Regression Diagnostics with Predicted Residuals of Linear Model with Improved Singular Value Classification Applied to Forecast the Hydrodynamic Efficiency of Wave Energy Converters
In the preliminary stages of design of the oscillating water column (OWC) type of wave energy converters (WECs), we need a reliable cost- and time-effective method to predict the hydrodynamic efficiency as a function of the design parameters. One of the cheapest approaches is to create a multiple li...
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| Format: | Article |
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MDPI AG
2021-03-01
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| Series: | Applied Sciences |
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| Online Access: | https://www.mdpi.com/2076-3417/11/7/2990 |
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| author | Kiril Tenekedjiev Nagi Abdussamie Hyunbin An Natalia Nikolova |
| author_facet | Kiril Tenekedjiev Nagi Abdussamie Hyunbin An Natalia Nikolova |
| author_sort | Kiril Tenekedjiev |
| collection | DOAJ |
| description | In the preliminary stages of design of the oscillating water column (OWC) type of wave energy converters (WECs), we need a reliable cost- and time-effective method to predict the hydrodynamic efficiency as a function of the design parameters. One of the cheapest approaches is to create a multiple linear regression (MLR) model using an existing data set. The problem with this approach is that the reliability of the MLR predictions depend on the validity of the regression assumptions, which are either rarely tested or tested using sub-optimal procedures. We offer a series of novel methods for assumption diagnostics that we apply in our case study for MLR prediction of the hydrodynamics efficiency of OWC WECs. Namely, we propose: a novel procedure for reliable identification of the zero singular values of a matrix; a modified algorithm for stepwise regression; a modified algorithm to detect heteroskedasticity and identify statistically significant but practically insignificant heteroscedasticity in the original model; a novel test of the validity of the nullity assumption; a modified Jarque–Bera Monte Carlo error normality test. In our case study, the deviations from the assumptions of the classical normal linear regression model were fully diagnosed and dealt with. The newly proposed algorithms based on improved singular value decomposition (SVD) of the design matrix and on predicted residuals were successfully tested with a new family of goodness-of-fit measures. We empirically investigated the correct placement of an elaborate outlier detection procedure in the overall diagnostic sequence. As a result, we constructed a reliable MLR model to predict the hydrodynamic efficiency in the preliminary stages of design. MLR is a useful tool at the preliminary stages of design and can produce highly reliable and time-effective predictions of the OWC WEC performance provided that the constructing and diagnostic procedures are modified to reflect the latest advances in statistics. The main advantage of MLR models compared to other modern black box models is that their assumptions are known and can be tested in practice, which increases the reliability of the model predictions. |
| first_indexed | 2024-03-10T12:52:04Z |
| format | Article |
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| institution | Directory Open Access Journal |
| issn | 2076-3417 |
| language | English |
| last_indexed | 2024-03-10T12:52:04Z |
| publishDate | 2021-03-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Applied Sciences |
| spelling | doaj.art-2f7552ad4754425dac545addd7c071f62023-11-21T12:59:51ZengMDPI AGApplied Sciences2076-34172021-03-01117299010.3390/app11072990Regression Diagnostics with Predicted Residuals of Linear Model with Improved Singular Value Classification Applied to Forecast the Hydrodynamic Efficiency of Wave Energy ConvertersKiril Tenekedjiev0Nagi Abdussamie1Hyunbin An2Natalia Nikolova3Australian Maritime College (National Centre for Maritime Engineering and Hydrodynamics), University of Tasmania, Launceston 7250, Tasmania, AustraliaAustralian Maritime College (National Centre for Maritime Engineering and Hydrodynamics), University of Tasmania, Launceston 7250, Tasmania, AustraliaAustralian Maritime College (National Centre for Maritime Engineering and Hydrodynamics), University of Tasmania, Launceston 7250, Tasmania, AustraliaAustralian Maritime College (National Centre for Ports and Shipping), University of Tasmania, Launceston 7250, Tasmania, AustraliaIn the preliminary stages of design of the oscillating water column (OWC) type of wave energy converters (WECs), we need a reliable cost- and time-effective method to predict the hydrodynamic efficiency as a function of the design parameters. One of the cheapest approaches is to create a multiple linear regression (MLR) model using an existing data set. The problem with this approach is that the reliability of the MLR predictions depend on the validity of the regression assumptions, which are either rarely tested or tested using sub-optimal procedures. We offer a series of novel methods for assumption diagnostics that we apply in our case study for MLR prediction of the hydrodynamics efficiency of OWC WECs. Namely, we propose: a novel procedure for reliable identification of the zero singular values of a matrix; a modified algorithm for stepwise regression; a modified algorithm to detect heteroskedasticity and identify statistically significant but practically insignificant heteroscedasticity in the original model; a novel test of the validity of the nullity assumption; a modified Jarque–Bera Monte Carlo error normality test. In our case study, the deviations from the assumptions of the classical normal linear regression model were fully diagnosed and dealt with. The newly proposed algorithms based on improved singular value decomposition (SVD) of the design matrix and on predicted residuals were successfully tested with a new family of goodness-of-fit measures. We empirically investigated the correct placement of an elaborate outlier detection procedure in the overall diagnostic sequence. As a result, we constructed a reliable MLR model to predict the hydrodynamic efficiency in the preliminary stages of design. MLR is a useful tool at the preliminary stages of design and can produce highly reliable and time-effective predictions of the OWC WEC performance provided that the constructing and diagnostic procedures are modified to reflect the latest advances in statistics. The main advantage of MLR models compared to other modern black box models is that their assumptions are known and can be tested in practice, which increases the reliability of the model predictions.https://www.mdpi.com/2076-3417/11/7/2990performance predictionmultiple linear regressionimproved design matrix SVDstepwise regressionheteroscedasticityoutlier detection |
| spellingShingle | Kiril Tenekedjiev Nagi Abdussamie Hyunbin An Natalia Nikolova Regression Diagnostics with Predicted Residuals of Linear Model with Improved Singular Value Classification Applied to Forecast the Hydrodynamic Efficiency of Wave Energy Converters Applied Sciences performance prediction multiple linear regression improved design matrix SVD stepwise regression heteroscedasticity outlier detection |
| title | Regression Diagnostics with Predicted Residuals of Linear Model with Improved Singular Value Classification Applied to Forecast the Hydrodynamic Efficiency of Wave Energy Converters |
| title_full | Regression Diagnostics with Predicted Residuals of Linear Model with Improved Singular Value Classification Applied to Forecast the Hydrodynamic Efficiency of Wave Energy Converters |
| title_fullStr | Regression Diagnostics with Predicted Residuals of Linear Model with Improved Singular Value Classification Applied to Forecast the Hydrodynamic Efficiency of Wave Energy Converters |
| title_full_unstemmed | Regression Diagnostics with Predicted Residuals of Linear Model with Improved Singular Value Classification Applied to Forecast the Hydrodynamic Efficiency of Wave Energy Converters |
| title_short | Regression Diagnostics with Predicted Residuals of Linear Model with Improved Singular Value Classification Applied to Forecast the Hydrodynamic Efficiency of Wave Energy Converters |
| title_sort | regression diagnostics with predicted residuals of linear model with improved singular value classification applied to forecast the hydrodynamic efficiency of wave energy converters |
| topic | performance prediction multiple linear regression improved design matrix SVD stepwise regression heteroscedasticity outlier detection |
| url | https://www.mdpi.com/2076-3417/11/7/2990 |
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