MS18.2 - System Identification and Damage Detection

Operational modal analysis is a technique developed to estimate the modal parameters of a given structural or mechanical system using vibration data recorded with sensors. There are many approaches to the problem: parametric and non-parametric; time domain and frequency domain; maximum likelihood and least squares; Bayesian and non-Bayesian, … This work presents the estimation of modal parameters using Bayesian estimation in time domain. Bayesian estimation is based in three steps: 1. Prior distributions: is the distribution of the modal parameters before the vibration data is recorded; 2. Likelihood function: is the distribution of the recorded data conditional on the modal parameters; 3. Posterior distributions: is the distribution of the modal parameters taking into account the recorded data. The objective in Bayesian estimation is to find the posterior distributions of the parameters. In this work, the posterior distributions of modal parameters are computed using the following assumptions: 1. Normal distributions are used for prior distributions. 2. The likelihood function is derived using the state space model and the Kalman filter; 3. Posterior distributions are computed using Markov Chain Montecarlo sampling by mean of the state-of-the-art software Stan. The objective of the paper is to analyze the performance of this approach in Operational Modal Analysis.

We propose an approach to define alarm thresholds for vibration-based structural health monitoring (SHM) systems. The approach uses the frequencies of vibration, generally estimated from recorded accelerations, and it is based on the concept of Minimum Detectable Damage (MDD), namely the smallest damage size in each structural element associated with given probability of detection (POD) and false alarm (PFA). We here demonstrate the approach using pseudo-measured frequencies computed from finite element models of healthy and damaged structures. In particular, for each considered scenario (healthy or damaged), a dataset of modal frequencies is computed accounting for the variability introduced by temperature fluctuations and measurement noises. The approach considers first a baseline dataset of pseudo modal frequencies computed for a yearly thermal cycle on a healthy structure. The application of the Principal Component Analysis (PCA) on this dataset leads to (i) the projection of data on the maximal variance directions, (ii) the projection operator, and (iii) the residual between each sample (the frequencies for a given scenario) and its original one. For each sample, a Damage Index (DI) is computed as the Mahalanobis distance between the residual of sample and the residuals of the entire baseline samples. At this point, the threshold of the SHM system is defined as the DI value for a given PFA. Next, the approach considers dataset of pseudo frequencies computed for a yearly thermal cycle on damaged structures. For each sample of the dataset, the residual is computed using the projection operator of the baseline and its DI value by using the Mahalnobis distance having the covariance matrix based on the baseline data. Based on the DIs of the damaged structure, the POD is computed for the considered system threshold. This operation is repeated by increasing the level of damage. The MDD is thus defined as the level of damage associated to a desired value of POD. Finally, a probabilistic approach based on the binomial probability distribution is proposed to set the SHM alarm by distinguishing above threshold DIs between false alarms and true damages. The proposed idea is tested on a steel truss bridge, where the MDD for each element is estimated by considering PFA=2.5 % and POD=97.5 %.

Structural damage detection is an inverse problem to identify and quantify structural damage from measurement data by discovering the change of structural mechanical parameters such as stiffness and damping coefficients. Recently, a novel deep learning framework named physics-informed neural networks (PINNs) has been proposed and successfully applied to solve inverse problems of various linear/nonlinear partial differential equations (PDEs) by integrating physical information such as constraints and governing equations as prior information. In this study, we proposed a PINNs framework to exploit a new direction of structural damage detection. Specifically, a multi-output neural network model is built to predict the dynamic response such as displacement, velocity, and acceleration of the structure. The mechanical parameters to be discovered are initialized and updated together with the neural network model parameters. Then, the structural physical model and boundary conditions are embedded by calculating the residuals of governing equations and boundary conditions as parts of the loss function to constrain the relationships between the dynamic responses. The residual between the predicted dynamic response and measurement data is also used as another part of the loss function. The total loss function is minimized by an optimizer so the predicted dynamic response from the model can satisfy the constraints of the governing equations and boundary conditions and represent the measured response simultaneously. Through numerical experiments of a single-degree-of-freedom system, we demonstrate that the proposed method can successfully identify potential structural mechanical parameters and quantitatively detect structural damage. The influence of noise in the measurement data on the detection results is also analyzed. Through numerical experiments of a 6-DOF system, we demonstrate that the proposed method can be utilized to detect the structural damage of the complex structural system.