Estimation of failure probability of wave energy farms by group method of data handling: An indian scenario

The failure probability of the wave energy converters is exceptionally high, which again increases the operation cost of the entities. The cause of this high cost lies in the fact that various factors influence the production efficiency of the converters. To solve this problem, multiple converters are utilized in series and parallel formation to produce energy simultaneously. This multiple converter system, known as wave energy farms, also fails to increase efficiency and decrease the cost of operation sufficiently. The reason for this is that not only technical but socio-economic as well as different environmental factors have a significant role in this aspect, which remains undetected or under- or over-detected while calculating the potential wave energy. The present investigation tries to classify the different factors which are most influential in controlling the transfer efficiency of wave energy farms to solve the problem of erroneously detecting significant factors. The authors offer a new indicator for estimating the failure likelihood of wave energy farms in converting ocean wave energy into electricity by combining Multi-Criteria Decision Making and Polynomial Neural Networks with information collected from an unbiased ranking technique.

1 Introduction

With the current population and economic growth, it is predicted that in the near future, demand for energy will increase considerably by 17 TW (Rotty, 1979). Global climate change, as well as the warnings linked with it, constitute a serious threat to the world’s ecosystems. The possibility of reversing this trend relies on lowering CO₂ emissions into the environment. By investing in renewable energies such as wind and solar electricity, international treaties are playing a critical role. However, there is another renewable energy cluster with great potential and a bright future. This is the energy created by waves, which is quickly gaining traction as a viable alternative to reducing the environmental impact of fossil fuel use (Abanades et al., 2014). Wave energy has a number of advantages, including, but not limited to, large energy capacity One of the most concentrated, reliable, and long-lasting energy sources, wave energy is available in many nations but is underutilized (Mackay et al., 2010).

As a result, the utilization of wave renewable energy offers enormous potential for lowering greenhouse gas emissions. More wave energy providers are showcasing their products to draw investors in a competitive manner as a result of the growing marine renewable sector. Information about WEC is frequently confidential. Developers want to place a device in the best possible way, but investors just want to make money. The rivalry also causes WECs on the market to have very dynamic properties. Therefore, research is necessary to improve evaluations of novel WECs and offer recommendations for matching WECs and locales (Choupin et al., 2021). Because the wave energy converter (WEC) produces no gaseous, liquid, or solid emissions, wave power is less environmentally damaging than most other forms of energy generation (Brooke, 2003). Wave farms vary depending on the device type, condition of the ocean, farm size, proximity to shore and grid connection, and device and plant cost estimation of the farm layout.

Wave farms (Guanche et al., 2014) are arrays of wave energy converters that are arranged in either series or parallel connections to cumulatively convert the available potential of wave energy resources. The efficiency of conversion mainly depends on the performance efficiency of the converters (Bódai and Srinil, 2015), the transmission loss incurred in the connecting cables (Sharkey et al., 2013), the park effect (Katsaprakakis and Christakis, 2014; Gatzert and Kosub, 2016), and some other factors which depend on location, such as wind speed, duration of fetch (Carrasco et al., 2012), water quality (Ghosh et al., 2016), tourism potential (Greaves et al., 2016), etc. Due to various crucial characteristics, such as gap resonance, array arrangement, wave nonlinearity, 3-D flow field effect, power take-off (PTO) mechanism, and oblique wave incidence, the hydrodynamic behavior of multi oscillating wave surge converter devices is still not fully known (Cheng et al., 2021).

It is particularly difficult to determine how nonlinear multi-body hydrodynamic interaction would affect the harvested energy of OWSC devices. It is necessary to do systematic research into the additional nonlinear hydrodynamic performance of an array of OWSCs.

1.1 Objective and novelty

The goal of this research is to determine the best arrangement for wave energy farms so that the most quantity of utilizable energy can be transformed. The study’s unique contribution is the creation of an indicator that may objectively describe the performance efficiency of wave farms in terms of location, design, and cost. The creation of an instinctual indication was accomplished, and it was used to solve a problem for the first time.

2 Method applied

The present study includes the application of the Multi-criteria decision making (MCDM) and ANN-based GMDH methods. The latter method was used to incorporate adaptability, and MCDM was used to find the priority of the input parameter with respect to the study objective. Sections 2.1, 2.2 depict the strengths, weaknesses, and application of the MCDM and GMDH methods in the related fields.

