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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

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posted on 2023-05-21, 02:12 authored by Kiril Tenekedjiev, Nagi AbdussamieNagi Abdussamie, An, H, Nataliya Nikolova
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.

History

Publication title

Applied Sciences

Volume

11

Issue

7

Article number

2990

Number

2990

Pagination

1-32

ISSN

2076-3417

Department/School

Australian Maritime College

Publisher

MDPI AG

Place of publication

Switzertland

Rights statement

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 (https://creativecommons.org/licenses/by/4.0/).

Repository Status

  • Open

Socio-economic Objectives

Wave energy; Expanding knowledge in engineering

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