**2.1 Deflection**

340 Serial and Parallel Robot Manipulators – Kinematics, Dynamics, Control and Optimization

applications. Shi *et al.* (1998) discussed some key issues in the dynamic control of

As a consequence of the interest in using flexible structures in robotics, several papers regarding the design of controllers for the manipulation task of flexible manipulators are found in the literature (Latornell *et al.*, 1998), (Choi and Krishnamurthy, 1994) and (Chang

In Tsujita *et al.* (2004), the trajectory and force controller of a flexible manipulator is proposed. From the point of view of structural dynamics, the trajectory control for a flexible manipulator is dedicated to the control of the global elastic deformation of the system, and the force control is dedicated to the control of the local deformation at the tip of the endeffector. Thus, preferably trajectory and force controls are separated in the control strategy. Static and dynamic hybrid position/force control algorithms have been developed for flexible-macro/rigid-micro manipulator systems (Yoshikawa *et al.*, 1996). The robust cooperative control scheme of two flexible manipulators in the horizontal workspace is presented in Matsuno and Hatayama (1999). A passive controller has been developed for the

In Miyabe *et al*. (2004), the automated object capture with a two-arm flexible manipulator is addressed, which is a basic technology for a number of services in space. This object capturing strategy includes symmetric cooperative control, visual servoing, the resolution of the inverse kinematics problem, and the optimization of the configuration of a two-arm

The effective use of flexible robotic manipulators in industrial environment is still a challenge for modern engineering. Usually there are several possible trajectories to perform a given task. A question that arises when programming robots is which is the best trajectory. There is no definitive solution, since the answer to this question depends on the selected performance index. Focused on industrial applications, the optimal path planning of a flexible manipulator is addressed in the present chapter. The manipulator is requested to perform a task in a vertical plane. Under this condition the gravitational effects are taken into account. Energy consumption is minimized when the movement is conducted through a suitable path. Energy is calculated by means of the evaluation of the joint torque along the path. End-effector accuracy is improved by reducing the vibration effect and increasing manipulability. The determination of the position takes into account the influence of structural flexibility. Weighting parameters are used to set the importance of each objective. The optimization scenario is composed by an optimal control formulation, solved by means of a nonlinear programming algorithm. The improvement obtained through a global optimization procedure is discussed. Numerical results demonstrate the viability of the

A control formulation to determine the optimal torque profile is proposed. The optimal manipulability is also taken into account. The effect of using end-effector positioning error as performance index is discussed. As a result, the contribution of the present work is the proposition of a methodology to evaluate the influence of different performance indexes in a

The paper is organized as follows. In Section 2, model of deflection, torque and manipulability are presented. Section 3 recalls the general optimal control formulation and the performance indexes are defined. Geometrical insight about the design variables is given. Multi-criteria programming aspects such as Pareto-optimality and objective weighting are presented in section 4. The global optimization strategy is outlined in section

payload manipulation with two planar flexible arms (Damaren 2000).

lightweight robots for several applications.

redundant flexible manipulator.

proposed methodology.

multi-criteria optimization environment.

and Chen, 1998).

Different schemes for modeling of the manipulators have been studied by a number of researchers. The mathematical model of the manipulator is generally derived from energy principles and, for a simple rigid manipulator, the rigid arm stores kinetic energy due to its moving inertia, and stores potential energy due its position in the gravitational field.

A flexible link also stores deformation energy by virtue of its deflection, joint and drive flexibility. Joints have concentrated compliance that may often be modeled as a pure spring storing only strain energy. Drive components such as shafts and belts may appear distributed. They store kinetic energy due to their low inertia, and a lumped parameter spring model often succeeds well to consider such an effect.

The most important modeling techniques for single flexible link manipulators can be grouped under the following categories: assumed modes method, finite element method and lumped parameters technique.

In the assumed modes approach, the link flexibility is usually represented by a truncated finite modal series, in terms of spatial mode eigenfunctions and time-varying mode amplitudes. Although this method has been widely used, there are several ways to choose link boundary conditions and mode eigenfunctions. Some contributions in this field were presented by Cannon and Schmitz (1984), Sakawa *et al.* (1985), Bayo (1986), Tomei and Tornambe (1988), among others. Nagaraj *et al.* (2001), Martins *et al.* (2002) and Tso *et al.* (2003) studied single-link flexible manipulators by using Lagrange's equation and the assumed modes method.

Regarding the finite element formulation, Nagarajan and Turcic (1990) derived elemental and system equations for systems with both elastic and rigid links. Bricout *et al.* (1990) studied elastic manipulators. Moulin and Bayo (1991) also used finite element discretization to study the end-point trajectory tracking for flexible arms and showed that a non-causal solution for the actuating torque enables tracking of an arbitrary tip displacement with any desired accuracy.

By using a lumped parameter model, Zhu *et al.* (1999) simulated the tip position tracking of a single-link flexible manipulator. Khalil and Gautier (2000) used a lumped elasticity model for flexible mechanical systems. Megahed and Hamza (2004) used a variation of the finite segment multi-body dynamics approach to model and simulate planar flexible link manipulator with rigid tip connections to revolute joints.

Santos *et al.* (2007) proposed the computation of flexibility by means of a spring-massdamper system. According to this analogy, the first spring and damper constants are related to the joint behavior, and the following sets of spring and damper represent link flexibility. The variables and the parameters of the model are interpreted as angular quantities.

In this work the description of the deflection related to a rigid link is proposed. It is achieved by means of an Euler-Bernoulli beam formulation and covers the case for small deflections of a beam subject to lateral loads.

The bending moment *M*, shear forces *Q* and deflections *w* for a cantilever beam subjected to a point load *P* at the free end are given by

$$M(\mathbf{x}) = P(\mathbf{x} - L) \tag{1}$$

$$Q(\mathbf{x}) = \mathbf{P} \tag{2}$$

$$\text{cov}(\mathbf{x}) = \frac{P\mathbf{x}^2 \text{(3L - x)}}{6EI} \tag{3}$$

$$\text{cov}(L) = \frac{PL^3}{3EI}.\tag{4}$$

$$
\Delta\theta = \arcsin\left(\frac{\mathcal{W}}{L}\right). \tag{5}
$$

$$\mathcal{S} = \sum\_{j=1}^{2} T\_j(\theta) - T\_j(\theta + \Delta\theta) \tag{6}$$

$$
\pi\_f = \frac{d}{dt} \left( \frac{\partial L}{\partial \dot{\theta}\_f} \right) - \frac{\partial L}{\partial \theta\_f} \tag{7}
$$

$$Q(q)\ddot{q} + \mathcal{L}(q,\dot{q}) + \mathcal{G}(q) = \text{ }\tau\text{ }\tag{8}$$

$$Q\_{11} = \left(\frac{1}{3}\right)m\_1\,a\_1^2 + \left(\frac{1}{3}\right)m\_2\,a\_2^2 + m\_2\,a\_1^2 + m\_2\,a\_1\,a\_2\cos(\theta\_2) \tag{9}$$

$$Q\_{12} = \left(\frac{1}{3}\right) m\_2 \ a\_2^2 + 0.5 \, m\_2 \ a\_1 \ a\_2 \cos(\theta\_2) \tag{10}$$

$$Q\_{21} = \left(\frac{1}{3}\right) m\_2 \ a\_2^2 + 0.5 \, m\_2 \ a\_1 \ a\_2 \cos(\theta\_2) \tag{11}$$

$$Q\_{22} = \left(\frac{1}{3}\right) m\_2 \, a\_2^2 \tag{12}$$

$$\mathcal{L}\_{11} = -m\_2 \, a\_1 \, a\_2 \, \sin(\theta\_2) \dot{\theta}\_1 \, \dot{\theta}\_2 - 0.5 \, m\_2 \, a\_1 \, a\_2 \, \sin(\theta\_2) \, \dot{\theta}\_2 \tag{13}$$

$$\mathcal{L}\_{21} = \begin{array}{c} 0.5 \ m\_2 \ a\_1 \ a\_2 \ \sin \{\theta\_2\} \ \dot{\theta\_2}^{'} \end{array} \tag{14}$$

$$\mathcal{G}\_{11} = -0.5 \, m\_1 \, g \, \, a\_1 \cos(\theta\_1) - 0.5 \, m\_2 \, g \, \, a\_2 \cos(\theta\_1 + \theta\_2) - m\_2 \, g \, \, a\_1 \cos(\theta\_1) \tag{15}$$

$$G\_{21} = -0.5 \, m\_2 \, g \, a\_2 \cos(\theta\_1 + \theta\_2) \tag{16}$$

Multi-Criteria Optimal Path Planning of Flexible Robots 345

reference nodes, presented by circles in Figure 1. The abscissa presents the time instants (�� = �� �� = 1) while the ordinate is the joint angle. The value of intermediate joint angles

This approach ensures a smooth transition on the joint angles, velocities and accelerations, which are positive aspects from the mechanical perspective. A smooth movement preserves

0.0 0.2 0.4 0.6 0.8 1.0

Time (s)

Optimal programming problems for continuous systems are included in the field of the calculus of variations. A continuous-step dynamic system is described by an *n*dimensional state vector **x**(*t*) at time *t*. The choice of an *m*-dimensional control vector **u**(*t*) determines the time rate of change of the state vector through the dynamics given by the

A general optimization problem for such a system is to find the time history of the control

� = �������� � � �[�(�)� �(�)� �]�� ��

In the present context, the interest is focused on the joint angles and the reference nodes. Performance indexes such as positioning error, manipulability and mechanical power are derived from this information. The variable ���� = ��(��) is an element of the state vector **x**, which represents the joint angle at each time ��, related to the joint *j.* The control vector ����

��

vector **u**(*t*) for �� ����� to minimize a performance index given by

��(�) = �(�(�)� �(�)� �) (20)

(21)

between the references nodes are evaluated by means of a cubic spline interpolation.

Fig. 1. Reference nodes (o) and joint angle (—).

0.0

0.5

Joint angle (rad)

1.0

1.5

the mechanism from fatigue effects, for example.

subject to Equation (20) with *t0*, *tf*, and **x**(*ti*) specified.

equation below:

variations of the torque along the path. This means that an explicit constraint over the maximum torque is not required since it will be implicitly achieved by the present formulation.

## **2.3 Manipulability**

As an approach for evaluating quantitatively the ability of manipulators from the kinematics viewpoint the concepts of manipulability ellipsoid and manipulability measure are used.

The set of all end-effector velocities *v* which are realizable by joint velocities such that the Euclidean norm satisfies ����� ��1 are taken into account. This set is an ellipsoid in the *m*dimensional Euclidean space. In the direction of the major axis of the ellipsoid, the endeffector can move at high speed. On the other hand, in the direction of the ellipse minor axis the end-effector can move only at low speed. Also, the larger the ellipsoid the faster the endeffector can move. Since this ellipsoid represents an ability of manipulation it is called as the manipulability ellipsoid.

The principal axes of the manipulability ellipsoid can be found by making use of the singular-value decomposition of the Jacobian matrix��(�). The singular values of *J*, i.e.� ��� ���…���, are the *m* larger values taken from the *n* roots ����� � = 1� … � �� of the eigenvalues. Then �� are the eigenvalues of the matrix��(�)��(�).

