Subset Selection with Whitening and Tikhonov Regularization (SSWT): A Novel and Robust Sensitivity-Based Method for Static Damage Detection Under Load and Measurement Uncertainty

Naseralavi, Seyed Sadegh; Rostami, Sobhan

doi:10.48301/jear.2025.506387.1092

Subset Selection with Whitening and Tikhonov Regularization (SSWT): A Novel and Robust Sensitivity-Based Method for Static Damage Detection Under Load and Measurement Uncertainty

Document Type : Original Article

Authors

Seyed Sadegh Naseralavi ¹

Sobhan Rostami ²

¹ Department of Civil Engineering, Technical and Engineering Faculty, Valiasr University, Rafsanjan, Kerman, Iran.

² Department of Civil Engineering, Technical and Vocational University (TVU), Tehran, Iran.

10.48301/jear.2025.506387.1092

Abstract

This paper introduces a novel two-stage algorithm for structural damage detection under static loading conditions, explicitly addressing uncertainties in both applied loads and sensor measurements. We rigorously demonstrate that the combined effect of load and sensor errors can be equivalently represented as sensor errors with a specifically defined covariance matrix. The first stage of the proposed method focuses on identifying the location of damaged elements. This is achieved by initially transforming the error covariance matrix into an identity matrix via a linear whitening transformation, effectively converting the ellipsoidal error probability density function (PDF) into a spherical form. Subsequently, the damaged elements are identified by locating those whose displacement sensitivity vectors most effectively span the subspace containing the displacement change vector. The second stage then quantifies the extent of damage using Tikhonov regularization, without requiring iterative model updating. The efficacy of the proposed Subspace Selection with Whitening and Tikhonov Regularization (SSWT) algorithm is rigorously validated through numerical simulations on a truss structure subjected to various damage scenarios and under the influence of uncertainties in both sensors and applied loads. The results unequivocally demonstrate the superior performance of SSWT compared to existing methods in the literature.

Keywords

structural damage detection

static analysis

uncertainty quantification

whitening transformation

Tikhonov regularization

sensitivity analysis

subset selection

Subjects

Civil Engineering

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