**Table 1.**

*Weather stations used in study.*

the data of the reference WS of each wind farm (WS1 and WS9) are combined with the data of each of the seven other weather stations, WS-2 to WS-8 (**Table 1**). Therefore, for Case B, 175 different models are generated (25 × 7). After applying these models to each wind farm, their results are then compared.

The number of neurons in the input layer also varies, depending on the value of *n*, from 15 (*n* = 3) to 180 (*n* = 36).

The variation in the number of output layer neurons is the same as in Case A.

#### **2.3 Metrics used to compare the different models**

To compare the performance of the different models generated for Cases A and B, metrics (1) and (2) were used:

$$\text{MARE} = \frac{\mathbf{1}}{m} \sum\_{j=1}^{m} \frac{\mathbf{1}}{(T - r)} \sum\_{i=1}^{T-r} \left( \frac{\left| P\_j - \dot{P}\_j \right|}{P\_j} \right)\_i = \frac{\mathbf{1}}{m} \text{MARE}\_j \tag{1}$$

$$R = \frac{1}{m} \sum\_{j=1}^{m} \frac{\sum\_{i=1}^{T-r} \left(P\_{j\_i} - \overline{P\_j}\right) \times \left(\dot{P}\_{jt} - \overline{\dot{P}\_j}\right)}{\sqrt{\left[\sum\_{i=1}^{T-r} \left(P\_{jt} - \overline{P\_j}\right)^2\right] \times \left[\sum\_{i=1}^{T-r} \left(\dot{P}\_{jt} - \overline{\dot{P}\_j}\right)^2\right]}} = \frac{1}{m} \sum\_{j=1}^{m} R\_j \tag{2}$$

**89**

**Table 2.**

*Optimization of the ANNs Models Performance in the Short-Term Forecasting of the Wind…*

The combined use of the two previous metrics is considered sufficient for the evaluation of the performance of the models and they have been widely used [38–41]. Alternatively, for the evaluation of future models, combinations of other metrics could be used [42]. For example, a combination of the Normalized Mean Absolute Error (NMAE) and the Index of Agreement (IoA) could be used.

The meteorological data (wind speed and direction) recorded by nine WSs located in four of the seven islands of the Canary Archipelago (**Table 1**) are used in this study. The mean hourly wind speed and direction data from 2008 are used in all cases. The heights of the WSs are expressed in metres above ground

To validate and compare the results obtained with the different models, information corresponding to two wind farms (WF) located on two of the seven islands of the Canary Archipelago is used. **Tables 2** and **3** shows the geographic coordinates of the wind turbines (WT) of the two wind farms (WF1 and WF2). The hourly

Stations WS1 and WS9 (**Table 1**) are the reference weather stations of wind farms WF1 and WF2, respectively. The WS1 and WS9 data and the wind power production values are provided by the respective owners of the wind farms. The data from the seven additional WSs used in the study are provided by the Canary Islands Technological Institute (Spanish initials: ITC), a publicly owned R&D company run by the Regional Government of the Canary Islands and Spain's State Meteorological

**Table 4** shows the results obtained for the coefficients of linear correlation (3)

1 1

where *CC* is the Pearson's coefficient of correlation between the wind speeds of two WSs; *NG* is the total number of data of the series. In this case, as a series of hourly data equivalent to one year is available, *NG* is equal to 8760. *V*i and *Vi*

**Code** *x* **(m)** *y* **(m)** *z* **(m)** WF1-WT1<PHONE_NUMBER>314 3 WF1-WT2<PHONE_NUMBER>301 1 WF1-WT3<PHONE_NUMBER>067 5 WF1-WT4<PHONE_NUMBER>038 2

= =

*i i i NG NG i i i i*

∑ ′

1

−× − =

∑ ∑

the speeds at instant *i* of the two WSs subject to correlation; *V* and *V*′ are the mean wind speeds of the two WSs subject to correlation for the available data series.

*NG*

=

( ) ( )

*VV V V*

( ) ( )

− × − ′

*VV V V*

2 2

′

(3)

′ are

′

wind farm power output data for 2008 are used for this study.

between the mean hourly wind speeds of the different WSs.

*CC*

Agency (Spanish initials: AEMET).

*Geographic coordinates of wind turbines in WF1.*

*DOI: http://dx.doi.org/10.5772/intechopen.97190*

**3. Materials**

level (magl).

where: MARE is the mean absolute relative error for the forecast horizon; *T* is the number of data in the test stage (see **Figure 1**); *r = T-m-n*; MAREj is the mean absolute relative error for the forecasting period *j*; Pj and *P j* are the actual and estimated wind farm power output in the forecasting period j, respectively; R is the mean value of Pearson's coefficient of correlation between the estimated and actual wind farm power output for the forecast horizon; and Rj is the mean Pearson correlation coefficient between the estimated and actual wind farm power output values for the forecasting period *j*.

*Optimization of the ANNs Models Performance in the Short-Term Forecasting of the Wind… DOI: http://dx.doi.org/10.5772/intechopen.97190*

The combined use of the two previous metrics is considered sufficient for the evaluation of the performance of the models and they have been widely used [38–41]. Alternatively, for the evaluation of future models, combinations of other metrics could be used [42]. For example, a combination of the Normalized Mean Absolute Error (NMAE) and the Index of Agreement (IoA) could be used.

