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<p>The existing autoregressive moving average with exogenous inputs (ARMAX) model, which is derived from the equation of motion of the shear-type structures, establishes a direct relationship between model coefficient and damage severity, enabling successful damage localization and quantification. However, the above approach is limited to shear-type structures with a single degree of freedom per node and a lumped mass matrix, which limits its applicability to complex structures. To overcome this limitation, this paper proposes an improved ARMAX model to extend damage identification methods to a wider range of structural types. Specifically, this model is based on the equations of motion of the structures with multiple degrees of freedom per node and a consistent mass matrix. The ARMAX model derived from the structural equation of motion has a clear physical meaning, and the order and coefficient of the autoregressive (AR) term are determined to be 1. To further improve damage identification accuracy, a physically constrained order determination technique is proposed. This technique employs a grid search to fix the AR coefficient at 1 to capture the inherent structural characteristics, thereby guiding the selection of the order of the moving average term. Finally, the ARMAX model coefficient is used to construct the damage feature to detect, locate, and quantify structural damage. Numerical simulation and experimental results demonstrate that this method can not only identify damage in various structural types but also improve damage identification accuracy.</p>

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An ARMAX model with a physically constrained order determination technique for structural damage identification

  • 期刊论文

  • 发表日期：

    2025年8月14日

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  • Xueli Song,
  • Lingjuan Ma,
  • Rongpeng Li,
  • Wen Yi,
  • Yuzhu Xiao,
  • Fan Yang

摘要

The existing autoregressive moving average with exogenous inputs (ARMAX) model, which is derived from the equation of motion of the shear-type structures, establishes a direct relationship between model coefficient and damage severity, enabling successful damage localization and quantification. However, the above approach is limited to shear-type structures with a single degree of freedom per node and a lumped mass matrix, which limits its applicability to complex structures. To overcome this limitation, this paper proposes an improved ARMAX model to extend damage identification methods to a wider range of structural types. Specifically, this model is based on the equations of motion of the structures with multiple degrees of freedom per node and a consistent mass matrix. The ARMAX model derived from the structural equation of motion has a clear physical meaning, and the order and coefficient of the autoregressive (AR) term are determined to be 1. To further improve damage identification accuracy, a physically constrained order determination technique is proposed. This technique employs a grid search to fix the AR coefficient at 1 to capture the inherent structural characteristics, thereby guiding the selection of the order of the moving average term. Finally, the ARMAX model coefficient is used to construct the damage feature to detect, locate, and quantify structural damage. Numerical simulation and experimental results demonstrate that this method can not only identify damage in various structural types but also improve damage identification accuracy.