Automated modal parameter estimation using correlation analysis and bootstrap sampling

Abstract

The estimation of modal parameters from a set of noisy measured data is a highly judgmental task, with user expertise playing a significant role in distinguishing between estimated physical and noise modes of a test-piece. Various methods have been developed to automate this procedure. The common approach is to identify models with different orders and cluster similar modes together. However, most proposed methods based on this approach suffer from high-dimensional optimization problems in either the estimation or clustering step. To overcome this problem, this study presents an algorithm for autonomous modal parameter estimation in which the only required optimization is performed in a three-dimensional space. To this end, a subspace-based identification method is employed for the estimation and a non-iterative correlation-based method is used for the clustering. This clustering is at the heart of the paper. The keys to success are correlation metrics that are able to treat the problems of spatial eigenvector aliasing and nonunique eigenvectors of coalescent modes simultaneously. The algorithm commences by the identification of an excessively high-order model from frequency response function test data. The high number of modes of this model provide bases for two subspaces: one for likely physical modes of the tested system and one for its complement dubbed the subspace of noise modes. By employing the bootstrap resampling technique, several subsets are generated from the same basic dataset and for each of them a model is identified to form a set of models. Then, by correlation analysis with the two aforementioned subspaces, highly correlated modes of these models which appear repeatedly are clustered together and the noise modes are collected in a so-called Trashbox cluster. Stray noise modes attracted to the mode clusters are trimmed away in a second step by correlation analysis. The final step of the algorithm is a fuzzy c-means clustering procedure applied to a three-dimensional feature space to assign a degree of physicalness to each cluster. The proposed algorithm is applied to two case studies: one with synthetic data and one with real test data obtained from a hammer impact test. The results indicate that the algorithm successfully clusters similar modes and gives a reasonable quantification of the extent to which each cluster is physical.

A single‐mode recursive validation method for modal identification of linear time‐varying structures based on prior knowledge

“…21 Yaghoubi et al proposed an algorithm with multistage clustering, and a noniterative correlation-based clustering method is used in the intermediate stage to reduce the high-dimensional optimizations. 23 Nevertheless, iterative clustering methods are still in use. Yang et al presented an automated OMA method based on an eigensystem realization algorithm, which exploited the dissimilarity of modal parameters as the features for fuzzy C-means clustering to solve the difficulty about the spatial aliasing.…”

An improved bootstrap method introducing error ellipse for numerical analysis of fatigue life parameters

“…It estimates that the overall sample parameters are obtained by resampling samples, which is a new augmented sample statistical method. After 30 years of EC 38,1 development, the bootstrap method can be applied in various fields, such as hydrology (Zhang et al, 2014), aviation (Wang et al, 2014), mechanical engineering (Yaghoubi et al, 2018) and biological engineering (Robinson, 2007). The bootstrap theory is mainly composed of IID bootstrap (Inés and Ricardo, 2019) and independent data bootstrap.…”

Automated Harmonic Signal Removal Technique Using Stochastic Subspace-Based Image Feature Extraction

“…In recent years, the development of automated procedures for identifying modal parameters in operating conditions has become increasingly popular and stochastic subspace-based algorithms (SSI) methods have been selected as the most practical tool for this procedure due to the consistency in modal parameters’ estimation, especially under non-stationary noise excitations [ 5 , 6 , 7 , 8 , 9 , 10 , 11 , 12 , 13 , 14 , 15 ]. However, the use of subspace-based algorithms for OMA and structural health monitoring (SHM) will be problematic when applied to structures with rotating machines, due to the harmonic excitations.…”

“…Since a lot of human intervention is for monitoring purposes, clustering tools are proposed to automate modal identification by discriminating physical poles from others. The current clustering tools require at least one user-defined parameter, the maximum within-cluster distance between representations of the same physical mode from different system orders and the supplementary adaptive approaches have to be employed to optimize the selection of cluster validation criteria [ 8 , 11 , 21 , 29 ]. In addition, the values for thresholds and parameters are inconsistent due to natural variations in modal properties of structures that come from damage or environmental influences that bring more difficulties to existing approaches [ 30 ].…”