#### **3. Materials**

*Theory of Complexity - Definitions, Models, and Applications*

**Code Height (magl) Latitude**

the data of the reference WS of each wind farm (WS1 and WS9) are combined with the data of each of the seven other weather stations, WS-2 to WS-8 (**Table 1**). Therefore, for Case B, 175 different models are generated (25 × 7). After applying

The number of neurons in the input layer also varies, depending on the value of

**(north)**

WS1 40 27°54′08" 15°23′17" 16 WS2 10 27°51′36" 15°23′13" 3 WS3 10 28°27′10" 13°51′54" 24 WS4 10 28°57′07" 13°36′00" 10 WS5 13 28°01′36" 15°23′16" 5 WS6 10 28°07′30" 15°40′37" 472 WS7 10 27°56′08" 15°25′24" 186 WS8 10 28°02′35" 16°34′16" 51 WS9 40 29°05′47" 13°30′21" 457

**Longitude (west)**

**Altitude (m)**

The variation in the number of output layer neurons is the same as in Case A.

To compare the performance of the different models generated for Cases A and

1 1 1 −

*MARE MARE*

2 1 1 2

−× −

= = − −

*j j T r T r ji j ji j i i*

∑ ∑

*ji j j j m m i*

*PP P P R R m m PP PP*

−× −

where: MARE is the mean absolute relative error for the forecast horizon; *T* is the number of data in the test stage (see **Figure 1**); *r = T-m-n*; MAREj is the mean

estimated wind farm power output in the forecasting period j, respectively; R is the mean value of Pearson's coefficient of correlation between the estimated and actual wind farm power output for the forecast horizon; and Rj is the mean Pearson correlation coefficient between the estimated and actual wind farm power output

*P P*

*i*

*m Tr P m* (1)

*j*

*j*

*P j* are the actual and

(2)

− = = −

*j i j*

( )

*i*

= =

1 1

1 1

= =

*j m T r j*

1 1 ( )

= =

( )

∑ ∑

1

− =

*T r*

∑

absolute relative error for the forecasting period *j*; Pj and

∑ ∑

these models to each wind farm, their results are then compared.

**2.3 Metrics used to compare the different models**

*n*, from 15 (*n* = 3) to 180 (*n* = 36).

**Table 1.**

*Weather stations used in study.*

B, metrics (1) and (2) were used:

values for the forecasting period *j*.

**88**

The meteorological data (wind speed and direction) recorded by nine WSs located in four of the seven islands of the Canary Archipelago (**Table 1**) are used in this study. The mean hourly wind speed and direction data from 2008 are used in all cases. The heights of the WSs are expressed in metres above ground level (magl).

To validate and compare the results obtained with the different models, information corresponding to two wind farms (WF) located on two of the seven islands of the Canary Archipelago is used. **Tables 2** and **3** shows the geographic coordinates of the wind turbines (WT) of the two wind farms (WF1 and WF2). The hourly wind farm power output data for 2008 are used for this study.

Stations WS1 and WS9 (**Table 1**) are the reference weather stations of wind farms WF1 and WF2, respectively. The WS1 and WS9 data and the wind power production values are provided by the respective owners of the wind farms. The data from the seven additional WSs used in the study are provided by the Canary Islands Technological Institute (Spanish initials: ITC), a publicly owned R&D company run by the Regional Government of the Canary Islands and Spain's State Meteorological Agency (Spanish initials: AEMET).

**Table 4** shows the results obtained for the coefficients of linear correlation (3) between the mean hourly wind speeds of the different WSs.

$$\text{CC} = \frac{\sum\_{i=1}^{NG} \left( V\_i - \overline{V} \right) \times \left( V\_i' - \overline{V'} \right)}{\sqrt{\sum\_{i=1}^{NG} \left( V\_i - \overline{V} \right)^2} \times \sqrt{\sum\_{i=1}^{NG} \left( V\_i' - \overline{V'} \right)^2}} \tag{3}$$

where *CC* is the Pearson's coefficient of correlation between the wind speeds of two WSs; *NG* is the total number of data of the series. In this case, as a series of hourly data equivalent to one year is available, *NG* is equal to 8760. *V*i and *Vi* ′ are the speeds at instant *i* of the two WSs subject to correlation; *V* and *V*′ are the mean wind speeds of the two WSs subject to correlation for the available data series.

#### **Table 2.**

*Geographic coordinates of wind turbines in WF1.*

#### *Theory of Complexity - Definitions, Models, and Applications*

#### **Table 3.**

*Geographic coordinates of wind turbines in WF2.*

**Table 4.**

*Coefficient of linear correlation between wind speeds of different weather stations in 2008.*

### **4. Results and discussion**

The discussion of the results centres on the two cases proposed in the methodology. For the various figures corresponding to the results, *t*-3 indicates that 2 periods prior to the forecasting period are chosen in addition to the forecasting period (*t*i, *t*i-1, *t*i-2), and *t* + 3 indicates a forecasting horizon of 3 periods, *t*i + 1, *t*i + 2, *t*i + 3, starting from the period for which the forecasting is being made, and so on for all combinations.

#### **4.1 Discussion of results for case A**

**Figures 4** and **5** show the results for the MARE and R metrics for the 25 generated models. In practically all cases, the MARE and R values improve as *n* increases. The only exception is for case *t*-36 in comparison with *t*-24, where the improvement is minimal or not observed. In addition, the degree of improvement increases as *m* increases (*t* + 12, *t* + 24 and *t* + 36).