2.1 Multi-criteria decision making

The MCDM is used to make objective decisions and determine the significance of selected characteristics for the study’s specific goal. In this study, MCDMs such as Fuzzy-AHP (Shaw et al., 2012) and ANP (Aragonés-Beltrán et al., 2014) were used to determine the importance of selected characteristics in relation to the investigation’s goal.

2.1.1 Fuzzy-AHP

The computation approach developed by Saaty (Saaty, 1980) for the analytical hierarchy process was based on crisp judgment. On the basis of fuzzy set theory and hierarchical structure analysis, many fuzzy AHP approaches have been devised. In the application process, Saaty proposed the significance scale, which uses numbers from 1 to 9 while the decision-maker performs paired comparisons. Most real-life decisions, on the other hand, have unknown outcomes (Chang, 1996).

The weights for evaluative elements are determined using fuzzy AHP, which is based on fuzzy interval arithmetic using fuzzy triangular numbers and confidence indexes, and an interval means method (Buckley, 1985; HMd and Wu, 2011). To enhance decision-making, some academics have combined fuzzy theory with AHP.

2.1.2 Analytical network process

Analytical network process (ANP) is a flexible decision-making strategy that works with both quantitative and qualitative data and qualitative data. Saaty introduced ANP as a novel MCDM technique to solve the real-world concerns of interaction and feedback among criteria and options (Saaty, 2004). ANP is a nonlinear dynamic structure that is based on the Markov Chain notion and is an extension of AHP (Saaty, 1999). We discovered that while dealing with ANP, the standard way of normalizing the non-weighted super matrix was not appropriate since, in the actual world, varying degrees of impact exist within clusters of factors/criteria. As a result, the weighted super matrix’s weighted assumption of equal weights for each cluster is impractical and has to be modified (Luo et al., 2010). Three matrix analyses are included in the ANP method: the super matrix, the weighted super matrix, and the limit matrix (Yang et al., 2003). Table 1 depicts the advantages, disadvantages, and application of the ANP method.

TABLE 1

TABLE 1. Table showing advantages, disadvantages, and application of Fuzzy-AHP method.

2.2 Ranking method

Duncan was the first to suggest an economical design for X control charts (Duncan, 1956). By adding statistical restrictions into the economic model, Saniga was the first to propose the economic-statistical design of X bar and R charts (Saniga, 1989). Multiple objectives, including cost function and statistical features, are maximized simultaneously in their method. As a result, the best control chart design is modeled as a Multi-criteria decision making (MCDM) issue (Allen, 2006) (Table 2).

TABLE 2

TABLE 2. Table showing the features of the twelve development models.

The present investigation also uses some statistical control charts to find the rank of the selected factors in an unbiased and non-preferential way.

The control charts are used to detect system performance outliers. The charts are used in this study to determine the relevance of the index’s optimal performance and the associated features of the input parameters without outliers. The separation of the factors in terms of their contribution to optimizing the index performance. The X-bar, R, and P control charts were used separately to rank the variables as per their contribution to the study objective.

2.3 Group method data handling algorithms

Ivakhnenko (Ivakhnenko, 1971) created the Group method data handling algorithms (GMDH) model, which is one of the learning machine models based on the polynomial theory of complex systems. The most important input parameters, the number of layers, the number of neurons in the middle layers, and the network’s ideal topology design are all automatically defined by this network. As a result, the GMDH network is a model of active neurons that self-organize. During the training step, the GMDH network’s topology is set using a polynomial model that yields the least amount of error between the predicted value and the observed output.

The neuro-fuzzy GMDH network is a highly versatile algorithm that may be integrated with other iterative and evolutionary algorithms with ease (Nariman-Zadeh et al., 2002). The GMDH neural network is a self-organizing, unidirectional structure with many layers made up of neurons with comparable structures.

After selecting the model criterion in line with the modeling and information division’s aims, GMDH will automatically confirm the model. If several types of input units are used, this modeling approach will generate multiple types of models. This automated modeling method has been used to create Bayesian networks (Xiao et al., 2009) and Mamdani-type fuzzy models (Lemke and Müller, 2003).

The noise-immunity of GMDH is another attractive feature. We all know that when data contains noise, the greatest danger is over-fitting (Tan et al., 2006), which means that models become too complicated and generalizable. This issue, however, may be overcome in the case of GMDH.