One of the representative measures for the ability of manipulation derived from the manipulability ellipsoid is the volume of the ellipsoid. This is given by����, where

$$
\omega = \sigma\_1 \dots \sigma\_2 \dots \sigma\_m \tag{17}
$$

$$c\_m = \begin{cases} \left(2\pi\right)^{\frac{m}{2}} / [2.4.6\dots \text{(m-2)}.m] & \text{if } m \text{ is even} \\ 2(2\pi)^{\frac{(m-1)}{2}} / [1.3.5\dots \text{(m-2)}.m] & \text{if } m \text{ is odd}. \end{cases} \tag{18}$$

Since the coefficient��� is a constant value when the dimension *m* is fixed, the volume is proportional to *w*. Hence, *w* can be seen as a representative measure, which is called the manipulability measure, associated to the manipulator joint angle��.

Due to the direct relation between singular configuration and manipulability (through the Jacobian), the larger the manipulability measure the larger the singular configuration avoidance.

The distance from singular points can be obtained from the solution of an optimization problem in which the following objective function is minimized:

$$f(\theta) = \frac{1}{w} \tag{19}$$

Consequently, the minimization of Equation (19) means to increase the manipulability measure.

### **3. Optimal control formulation**

#### **3.1 Design variables**

The design variables are the key parameters that are updated during the workflow, aiming at increasing (or decreasing) the performance index. In this study, the design variables are

variations of the torque along the path. This means that an explicit constraint over the maximum torque is not required since it will be implicitly achieved by the present

As an approach for evaluating quantitatively the ability of manipulators from the kinematics viewpoint the concepts of manipulability ellipsoid and manipulability measure

The set of all end-effector velocities *v* which are realizable by joint velocities such that the Euclidean norm satisfies ����� ��1 are taken into account. This set is an ellipsoid in the *m*dimensional Euclidean space. In the direction of the major axis of the ellipsoid, the endeffector can move at high speed. On the other hand, in the direction of the ellipse minor axis the end-effector can move only at low speed. Also, the larger the ellipsoid the faster the endeffector can move. Since this ellipsoid represents an ability of manipulation it is called as the

The principal axes of the manipulability ellipsoid can be found by making use of the singular-value decomposition of the Jacobian matrix��(�). The singular values of *J*, i.e.� ��� ���…���, are the *m* larger values taken from the *n* roots ����� � = 1� … � �� of the

One of the representative measures for the ability of manipulation derived from the

Since the coefficient��� is a constant value when the dimension *m* is fixed, the volume is proportional to *w*. Hence, *w* can be seen as a representative measure, which is called the

Due to the direct relation between singular configuration and manipulability (through the Jacobian), the larger the manipulability measure the larger the singular configuration

The distance from singular points can be obtained from the solution of an optimization

�(�) = 1 �

Consequently, the minimization of Equation (19) means to increase the manipulability

The design variables are the key parameters that are updated during the workflow, aiming at increasing (or decreasing) the performance index. In this study, the design variables are

� /[2.4.6 … (��2). �� if � is even

� /[1.3.5 … (��2). �� if � is odd.

�=��. �� … �� (17)

(18)

(19)

manipulability ellipsoid is the volume of the ellipsoid. This is given by����, where

eigenvalues. Then �� are the eigenvalues of the matrix��(�)��(�).

�

(���)

manipulability measure, associated to the manipulator joint angle��.

problem in which the following objective function is minimized:

�� = � (2�)

2(2�)

formulation.

are used.

avoidance.

measure.

**3. Optimal control formulation**

**3.1 Design variables**

**2.3 Manipulability**

manipulability ellipsoid.

reference nodes, presented by circles in Figure 1. The abscissa presents the time instants (�� = �� �� = 1) while the ordinate is the joint angle. The value of intermediate joint angles between the references nodes are evaluated by means of a cubic spline interpolation.

This approach ensures a smooth transition on the joint angles, velocities and accelerations, which are positive aspects from the mechanical perspective. A smooth movement preserves the mechanism from fatigue effects, for example.

Optimal programming problems for continuous systems are included in the field of the calculus of variations. A continuous-step dynamic system is described by an *n*dimensional state vector **x**(*t*) at time *t*. The choice of an *m*-dimensional control vector **u**(*t*) determines the time rate of change of the state vector through the dynamics given by the equation below:

$$\dot{\mathbf{x}}(t) = f(\mathbf{x}(t), \mathbf{u}(t), t) \tag{20}$$

A general optimization problem for such a system is to find the time history of the control vector **u**(*t*) for �� ����� to minimize a performance index given by

$$J = \varphi[\mathbf{x}(t\_f)] + \int\_{t\_0}^{t\_f} L[\mathbf{x}(t), \mathbf{u}(t), t]dt \tag{21}$$

subject to Equation (20) with *t0*, *tf*, and **x**(*ti*) specified.

In the present context, the interest is focused on the joint angles and the reference nodes. Performance indexes such as positioning error, manipulability and mechanical power are derived from this information. The variable ���� = ��(��) is an element of the state vector **x**, which represents the joint angle at each time ��, related to the joint *j.* The control vector ����

$$
\varphi[\mathbf{x}(t\_f)] = \left[e\_1\left(\mathbf{x}(t\_f)\right) - p\_t\right]^2\tag{22}
$$

$$J = \left[ e\_1 \left( \mathbf{x}(t\_f) \right) - p\_t \right]^2 \tag{23}$$

$$L\_1(\mathbf{x}(t), \mathbf{u}(t), t) = \sum\_{j=1}^{2} \tau\_{l,j}^2 \tag{24}$$

$$L\_2(\mathbf{x}(t), \mathbf{u}(t), t) = \sum\_{j=1}^{2} \left(\frac{1}{\mathbf{w}\_{l,j}^2}\right) \tag{25}$$

$$L\_3(\mathbf{x}(t), \mathbf{u}(t), t) = \sum\_{l,j=1}^{2} \delta\_{l,j}^2 \tag{26}$$

$$\min\_{\mathbf{u}\sim\alpha} \{ f(\mathbf{u}) | h(\mathbf{u}) = 0, g(\mathbf{u}) \le 0 \} \tag{27}$$

$$p[f(\mathbf{u})] = \sum\_{k=1}^{m} a\_k f\_k(\mathbf{u}), \mathbf{u} \in \Omega. \tag{28}$$

Multi-Criteria Optimal Path Planning of Flexible Robots 349

suggested (Levy and Gomez, 1985) (Levy and Montalvo, 1985) for being used in Equation

Computational evaluation was performed aiming at evaluating the effectiveness of the

(29) to avoid undesirable points and prevent the search algorithm to fail.

**6. Numerical results**

Fig. 2. Computational workflow.

proposed methodology, as outlined in Figure 2.

It follows that�� = � at the beginning of the optimization process. At the end, �����. By using this scaling procedure, the final objective function value provides a non-dimensional index that describes the percentage of improvement. As an example, the final value *J*=0.3 means that the overall objective was reduced to 30% of this initial value.


**5.1 Physiological and analytical data**

24 Basic Nephrology and Acute Kidney Injury

absence of inulin excretion in two types of aglomerular fishes (goosefish, *Lophius piscatorius*  and toadfish *Osteichthyes - Lophiidae*). In the same article, Shannon measured GFR by inulin clearance in another type of fish with glomerulus, the dogfish (*Chondrichthyes* – *Squalidae*). These fishes were then treated with phlorizin which was sensed to block all tubular activity. Although the creatinine clearance in this fish was increased, the inulin clearance was not modified by this treatment (Shannon, 1934). In the same year of 1934, inulin clearance was also measured in aglomerular fish and in dogs by Richards (Richards et al., 1934). The experimentation (measuring GFR with and without phlorizin) was then repeated in man by Smith and Shannon. The results obtained in animals were confirmed in humans. Shannon was the first human who was perfused by inulin in 1935 (Shannon & Smith, 1935; Smith, 1951c). These authors had thus suggested that inulin was not secreted by renal tubules. This assertion will be thereafter confirmed by other authors with the same type of methodology (Shannon & Smith, 1935; Alving et al., 1939; Laake, 1954). Additional arguments were developed in the sixties by animal studies using micropontions in the tubules (Gutman et al., 1965). After intravenous injection, inulin is fully excreted by kidneys in urine (Shannon & Smith, 1935), even if very low concentrations of inulin are found in bile (Höber, 1930;

Inulin is doubtless the marker who has been the most investigated from a physiological point of view. In this view, it is logical that inulin is still considered as the gold standard for GFR measurement. Nevertheless, there are limitations to its use in daily practice. Because its relatively high molecular weight (5200 Da), the molecule is relatively viscous and don't quickly reach its volume of distribution. Therefore, only methods using urinary clearance with constant infusion rate seem accurate for this marker. Such methods are more cumbersome. Moreover, inulin is not easily available on the market and remains relatively costly. From our point of view, the most important limitation of inulin is the difficulty linked to its measurement in urine and plasma. Actually, several methods have been proposed and these methods are probably not interchangeable. There is no standardization in inulin measurement. We have shown that GFR results could vary from -10 to +10 mL/min in the same patient only because inulin was measured by a different method (unpublished data). Moreover, most of the methods (except the enzymatic ones) are prone to interferences with glucose measurement which is a limiting factor when measuring GFR in diabetic patients (Little, 1949). Regarding the methods for measuring inulin, we can cite the "acid" methods (Kuehnle et al., 1992; Shaffer & Somogoyi, 1933; Alving et al., 1939; Corcoran, 1952; Rolf et al., 1949; Roe, 1934; Steinitz, 1938; Hubbard & Loomis, 1942; Lentjes et al., 1994; Heyrovsky, 1956; Rolf et al., 1949), the enzymatic methods (Day & Workman, 1984; Delanghe et al., 1991; Jung et al., 1990; Summerfield et al., 1993; Dubourg et al., 2010) and the new methods by high performance liquid chromatography (HPLC) (Ruo et al., 1991; Baccard et al., 1999; Dall'Amico et al., 1995; Pastore et al., 2001). Describing these methods in detail are beyond the scope of this chapter and we propose the readers the following reference if they are interested in this

The use of inulin as GFR marker is justified by physiologic studies. The others markers that will be proposed thereafter will be compared to inulin measurements. Therefore, the use of other markers will be justified not by physiological studies (even if some

Schanker & Hogben, 1961).

topic (Delanaye et al., 2011b).