**91**

*Optimization of the ANNs Models Performance in the Short-Term Forecasting of the Wind…*

For the forecasting horizons *t* + 12, *t* + 24, *t* + 36, the maximum improvements obtained for MARE between the values for *n* = 3 and *n* = 36, are 13.3%, 11.2% and 10%, respectively. For the same cases but for R, the corresponding improvements

To study the forecasting stability, an analysis has been made of the specific case of forecasting horizon *t* + 24, in which the number of periods to forecast is significant. **Figure 6** shows, for this specific case and differentiated according to *n,* the results of the variation of the relative error in the different forecasting periods,

The forecasting stability is analyzed for all the forecasting horizons (**Figure 7**). This analysis is made on the basis of the standard deviation of relative error in the

*j j*

where *SDV* is the mean standard deviation of the MARE for a forecasting time

It can be seen in **Figure 7** that for all the forecasting horizons, the SDV/MARE value decreases significantly as the number of prior hours *n* increases. This significant improvement in the stability of models is observed even for the lowest forecasting horizons. Only for the particular case of forecasting horizon *t +* 3 and when

*m*

( )

*MARE MARE*

1

2

∑ (4)

*MARE*j. It can be seen how the relative error stabilizes earlier as *n* increases.

1

= − = −

*m*

the horizon passes from *t*-24 to *t*-36, no improvement is observed.

*SDV*

*DOI: http://dx.doi.org/10.5772/intechopen.97190*

are 7.9%, 8.9% and 9.2%, respectively.

forecasting horizon:.

horizon *m*.

**Figure 4.**

**Figure 5.** *R results in case A.*

*MARE results in case A.*

*Optimization of the ANNs Models Performance in the Short-Term Forecasting of the Wind… DOI: http://dx.doi.org/10.5772/intechopen.97190*

**Figure 4.** *MARE results in case A.*

*Theory of Complexity - Definitions, Models, and Applications*

**No. Coefficient of linear correlation**

*Geographic coordinates of wind turbines in WF2.*

*Coefficient of linear correlation between wind speeds of different weather stations in 2008.*

**WS1 WS2 WS3 WS4 WS5 WS6 WS7 WS8 WS9**

WS1 1.00 0.84 0.27 0.34 0.74 0.73 0.77 0.50 0.51 WS2 0.81 1.00 0.19 0.25 0.79 0.74 0.87 0.44 0.54 WS3 0.27 0.19 1.00 0.70 0.16 0.16 0.18 0.16 0.11 WS4 0.34 0.25 0.70 1.00 0.20 0.21 0.22 0.20 0.11 WS5 0.74 0.79 0.16 0.20 1.00 0.49 0.78 0.21 0.44 WS6 0.73 0.74 0.16 0.21 0.49 1.00 0.61 0.62 0.54 WS7 0.77 0.87 0.18 0.22 0.78 0.61 1.00 0.39 0.46 WS8 0.50 0.44 0.16 0.20 0.21 0.62 0.39 1.00 0.35 WS9 0.51 0.54 0.11 0.11 0.44 0.54 0.46 0.35 1.00

**Code** *x* **(m)** *y* **(m)** *z* **(m)** WF2-WT1<PHONE_NUMBER>819 486 WF2-WT2<PHONE_NUMBER>752 478 WF2-WT3<PHONE_NUMBER>638 473 WF2-WT4<PHONE_NUMBER>548 464 WF2-WT5<PHONE_NUMBER>462 456 WF2-WT6<PHONE_NUMBER>369 448 WF2-WT7<PHONE_NUMBER>213 440 WF2-WT8<PHONE_NUMBER>194 425 WF2-WT9<PHONE_NUMBER>133 405

The discussion of the results centres on the two cases proposed in the methodology. For the various figures corresponding to the results, *t*-3 indicates that 2 periods prior to the forecasting period are chosen in addition to the forecasting period (*t*i, *t*i-1, *t*i-2), and *t* + 3 indicates a forecasting horizon of 3 periods, *t*i + 1, *t*i + 2, *t*i + 3, starting from the period for which the forecasting is being made, and so on for all

**Figures 4** and **5** show the results for the MARE and R metrics for the 25 generated models. In practically all cases, the MARE and R values improve as *n* increases. The only exception is for case *t*-36 in comparison with *t*-24, where the improvement is minimal or not observed. In addition, the degree of improvement increases as *m*

**90**

**Table 4.**

**Table 3.**

combinations.

**4. Results and discussion**

**4.1 Discussion of results for case A**

increases (*t* + 12, *t* + 24 and *t* + 36).

#### **Figure 5.** *R results in case A.*

For the forecasting horizons *t* + 12, *t* + 24, *t* + 36, the maximum improvements obtained for MARE between the values for *n* = 3 and *n* = 36, are 13.3%, 11.2% and 10%, respectively. For the same cases but for R, the corresponding improvements are 7.9%, 8.9% and 9.2%, respectively.

To study the forecasting stability, an analysis has been made of the specific case of forecasting horizon *t* + 24, in which the number of periods to forecast is significant. **Figure 6** shows, for this specific case and differentiated according to *n,* the results of the variation of the relative error in the different forecasting periods, *MARE*j. It can be seen how the relative error stabilizes earlier as *n* increases.

