On the use of gaussian mixture models for automated modal parameters estimation

The increasing interest in Machine Learning (ML) has revealed the potential for applications in many fields of engineering and science. As part of the ML theory, unsupervised learning algorithms help the analyst in the identification of hidden classes among unlabeled data. These algorithms aggregate data characterized by similar features to form data clusters. One of the most effective unsupervised learning methods is the Gaussian Mixture Modeling (GMM), which identifies classes as Multivariate Normal Distributions (MND) as determined among a dataset. Each sample is assigned with a probability to be part of a specific class (soft clustering), instead of being strictly assigned to it (hard clustering). In this paper, the GMM method is applied to automate the estimation of modal parameters from modal test data as obtained from parametric modal analysis methods. Poles are calculated for multiple model orders. Resulting poles are taken as a dataset for GMM application with an increasing number of clusters whose statistical parameters corresponds to the modal parameters (such as natural frequencies and damping ratios). The Akaike Information Criterion (AIC) is then applied to identify the optimal number of classes, and thus the optimal number of modes with related modal parameters. The procedure was applied on a simple Multiple Degrees Of freedom (MDOF) mass-spring-damper system. Simulated time response data was generated imposing a white noise input. Stochastic Subspace Identification (SSI) was applied on output data to extract poles and mode shapes for multiple model orders. Then, the GMM method was applied to identify poles clusters and related modal parameters. Analysis results highlighted a good correlation between identified clusters and modal parameters (natural frequency and damping), showing the procedure to be effective in modal parameters identification. The proposed method was also applied on a real test case, consisting in the automated modal identification and parameters extraction from Flight Vibration Test data. Although further improvements were required, a good capability to automatically capture modes and provide modal parameters was demonstrated, which is desirable for flight test.