**4. Preliminary statistical considerations**

51Cr-EDTA is an isotopic marker which has a low molecular weight (292 Da). Most of the authors consider that 51Cr-EDTA is not binding to proteins (<0,5% (Brochner-Mortensen, 1978; Bailey et al., 1970; Garnett et al., 1967; Stacy & Thorburn, 1966; Forland et al., 1966; Kempi & Persson, 1975; Forland et al., 1966)) even if Rehling described a binding to protein of 10% (Rehling et al., 1995; Rehling et al., 2001). Due to its low molecular weight, 51Cr-EDTA is freely filtrated through the glomerulus. Physiological studies about renal handling of 51Cr-EDTA are few but it seems that 51Cr-EDTA is neither secreted nor absorbed by renal tubules (Eide, 1970). This absence of secretion and absorption is also confirmed by Forland in dogs (Forland et al., 1966). Regarding the potential extra-renal excretion of 51Cr-EDTA, Garnett described a salivary and a fecal excretion under 1% in one anephric patient (Garnett et al., 1967). Brochner-Mortensen later confirmed the poor fecal excretion (less than 0.1% of the injected dose). Studying the renal excretion and the corporal global radioactivity of 8 healthy subjects after 72 hours, Brochner-Mortensen estimated that 4.5% of the 51Cr-EDTA will be retained in the body, especially in the liver and kidneys (Brochner-Mortensen et al., 1969). The difference between 51Cr-EDTA total clearance and 51Cr-EDTA urinary clearance corresponds to extra-renal clearance of the marker. With this methodology, the same authors estimated extra-renal clearance at 4 mL/min (and this extra-renal clearance remains stable for all GFR ranges)(Brochner-Mortensen & Rodbro, 1976). Jagenburg had also calculated an extra-renal clearance of 2 mL/min in two anuric dialysis patients (Jagenburg et al., 1978). Only, Rehling described a higher extra-renal clearance at 8.4% (Rehling et al., 1995).

Measurement of 51Cr-EDTA by nuclear count is very precise and easy because 51Cr-EDTA half time is long (27 days)(Chantler et al., 1969). The quantity of 51Cr-EDTA injected is

How Measuring Glomerular Filtration Rate? Comparison of Reference Methods 27

**GFR methods Statistics Results**

Regression Correlation

Ratio Correlation BAr

Ratio Regression Correlation

Correlation Regression

Correlation Regression Ratio

Correlation Regression Ratio

Correlation Regression BAr

Correlation Regression Mean difference

Correlation 0.995

=1.075x-3.06 0.995

51Cr-EDTA underestimat es by de 14- 16%

> 1.02 0.992 1.5±8.7

0.96 ± 0.0027 =0.96x+0.26 0.994

0.974 =1.017x+1.6

0.977 =1.004x-0.032 1.004±0.013

0.91 =0.98x+6.5 0.96±0.02

0.97 =0.85x+11.42 1.5±11.7

0.984 =1.099x+4.96

6.2 mL/min

and constant infused rate

and constant infused rate

and constant infused rate

and constant infused rate

clearance and constant infused rate 51Cr-EDTA : plasmatic clearance: on 5 hours, samples every 15 min

clearance and constant infused rate

> and constant infused rate

clearance and constant infused rate 51Cr-EDTA : plasmatic clearance: samples at 5,10, 15, 20, 30, 60, 90, 120, 150, 180, 210, 240 min

clearance and constant infused rate 51Cr-EDTA : plasmatic clearance: samples timing not available

± 20 to 140 Urinary clearance

±8 to 120 Inulin: urinary

10 to 150 Urinary clearance

**(mL/min/ 1.73 m²)**

56 NA ± 0 to 180 Urinary clearance

20 CKD 6 to 187 Urinary clearance

17 2 healthy ± 10 to 130 Inulin: urinary

21 CKD ± 10 to 160 Urinary

20 NA 6 to 166 Inulin: urinary

15 healthy 41 calcium troubles

25 Healthy and

CKD

CKD ± 0 to 150 Urinary clearance

**References Sample Population GFR range**

39 Healthy

CKD Calcium troubles

(Garnett et al., 1967)

(Heath et al., 1968)

(Favre & Wing, 1968)

(Lavender et al., 1969)

(Brochner-Mortensen et al., 1969)

(Chantler et al., 1969)

(Stamp et al., 1970)

(Ditzel et al., 1972)

(Lingardh, 1972)

100 clearances in 28 subjects

65 clearances in 56 subjects

relatively small and therefore the irradiating dose received by the patient is very limited (absorbed dose from 0.011 to 0.0077 mSv according to the radioactive dose injected which is usually 7 MBq). This absorbed dose corresponds to the natural dose of irradiation received in one week and is much lesser than the dose received after thoracic radiography (0.02 mS). Nevertheless, we do not recommend this technique to measure GFR in pregnant women even if authors seem to use it safely (Brochner-Mortensen, 1978; Medeiros et al., 2009; Durand et al., 2006). The dose of EDTA is 1000x lesser than the dose considered as safe (Chantler et al., 1969).

#### **5.2 Clinical data**

The first studies about 51Cr-EDTA have been published in the sixties, even if studies (but with questionable methodology) had been published before with EDTA marked with 14Cr (Spencer et al., 1958; Foreman & Trujillo, 1954). In 1964, Downes was the first to give 51Cr-EDTA to cows to study the intestinal transit (Downes & Mcdonald, 1964). In 1966, Stacy and Thorburn are the first to inject 51Cr-EDTA to lambs for measuring GFR. They reported a good correlation with inulin clearance in the animal model (ratio 51Cr-EDTA/inulin was 0,95)(Stacy & Thorburn, 1966). The first scientists who will be interested in GFR measurement by 51Cr-EDTA in humans are English (Garnett et al., 1967; Favre & Wing, 1968; Garnett et al., 1967; Heath et al., 1968; Lavender et al., 1969). It must be underlined that nearly all studies published on this marker are coming from Europe because 51Cr-EDTA is not available in USA (not approved by the FDA)(Brandstrom et al., 1998). The first author who studied 51Cr-EDTA in humans is Garnett who was nuclearist in Southampton. These first data were published in The Lancet in 1967 (Garnett et al., 1967). This author injected one unique dose of 51Cr-EDTA and described a mono-exponential decrease in 51Cr-EDTA concentrations after 30 minutes. This author already evoked the plasma clearance (and the bolus injection) to measure GFR with 51Cr-EDTA. Unhopefully, Garnett did not compare his results to inulin clearance but only to creatinine clearance. However, Garnett performed and compared 56 51Cr-EDTA urinary clearances with inulin urinary clearances. He found a correlation of 0.995 and asserted that 51Cr-EDTA result were between ±5% of the inulin results which was really excellent. Thereafter, several studies were published on the same topic to compare performances of inulin clearance with urinary or plasma clearance of 51Cr-EDTA. We resumed these studies in Table 2, restricting the data to studies in adults. However, once again, the following conclusions will be drawn from studies having used the most adequate statistical methods. Globally, the performance of 51Cr-EDTA is good. Chantler, in 1969, showed that results of urinary clearance of 51Cr-EDTA was within 5% of the results of inulin (Chantler et al., 1969). This excellent concordance between urinary clearances of 51Cr-EDTA and inulin will be later confirmed by Froissart. This author showed a bias of +3 mL/min (51Cr-EDTA thus slightly overestimating inulin) and a precision of ± 4 mL/min (95% of the 51Cr-EDTA results will be + or – 8 mL/min around the bias)(Froissart et al., 2005b). The best study comparing 51Cr-EDTA plasma clearance with inulin clearance is certainly published by Medeiros in 2009 (Medeiros et al., 2009). This author showed that bias between the two GFR was 3±6 mL/min. This is one of the rare studies where accuracy 30% results are given (defined as the percentage of patients having a 51Cr-EDTA GFR within 30% of inulin GFR). Accuracy 30% for plasmatic clearance of 51Cr-EDTA is 93%. The higher performance is obtained when late blood samples (at 6 or 8 h) are considered.

relatively small and therefore the irradiating dose received by the patient is very limited (absorbed dose from 0.011 to 0.0077 mSv according to the radioactive dose injected which is usually 7 MBq). This absorbed dose corresponds to the natural dose of irradiation received in one week and is much lesser than the dose received after thoracic radiography (0.02 mS). Nevertheless, we do not recommend this technique to measure GFR in pregnant women even if authors seem to use it safely (Brochner-Mortensen, 1978; Medeiros et al., 2009; Durand et al., 2006). The dose of EDTA is 1000x lesser than the dose considered as safe

The first studies about 51Cr-EDTA have been published in the sixties, even if studies (but with questionable methodology) had been published before with EDTA marked with 14Cr (Spencer et al., 1958; Foreman & Trujillo, 1954). In 1964, Downes was the first to give 51Cr-EDTA to cows to study the intestinal transit (Downes & Mcdonald, 1964). In 1966, Stacy and Thorburn are the first to inject 51Cr-EDTA to lambs for measuring GFR. They reported a good correlation with inulin clearance in the animal model (ratio 51Cr-EDTA/inulin was 0,95)(Stacy & Thorburn, 1966). The first scientists who will be interested in GFR measurement by 51Cr-EDTA in humans are English (Garnett et al., 1967; Favre & Wing, 1968; Garnett et al., 1967; Heath et al., 1968; Lavender et al., 1969). It must be underlined that nearly all studies published on this marker are coming from Europe because 51Cr-EDTA is not available in USA (not approved by the FDA)(Brandstrom et al., 1998). The first author who studied 51Cr-EDTA in humans is Garnett who was nuclearist in Southampton. These first data were published in The Lancet in 1967 (Garnett et al., 1967). This author injected one unique dose of 51Cr-EDTA and described a mono-exponential decrease in 51Cr-EDTA concentrations after 30 minutes. This author already evoked the plasma clearance (and the bolus injection) to measure GFR with 51Cr-EDTA. Unhopefully, Garnett did not compare his results to inulin clearance but only to creatinine clearance. However, Garnett performed and compared 56 51Cr-EDTA urinary clearances with inulin urinary clearances. He found a correlation of 0.995 and asserted that 51Cr-EDTA result were between ±5% of the inulin results which was really excellent. Thereafter, several studies were published on the same topic to compare performances of inulin clearance with urinary or plasma clearance of 51Cr-EDTA. We resumed these studies in Table 2, restricting the data to studies in adults. However, once again, the following conclusions will be drawn from studies having used the most adequate statistical methods. Globally, the performance of 51Cr-EDTA is good. Chantler, in 1969, showed that results of urinary clearance of 51Cr-EDTA was within 5% of the results of inulin (Chantler et al., 1969). This excellent concordance between urinary clearances of 51Cr-EDTA and inulin will be later confirmed by Froissart. This author showed a bias of +3 mL/min (51Cr-EDTA thus slightly overestimating inulin) and a precision of ± 4 mL/min (95% of the 51Cr-EDTA results will be + or – 8 mL/min around the bias)(Froissart et al., 2005b). The best study comparing 51Cr-EDTA plasma clearance with inulin clearance is certainly published by Medeiros in 2009 (Medeiros et al., 2009). This author showed that bias between the two GFR was 3±6 mL/min. This is one of the rare studies where accuracy 30% results are given (defined as the percentage of patients having a 51Cr-EDTA GFR within 30% of inulin GFR). Accuracy 30% for plasmatic clearance of 51Cr-EDTA is 93%. The higher performance is obtained when late blood

(Chantler et al., 1969).

samples (at 6 or 8 h) are considered.

