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Regression diagnostics with predicted residuals of linear model with improved singular value classification applied to forecast the hydrodynamic efficiency of wave energy converters


Tenekedjiev, K and Abdussamie, N and An, H and Nikolova, N, 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, 11, (7) Article 2990. ISSN 2076-3417 (2021) [Refereed Article]

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

DOI: doi:10.3390/app11072990


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.

Item Details

Item Type:Refereed Article
Keywords:performance prediction, multiple linear regression, improved design matrix SVD, stepwise regression, heteroscedasticity, outlier detection
Research Division:Mathematical Sciences
Research Group:Statistics
Research Field:Applied statistics
Objective Division:Energy
Objective Group:Renewable energy
Objective Field:Wave energy
UTAS Author:Tenekedjiev, K (Professor Kiril Tenekedjiev)
UTAS Author:Abdussamie, N (Dr Nagi Abdussamie)
UTAS Author:Nikolova, N (Professor Nataliya Nikolova)
ID Code:146412
Year Published:2021
Web of Science® Times Cited:2
Deposited By:Maritime and Logistics Management
Deposited On:2021-09-06
Last Modified:2021-10-14
Downloads:16 View Download Statistics

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