The forecasting stability is analyzed for all the forecasting horizons (**Figure 7**). This analysis is made on the basis of the standard deviation of relative error in the forecasting horizon:.

$$SDV = \sqrt{\frac{\sum\_{j=1}^{m} \left(MARE\_j - MARE\right)^2}{m - 1}}\tag{4}$$

where *SDV* is the mean standard deviation of the MARE for a forecasting time horizon *m*.

It can be seen in **Figure 7** that for all the forecasting horizons, the SDV/MARE value decreases significantly as the number of prior hours *n* increases. This significant improvement in the stability of models is observed even for the lowest forecasting horizons. Only for the particular case of forecasting horizon *t +* 3 and when the horizon passes from *t*-24 to *t*-36, no improvement is observed.

**Figure 6.** *MARE variation of different prediction periods: Case of a forecasting horizon t + 24.*

**Figure 7.** *Stability of relative error SDV in forecasting horizon.*

By way of example, we will now proceed to analyze the specific cases of the forecasting models *t* + 12 and *t +* 24. To date, in the ANN models studied in the literature, the number of prior periods *n* chosen to generate the models has always been fixed. Assume that the *n* chosen for a standard model is 12. In this case, the MARE value is 0.2866 for the *t* + 12 model and 0.3382 for the *t* + 24 model (**Figure 4**). The corresponding values for the stability of the relative error are 17.4% and 14.4% (**Figure 7**), respectively. According to the analysis made with Case A, the performance of these models can be improved by choosing a higher value of *n*. If *n* is 24, the MARE values decrease to 0.2783 and 0.3206, respectively (**Figure 4**). Similarly, for an *n* of 24, the stability of the relative error in the forecasting improves to the values of 15.8% and 12.8%, respectively (**Figure 7**).

#### **4.2 Discussion of results for case B**

For the analysis of Case B, the MARE and R results of this case, with two WSs, are compared with those of Case A, with one WS. For this purpose, (5) and (6) are used.

**93**

**Figure 9.**

**Figure 8.**

*Optimization of the ANNs Models Performance in the Short-Term Forecasting of the Wind…*

2 7 1

*MARE MARE*

1 1

*R R*

− = ∑ × 2 7 1

*p with WS*

1 1

= *R*

= *MARE*

*p with WS*

( ) ( ) ( )

7 (6)

*with WSs p with WS*

1 100%

− ∆ = ∑ × (5)

> ( ) ( ) ( ) *with WSs p with WS*

It can be seen in **Figures 8** and **9** how all the models generated for Case B obtain an additional improvement in performance to that already obtained for Case A. This additional improvement is in relation to ANN models developed to date which

It can also be observed that, in general, the degree of improvement increases as *m* increases. This degree of improvement slows down for forecasting horizons

The maximum additional improvements in model performance are seen in forecasting horizons *t* + 24 and *t* + 36 (7.5% and 5.5% for MARE and 3.7% and 5.4% for R, respectively). Even for the shortest forecasting horizons, *t* + 3 and *t* + 6, the maximum improvements in the MARE metric are significant (3% and 4.9%, respectively). Continuing with the specific example proposed in the analysis of results for Case A (using models *t* + 12 and *t* + 24), **Figure 10** shows the additional improvements in performance that can be obtained through the incorporation in the input layer of

1 100%

*DOI: http://dx.doi.org/10.5772/intechopen.97190*

*MARE*

always use exclusive data from a single WS.

longer than 24 hours.

data from a second WS (Case B).

*Comparison of MARE results for cases A and B.*

*Comparison of results obtained for R for cases A and B.*

7

*R*

∆

*Optimization of the ANNs Models Performance in the Short-Term Forecasting of the Wind… DOI: http://dx.doi.org/10.5772/intechopen.97190*

$$\Delta\text{ }\text{MAREE} = \frac{1}{7} \sum\_{p=1}^{7} \frac{\text{MAREE}\_{p\_{\text{(walk 1WS)}}} - \text{MAREE}\_{\text{(walk 1WS)}}}{\text{MAREE}\_{\text{(walk 1WS)}}} \times \text{1OO96} \tag{5}$$

$$
\Delta R = \frac{1}{7} \sum\_{p=1}^{7} \frac{R\_{p\_{\text{(wilt 1 WS)}}} - R\_{\text{(wilt 1 WS)}}}{R\_{\text{(wilt 1 WS)}}} \times \mathbf{100}\text{\%}\tag{6}
$$

It can be seen in **Figures 8** and **9** how all the models generated for Case B obtain an additional improvement in performance to that already obtained for Case A. This additional improvement is in relation to ANN models developed to date which always use exclusive data from a single WS.

It can also be observed that, in general, the degree of improvement increases as *m* increases. This degree of improvement slows down for forecasting horizons longer than 24 hours.

The maximum additional improvements in model performance are seen in forecasting horizons *t* + 24 and *t* + 36 (7.5% and 5.5% for MARE and 3.7% and 5.4% for R, respectively). Even for the shortest forecasting horizons, *t* + 3 and *t* + 6, the maximum improvements in the MARE metric are significant (3% and 4.9%, respectively).

Continuing with the specific example proposed in the analysis of results for Case A (using models *t* + 12 and *t* + 24), **Figure 10** shows the additional improvements in performance that can be obtained through the incorporation in the input layer of data from a second WS (Case B).