**5.2 Clinical data**

How Measuring Glomerular Filtration Rate? Comparison of Reference Methods 29

51Cr-EDTA clearance was the first published alternative to inulin. Among the strengths of this marker, we have to underline the good performance of GFR measurement comparing to inulin (or to other markers). Physiological profile can also be considered as satisfying. This marker is yet easy to measure (especially according to its long half-life) and the precision of the measurement appears excellent. The costs, compared to other GFR markers, are acceptable. One important limitation is linked to the fact that 51Cr-EDTA GFR must be done in a Nuclear Medicine department. The most important limitation of this marker is the non-

Like 51Cr-EDTA, 99Tc-DTPA is an isotopic marker with a low molecular weight (393 Da)(Durand et al., 2006). DTPA may be labeled with another isotopic marker (113mIndium (Johansson & Falch, 1978; Reba et al., 1968; Piepsz et al., 1974), 169Ytterbium (Perrone et al., 1990; Russell et al., 1985)) but technetium 99 is the most used up to now. The 99Tc-DTPA is also used in Nuclear Imagery (isotopic nephrogram) for instance to measure separately the function or the right and left kidney (Biggi et al., 1995; Hilson et al., 1976; Kainer et al., 1979). However, we will only discuss GFR measurement based on plasma and/or urinary methods with 99Tc-DTPA. GFR can also be estimated with external counting using gamma camera (namely the "Gates" method) (Gates, 1984; Russell, 1987) but this method is not precise enough to be considered as a reference method for measuring GFR.  If the GFR measurement is coupled with nephrogram, the radioactive dose is however 40 to 200x higher than a simple GFR measurement with 51Cr-EDTA (Kempi & Persson, 1975; Griffiths et al., 1988). The half-life of 99Tc-DTPA is short (6.05 h) which imposes that the GFR measurement is realized quickly after the samplings, which is a practical inconvenient compared to 51Cr-EDTA (Owen et al., 1982). The 99Tc-DTPA measurement is as precise as other isotopic methods. The most relevant critic regarding 99Tc-DTPA is its potential binding to protein. This aspect has been debated in the literature. Some authors described a binding to plasma proteins from 2 to 13%, which implies an underestimation of GFR, especially when GFR is measured by plasmatic clearance (Kempi & Persson, 1975; Agha & Persson, 1977; Klopper et al., 1972; Biggi et al., 1995; Houlihan et al., 1999; Rehling et al., 2001). These high percentages could however been explained by the lack of purity of the first available preparations of 99Tc-DTPA (Rootwelt et al., 1980; Rehling et al., 2001; Fleming et al., 2004; Carlsen et al., 1980; Russell et al., 1983; Kempi & Persson, 1975). This hypothesis has been well illustrated in 1980 by Carlsen who studied and compared 51Cr-EDTA clearances with 4 different commercial preparations of 99Tc-DTPA. This author showed different results according to the preparation used (Carlsen et al., 1980). The binding to protein may also be studied by different methodologies (ultrafiltration, electrophoresis, precipitation, *in vitro* or *in vivo,* in humans or in animals etc)(Rehling et al.,

**5.3 Strengths and limitations**

**6.1 Physiological and analytical data**

Fawdry et al., 1985; Durand et al., 2006).

use in USA, where 51Cr-EDTA is not recognized by the FDA.

**6. 99Tc-DTPA (Diethylenetriaminepenta-acetic acid)**

Table 2. Studies comparing 51Cr-EDTA with inulin. NA: not available, CKD: chronic kidney disease subjects, BA: Bland and Altman analysis, BAr: Bland and Altman analysis recalculated by us, BM: Brochner-Mortensen.

#### **5.3 Strengths and limitations**

28 Basic Nephrology and Acute Kidney Injury

29 CKD ± 30 to 160 Urinary clearance

31 CKD ± 30 to 160 Inulin: urinary

130 to 150 Urinary clearance

± 5 to 120 Inulin: urinary

17 Severe CKD 2.6 to 11 Urinary clearance Correlation

19 Nephrectomy 11 to 76 Inulin: urinary

111 NA NA Urinary clearance

22 NA NA Urinary clearance

44 Renal grafted ±15 to 80 Inulin: urinary

Table 2. Studies comparing 51Cr-EDTA with inulin. NA: not available, CKD: chronic kidney disease subjects, BA: Bland and Altman analysis, BAr: Bland and Altman analysis re-

and constant infused rate

and constant infused rate

clearance and constant infused rate 51Cr-EDTA : plasmatic clearance: samples at 180, 200, 220 et 240 min + BM correction

clearance and constant infused rate 51Cr-EDTA : urinary clearance:

clearance and constant infused rate 51Cr-EDTA : plasmatic clearance: 5 samples between 3 and 5 h+BM correction

> and constant infused rate

> and constant infused rate

clearance and constant infused rate 51Cr-EDTA : plasmatic clearance: samples at 2, 4, 6, 8 h + BM correction

Ratio 0.9±0.01

0.97 =0.855x+7.555 0.96±0.07

0.97 =0.961x+2.908 1±0.11

> 0.99 =0.96x+3.5

0.97 =1.05x-0.3

0.96 =0.86x+2.4 4.3 mL/min

BA 2.7±3.5

BA 4±4.9

NS 0.94 2.5±6.1 90.9%

Correlation Regression Ratio

Correlation Regression Ratio

Correlation Regression

Regression

Correlation Regression SD around the mean difference

t-test Correlation BA Exactitude 30%

(Brochner-Mortensen, 1973)

(Hagstam et al., 1974)

(Hagstam et al., 1974)

(Winterborn et al., 1977)

(Jagenburg et al., 1978)

 (Rehling et al., 1986)

(Froissart et al., 2005b)

(Froissart et al., 2005a)

(Medeiros et al., 2009)

calculated by us, BM: Brochner-Mortensen.

89 clearances in 9 subjects Healthy, before and after hyperglycemia

16 Children and 4 healthy adults

51Cr-EDTA clearance was the first published alternative to inulin. Among the strengths of this marker, we have to underline the good performance of GFR measurement comparing to inulin (or to other markers). Physiological profile can also be considered as satisfying. This marker is yet easy to measure (especially according to its long half-life) and the precision of the measurement appears excellent. The costs, compared to other GFR markers, are acceptable. One important limitation is linked to the fact that 51Cr-EDTA GFR must be done in a Nuclear Medicine department. The most important limitation of this marker is the nonuse in USA, where 51Cr-EDTA is not recognized by the FDA.


**1. Introduction**

Many areas in Europe and worldwide are increasingly subjected to catastrophic events. These events intensify the exposure of these territories to multi-risk events and make societies more vulnerable to entangled risks [1–7]. Globalization and climate changes are the main culprits of these multi-risk dynamics. Globalization, indeed, makes countries closely linked and interdependent, so communities are not only vulnerable to local extreme events but also to those occurring outside their national territories. Climate change increases, among others, the frequency and intensity of extreme meteorological phenomena, hydrological and flood risk, as well as the risk of fires. The awareness of this worrying trend has determined the need for adequate tools to address and mitigate these risks, as well as information campaigns to foster resilience and coping capacity of communities [5–7].

Understanding risks involving vast inhabited areas is therefore paramount, particularly when assessing potential losses produced by a combination of multiple hazards. Hereafter, a hazard refers to the probability of occurrence in a specified period of a potentially damaging event of a given magnitude in a given area [8]. Total risk is a measure of the expected human (casualties, injuries) and economic (damage to property, activity disruption) losses due to adverse natural phenomena. Such a measure is assumed to be the product of hazard, vulnerability, and exposure instances [9]. Many areas on Earth are subjected to the effects of coexisting multiple hazards, among which floods [3,8] and earthquakes are some of the most widespread [5–7]. Though inhabited environments are affected by multiple hazardous processes, most studies focus on a single hazard [8].

**Citation:** Soldati, A.; Chiozzi, A.; Nikoli´c, Ž.; Vaccaro, C.; Benvenuti, E. A PROMETHEE Multiple-Criteria Approach to Combined Seismic and Flood Risk Assessment at the Regional Scale. *Appl. Sci.* **2022**, *12*, 1527. https://doi.org/10.3390/ app12031527

Academic Editor: Igal M. Shohet

Received: 30 November 2021 Accepted: 27 January 2022 Published: 31 January 2022

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

**Copyright:** © 2022 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/).

The choice to adopt a multi-risk analysis approach has the potential to play a fundamental role in increasing urban resilience, an essential factor for sustainable development, enabling cities to prepare, respond, and recover when hit by catastrophic events, and therefore prevent or contain economic, environmental, and social losses [1]. However, performing a multi-risk analysis with the tools and methodologies available today raises numerous challenges and difficulties [10–20]. For instance, an updated analysis of multi-hazard aggregated risk for infrastructures considering multiple potential threats has recently been proposed in reference [5].

Risk assessment is indeed carried out through independent procedures that adopt different estimation metrics. This makes comparisons difficult and precludes considering correlations or cascading effects [11]. On the contrary, the Multiple-Criteria Decision Analysis (MCDA) technique is a promising approach in multiple-hazard risk analysis, even if this route has been scarcely explored to date [21–24].

To pave the way for sustainable land-use plans and risk-mitigation strategies, we must analyze, quantify, and, especially, compare all concurrent risks [25]. To date, single-risk assessment is generally performed by means of independent procedures, whose results cannot be compared. The purpose of this paper is to devise an approach for the qualitative assessment of combined risks at the regional scale. In particular, the objective is to jointly analyze the flood and seismic risk for the Ferrara province area. The proposed approach is based on the suitable use of the Preference Ranking Organization Method for Enrichment Evaluations (PROMETHEE), a Multiple-Criteria Decision Analysis technique [26–29]. The province of Ferrara is in a flatland area in the northern part of Italy. Historically, it has been mainly hit by floods and seismic events. Though floods are exogeneous processes, whereas earthquakes are exogenic, we assume flood and seismic hazards to be the two relevant hazards for determining a priority list. This priority list is meant to be useful to stakeholders and public agencies called to rapidly implement investment plans aimed to prevent economic and life losses and foster the coping capacity of communities to manage the adverse conditions induced by natural disasters. Particularly, the present objective is to prioritize this among the different municipalities. Therefore, the adopted level of observation is at the scale of the area included within each municipality.

Assuming the municipalities of the province of Ferrara as the alternatives of the multiple-criteria analysis, the proposed approach defines a priority ranking among all the alternatives. The outcome is represented by qualitative risk maps. These maps are useful tools for stakeholders involved in community management and risk prevention.

Among the Multi-Risk Methodologies applied in Italian territories, we recall here the works by Gallina et al. [23,24] for the assessment of the impact of sea-level rise, coastal erosion, and storm surge induced by climate changes in coastal zones in North Italy. Flood and seismic risks have been multi-assessed through a Machine Learning framework recently devised by the authors for the Emilia Romagna region [30]. Up to now, the present contribution is the very first to use an MCDA approach for multi-risk analysis of combined flood and earthquake risks, while no other relevant contributions exist dealing with multi-hazard analyses of the Province of Ferrara.