3 Methodology

3.1 Brief description

Following an examination of the literature, the twenty-one most critical factors for the efficiency of a wave energy converter farm design were chosen. These factors are wave height, shipping density, wave period, water depth, distance from the coast, wind speed, salinity, regularity of wave, number of WEC, the distance between WEC, wave incidence direction, array layout, length of cable connecting to shore, buoy diameter, rated power, converter efficiency, unit cost, operating and maintenance costs, capital costs, taxes and rate of energy charge per unit.

The current research took two steps to create an indicator for representing farm performance in terms of the installation site, converter design, and system cost.

The control charts X bar, R, and P were used in the first phase based on their significance to the study goals. The Fuzzy-AHP and ANP MCDM techniques were then used to determine the priority value of each of the parameters. The MCDM technique is divided into three parts, which will be detailed in the next section.

3.2 Application of multi-criteria decision making

The application of MCDM involves three steps, which are described in the next section.

3.2.1 Criteria selection

The criteria were selected based on the study objective. In the present study, the location (L), Design (D), and Cost (C) were selected as the criteria on which the parameters will be compared.

3.2.2 Alternative selection

All the selected parameters were considered as alternatives to the decision-making method. Based on the rank obtained using the control chart method, each of the possibilities is compared to one another.

3.3 Application of aggregation method

After comparing each of the alternatives against each other based on the criteria and with respect to the study aim, the criteria and alternatives were utilized to identify the equal weight of the given parameters.

The criteria were then compared to one another based on the available possibilities, all while keeping the study’s purpose in mind. To evaluate the weight of importance for each of the elements, both findings were cross multiplied based on the criteria and in relation to the study’s purpose.

The weight vector or priority values of the parameters were used to convey the relevance of the parameters at the end of this strategy, which is directly proportional to the significance of the variables.

Weight Function as the Indicator: The W-value, or Indicator for Performance Evaluation of Wave Energy Converter Array Design, was calculated by Eq. 1

$W_{value}=\frac{\sum w_n{b}_n}{\sum w_m{b}_m}(1)$

where “w_n” and bn denote the degree of the weight of importance, beneficiary and non-beneficiary variables, respectively, and n and m indicate the number of the beneficiary and non-beneficiary variables.

3.4 Development of the group method data handling model

With twenty-one inputs and one output, the GMDH model was created. The models’ datasets were standardized, and 60 percent of the data was utilized for training, while the remaining 40 percent was preserved for testing. A total of twelve models were created using a variety of control charts, MCDMs, and data transformations. Table 1 demonstrates how the models were created in different methods to anticipate the same goals.

Mean Absolute Error (MAE) (Willmott and Matsuura, 2005), Root Mean Square Error (RMSE) (Despotovic et al., 2016), Mean Relative Error (MRE) (Gray et al., 2016), and Correlation(R) (Pascual-González et al., 2016) were used to evaluate the performance of all forty-eight models.

Model accuracy is known to be inversely proportional to the former measures, but model performance is known to be directly proportional to the latter measurements. The model’s performance during the checking (c) or testing phase is a better predictor of model dependability than the model’s performance during the training (t) phase (Noori and Kalin, 2016).

According to the EI, three models were chosen for additional validation after they were shown to be superior to the forty-eight models produced for this investigation.

Root Mean Square Error (RMSE), Mean Relative Error (MRE), and Percent bias (PBIAS) (Gupta et al., 1999) between predicted and observed data were used to assess the dependability of the selected three models. The Performance Index (PI) was created to represent the models’ performance. Equ.2.

$\left[\mathrm{P}\mathrm{I}=\left\{\frac{{\mathrm{R}}_{\mathrm{t}}}{{\mathrm{M}\mathrm{A}\mathrm{E}}_{\mathrm{t}}+{\mathrm{M}\mathrm{R}\mathrm{E}}_{\mathrm{t}}+{\mathrm{R}\mathrm{M}\mathrm{S}\mathrm{E}}_{\mathrm{t}}+{\mathrm{P}\mathrm{B}\mathrm{I}\mathrm{A}\mathrm{S}}_{\mathrm{t}}}\ast 0.6\right\}+\left\{\frac{{\mathrm{R}}_{\mathrm{T}}}{{\mathrm{M}\mathrm{A}\mathrm{E}}_{\mathrm{T}}+{\mathrm{M}\mathrm{R}\mathrm{E}}_{\mathrm{T}}+{\mathrm{R}\mathrm{M}\mathrm{S}\mathrm{E}}_{\mathrm{T}}+{\mathrm{P}\mathrm{B}\mathrm{I}\mathrm{A}\mathrm{S}}_{\mathrm{T}}}\ast 0.4\right\}\right](2)$

where t is for testing and T is for the training phase.

