Output-Only Modal Parameter Recursive Estimation of Time-Varying Structures via a Kernel Ridge Regression FS-TARMA Approach

Zhi-Sai Ma,Li Liu,Lei Yu,Si-Da Zhou

doi:10.1155/2017/8176593

Abstract

Modal parameter estimation plays an important role in vibration-based damage detection and is worth more attention and investigation, as changes in modal parameters are usually being used as damage indicators. This paper focuses on the problem of output-only modal parameter recursive estimation of time-varying structures based upon parameterized representations of the time-dependent autoregressive moving average (TARMA). A kernel ridge regression functional series TARMA (FS-TARMA) recursive identification scheme is proposed and subsequently employed for the modal parameter estimation of a numerical three-degree-of-freedom time-varying structural system and a laboratory time-varying structure consisting of a simply supported beam and a moving mass sliding on it. The proposed method is comparatively assessed against an existing recursive pseudolinear regression FS-TARMA approach via Monte Carlo experiments and shown to be capable of accurately tracking the time-varying dynamics in a recursive manner.

Highlights

The need for damage identification or fault diagnosis of a structure is pervasive throughout the aerospace, shipbuilding, manufacturing, infrastructure, and transportation engineering communities
The exponentially weighted RPLR-FS-time-dependent autoregressive moving average (TARMA) method loses those advantages of the deterministic parameter evolution (DPE) methods and sometimes even underperforms its unstructured parameter evolution (UPE) counterpart, that is, the exponentially weighted RPLR-TARMA method [9, 13]
The modal parameter estimation of the experimental time-varying structure is subsequently considered based on three methods including the RPLR-FSTARMA method, the exponentially weighted RPLR-TARMA method, and the proposed KRR-FS-TARMA method

Summary

Introduction

The need for damage identification or fault diagnosis of a structure is pervasive throughout the aerospace, shipbuilding, manufacturing, infrastructure, and transportation engineering communities. In contrast with the UPE/SPE methods, the DPE methods are based on explicit models of the parameter variation These models are achieved by approximating the parameter trajectory by a linear combination of known basis functions, belonging to specific functional subspaces. Different recursive DPE methods have been developed in recent years, their tracking capability of time-varying dynamics may be limited and more efforts are still needed [10,11,12,13,14,15,16,17,18,19,20] From this point of view the FSTARMA model-based recursive methods are promising and are investigated in this work.

FS-TARMA Model-Based Modal Parameter Estimation

Recursive Pseudolinear Regression FS-TARMA Approach

Kernel Ridge Regression FS-TARMA Approach

Numerical Validation

The Exponentially Weighted RPLR-TARMA Method

Experimental Validation

Conclusions