Theoretical conceptualization for novel multivariate reliability design, with clustering effects accounted for

Tracking #: 940-1920

Authors:

	Name	ORCID
	Oleg Gaidai	https://orcid.org/0000-0002-3196-8562

Responsible editor:

Sofya Titarenko

Submission Type:

Research Paper

Abstract:

Univariate Extreme Value Theory (EVT) is frequently used to assess the structural risk of failure or damage resulting from excessive environmental loads in structural design. In reality, failure or damage is caused not by univariate (1D) load but by a combination of cross-correlated covariates. This research work presents a state-of-the-art, multimodal reliability approach for multivariate structural design. Analysis of the joint probability distribution tail of an M-dimensional random process is the focus of multivariate EVT and extrapolation schemes. Expansion of EVT and Generalized Extreme Value (GEV) based Probability Density Function (PDF) from univariate (1D) towards bivariate (2D) systems encounters both theoretical and practical obstacles. For the first, 1D EVT is not straightforwardly extended to 2D cases, not to mention challenges pertaining to dynamic systems' dimensionality above 2D. Extension from 1D to 2D is typically done using a particular copula selection, which in itself introduces additional bias and inaccuracy. The multi-modal Gaidai reliability approach, presented here, does not rely on copula selection, hence being genuinely ∞D, and yet mathematically exact. The primary goal of the presented investigation was to develop a novel design philosophy, incorporating a generic state-of-the-art multivariate reliability method for a high-dimensional energy-generating dynamic system’s failure or damage risk assessment, allowing pertinent information regarding excessive dynamics to be extracted from available time histories that were recorded physically or simulated numerically. The multivariate design approach is a priori more conservative than existing univariate ones. Novelty: proposed holistic multi-modal reliability methodology allows for accurate yet efficient prognostics of failure, hazard or damage risk for a range of multi-modal nonlinear renewable energy dynamic systems, accounting for memory effects. The presented multidimensional reliability methodology's potential application will include big data and renewable energy harvesting and grid design applications when the number of system’s cross-correlated components (dimensions) exceeds 2.

Manuscript:

ds-paper-940.docx

Data repository URLs:

https://github.com/OlegGaidai/

Date of Submission:

Tuesday, December 9, 2025

Date of Decision:

Wednesday, March 25, 2026

Nanopublication URLs:

Decision:

Undecided

Solicited Reviews:

Review #1 submitted on 13/Mar/2026

By Baitshephi Mashabe

Review Details

Reviewer has chosen not to be Anonymous

Overall Impression: Good
Suggested Decision: Undecided
Technical Quality of the paper: Good
Presentation: Good
Reviewer`s confidence: Medium
Significance: High significance
Background: Reasonable
Novelty: Clear novelty
Data availability: With exceptions that are admissible according to the data availability guidelines, all used and produced data are FAIR and openly available in established data repositories
Length of the manuscript: The length of this manuscript is about right

Summary of paper in a few sentences:

[N/A]

Reasons to accept:

The manuscript proposes a theoretical framework for multivariate reliability design that accounts for clustering effects and provides an application comparing the proposed approach with several copula-based methods. The authors aim to introduce this novel approach to address limitations in existing approaches to multivariate extreme value modeling and reliability analysis. The proposed framework appears methodologically sound, and the results are clearly presented. The manuscript is generally well structured and readable.

Reasons to reject:

[N/A]

Nanopublication comments:

Further comments:

[Page 9, line 315: Typo – “in in” appears; please delete one “in”.

Page 9, line 332: In the equation, it appears that n_{Y}^{λ} may be missing. Please verify.

Page 9, line 341: In equation (7), the variable Z is not clearly defined.

Page 10: Please check the equation numbering, as equation (18) could not be located.

Page 10, line 361: The phrase “is summarized” can be removed from the first sentence to avoid repetition.

Page 13, line 433: Please confirm whether the return period should be 11-year or 1-year.

Page 17, line 511: Please check whether “and” is missing between 4 and 5. Please check for any other typographical errors and correct them accordingly.

In addition, some conceptual statements regarding the limitations of extreme value theory appear too strong and potentially misleading. In particular, the manuscript suggests that multivariate reliability models are limited to two dimensions and that extreme value theory is fundamentally restricted by its one-dimensional nature. However, multivariate extreme value theory is well established for general d-dimensional settings, although practical applications often focus on low-dimensional cases due to data sparsity and estimation challenges. The authors should clarify or moderate these statements and provide appropriate references. Additionally, the claim that one-dimensional extreme value methods cannot assess whether data are sufficiently asymptotic should be reconsidered. While EVT is asymptotic in nature, several diagnostic tools (e.g., return level plots, probability plots, and quantile plots) are commonly used in practice to assess model adequacy.

Review #2 submitted on 23/Mar/2026

Review Details

Reviewer has chosen to be Anonymous

Overall Impression: Weak
Suggested Decision: Reject
Technical Quality of the paper: Average
Presentation: Weak
Reviewer`s confidence: Medium
Significance: Moderate significance
Background: Reasonable
Novelty: Limited novelty
Data availability: All used and produced data (if any) are FAIR and openly available in established data repositories
Length of the manuscript: This manuscript is too long for what it presents and should therefore be considerably shortened (below the general length limit)

Summary of paper in a few sentences:

This study introduces a new multivariate (multi-dimensional) reliability assessment method for complex energy-generating systems. Unlike existing single-variable approaches, it analyses multiple correlated components simultaneously to more accurately predict the risk of failure or damage. The method is designed to handle large datasets and has practical applications in renewable energy systems and grid design.

Reasons to accept:

Reasons to reject:

The paper requires substantial improvements in presentation. The introduction is too long, with the research gaps discussed twice — the differences between these two discussions should be clarified or the repetition removed. Additionally, the first paragraph on page 5 does not connect clearly to the preceding context, and its purpose and outline should be made more explicit.

On page 10, a theorem is presented without proof. If this is a new theorem, a proof must be provided; if it is an existing result, the appropriate reference should be cited.

Consistency in terminology is also an issue throughout the manuscript. Several terms appear in multiple forms — for example, "multi-modal" and "multimodal", "Multi-variate" and "Multivariate" — and these should be standardised throughout.

On page 7, the justification for introducing the 4-parameter Weibull model is unclear. The standard Weibull model has two parameters, and adding further parameters risks overfitting — the rationale for this choice should be explicitly justified. Furthermore, in line 252, the term "extrapolation scheme" is used without definition and should be clarified. It should also be confirmed that the correct equation is cited in this context.

A significant concern is the inconsistency between the paper's stated objective and its actual scope. While the main objective is clearly emphasised as developing a multivariate reliability design framework, the numerical and theoretical investigations appear to be largely limited to 2D EVD. This inconsistency represents a notable limitation of the study and should be explicitly acknowledged and addressed by the authors.