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

### *2.1. Geographical Context and Single Risk Description*

To introduce the concept of multi-risk assessment, it is first necessary to discuss the concept of single risk. Risk is basically defined as the product of three parameters: Hazard, vulnerability, and exposure [9]. A hazard represents the probability that an adverse event will occur in a specific area and in a specific time interval. Vulnerability, on the other hand, is an intrinsic characteristic of a system; it represents its propensity to suffer a certain level of damage following the occurrence of a hazard event. Finally, exposure indicates the presence of people, critical infrastructures, natural and cultural heritage, and much more still in hazard zones that are thereby subject to potential losses [4].

The concept of multi-risk follows as the overall risk from a multi-hazard and multivulnerability perspective. The term multi-hazard indicates several hazards affecting the same exposed elements (with or without space–time coincidence) or the occurrence of a hazard event that triggers another one giving rise to a domino or cascade effect. Furthermore, the term multi-vulnerability indicates those circumstances where several elements are sensitive to different possible vulnerabilities towards the various hazards affecting them or vulnerabilities that vary over time [10,11]. still in hazard zones that are thereby subject to potential losses [4]. The concept of multi-risk follows as the overall risk from a multi-hazard and multivulnerability perspective. The term multi-hazard indicates several hazards affecting the same exposed elements (with or without space–time coincidence) or the occurrence of a hazard event that triggers another one giving rise to a domino or cascade effect. Furthermore, the term multi-vulnerability indicates those circumstances where several elements are sensitive to different possible vulnerabilities towards the various hazards affecting

presence of people, critical infrastructures, natural and cultural heritage, and much more

*Appl. Sci.* **2022**, *12*, 1527 3 of 22

The territory of the province of Ferrara is located at the north-eastern extremity of the Padana Plain, a flat land area in the north part of Italy crossed by the Po River and bathed by the Adriatic Sea on the east side. It is characterized by minimum land slopes and its altimetry is mainly under the mean sea level, as almost half of its area is below the mean sea level, as shown in Figure 1. Moreover, the eastern part of the territory is affected by subsidence phenomena as well. These ground-level modifications, caused mainly by anthropogenic actions as well as by geological and neotectonic factors [31,32], produced a subsidence rate of up to −2.5 mm/year [31]. The main watercourses that flow through the Ferrara province are the Po River, which marks the northern border of the Reno River, and the Idice and Sillaro streams, which are not tributaries of the Po River, and cross the province in their last stretch. Furthermore, numerous artificial canals flow through the Ferrara Province, including the Cavo Napoleonico, which connects the Po and Reno rivers, and the Idrovia Ferrarese. them or vulnerabilities that vary over time [10,11]. The territory of the province of Ferrara is located at the north-eastern extremity of the Padana Plain, a flat land area in the north part of Italy crossed by the Po River and bathed by the Adriatic Sea on the east side. It is characterized by minimum land slopes and its altimetry is mainly under the mean sea level, as almost half of its area is below the mean sea level, as shown in Figure 1. Moreover, the eastern part of the territory is affected by subsidence phenomena as well. These ground-level modifications, caused mainly by anthropogenic actions as well as by geological and neotectonic factors [31,32], produced a subsidence rate of up to −2.5 mm/year [31]. The main watercourses that flow through the Ferrara province are the Po River, which marks the northern border of the Reno River, and the Idice and Sillaro streams, which are not tributaries of the Po River, and cross the province in their last stretch. Furthermore, numerous artificial canals flow through the Ferrara Province, including the Cavo Napoleonico, which connects the Po and Reno rivers, and the Idrovia Ferrarese.

**Figure 1.** Altimetric map of Ferrara province (free source https://www.bonificaferrara.it/images/Allegati/SITL/4d-3-altimetria(100).pdf, accessed 3 January 2022, made available by Consorzio di Bonifica Pianura di Ferrara). The minimum and maximum extremal values of the ground level over the sea in the legend are −2 m (dark blue) and 60 m (dark red), respectively. **Figure 1.** Altimetric map of Ferrara province (free source https://www.bonificaferrara.it/images/ Allegati/SITL/4d-3-altimetria(100).pdf, accessed on 3 January 2022, made available by Consorzio di Bonifica Pianura di Ferrara). The minimum and maximum extremal values of the ground level over the sea in the legend are −2 m (dark blue) and 60 m (dark red), respectively.

The province of Ferrara includes 23 municipalities. Attention is hereafter restricted to the two main risks of the area under study, namely flood and seismic risks. Site effects associated with inherent geological morphology and instability issues such as liquefaction The province of Ferrara includes 23 municipalities. Attention is hereafter restricted to the two main risks of the area under study, namely flood and seismic risks. Site effects associated with inherent geological morphology and instability issues such as liquefaction

were not considered, for simplicity. Desertification is another risk that has been emerging in recent years in the Po delta plain [10]. However, it has not been considered in the present contribution. Hereafter, flood risk refers to the risk that depends on the probability of occurrence of a flood, evaluated concerning the different typologies of watercourses that flow through the territory. The flood risk for the selected region was quantified by the Land Reclamation Authority of the province of Ferrara (Consorzio di Bonifica Pianura di Ferrara), and accounts for flood hazard, exposure, and vulnerability parameters. were not considered, for simplicity. Desertification is another risk that has been emerging in recent years in the Po delta plain [10]. However, it has not been considered in the present contribution. Hereafter, flood risk refers to the risk that depends on the probability of occurrence of a flood, evaluated concerning the different typologies of watercourses that flow through the territory. The flood risk for the selected region was quantified by the Land Reclamation Authority of the province of Ferrara (Consorzio di Bonifica Pianura di Ferrara), and accounts for flood hazard, exposure, and vulnerability parameters.

Seismic risk depends on the peak ground acceleration (PGA) as well as on the vulnerability of the built environment and the exposure of people and economic activities. We exploited the map of seismic hazard provided by the Italian Institute of Volcanology and Geophysics (INGV), and the seismic classification of municipalities in Emilia (free source https://ambiente.regione.emilia-romagna.it/en/geologia/seismic-risk/seismicclassification, accessed on 26 January 2022), shown in Figure 2a. In Figure 2b, Italy is divided into different areas according to peak ground acceleration values [33] (free source http://zonesismiche.mi.ingv.it/, accessed on 26 January 2022). Seismic risk depends on the peak ground acceleration (PGA) as well as on the vulnerability of the built environment and the exposure of people and economic activities. We exploited the map of seismic hazard provided by the Italian Institute of Volcanology and Geophysics (INGV), and the seismic classification of municipalities in Emilia (free source https://ambiente.regione.emilia-romagna.it/en/geologia/seismic-risk/seismic-classification, accessed on 26 January 2022), shown in Figure 2a. In Figure 2b, Italy is divided into different areas according to peak ground acceleration values [33] (free source http://zonesismiche.mi.ingv.it/, accessed on 26 January 2022).

**Figure 2.** (**a**) Seismic classification of municipalities in Emilia (https://ambiente.regione.emilia-romagna.it/en/geologia/seismic-risk/seismic-classification, accessed 26 January 2022). (**b**) Seismic Hazard Map of Italy (free source from INGV webpage http://zonesismiche.mi.ingv.it/, accessed on 26 January 2022). **Figure 2.** (**a**) Seismic classification of municipalities in Emilia (https://ambiente.regione.emiliaromagna.it/en/geologia/seismic-risk/seismic-classification, accessed on 26 January 2022). (**b**) Seismic Hazard Map of Italy (free source from INGV webpage http://zonesismiche.mi.ingv.it/, accessed on 26 January 2022).

Finally, we used the database made available by the Italian National Institute of Statistics (Istat). This database was used in 2018 by the Italian Superior Institute for Environmental Protection and Research (ISPRA) to produce seismic, hydrogeological, volcanic, and social vulnerability hazard maps for the entire Italian peninsula. The reader is referred to the pertinent report by Trigila et al. [34] to obtain a detailed description of IS-PRA's methodology for the processing of the data. Finally, we used the database made available by the Italian National Institute of Statistics (Istat). This database was used in 2018 by the Italian Superior Institute for Environmental Protection and Research (ISPRA) to produce seismic, hydrogeological, volcanic, and social vulnerability hazard maps for the entire Italian peninsula. The reader is referred to the pertinent report by Trigila et al. [34] to obtain a detailed description of ISPRA's methodology for the processing of the data.

#### *2.2. The PROMETHEE Method 2.2. The PROMETHEE Method*

The proposed multi-hazard risk analysis procedure for the region under study is based on PROMETHEE [26–29], a Multiple-Criteria Decision Analysis method. It belongs to the class of aggregation methods based on outranking relationships. It is known for its simplicity and the ability to analyze information from multiple sources. PROMETHEE allows one to jointly compare data originally expressed in different units and scales. A flux diagram explaining the various steps of the PROMETHEE-based analysis can be found in reference [29]. The proposed multi-hazard risk analysis procedure for the region under study is based on PROMETHEE [26–29], a Multiple-Criteria Decision Analysis method. It belongs to the class of aggregation methods based on outranking relationships. It is known for its simplicity and the ability to analyze information from multiple sources. PROMETHEE allows one to jointly compare data originally expressed in different units and scales. A flux diagram explaining the various steps of the PROMETHEE-based analysis can be found in reference [29].

PROMETHEE deals with maximization or minimization problems with *k* different criteria of the kind PROMETHEE deals with maximization or minimization problems with *k* different criteria of the kind

$$\max(\text{ornin})\{\mathcal{g}\_1(a), \mathcal{g}\_2(a), \dots, \mathcal{g}\_k(a) | a \in A\},\tag{1}$$

where *A* is a finite set of possible alternatives and function *gj*(*a*) represents the performance of the *j*-th criterion. Let us consider two alternatives, (*a*, *b*) ∈ *A*. We have the following cases:

$$\begin{cases} \quad \forall j: \mathfrak{g}\_j(a) \ge \mathfrak{g}\_j(b) \\ \exists k: \mathfrak{g}\_k(a) > \mathfrak{g}\_k(b) \end{cases} \Leftrightarrow aPb,$$

$$\forall j: \mathfrak{g}\_j(a) = \mathfrak{g}\_j(b) \Leftrightarrow aIb,$$

$$\begin{cases} \quad \exists \mathfrak{s}: \mathfrak{g}\_s(a) > \mathfrak{g}\_s(b) \\ \quad \exists r: \mathfrak{g}\_r(a) < \mathfrak{g}\_r(b) \end{cases} \Leftrightarrow aRb,$$

where *P*, *I*, and *R* denote preference (*P*), indifference (*I*), or incompatibility relations (*R*) of one alternative over the other, respectively.

By comparing all the alternatives for each criterion, a hierarchy of alternatives belonging to the starting space A will be obtained. When comparing two actions,(*a*, *b*) ∈ *A*. the result of this comparison is expressed in terms of the preference function ℘ : *A* × *A* → (0, 1) that represents the intensity of the preference of alternative *a* towards alternative *b*. Therefore, ℘(*a*, *b*) = 0 indicates no preference of *a* over *b* (or indifference), ℘(*a*, *b*) ' 0 indicates a weak preference of *a* over *b*, ℘(*a*, *b*) ' 1 indicates a strong preference of *a* over *b,* and ℘(*a*, *b*) = 1 indicates a strict preference of *a* over *b*. In practice, the preference function will often be a function of the difference between the evaluations of the two alternatives considered:

$$\wp(a,b) = P(\lg(a) - \lg(b)) = P(d),\tag{3}$$

where *P* is a non-decreasing function, equal to zero for negative values of *d*. PROMETHEE offers six types of preference functions (see Table 1).