**Figure 8.** *Comparison of MARE results for cases A and B.*

**Figure 9.** *Comparison of results obtained for R for cases A and B.*

*Theory of Complexity - Definitions, Models, and Applications*

*MARE variation of different prediction periods: Case of a forecasting horizon t + 24.*

**92**

are used.

(**Figure 7**).

**Figure 6.**

**Figure 7.**

*Stability of relative error SDV in forecasting horizon.*

**4.2 Discussion of results for case B**

By way of example, we will now proceed to analyze the specific cases of the forecasting models *t* + 12 and *t +* 24. To date, in the ANN models studied in the literature, the number of prior periods *n* chosen to generate the models has always been fixed. Assume that the *n* chosen for a standard model is 12. In this case, the MARE value is 0.2866 for the *t* + 12 model and 0.3382 for the *t* + 24 model (**Figure 4**). The corresponding values for the stability of the relative error are 17.4% and 14.4% (**Figure 7**), respectively. According to the analysis made with Case A, the performance of these models can be improved by choosing a higher value of *n*. If *n* is 24, the MARE values decrease to 0.2783 and 0.3206, respectively (**Figure 4**). Similarly, for an *n* of 24, the stability of the relative error in the forecasting improves to the values of 15.8% and 12.8%, respectively

For the analysis of Case B, the MARE and R results of this case, with two WSs, are compared with those of Case A, with one WS. For this purpose, (5) and (6)

#### **Figure 10.**

*Improvements in error for two specific models due to implementation of cases A and B.*

Points A and B represent the error obtained when using a fixed *n* of 12 and only data from the reference WS of the wind farm. Points A1 and B1 represent the improvements obtained in the error when *n* is increased to 24. Points A2 and B2 represent the additional improvements obtained in the error when, in Case B, the data from a second WS are incorporated in the input layer of the ANN. For the two specific examples given, the overall improvements obtained by combining Cases A and B amount to 8.78% and 6.04%, respectively.

#### **5. Conclusion**

A series of interesting conclusions can be drawn from the results of this study with respect to possible improvements in the performance of ANN models for the short-term forecasting of wind farm power output.

The performance of the new ANN models generated for each forecast horizon improves with the increase in the number of prior 1-*h* periods (periods prior to the prediction hour), *n*, chosen for incorporation of the input layer parameters. For the forecasting horizons *t +* 12, *t* + 24 and *t* + 36, the maximum improvements obtained for MARE are 13.3%, 11.2% and 10%, respectively; and for R, the corresponding improvements are 7.9%, 8.9% and 9.2%, respectively.

A study is also made of the stability of the mean relative error for the different forecasting periods and for each forecasting horizon *m*. As *n* increases the stability of the error in the forecasting improves significantly for all forecasting horizons.

Additionally, in all the new models generated, the incorporation in the input layer of ANN of meteorological data from a second WS also improves the performance of the traditional models generated exclusively with data from the reference station of the wind farm. In general terms, the degree of improvement in model performance increases with *m*, attaining improvements in the MARE and R of up to 7.5% and 5.4%, respectively.

In view of the conclusions drawn from the present study, the original contributions described in this manuscript could be implemented in existing ANN models to optimize their results.

#### **Acknowledgements**

This research has been co-funded by ERDF funds, INTERREG MAC 2014-2020 programme, within the ENERMAC project (MAC/1.1a/117). No funding sources

**95**

**Author details**

Sergio Velázquez-Medina1

Canaria, Canary Islands, Spain

Palmas de Gran Canaria, Canary Islands, Spain

provided the original work is properly cited.

*Optimization of the ANNs Models Performance in the Short-Term Forecasting of the Wind…*

had any influence on study design, collection, analysis, or interpretation of data,

manuscript preparation, or the decision to submit for publication.

\* and Ulises Portero-Ajenjo2

1 Department of Electronics and Automatics Engineering, Universidad de Las

2 School of Industrial and Civil Engineering, University of Las Palmas de Gran

© 2021 The Author(s). Licensee IntechOpen. This chapter is distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/ by/3.0), which permits unrestricted use, distribution, and reproduction in any medium,

\*Address all correspondence to<EMAIL_ADDRESS>
*DOI: http://dx.doi.org/10.5772/intechopen.97190*

The authors declare no conflict of interest.

**Conflict of interest**

*Optimization of the ANNs Models Performance in the Short-Term Forecasting of the Wind… DOI: http://dx.doi.org/10.5772/intechopen.97190*

had any influence on study design, collection, analysis, or interpretation of data, manuscript preparation, or the decision to submit for publication.


4. Case study: Design of the centrifugal compressor

The case study presented in the literature [5] is considered for the present illustration for the design and numerical analysis of the centrifugal compressor. Main objective of the current work is to design a centrifugal compressor capable of delivering a pressure ratio of 5.4 with a mass flow ingestion rate of 5.73 kg/sec. The compressor is targeted to achieve 82% total-total efficiency with design constraints of 280 mm for the impeller and 340 mm for the diffuser in terms of diameter. Also, the compressor has to generate flow parameters relative to functional downstream components.

### 4.1. Centrifugal compressor specifications

The input parameters of the centrifugal compressor are tabulated in Table 1.

Table 1. Geometrical and functional specifications of analysed turbo-machinery.

