[Paper Review] A SHM method for detecting damage with incomplete observations based on VARX modelling and Granger causality

Unai Ugalde, Javier Anduaga+2 more|arXiv (Cornell University)|Feb 1, 2016

Structural Health Monitoring Techniques20 references3 citations

TL;DR

This paper proposes a structural health monitoring (SHM) method that reduces sensor count by using Vector AutoRegressive with eXogenous inputs (VARX) modeling and Granger causality to identify minimal, information-preserving sensor sets. By analyzing conditional Granger causality between substructure degrees of freedom (DOFs), the method selects optimal sensors for damage detection via residual comparison between measured and model-predicted responses, validated on a lattice finite element model with reduced sensor requirements and high detection accuracy.

ABSTRACT

A SHM method is proposed that minimises the required number of sensors for detecting damage. The damage detection method consists of two steps. In an initial characterization step, substructuring approach is applied to the healthy structure in order to isolate the substructures of interest and later, each substructure is identified by a Vector Auto Regressive with eXogenous inputs (VARX) model measuring all DOFs. Then, pairwise conditional Granger causality analysis is carried out with data measured from substructural DOFs to evaluate the information loss when measurements from all DOFs are not available. This analysis allows selecting those accelerometers that can be suppressed minimising the information loss. In the evaluation phase, vibration data from the reduced set of sensors is compared to the estimated data obtained from the healthy substructure's VARX model, and as a result a damage indicator is computed. The proposed detection method is validated by finite element simulations in a lattice structure model.

Motivation & Objective

• To minimize the number of sensors required for effective structural health monitoring (SHM) in civil and mechanical structures.
• To address the challenge of incomplete sensor observations in SHM by identifying critical measurement points that preserve essential dynamic information.
• To develop a systematic method for selecting optimal sensor locations based on information flow analysis between structural subcomponents.
• To enable reliable damage detection using a reduced sensor set by comparing real-time vibration data with predictions from a healthy substructure model.
• To validate the method's effectiveness through finite element simulations on a lattice structure under varying damage scenarios.

Proposed method

• The method begins with substructuring the healthy structure into substructures of interest to isolate dynamic behavior.
• Each substructure is modeled using a Vector AutoRegressive with eXogenous inputs (VARX) model that captures the dynamics across all degrees of freedom (DOFs).
• Pairwise conditional Granger causality is computed between DOFs to quantify information flow and assess the impact of omitting specific sensors.
• Sensors are ranked and selectively removed based on their contribution to information flow, minimizing information loss while reducing sensor count.
• In the evaluation phase, vibration data from the reduced sensor set is compared to predictions from the healthy VARX model to compute a damage indicator.
• The damage indicator is computed as the residual between measured and estimated responses, with significant deviations indicating potential damage.

Experimental results

Research questions

• RQ1 What is the minimal set of sensors required to maintain effective damage detection in structures with incomplete observations?
• RQ2 How can information flow between structural subcomponents be quantified to guide optimal sensor placement?
• RQ3 To what extent can Granger causality analysis identify redundant sensors without compromising damage detection performance?
• RQ4 How does the proposed method maintain detection accuracy when sensor count is reduced through information-theoretic selection?
• RQ5 Can the VARX-Granger causality framework reliably detect damage in a finite element model with limited sensor data?

Key findings

• The proposed method successfully identifies a reduced set of sensors that preserve critical dynamic information, significantly lowering sensor count without sacrificing detection capability.
• Conditional Granger causality analysis effectively quantifies the information contribution of each DOF, enabling systematic sensor selection based on causal influence.
• The damage indicator derived from residual analysis between measured and predicted responses reliably detects damage in the finite element model.
• The method maintains high detection accuracy even with incomplete observations, demonstrating robustness to sensor reduction.
• Validation on a lattice structure model confirms that the selected sensor set achieves comparable performance to full-sensor monitoring.
• The approach enables a systematic, data-driven selection of sensors that minimizes information loss while reducing measurement costs.