Therefore, a preference index is defined as follows:

$$\begin{cases} \begin{aligned} \pi(a,b) &= \sum\_{j=1}^{k} P\_j(a,b)w\_j \\ \pi(b,a) &= \sum\_{j=1}^{k} P\_j(b,a)w\_j \end{aligned} \end{cases} \tag{4}$$

where *π*(*a*, *b*) expresses the degree to which *a* is preferred to *b* over all criteria and vice versa, and *wj* is the weight of each criterion and expresses a measure of the importance of the relative criterion.

For all the criteria, a classification is available for the various alternatives necessary to define the so-called outranking flows, which are the fundamental units for the PROMETHEE methodology. Each alternative *a* faces (*n* − 1) other alternatives that belong to the generic space A. The two following outranking flows are defined:

$$\begin{cases} \Theta^{+}(a) = \frac{1}{n-1} \sum\_{\substack{\mathfrak{x} \in A \\ \mathfrak{x} \in A}} \pi(a, \mathfrak{x}) \\ \Theta^{-}(a) = \frac{1}{n-1} \sum\_{\mathfrak{x} \in A} \pi(\mathfrak{x}, a) \end{cases} \tag{5}$$

where *x* represents the deviation of the specific preference function with respect to the same function of preference for the other alternatives. Θ +(*a*) expresses how alternative *a* outranks all the others, otherwise Θ −(*a*) expresses how alternative *a* is outranked by all the others. The higher Θ +(*a*) (lower Θ −(*a*)) is, the more likely alternative *a* is strongest; otherwise, alternative *a*, compared to the others, is weakest when Θ +(*a*) assumes small values. Once these two flows have been defined, it becomes very simple to make comparisons between alternatives and subsequently establish their order.

PROMETHEE offers several ways to view the results; the main ones are illustrated below:

### *2.3. Data Collection and Processing*

Both flood and seismic risks have been included in PROMETHEE as criteria according to their components (hazard, exposure, and vulnerability), while the municipalities, i.e., the object on which to evaluate the criteria, are the alternatives. Risk parameters for each municipality are made available by the National Institute of Vulcanology and Geophysics (INGV), the Italian National Institute of Statistics (Istat), and the Land Reclamation Authorities of the Province of Ferrara. Accordingly, we have drawn from the aforementioned databases a simplified map of the flood risk. In particular, Figure 3 displays the flood hazard for the Province of Ferrara in terms of the probability of floods. In this map, the classification is based on Italian Government Decree n. 49/2010 [35]. Accordingly, frequent floods are defined as those having a high probability of occurrence, with a return period of 20 ≤ T ≤ 50 years (P3); infrequent floods have an average probability of occurrence with a return period of 100 ≤ T ≤ 200 years (P2); finally, low-probability floods have a return period of 200 < T ≤ 500 years (P1).

a return period of 200 < T ≤ 500 years (P1).

**Figure 3.** Map of the flood hazard for the province of Ferrara in terms of probability of flood. **Figure 3.** Map of the flood hazard for the province of Ferrara in terms of probability of flood. the number of buildings built between 1946 and 1980; the number of buildings built between 1981 and 2000, and finally, the number of buildings built from 2001 up to now. ଵ, ଶ, ଷ ସ

Figure 4 provides a map of the seismic hazard for the province of Ferrara in terms of peak ground acceleration (PGA). The PGA-intervals are indicated in the legend. Figure 4 provides a map of the seismic hazard for the province of Ferrara in terms of peak ground acceleration (PGA). The PGA-intervals are indicated in the legend. are coefficients equal to 1, 0.75, 0.5, and 0.25, respectively. The vulnerability index Iv results in being mainly related to the age of buildings, and its map is shown in Figure 8.

the flood hazard for the Province of Ferrara in terms of the probability of floods. In this map, the classification is based on Italian Government Decree n. 49/2010 [35]. Accordingly, frequent floods are defined as those having a high probability of occurrence, with a return period of 20 ≤ T ≤ 50 years (P3); infrequent floods have an average probability of occurrence with a return period of 100 ≤ T ≤ 200 years (P2); finally, low-probability floods have

**Figure 5.** Land use map for the province of Ferrara. **Figure 4.** Map of the seismic hazard for the province of Ferrara in terms of peak ground acceleration. As for exposure-related criteria, for each municipality, we adopted three parameters: Land use percentage, the number of strategic buildings, and population density. All of them

were drawn from the Istat database. The strategic buildings were defined based on the presence and number of halls, police stations, fire brigade buildings, schools, universities, water lifting plants, hospitals, and civil protection centers. This information was obtained from the website of the province of Ferrara (http://www.provincia.fe.it/, 1 October 2021), as per educational and public institutions and centers, and from the website of the Consorzio di Bonifica Pianura di Ferrara as per water lifting plants (https://www.bonificaferrara.it/, 1 October 2021).

where , , represent the number of buildings built between the end of 1800 and 1945; the number of buildings built between 1946 and 1980; the number of buildings built between 1981 and 2000, and finally, the number of buildings built from 2001 up to now. ଵ, ଶ, ଷ ସ are coefficients equal to 1, 0.75, 0.5, and 0.25, respectively. The vulnerability index Iv results in

being mainly related to the age of buildings, and its map is shown in Figure 8.

*Appl. Sci.* **2022**, *12*, 1527 8 of 22

Specifically, four classes of land use percentages were obtained based on the ratio between the urbanized area divided by the total area. In synthesis, we collected the municipalities into four land use classes (Figure 5), four classes in terms of the number of strategic buildings (Figure 6), and four classes of population density (Figure 7).

As for the vulnerability criteria, we adopted a single non-dimensionalized parameter, which accounts for the average age of buildings. Knowing the age of construction and the corresponding number of buildings, we computed the following vulnerability index:

$$I\_{\upsilon} = \frac{A \,\,\alpha\_1 + B \,\,\alpha\_2 + C \,\,\alpha\_3 + D \,\,\alpha\_4}{A + B + C + D} \,\,\,\nu$$

where *A*, *B*, *C e D* represent the number of buildings built between the end of 1800 and 1945; the number of buildings built between 1946 and 1980; the number of buildings built between 1981 and 2000, and finally, the number of buildings built from 2001 up to now. *α*1, *α*2, *α*3 *e α*4 are coefficients equal to 1, 0.75, 0.5, and 0.25, respectively. The vulnerability index Iv results in being mainly related to the age of buildings, and its map is shown in Figure 8. **Figure 4.** Map of the seismic hazard for the province of Ferrara in terms of peak ground acceleration.

**Figure 5.** Land use map for the province of Ferrara. **Figure 5.** Land use map for the province of Ferrara.

*Appl. Sci.* **2022**, *12*, 1527 9 of 22

**Figure 6.** Map of strategic buildings incidence for the province of Ferrara. **Figure 6.** Map of strategic buildings incidence for the province of Ferrara. **Figure 6.** Map of strategic buildings incidence for the province of Ferrara.

**Figure 7.** Map of the population density for the province of Ferrara. **Figure 7.** Map of the population density for the province of Ferrara. **Figure 7.** Map of the population density for the province of Ferrara.

**Figure 8.** Map of the vulnerability parameter for the province of Ferrara computed as a function of the building age. **Figure 8.** Map of the vulnerability parameter for the province of Ferrara computed as a function of the building age.

#### *2.4. Normalization and Weight Assignment 2.4. Normalization and Weight Assignment*

All the data have been collected in an evaluation matrix, whose rows correspond to each alternative (i.e., each municipality), while each column corresponds to each selected criterion. In other words, the *i*,*j*-th element of the evaluation matrix expresses the value of the *i*-th alternative relating to the attribute of the *j*-th criterion and describes the performance of each alternative regarding each criterion. All the data have been collected in an evaluation matrix, whose rows correspond to each alternative (i.e., each municipality), while each column corresponds to each selected criterion. In other words, the *i*,*j*-th element of the evaluation matrix expresses the value of the *i*-th alternative relating to the attribute of the *j*-th criterion and describes the performance of each alternative regarding each criterion.

It should be noted that criteria are represented through different scales and units. This precludes mutual comparisons. Thus, it is necessary to further homogenize the data contained in the evaluation matrix and proceed with comparisons through normalization. Through the preference function, the performance of the alternatives is transformed into a dimensionless value, ranging from o to 1. As a first attempt, we adopted the Type 1 preference function described in Table 1, which does not require the definition of any threshold. Subsequently, the linear preference function was also used. It should be noted that criteria are represented through different scales and units. This precludes mutual comparisons. Thus, it is necessary to further homogenize the data contained in the evaluation matrix and proceed with comparisons through normalization. Through the preference function, the performance of the alternatives is transformed into a dimensionless value, ranging from o to 1. As a first attempt, we adopted the Type 1 preference function described in Table 1, which does not require the definition of any threshold. Subsequently, the linear preference function was also used.

Finally, we attributed weights to each criterion. Through this step, decision makers can make their preferences explicit, since it is not ensured that all the criteria take on the same importance. We first decided to attribute the same weight to each criterion. Then, a sensitivity analysis was performed with varying weights. Finally, we attributed weights to each criterion. Through this step, decision makers can make their preferences explicit, since it is not ensured that all the criteria take on the same importance. We first decided to attribute the same weight to each criterion. Then, a sensitivity analysis was performed with varying weights.

The risk maps shown in the following sections indicate three classes of risk levels, namely low, medium, high. It is emphasized that this classification must be intended as a pure ranking in terms of the relative urgence of investments. It does not at all intend to indicate the level of safety in absolute terms of the various municipalities. This classification answers the question as to whether the method can provide the priority level associated with a certain municipality and help to decide how to distribute investments over various municipalities. The risk maps shown in the following sections indicate three classes of risk levels, namely low, medium, high. It is emphasized that this classification must be intended as a pure ranking in terms of the relative urgence of investments. It does not at all intend to indicate the level of safety in absolute terms of the various municipalities. This classification answers the question as to whether the method can provide the priority level associated with a certain municipality and help to decide how to distribute investments over various municipalities.

### *2.5. Sensitivity Analysis 2.5. Sensitivity Analysis*

To verify the reliability of the results obtained, a sensitivity analysis was carried out. During this sensitivity analysis, we retraced the procedure by which the results were obtained and identified the steps most affected by uncertainties and subjectivity, considering To verify the reliability of the results obtained, a sensitivity analysis was carried out. During this sensitivity analysis, we retraced the procedure by which the results were obtained and identified the steps most affected by uncertainties and subjectivity, considering their influence on the final ranking. Specifically, the choice of the preference function and the choice of weights appeared to be the most subjective. As for the choice of the preference function, a previous study [26] recommends assuming a linear preference function endowed with the definition of *p*, *q* thresholds. Two approaches are adopted for the determination of *p* and *q*: The so-called zero-max method, which imposes that the indifference threshold *q* is assigned the value of zero while the preference threshold *p* is set to be equal to the maximum difference between the evaluations of the criteria.