Preliminary design of the impeller and vaned diffuser is carried out by adapting a onedimensional model approach. Comprehensive design of the centrifugal compressor stage was generated using ANSYS BladeGen module.


**5. Discussion and conclusion**

The quantitative results show that the gifted students significantly outperformed the general students in number sense and had a high effect size. Previous studies have shown a positive relationship between number sense and mathematics achievement [15, 39]. Earlier studies also agreed that students who have good number sense should be able to develop and apply flexible and efficient strategies (including mental computation and estimation) to handle numerical problems [9, 17, 38, 39]. In addition,

#### *Number Sense Performance of Gifted and General Fourth Graders in Taiwan DOI: http://dx.doi.org/10.5772/intechopen.111752*

several studies reported that the gifted students have the ability to use various methods efficiently and flexibly when solving problems [13, 25, 27, 29]. Therefore, the result that the gifted students significantly outperformed the general students in number sense is reasonable. In addition, the data also show no significant difference between each number sense component for the gifted students. This is probably due to the facts that the gifted students can develop more flexible and efficient methods to solve problems. Therefore, they have more balanced development on each number sense component. However, a significant difference was found between each number sense component for the general students.

The general students' performance on F4 (recognizing the relative number size) was significantly higher than that on F2 (being able to decompose and compose numbers). This is probably because Taiwanese mathematics textbooks typically have several "recognizing the relative number size"-related problems, and Taiwanese students have limited exposure to problems in mathematics that require them to compose and decompose numbers. Therefore, these Taiwanese students performed well on "recognizing the relative number size"-related problems due to they have ample opportunities to solve these kinds of problems. This result is consistent with the findings of a previous study [38, 39]. In addition, decomposing and composing numbers to solve problems need more flexible thinking; therefore, it is reasonable to believe that general students not performed well on this number sense component. Moreover, the teachers of the gifted students also provided several challenging problems to deepen their mathematical learning and thinking. However, these problems are not necessarily related to decomposing and composing numbers.

The interview results showed that the gifted students outperformed the general students in using the number sense-based method. It is reasonable to believe that gifted students can flexibly apply number sense-based methods, including the use of benchmark, estimation, and so on to solve problems. This supports Sands' finding [40] that showed that the gifted students tend to develop multiple methods to solve problems which relate to flexibility in thinking. Therefore, the result that the gifted students outperformed the general students in using the number sense-based method is reasonable. Moreover, the general students obviously had more misconceptions regarding number sense than the gifted students did. This result is probably due to insufficient basic mathematics knowledge exist among the general students. In fact, there is still the lingering question of curricula, learning opportunities, etc. This will lead more studies in the future.

This study was conducted to examine whether the gifted students outperform general students on number sense. Additionally, variations in the use of number sense methods between the gifted and general students when solving number sense-related problems were examined. Although limited by a small sample size, this study provides three major contributions to mathematics education:

students are significantly higher in applying number sense-based method to solve problems than the general students.

3.The findings showed that the gifted students performed equally well on each number sense component. This is special and different from the earlier studies that students in Taiwan did not perform equally well on each number sense components [39]. Earlier studies showed that general students performed poor on judging the reasonableness of a computational result (Authors).

We do hope the findings in this study may contribute the future teaching and research relating to number sense and the gifted students.


**8. Acknowledgments**

This work was supported by the Chinese Academy of Sciences (the 100 talents program and KJCX2-EW-N06-04), Natural Science Foundation of China (11004228), and Innovation Method Fund of China (2010IM030600).


**8.2 Project planning phase**

The Project Planning Phase is defined as creating and maintaining a workable plan to accomplish the purpose of the project. This involves developing a project management plan which encompasses all of the project knowledge areas [29].

### *8.2.1 BIM integration with emerging technologies used in the project planning phase*

project. This helps contractors estimate projects more accurately [34]. AI can be used to ensure structural steel adheres to guidelines set by standards and building codes for fire resistance and safety. Providing more precision in performance on steel structures against fire. In addition, AI can be used to understand what will happen to various types of materials like concrete, masonry, steel and wood under maximum temperature conditions [35].


*Review* **The Role of Liver Imaging in Hereditary Hemorrhagic Telangiectasia**

**Joelle Harwin 1, Mark D. Sugi 1,2, Steven W. Hetts 1,2, Miles B. Conrad 1,2 and Michael A. Ohliger 1,2,\***

Received: 7 October 2020; Accepted: 4 November 2020; Published: 21 November 2020

**Abstract:** Hereditary hemorrhagic telangiectasia (HHT) is an autosomal dominant vascular disorder characterized by spontaneous epistaxis, telangiectasia, and visceral vascular malformations. Hepatic vascular malformations are common, though a minority are symptomatic. Symptoms are dependent on the severity and exact type of shunting caused by the hepatic malformation: Arteriosystemic shunting leads to manifestations of high output cardiac failure, and arterioportal shunting leads to portal hypertension. Radiologic imaging, including ultrasound, computed tomography (CT), and magnetic resonance imaging (MRI), is an important tool for assessing liver involvement. Doppler ultrasonography is the first-line screening modality for HHT-related liver disease, and it has a standardized scale. Imaging can determine whether shunting is principally to the hepatic vein or the portal vein, which can be a key determinant of patients' symptoms. Liver-related complications can be detected, including manifestations of portal hypertension, focal liver masses as well as ischemic cholangiopathy. Ultrasound and MRI also have the ability to quantify blood flow through the liver, which in the future may be used to determine prognosis and direct antiangiogenic therapy.