Table 1 shows the nomenclature, which starts with the number of inputs, then the first letter of the training process, the data transformation function, and finally, the model number.

3.5 Sensitivity analysis

The most efficient model’s sensitivity will always be proportional to the importance of the parameters in the model output. For a model to be trustworthy and efficient in predicting its output with dependability, the sensitivity and significance must be consistent and associated. The model was subjected to a sensitivity analysis, and it was discovered to have the highest EI of all the models produced for this study.

3.6 Case study

In Figure 1 represents the geographical locations of five points (location 1 to location 5), which are used to define the wave energy converter efficiency analysis.

FIGURE 1

FIGURE 1. Locations of the study area (Noori and Kalin, 2016)

Several industries are currently developing and implementing novel technologies in wave energy generation across the world. AquaEnergy Group, Ltd. (AquaEnergy), an ocean wave corporation, describes its categorization growth and optimization efforts in this study. Ocean energies have witnessed a resurgence in attention in recent years, owing to a growing recognition that we will need all types of clean energy to lessen our reliance on fossil fuels.

4 Results and discussion

The weight vector of the parameters was calculated to analyze the X bar, R, P control chart, and citation frequency; the citation frequency refers to the number of citations divided by the number of the literature surveyed, as defined in Table 3. The twelve models were specified as AHP, ANP, AHP-ANP, Statistical method with AHP, Statistical method with ANP, Statistical method with AHP-ANP, Fuzzy AHP, Fuzzy ANP, Fuzzy –AHP, Fuzzy-ANP, Fuzzy-AHP-ANP, Statistical method with Fuzzy-AHP, Statistical method with Fuzzy-ANP and Statistical method with Fuzzy-AHP-ANP in Table 4. The performance of the twelve models in the prediction of wave energy farm performance is depicted in Table 5. Figures 2, 3 depict the comparison of predicted and observed output during the training and testing or predictive phase and the distribution of residuals derived from the predicted and observed output, respectively.

TABLE 3

TABLE 3. Table showing the rank of the parameter of X bar, R, and P control chart.

TABLE 4

TABLE 4. Table showing the parameters as determined by various MCDM methods.

TABLE 5

TABLE 5. Table results of the 12 models developed for prediction of efficiency of wave energy farms.

FIGURE 2

FIGURE 2. Figure showing the distribution of residual value for the model #21ANG1.

FIGURE 3

FIGURE 3. Figure showing the distribution of residuals derived from observed and predicted output for #21ANG1.

According to the results of the fuzzy-AHP and ANP strategies, the potency of the wave energy farm was found to be the highest three most vital factors among the twenty-one thought-about parameters.

The study’s performance analysis found that Model No. 21ANG1 was the most dependable of all the models studied, followed by Model No. 21FAHG1. Both of the essential models were GMDH-trained, utilized non-linear neuron function, and modified the output. Models three and seven, which were discovered to be the study’s second and third most important models, incorporated variable ranking as well as output transformation, and the model was trained with GMDH. All the models that employed all twenty-one input variables were included in the analysis.

The model 21ANG1 was found to be better than the other models in Table 5. According to the results, one model was selected for prediction as performance will depend on the method of variable ranking and may change if the method is changed in Table 5. If the MCDM approach is altered, the performance accuracy of the chosen model may change as well. Thus it was assumed that if the method of MCDM remains unchanged, the accuracy of the model will be uniform in any system as the model was trained with a normalized data set that is independent of scale problems.

Chennai has the highest probability of failure among the sites, according to the conclusions of the case study research. In addition, criterion and alternative selection has a significant impact on the model findings in Table 6.

TABLE 6

TABLE 6. Table showing the performance analysis of five locations.

The importance of the variables was considered based on normal conditions; it depicts no information regarding the process to optimal performance efficiency of the converter. However, the importance variable by estimated MCDM depends on the information retrieved from the literature survey of a certain number of reports.

Figure 3 shows the comparison of predicted and output data, as estimated by the selected model. The distribution of residual value is depicted in Figure 2.

4.1 Objective equations

Using twenty-one input and one output parameter, the wave energy farm designs of five sites were estimated. The network was trained using the GMDH technique and Supplementary Equation S54 in Supplementary Annexure S1 shows the number of hidden layers and the value of the weight vector for each input.