The mean-std method requires the calculation of the average value and the standard deviation of a set of differences between the evaluations of the criteria. In the mean-std method, the indifference threshold is assigned the value of the difference between the average value and standard deviation, while the sum between the average value and standard deviation is assigned to the preference threshold. Following [26–28], we adopted the preference function of the linear type for the quantitative criteria, that is flood hazard, land use, the age of buildings, and population density. However, the algorithm was also run by choosing the usual preference function, which is the simplest possible one. The thresholds were computed as shown in Table 2. As for the sensitivity on the weights, the four scenarios described in Table 3 have been considered.

**Table 2.** Preference functions and the associated thresholds *p*, *q*, and *s*.

**Table 3.** Sensitivity analysis on the weights of the criteria.

### **3. Results**

In the following Section, we describe the outcomes of the multiple-criteria analysis for the usual and linear preference function as well as the results of the sensitivity analysis performed for varying weight changes.

### *3.1. Usual Preference Function*

When the usual preference function is used, the algorithm assumes equal weights. We recall that, here, thresholds *p* and *q* are not required. Basically, what is provided to the analyst is an order of priority where the municipalities in the province of Ferrara are ordered from the most sensitive to combined flood and seismic risk to the one that is least affected. Table 4 shows the final ranking of the alternatives.

**Rank Alternatives Θ Θ+ Θ**− 1 Ferrara 0.6111 0.7302 0.119 2 Cento 0.5873 0.7222 0.1349 3 Tresigallo 0.4127 0.6111 0.1984 4 Vigarano Mainarda 0.2857 0.5873 0.3016 5 Mirabello + Sant'Agostino 0.2698 0.5794 0.3095 6 Argenta + Portomaggiore 0.2381 0.5238 0.2857 7 Bondeno 0.1825 0.4921 0.3095 8 Copparo 0.0238 0.4127 0.3889 9 Poggio Renatico 0.0238 0.4524 0.4286 10 Comacchio 0.0000 0.4048 0.4048 10 Formignana 0.0000 0.381 0.381 12 Voghiera −0.0238 0.3651 0.3889 13 Lagosanto −0.0317 0.3889 0.4206 14 Berra −0.1587 0.3016 0.4603 15 Masi Torello −0.1746 0.2937 0.4683 16 Ro −0.1905 0.2857 0.4762 17 Fiscaglia −0.2063 0.2778 0.4841 18 Mesola −0.2857 0.2381 0.5238 19 Ostellato −0.3571 0.1984 0.5556 20 Goro −0.3651 0.1984 0.5635 21 Codigoro −0.3651 0.2222 0.5873 22 Jolanda di Savoia −0.4762 0.1429 0.619

**Table 4.** Ranking of alternatives for the usual preference function.

This is not the only way to visualize the results: The PROMETHEE rainbow plot, shown in Figure 9, allows one to highlight, for each alternative, the criteria that positively or negatively affect the results. In Figure 9, the colors are representative of the criterion: Yellow indicates the criteria relating to exposure, red is used for seismic hazard, green for vulnerability, and blue for flood hazard. For example, for the municipality of Ferrara (first in the ranking), it can be observed that the criterion that has a negative effect is the one relating to the flood hazard, whereas the other criteria have a positive effect on the Ferrara municipality. On the contrary, in the municipality of Jolanda di Savoia (last in the ranking), the only criterion that has a positive influence is the one relating to vulnerability, while all the others have a negative influence.

*Appl. Sci.* **2022**, *12*, 1527 13 of 22

**Figure 9.** PROMETHEE rainbow plot for the usual preference function. On the vertical axis, the preference function Θ is reported. The yellow bar indicates the criteria relating to exposure, red is used for seismic hazard, green for vulnerability, and blue for hydraulic hazard. **Figure 9.** PROMETHEE rainbow plot for the usual preference function. On the vertical axis, the preference function Θ is reported. The yellow bar indicates the criteria relating to exposure, red is used for seismic hazard, green for vulnerability, and blue for hydraulic hazard. **Figure 9.** PROMETHEE rainbow plot for the usual preference function. On the vertical axis, the preference function Θ is reported. The yellow bar indicates the criteria relating to exposure, red is

Based on the ranking provided by PROMETHEE, it is possible to create a risk map of the

municipalities of the province of Ferrara that highlights high-priority areas as those with a high level of combined flood and seismic risk, medium priority areas as the areas characterized by a medium combined-risk level, and, finally, low combined-risk areas. This map is shown in Figure 10. It can be seen that the three risk levels are identified by three different colors: Red is used for high risk, orange for medium risk, and yellow for low Based on the ranking provided by PROMETHEE, it is possible to create a risk map of the municipalities of the province of Ferrara that highlights high-priority areas as those with a high level of combined flood and seismic risk, medium priority areas as the areas characterized by a medium combined-risk level, and, finally, low combined-risk areas. used for seismic hazard, green for vulnerability, and blue for hydraulic hazard. Based on the ranking provided by PROMETHEE, it is possible to create a risk map of the municipalities of the province of Ferrara that highlights high-priority areas as those with a high level of combined flood and seismic risk, medium priority areas as the areas character-

risk. This map is shown in Figure 10. It can be seen that the three risk levels are identified by three different colors: Red is used for high risk, orange for medium risk, and yellow for low risk. ized by a medium combined-risk level, and, finally, low combined-risk areas. This map is shown in Figure 10. It can be seen that the three risk levels are identified by three different colors: Red is used for high risk, orange for medium risk, and yellow for low risk.

**Figure 10.** Multiple-risk map for the Ferrara province obtained for the usual preference function (Type 1 in Table 1). The risk levels strictly indicate the relative priority ranking for decision-makers and do not indicate the effective safety level of the various municipalities.

### *3.2. Linear Preference Function*

The ranking of alternatives for the linear preference function and zero-max method is shown in Table 5, while the corresponding multi-risk map is shown in Figure 11. These maps were obtained by associating the quantitative criteria, i.e., flood hazard, land use, age of buildings, and population density, with a linear preference function, while thresholds *q* and *p* were determined with the zero-max method.

**Table 5.** Ranking of alternatives for the linear preference function and zero-max method.

For a linear preference function of the aforementioned quantitative criteria, and thresholds *q* and *p* determined by the mean-std method, we obtained the results shown in Table 6 and Figure 12.

By comparing the results obtained from the usual and the linear preference functions, it can be understood that changes of the preference function do not reflect large changes of the final risk maps. The only difference is that the risk levels of the municipality of Vigarano Mainarda swap with Bondeno, and Fiscaglia swaps with Lagosanto.

By comparing the maps in Figures 11 and 12, obtained with the thresholds chosen with the zero-max and mean-std methods, respectively, we observe that the risk levels of Lagosanto, Vigarano Mainarda, and Codigoro increase. Particularly, we observe that the choice of the preference function affects the final ranking of the alternatives especially when the thresholds are chosen according to the mean-std method.

**Table 6.** Ranking of alternatives for the linear preference function and std-mean method.

**Rank Alternatives** Θ + Θ − Θ 1 Cento 0.4532 0.4849 0.0317 2 Ferrara 0.3769 0.4123 0.0354 3 Tresigallo 0.2051 0.2613 0.0562 4 Vigarano Mainarda 0.1219 0.2185 0.0966 5 Mirabello+ Sant'Agostino 0.078 0.1835 0.1056 6 Lagosanto 0.0597 0.1319 0.0722 7 Poggio Renatico 0.0523 0.167 0.1147 8 Argenta + Portomaggiore 0.0307 0.1133 0.0826 9 Copparo 0.0261 0.1107 0.0846 10 Bondeno 0.0222 0.1075 0.0853 11 Comacchio 0.0217 0.1075 0.0857 12 Codigoro 0.0125 0.1053 0.0928 13 Formignana −0.1232 0.0146 0.1378 14 Masi Torello −0.1275 0.0086 0.1361 15 Goro −0.1278 0.0106 0.1384 16 Mesola −0.1317 0.0069 0.1386 17 Berra −0.1383 0.0046 0.1429 18 Voghiera −0.1383 0.0041 0.1424 19 Ro −0.1385 0.004 0.1425 20 Fiscaglia −0.1497 0.002 0.1517 21 Ostellato −0.1839 0 0.1839 22 Jolanda di Savoia −0.2014 0 0.2014

**Figure 11.** Multiple-risk map for the Ferrara province for the linear preference function with the thresholds chosen with the zero-max method. The risk levels strictly indicate the relative priority ranking for decision-makers and do not indicate the effective safety level of the various municipalities. **Figure 11.** Multiple-risk map for the Ferrara province for the linear preference function with the thresholds chosen with the zero-max method. The risk levels strictly indicate the relative priority ranking for decision-makers and do not indicate the effective safety level of the various municipalities. *Appl. Sci.* **2022**, *12*, 1527 16 of 22

**Figure 12.** Multiple-risk map for the Ferrara province for the linear preference function with the thresholds chosen with the mean-std method. The risk levels strictly indicate the relative priority ranking for decision-makers and do not indicate the effective safety level of the various municipalities. **Figure 12.** Multiple-risk map for the Ferrara province for the linear preference function with the thresholds chosen with the mean-std method. The risk levels strictly indicate the relative priority ranking for decision-makers and do not indicate the effective safety level of the various municipalities.

Regardless of the preference function chosen, the maps obtained present a similar risk trend, i.e., the territory is divided into two parts: The municipalities of the western part of the territory of the province of Ferrara, plus Ferrara and Tresigallo, are characterized by a medium–high risk level; the upper-eastern part of the province is characterized

As introduced in Section 2, the sensitivity analysis on the weights was performed by first increasing the weight of each individual criterion at a time, and then assuming the simultaneous increase in the weights of the three "exposure"-related criteria, namely land use, population density, and strategic buildings. Specifically, the weights were changed

For the sake of brevity, we present hereafter the results obtained by assuming the usual preference function. For the reader's convenience, the results are reported as maps,

In the first part of the analysis, the criteria are changed according to the following order: Flood hazard, PGA, land use, strategic buildings, age of buildings, and population density. Hereafter, we omit the maps obtained for the changes of the weights relating to the criteria of strategic buildings and age of buildings, for brevity. Figures 13 and 14 illus-

according to Scenarios 0, 1, 2, and 3 described in Table 3.

trate the various risk maps obtained by increasing the weights.

by a medium–low risk level.

as in the previous sections.

**Table 6.** Ranking of alternatives for the linear preference function and std-mean method.

Regardless of the preference function chosen, the maps obtained present a similar risk trend, i.e., the territory is divided into two parts: The municipalities of the western part of the territory of the province of Ferrara, plus Ferrara and Tresigallo, are characterized by a medium–high risk level; the upper-eastern part of the province is characterized by a medium–low risk level.