**Keywords:** HHT; liver; MRI; ultrasound; AVM; bevacizumab; Osler–Weber–Rendu


*2.4.1 Gamma spectra acquisition*

As mentioned above, the gamma peak with a centroid at 4.44 MeV is used to define soil carbon content. Gamma spectra containing peaks of interest with centroids at 4.44 and 1.78 MeV (used to correct silicon-28 interference in the carbon peak) are measured by gamma detectors. Gamma spectra measurements are the accumulation of gamma detector response in corresponding memory cells. Each memory cell accumulates the response (in counts) corresponding to a specific gamma ray energy interval. Gamma rays produced by 14 MeV neutrons have an energy less than this value. The studied energy interval is divided into 1024 cells (or channels) with channel widths of 10 keV. Gamma ray production under neutron irradiation is a statistical process. Thus, spectra acquisition should continue for some time to achieve required accuracy. The average count rate (counts per second, cps) depends on neutron flux intensity, number of nuclei of interest in the sample (soil), efficiency of neutron-nuclei interactions, and detector(s) volume and efficiency of gamma ray registration. From a radiation safety viewpoint, total neutron yields exceeding 2 107 neutrons per second should not be used in a field system. In general, soil carbon content is no more than 5–10 w%, and agricultural soil density varies from 1200 to 1600 kg/m3 . Under these conditions, gamma detectors with relatively large volumes should be used to achieve suitable count rates in channels of interest. In the described mobile PFTNA system, three gamma detectors with a total volume of 7.5 dm3 were used. To achieve a soil carbon content accuracy no worse than 0.5 w%, the accuracy of carbon peak area determinations should be no worse than 10 cps. The carbon peak area is around 200 cps when soil carbon content is 2–3 w%. To reach the desired accuracy for the described equipment, measurement time should be no less than 15 min [11]. For elements having a soil content greater than carbon, determinations with this same accuracy require shorter spectra acquisition time. For example, the higher soil content of silicon (30 w%) requires a spectra acquisition time of 1 min or less.


**2. Nutritional disorders and production diseases**

Production diseases are a negative side effect of the production processes. They are not merely a peripheral phenomenon, although often mistakenly dealt with as such, but are related, amongst other things, to the issues of animal welfare and food safety. Pds adversely affect productivity and reproduction and can have severe economic implications due to related failure and prevention costs [4]. Moreover, products of diseased animals are of inferior quality, a fact recognized by consumers, who are aware of the problems in animal production. Thus, the high prevalence of Pds gives rise to questions and discussions about production processes and what responsible management actually entails. Pds have been under discussion in animal science since the first Int. Conference on Production Diseases in Farm Animals in1968, an event which has occurred periodically ever since [5].

Disturbances of one or multiple metabolic processes related to the regulation of a particular metabolite in the body fluids are known as metabolic disorders [6] and are a manifestation of the cow's inability to cope with metabolic demands [7]. Clinical diseases closely related to a suboptimal nutritional management are, amongst other things, ketosis, milk fever, metritis, mastitis, and lameness [8]. The known interactions between various metabolic stressors, and their relationships to other diseases, particularly infectious and inflammatory diseases of early lactation, have become "a central focus of interest in the study of metabolic diseases in dairy cattle" [9]. Nutritional disorders and comorbidities have been comprehensively discussed elsewhere [10]. In the following, they are considered as production diseases.

Pds occur throughout the lifetime of dairy cattle but are never so pronounced than in the transition phase, the 6 to 8-week period centered on parturition, and which is known as the most challenging and critical period for a dairy cow during the lactation cycle [11]. Within this period, major physiological, nutritional, metabolic and immunological changes occur. The production cycle of the cow shifts from a non-lactating state to the onset of extensive milk synthesis [12, 13]. Cows have to adjust metabolically to the sudden increase in energy and nutrient requirements and supply. Gaps between nutrient demand and supply can coincidentally occur with substantial variations in the nutrient content of the diet and in the daily intake of dry matter (DMI). Dealing with this requires comprehensive adaptation and regulation of the metabolism. Desirable outcomes for farm management are: cows that are successful in adapting metabolically to challenges inside and outside of the organism with minimal to no disease events and a reduction in avoidable culling as well as cows with efficient productive and reproductive performances. Past intensive research conducted into nutritional requirements, physiological adaptation and metabolic associations with periparturient diseases of cows has not led to any substantial reduction in the prevalence of Pds. Despite the fact that solutions are still not clearly evident, most in the dairy industry continue to believe that there are tremendous opportunities to improve the health and reproductive performance of transition cows without compromising milk production [14].

**55**

*Nutrition and Health-Management in Dairy Production DOI: http://dx.doi.org/10.5772/intechopen.89447*

**3. Allocation of nutrients by the farm management**

average performance level of a herd or feeding group of dairy cows.

due to imprecision in mixing and/or in allocation procedures.

