 2002+ calculation per functional unit, Pt/kWh.

According to the share analysis on the damage categories level, the results obtained for the analyzed systems are similar for Variants I-VIII, with the highest contribution from the Human health, Climate change and Resources categories. This is caused mostly by the similarities in construction and the supporting conventional energy used (Figure 5).

#### *3.4. Solar Hot Water Systems: Multi-Criteria Analysis*

The analysis performed in this study aimed to compare several alternatives of solar hot water system construction on the basis of SPBT, EPBT and IMPACT 2002+ indicators. Assuming equal weights for all the analyzed criteria, the MCA results were presented by means of the Weighted Sum Method indicator as a percentage of the difference between the actual and minimal parameter related to the difference between the maximal and minimal parameter (Table 4).

**Figure 5.** Share analysis of IMPACT2002+ indicator on damage category level.

According to the data in Table 4, the best option is Variant V of installation, where all of the analyzed parameters were minimal due to the high efficiency of the system. Conversely, Variant IV can be assessed as the worst due to the longest payback periods and the highest environmental impact indicator. Following the specification of the analyzed systems, one can state that the most meaningful parameter is the type of solar collector. This contributed to approximately a 60% difference between systems (Variant I–IV vs. Variant V–VIII). The other analyzed parameters, such as water tank capacity (16–17% difference), and pipe material (13–15%) were also important. In turn, compared to the literature values, the analyzed solutions are characterized by higher payback times. This is connected with the method of analysis, e.g., covering the additional conventional energy spent on system operation, as well as various climate conditions.

#### **4. Conclusions**

According to the presented results, the most favorable solution included a heat-pipeevacuated tube collector, copper pipes and 200 dm3 water tank. Although the selection of a higher-capacity tank led to the optimization of solar energy conversion efficiency, the increase in this parameter was not crucial for the conducted research. However, it should be underlined that the values of the calculated indicators are comparable for all cases. For example, the payback times for both energy and financial inputs differed by no more than 11 months. Therefore, the analyzed systems can be assessed as green solutions, significantly minimizing the environmental impact connected with conventional energy usage.

The multi-criteria analysis, covering several aspects of systems' life cycle, can be used as a tool for the optimization of their selection in the green designing process. Moreover, the additional criteria used for sustainable designing can significantly improve the environmental balance of the analyzed technologies.

**Author Contributions:** Conceptualization, A.Z.; methodology, A. ˙ Z.; software, A. ˙ Z. and J.G.; valida- ˙ tion, A.Z.; formal analysis, A. ˙ Z. and J.G.; investigation, A. ˙ Z.; resources, A. ˙ Z.; data curation, A. ˙ Z.; ˙ writing—original draft preparation, A.Z.; writing—review and editing, A. ˙ Z. and J.G.; supervision, ˙ A.Z. and J.G.; project administration, A. ˙ Z. and J.G. All authors have read and agreed to the published ˙ version of the manuscript.

**Funding:** The publication is supported from founds FD-20/IS-6/012 and FD-20/IS-6/042 granted by Faculty of Environmental Engineering, Lublin University of Technology.

**Data Availability Statement:** Not applicable.

**Conflicts of Interest:** The authors declare no conflict of interest.

#### **References**

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**Author details**

Juriy Andreevich Tashkinov Donbass National Academy of Civil Engineering and Architecture, Khartsyzsk, Ukraine

\*Address all correspondence to<EMAIL_ADDRESS>
© 2021 The Author(s). Licensee IntechOpen. This chapter is distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/ by/3.0), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


*2.1. Phase Quantization*

The above computed phase is the ideal phase shift of each unit cell. However, only a limited phase shift can actually be provided with the coding unit cell. Hence, it is inevitable that we have to consider the phase quantization for the coding metasurface [13]. One can realize from Equation (3) that the phase compensation might be not within the range between 0 and 2*π*. Then, it should be shifted to be in the range of [0, 2*π*] before being quantized. Considering 1-bit coding unit cell, the shifted and quantized phase can be given as:

$$
\phi\_{mn}^{-} = \phi\_{mn} - 2\pi \left[\frac{\phi\_{mn}}{2\pi}\right],
\tag{4}
$$

$$
\boldsymbol{\phi}\_{mn}^{\circ} = \begin{cases}
\boldsymbol{\pi} & \text{if } \boldsymbol{\pi}/2 \le \boldsymbol{\phi}\_{mn}^{\circ} \le 3\boldsymbol{\pi}/2 \\
\boldsymbol{0} & \text{elsewhere} \end{cases}
\tag{5}
$$

After quantization, the reflection phase of the unit cell has just two states: 0◦ or 180◦, corresponding to the coding "1" and coding "0", respectively. To demonstrate the focusing ability of the coding metasurface, we computed the ideal phase and quantized phase distribution of the 16 × 16 coding metasurface using the above phase compensation method and the corresponding beam pattern as presented in Figure 2. The metasurface is assumed to be placed in XOY plane and is excited by a point source. Although the relative power generated by the ideal phase distribution (245) is much higher compared to one of the quantized phase distribution (around 170), both cases are capable of performing good beam steering. It is clear that beam synthesis can be acquired by 1-bit coding metasurface.

**Figure 2.** Reflection phase distribution and 3D pattern of the coding metasurface with an electromagnetic (EM) source located at (0 cm, 0 cm, 10 cm) and beam focusing at (0◦, 30◦): (**a**) ideal reflection phase distribution; (**b**) quantized phase distribution; (**c**) the beam pattern w.r.t ideal phase distribution; (**d**) the beam pattern w.r.t quantized phase distribution.


**6. Conclusions**

In this paper, a model combined by HHT and VMD is proposed to extract multidimensional dynamic responses characteristics of time, frequency, and energy of offshore oil platforms. A series of shaking-table tests and field tests in an offshore oil platform in Shengli Oilfield at Dongying City were performed using a single GPS receiver and a single accelerometer. By comparing analysis results between PSD and VMD–HHT, we found that dynamic response characteristics of ship collisions cannot be extracted entirely relying only on PSD. In contrast, VMD–HHT could effectively extract the characteristics of time, frequency, and energy simultaneously. Based on the analysis results of VMD–HHT, the dynamic displacements were reconstructed using the accelerometer in the MIMU, and the maximum displacement calculated by VMD–HHT based FDIA was 6 mm. Moreover, acceleration and angular rate obtained by MIMU had a high similarity and clear axial correlation, and such integration could also be used to calculate the torsion angle of offshore oil platforms; the maximum torsion angle is up to 1.1◦.

This novel proposed method could aid in the avoidance of collisions of offshore oil platforms and be further applied in oil exploitation and platform maintenance and monitoring. However, VMD–HHT model will not be able to effectively extract feature information when the noise frequency is close to the frequency of dynamic response events.

**Author Contributions:** Conceptualization, J.W. and X.L.; methodology, J.W.; validation, J.W., X.L. and W.L.; investigation, J.W.; resources, J.W. and C.H.; data curation, F.L.; writing—original draft preparation, X.L.; writing—review and editing, J.W., X.L., W.L., F.L. and C.H.; funding acquisition, J.W. All authors have read and agreed to the published version of the manuscript.

**Funding:** This research was funded by The National Natural Science Foundation of China, Grant Number 41874029, and The National Key Research and Development Program of China, Grant Number 2020YFD1100201.

**Data Availability Statement:** Not applicable.

**Conflicts of Interest:** The authors declare no conflict of interest.