$Y1=-0.10507-N707*N2*0.103405+N{707}^2*0.0782601+N2*1.08516+N{2}^2*0.0159021$

where $Y1$ = model output and $N2$ and $N707$ are the sub-model output as given in Supplementary Annexure S1.

4.2 Multiple linear regression model

The objective equation of model was developed by

$Y=\mathrm{b}0+\mathrm{b}1*\mathrm{x}+\mathrm{b}2*\mathrm{x}+\mathrm{b}3*\mathrm{x}+\mathrm{b}4*\mathrm{x}+\mathrm{b}5*\mathrm{x}+\mathrm{b}6*\mathrm{x}.$

In the current analysis, it was discovered that the GMDH trained model had acceptable performance metrics. To establish a relationship between the dependent and independent variables, a multiple linear regression was run on the dataset. The PI test for the MLRM model is not as significant as 0.122945. Correlation was calculated to be 0.992075, indicating that the developed model suited the dataset well. The MLRM model performed better at predicting in Table 7 than the regression model, which was determined by the MSE, which was obtained for both cases and was 0.03498 for the regression model and 0.0367 for the GHDH model. To validate the model, the created GHDH and regression model were both given the test dataset. The regression model was created utilizing the entire dataset, which included the test data points, but the MLRM model was never exposed to the test dataset during training. The GMDH method required to include data points that were near to the minimum and maximum values of the dependent variable when creating the test dataset.

TABLE 7

TABLE 7. Performance index of multiple linear regression model.

4.3 Sensitivity analysis

Each number in the sensitivity analysis represents the difference between the expected result and the level of uncertainty associated with a single input variable. It was observed that with a change in each of the input variables (i.e., wave height, shipping density, wave period, water depth, distance from the coast, wind speed, salinity, regular wave, number of WECs, the distance between WECs, wave incidence direction, array layout, length of cable connecting to shore, buoy diameter, rated power, converter efficiency, unit cost, operating and maintenance costs, capital costs, taxes and rate of energy charge per unit) there is a change in output, which depicts the sensitivity of the model with respect to each of its inputs in Figure 4. The most sensitive parameter was wave period, and the least sensitive was array layout.

FIGURE 4

FIGURE 4. Figure depicting the input variable’s sensitivity analysis.

6 Conclusion

The goal of this research is to evaluate the likelihood of wave energy farms failing. In this case, 12 alternative models were created using MCDM approaches and polynomial neural networks. Each model’s performance was estimated using performance indicators such as RMSE, MAE, r, and PBIAS. The model with the best performance efficiency was used to forecast the chance of failure. The selected model was also utilized to determine the likelihood of failure in five areas along the Indian coastal strip. The length of the cable connecting the converter (as determined by the X and P chart methods), the distance between WEC (as determined by the R Chart method), and converter efficiency (as determined by the citation frequency) were found to be the most important parameters in terms of failure probability.

Among the 12 models, the 21ANG1 developed model was found to have the highest performance efficiency (18.959). According to the sensitivity analysis results, the sensitivity and weight of importance of the variables are in exact coherence. The case study results show that the Chennai region has the highest failure probability compared to the other four regions, whereas the Kikanada coastal belt has the lowest chance of failure. This means that farms installed in the Kikanada region have the potential for higher conversion efficiency than in the Chennai region. Although the model has some drawbacks, such as if the method of ranking or decision making is changed, then the importance of the parameter may also change, and this will also impact the results. Again, the selected factors may also change if more resources are analyzed. Such drawbacks can be compensated for if specific policies are initiated so that uniformity among all the feasibility methods can be maintained.

Data availability statement

The datasets presented in this study can be found in online repositories. The names of the repository/repositories and accession number(s) can be found in the article/Supplementary Material.

Author contributions

All authors listed have made a substantial, direct, and intellectual contribution to the work and approved it for publication.

Acknowledgments

The authors thank the support of the National Research and Development Agency of Chile (ANID), ANID/Fondap/15110019.

Conflict of interest

The authors declare that the research was conducted in the absence of any commercial or financial relationships that could be construed as a potential conflict of interest.

Publisher’s note

All claims expressed in this article are solely those of the authors and do not necessarily represent those of their affiliated organizations, or those of the publisher, the editors and the reviewers. Any product that may be evaluated in this article, or claim that may be made by its manufacturer, is not guaranteed or endorsed by the publisher.

Supplementary material

The Supplementary Material for this article can be found online at: https://www.frontiersin.org/articles/10.3389/fenrg.2022.1009987/full#supplementary-material

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