**4. Resource allocation within dairy cows**

It is beyond dispute that allocation of nutrient resources to the farm animals by farm management is of high importance for the realization of both a high level of productivity and a low level of Pds. However, in farming practice the nutrient allocation is not always demand- and target-oriented. In general, the diet offered is either in the form of a total mixed ration ad libitum or in a combination of a feed mixture ad libitum, both supplemented with an assigned amount of concentrate via an electronic feeder. The allocated amounts of concentrate are deduced from a more or less accurately estimated level of milk performance of each individual dairy cow, while the total or partly mixed rations are generally formulated according to the

This approach, however, neglects the large variation in the requirements of the animals due to, amongst other things, inter and intra-individual variation in milk yield, body weight and, last but not least, variation in feed intake. Grouping strategy and feeding behavior as well as social rank between the animals have a considerable impact on the competition between them for space and feed, and thus on feed intake [15]. Accordingly, a large inter and intra-individual variation of feed intake is observed in farm practice [16]. The amount of daily nutrient and energy intake is a result of the interactions between the composition of the diet itself, the environment in which a diet is offered and various intrinsic processes [17]. On the other hand, the same dry matter intake (DMI) per cow and day can be achieved by altered frequencies and durations of eating time and meal sizes. Nutrient and energy intake can change dramatically in response to changes in diet composition or metabolic state. Feeding regimes on a farm might appear to be regular but hidden variations in the nutrient and energy supply can occur to a greater or lesser degree. Furthermore, the feeding rations offered can be quite variable in their composition, for example in the portion of roughage and concentrate, throughout the course of time, thus correspondingly in the availability for the animals within the digestive tract [18]. Furthermore, the proportion of single components can vary considerably

In light of the numerous sources of variation, feeding rations offered in farm practice cannot precisely meet the requirements of an individual cow within a feeding group or herd. The gap between demand and supply underlies a considerable variation between the animals. In general, farm management lacks insight into the degree of the inter and intra-individual variations and discrepancies. Knowledge about the impacts of nutrient supply is often restricted to the outcomes of feeding regimes in terms of the individual milk yields and content on a monthly, seldom on a daily, basis. Many farmers have knowledge about the composition and ingredients of the feeding ration and they can base estimations about the required feed intake on the analyzed portions of the diet [19]. However, these estimated equations are only valid for one virtual cow but represent the average of a feeding group. Considering that the interactions between the numerous influencing factors, of which only few have been mentioned, create a virtually unlimited number and variety of combinations (even within one single cow, let alone a herd), the discrepancies between demand and supply can only be poorly predicted by traditional models of feed intake regulation [20].

Available energy is used by animals during biological processes (chemical, active transport, mechanical, electrical and thermal work) which are essential for building, sustaining and enhancing biological structures [21]. To grasp the complex processes

*Livestock Health and Farming*

since [5].

diseases.

processes across the dairy industry. In raising this basic question, it is not the intention of the following script to repeat or summarize the general recommendations found in literature and text books that claim to provide options for reducing these serious problems. Instead, the objective is to question predominant thinking patterns and to reflect on the weak points and driving forces that might be responsible

Production diseases are a negative side effect of the production processes. They are not merely a peripheral phenomenon, although often mistakenly dealt with as such, but are related, amongst other things, to the issues of animal welfare and food safety. Pds adversely affect productivity and reproduction and can have severe economic implications due to related failure and prevention costs [4]. Moreover, products of diseased animals are of inferior quality, a fact recognized by consumers, who are aware of the problems in animal production. Thus, the high prevalence of Pds gives rise to questions and discussions about production processes and what responsible management actually entails. Pds have been under discussion in animal science since the first Int. Conference on Production Diseases in Farm Animals in1968, an event which has occurred periodically ever

Disturbances of one or multiple metabolic processes related to the regulation of a particular metabolite in the body fluids are known as metabolic disorders [6] and are a manifestation of the cow's inability to cope with metabolic demands [7]. Clinical diseases closely related to a suboptimal nutritional management are, amongst other things, ketosis, milk fever, metritis, mastitis, and lameness [8]. The known interactions between various metabolic stressors, and their relationships to other diseases, particularly infectious and inflammatory diseases of early lactation, have become "a central focus of interest in the study of metabolic diseases in dairy cattle" [9]. Nutritional disorders and comorbidities have been comprehensively discussed elsewhere [10]. In the following, they are considered as production

Pds occur throughout the lifetime of dairy cattle but are never so pronounced than in the transition phase, the 6 to 8-week period centered on parturition, and which is known as the most challenging and critical period for a dairy cow during the lactation cycle [11]. Within this period, major physiological, nutritional, metabolic and immunological changes occur. The production cycle of the cow shifts from a non-lactating state to the onset of extensive milk synthesis [12, 13]. Cows have to adjust metabolically to the sudden increase in energy and nutrient requirements and supply. Gaps between nutrient demand and supply can coincidentally occur with substantial variations in the nutrient content of the diet and in the daily intake of dry matter (DMI). Dealing with this requires comprehensive adaptation and regulation of the metabolism. Desirable outcomes for farm management are: cows that are successful in adapting metabolically to challenges inside and outside of the organism with minimal to no disease events and a reduction in avoidable culling as well as cows with efficient productive and reproductive performances. Past intensive research conducted into nutritional requirements, physiological adaptation and metabolic associations with periparturient diseases of cows has not led to any substantial reduction in the prevalence of Pds. Despite the fact that solutions are still not clearly evident, most in the dairy industry continue to believe that there are tremendous opportunities to improve the health and reproductive performance

of transition cows without compromising milk production [14].

for preventing effective progress in the reduction of Pds in dairy farming.

**2. Nutritional disorders and production diseases**

**54**