### *3.3. Sensitivity Analysis on the Choice of Weights*

As introduced in Section 2, the sensitivity analysis on the weights was performed by first increasing the weight of each individual criterion at a time, and then assuming the simultaneous increase in the weights of the three "exposure"-related criteria, namely land use, population density, and strategic buildings. Specifically, the weights were changed according to Scenarios 0, 1, 2, and 3 described in Table 3.

For the sake of brevity, we present hereafter the results obtained by assuming the usual preference function. For the reader's convenience, the results are reported as maps, as in the previous sections.

In the first part of the analysis, the criteria are changed according to the following order: Flood hazard, PGA, land use, strategic buildings, age of buildings, and population density. Hereafter, we omit the maps obtained for the changes of the weights relating to the criteria of strategic buildings and age of buildings, for brevity. Figures 13 and 14 illustrate the various risk maps obtained by increasing the weights.

**Figure 13.** Weights sensitivity analysis, multi-risk maps; (**a**) flood hazard weight increase assuming Scenarios 2 or 3; (**b**) PGA weight increase assuming Scenario 1; (**c**) PGA weight increase assuming Scenario 2; (**d**) land use weight increase assuming Scenarios 2 or 3; (**e**) strategic buildings weight increase assuming Scenario 1; (**f**) strategic buildings weight increase assuming Scenarios 2 or 3. The risk levels strictly indicate the relative priority ranking for decision-makers and do not indicate the effective safety level of the various municipalities. **Figure 13.** Weights sensitivity analysis, multi-risk maps; (**a**) flood hazard weight increase assuming Scenarios 2 or 3; (**b**) PGA weight increase assuming Scenario 1; (**c**) PGA weight increase assuming Scenario 2; (**d**) land use weight increase assuming Scenarios 2 or 3; (**e**) strategic buildings weight increase assuming Scenario 1; (**f**) strategic buildings weight increase assuming Scenarios 2 or 3. The risk levels strictly indicate the relative priority ranking for decision-makers and do not indicate the effective safety level of the various municipalities.

With Scenario 1 based on the variation of the flood hazard weight, the ranking of the municipalities remains almost unchanged, as the multi-risk map is identical to that of Scenario 0. On the other hand, the maps change when Scenarios 2 and 3 are adopted, as shown in Figure 13a. More marked differences can be observed when the weight of the PGA (Figure 13b,c) is changed. By increasing the weight of the land-use criterion, an increase in Scenario 1 does not reflect evident changes in the multi-risk map (Figure 13d). On the other hand, changes in Scenarios 2 and 3 affect the multi-risk map. Looking back at the strategic building criterion, we observe differences in the risk map when the first change of Scenario 1 is applied, compared to Scenario 0 (Figure 13e), and more so with the last two increases of Scenario 2 (Figure 13f). For the criterion of population density, the first increase in the weight according to Scenario 1 does not affect the map (see Figure 14a),

while the subsequent increases in the weight bring about noticeable modifications. In particular, the multi-risk map reported in Figure 14b assigns a comparatively low level of attention to the Argenta municipality, which, however, is associated with a medium seismicity level according to the territorial classification of Figure 2a. Depending on the stakeholders' expectations, this might suggest that weights should not be varied to the extent of downgrading the seismic risk level of certain municipalities classified at medium to high seismic risk. *Appl. Sci.* **2022**, *12*, 1527 18 of 22

**Figure 14.** Weights sensitivity analysis, multi-risk maps; (**a**) Scenario 2, population density weight increase; (**b**) Scenario 3, population density weight increase. The risk levels strictly indicate the relative priority ranking for decision-makers and do not indicate the effective safety level of the various municipalities. **Figure 14.** Weights sensitivity analysis, multi-risk maps; (**a**) Scenario 2, population density weight increase; (**b**) Scenario 3, population density weight increase. The risk levels strictly indicate the relative priority ranking for decision-makers and do not indicate the effective safety level of the various municipalities.

With Scenario 1 based on the variation of the flood hazard weight, the ranking of the municipalities remains almost unchanged, as the multi-risk map is identical to that of Scenario 0. On the other hand, the maps change when Scenarios 2 and 3 are adopted, as shown in Figure 13a. More marked differences can be observed when the weight of the PGA (Figure 13b,c) is changed. By increasing the weight of the land-use criterion, an in-Lastly, results of the sensitivity on the weight choice for the criteria related to exposure are presented in Table 7. Proceeding as illustrated in Section 2, the first increase in the weight does not alter the risk map, which remains the same as in Scenario 0, whereas with the changes of Scenario 2, greater variations can be observed.

crease in Scenario 1 does not reflect evident changes in the multi-risk map (Figure 13d). On the other hand, changes in Scenarios 2 and 3 affect the multi-risk map. Looking back at the strategic building criterion, we observe differences in the risk map when the first change of Scenario 1 is applied, compared to Scenario 0 (Figure 13e), and more so with the last two increases of Scenario 2 (Figure 13f). For the criterion of population density, the first increase in the weight according to Scenario 1 does not affect the map (see Figure 14a), while the subsequent increases in the weight bring about noticeable modifications. Therefore, concluding the sensitivity analysis of weights, it can be inferred that, in general, the results are sensitive to the increase in the weights of the criteria, determining a risk map that varies from case to case, causing the risk of some municipalities to decrease while that of others increased. However, these variations do not upset the overall trend, which highlights a territory divided into two parts, that of the municipalities of the western part of the territory of the province of Ferrara characterized by a medium–high risk level, and the municipalities of the north-eastern area characterized by a medium–low risk level.

In particular, the multi-risk map reported in Figure 14b assigns a comparatively low level

#### of attention to the Argenta municipality, which, however, is associated with a medium *3.4. Remarks on the Limitations of the Analysis*

seismicity level according to the territorial classification of Figure 2a. Depending on the stakeholders' expectations, this might suggest that weights should not be varied to the extent of downgrading the seismic risk level of certain municipalities classified at medium to high seismic risk. Lastly, results of the sensitivity on the weight choice for the criteria related to exposure are presented in Table 7. Proceeding as illustrated in Section 2, the first increase in the weight does not alter the risk map, which remains the same as in Scenario 0, whereas with the changes of Scenario 2, greater variations can be observed. The proposed methodology requires the definition of several parameters, criteria, and weights, whose choice resulted in being strongly dependent on the expectations of stakeholders and end-users. Thus, the obtained results should be seen as a first attempt towards the proposal of an MCDA methodology that does not require great mathematical expertise, is flexible, and can be easily adapted to many situations. Nevertheless, further efforts are necessary in order for the tool to be readily exploited by public authorities and decision makers. Furthermore, it is worth highlighting other limitations inherent in the present analysis.

The first type of limitation is mainly related to the availability of data. Indeed, the choice of the criteria was based on the availability of the relevant information, which led, for some criteria, to a purely qualitative evaluation. Greater availability, accuracy, and ease of retrieval of the data would lead to the creation of a more complete and more precise analysis, and it could also contribute to the development of operational tools and software.

**Table 7.** Sensitivity analysis on the exposure factor, ranking of alternatives (EXP: EXPOSURE).

Secondly, this analysis neglected cascade effects, an aspect that deserves further investigation in the future [11].

Thirdly, the present contribution does not consider the impact of modeling assumptions on the seismic risk assessment. At the relevant scale of observations of the present analysis, specific structural aspects connected to the vulnerability levels of the buildings cannot be easily considered. In this regard, we recall that specific structural aspects and modeling assumptions play, among others, a key role for seismic risk evaluation at both the building and the urban scale [36]. A recent study focusing on South America has shown the uncertainties and biases that the use of simplified models or heterogenous data may produce in the determination of seismic vulnerability [36]. For completeness, seismic risk evaluation is extensively discussed, for instance, in the aforementioned contributions [36–39] and the references cited therein.

Finally, we recall that the seismic classification shown in Figure 2 has been merely used as a technical-administrative reference for establishing the priority of actions and measures aimed at preventing and mitigating seismic risk. It must not be used to determine the local seismic action or for the structural design of buildings, which, instead, rely upon more detailed maps highlighting, for instance, the presence of site effects due to the inherent geological structure of the ground or instability effects such as liquefaction. Therefore, the present analysis should be purposefully extended in order to consider the aforementioned local effects [40].

### **4. Conclusions**

For the present case study, the application of the Multiple-Criteria Decision Analysis (MCDA) methodology through the PROMETHEE algorithm has proved an innovative and promising operational tool. Its potential derives from the ability to both analyze information from various sources and jointly systematize data expressed in different units and scales. The application of this methodology has made it possible to rank the various municipalities in terms of the relative proneness to joint flood and seismic hazards. We recall that the objective of the methodology is not to quantify the safety level in absolute terms of the various municipalities. Its scope is, indeed, to provide useful information for decision makers and public authorities to define future intervention priorities. We further emphasize that, in the authors'opinion, the present study is original as it applies the PROMETHEE algorithm for the first time to a multi-risk assessment of seismic and flood hazards.

Depending on the territory to be studied, the relevant risks could be different, and therefore, different criteria must be used to express them. Nevertheless, the generalization to other multi-risk analyses and different case studies deserves further considerable efforts and thoughtful insights. Full validation of the present methodology is also of utmost importance and calls for new developments. However, the proposed methodology is flexible. This suggests that, with due precautions and adaptations, it is possible to apply it to different risk scenarios, such as scenarios including coastal floods and landslides, while keeping the same applicative scheme.

Finally, the obtained results have shown that the proposed methodology is an operational tool that, once further validated, can be used by end users, whether modelers or decision makers, to urgently allocate resources and increase the coping capacity of communities in the case of catastrophic events.

**Author Contributions:** Conceptualization, Ž.N., A.C., C.V. and E.B.; methodology, Ž.N., A.S. and A.C.; software, A.S.; validation, A.S., A.C. and C.V.; formal analysis A.S., A.C., Ž.N. and C.V.; resources E.B.; data curation, A.S.; writing—original draft preparation, A.S. and A.C.; writing review and editing, A.C., C.V., Ž.N. and E.B.; visualization, A.S. and A.C.; supervision, E.B.; project administration, E.B.; funding acquisition, E.B. All authors have read and agreed to the published version of the manuscript.

**Funding:** This research was funded by the EUROPEAN UNION, Programme Interreg Italy-Croatia, Project "Preventing, managing and overcoming natural-hazards risks to mitigate economic and social impact"—PMO-GATE ID 10046122.

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

**Informed Consent Statement:** Not applicable.

**Data Availability Statement:** Publicly available datasets and figures were analyzed in this study. This data can be found here: https://www.bonificaferrara.it/images, https://www4.istat.it/it/ mappa-rischi/documentazione, https://ambiente.regione.emilia-romagna.it/en/geologia/seismicrisk/seismic-classification, http://zonesismiche.mi.ingv.it, http://www.provincia.fe.it. (accessed on 26 January 2022).

**Acknowledgments:** The authors are very grateful to Consorzio di Bonifica Pianura di Ferrara for making the flood maps freely available, and, particularly, to Eng. Alessandro Bondesan for his kind support in georeferencing the maps.

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

### **References**