Moving Window Differential Evolution Independent Component Analysis-Based Operational Modal Analysis for Slow Linear Time-Varying Structures

SSI-LSTM network for adaptive operational modal analysis of building structures

Operational modal analysis (OMA) is a procedure that allows the modal parameters of a structure to be extracted from the measured response to an unknown excitation generated during operation. Nonlinearity is inevitably and frequently encountered in OMA. The problem: The traditional OMA method based on linear modal theory cannot be applied to a nonlinear oscillation system. The solution: This paper aims to propose a nonlinear OMA method for nonlinear oscillation systems. The new OMA method is based on the following: (1) a self-excitation phenomenon is caused by nonlinear components; (2) the nonlinear normal modes (NNMs) of the system appear under a single-frequency harmonic excitation; and (3) using forced response data, the symbolic regression method (SR) can be used to automatically search for the NNMs of the system, whose modal parameters are implicit in the expression structure expressing each NNM. The simulation result of a three-degree-of-freedom (3-DOF) nonlinear system verifies the correctness of the proposed OMA method. Then, a disc-rod rotor model is considered, and the proposed OMA method’s capability is further evaluated.

Conventionally, modal monitoring of Wind Turbine Rotor Blades is primarily based on the evaluation of eigenfrequencies. Beyond this, combining a sensor network with the Operational Modal Analysis (OMA) method, mode shape and parallely a local component are utilized here. In addition it is expected that the damping, which is also determined by the OMA method, will give a lead on damage development at the rotor already at an early stage. Modal monitoring by means of measurement is combined with FEM simulation and with the comparison of results obtained from measurement and simulation. Moreover, this will establish a connection between the engineer and the design data of a rotor blade, which also are based on FEM analyzes. A further significant increase regarding error resolution is possible by combining the global modal methods with locally sensitive monitoring methods, based on guided elastic waves. These assume plate-like structures through which elastic waves propagate in the low-frequency ultrasonic range (10 - 100 kHz) in certain modes. These different wave modes interact distinctively with inner structural damages such as web fractures and delaminations. It is differentiated between piezoelectrically excited waves (acousto ultrasonics), and waves produced by energy released at fractures, delamination etc. (acoustic emission). Applying a moderate number of sensors, the combination of both methods can allow an effective monitoring of the global structure.

Structural Health Monitoring (SHM) is nowadays common in many branches of engineering since it allows to have a continuous or periodic report of the structural conditions and therefore to promptly intervene if there are incipient damages. The first step to perform a SHM is the identification of the dynamic parameters, i.e. natural frequencies, damping ratios and modal shapes, and it is a crucial step since a modification of the structural parameters can be a direct consequence of structural damages. Among the structural identification methods, Operational Modal Analysis (OMA) methods have received increasing attention from the researchers since they do not require the knowledge of the structural excitation that is due to ambient vibrations and that is usually modeled as a white noise. This aspect makes this kind of methods cheaper and simpler than the classical Experimental Modal Analysis (EMA) methods. In this paper an innovative OMA method is proposed. It is a semi - automated method that allows to identify natural frequencies, damping ratios and modal shapes of a structural system and that can be used also from users that have not knowledge in stochastic dynamics and signal analysis. First of all, the modal shapes are estimated through the use of signal filtering techniques applied on the stochastic properties of the output process and then natural frequencies and damping ratios can be estimated from the mono - component analytical signals obtained by performing a decomposition of the analytical signals matrix. The proposed method has been used to perform the dynamic identification of a real historic building situated in Palermo, i.e. Chiaramonte palace, and the results obtained have been compared with those obtained by using other OMA methods.

In order to identify the modal parameters of time invariant three-dimensional engineering structures with damping and small nonlinearity, a novel isometric feature mapping (Isomap)-based three-dimensional operational modal analysis (OMA) method is proposed to extract nonlinear features in this paper. Using this Isomap-based OMA method, a low-dimensional embedding matrix is multiplied by a transformation matrix to obtain the original matrix. We find correspondence relationships between the low-dimensional embedding matrix and the modal coordinate response and between the transformation matrix and the modal shapes. From the low-dimensional embedding matrix, the natural frequencies can be determined using a Fourier transform and the damping ratios can be identified by the random decrement technique or natural excitation technique. The modal shapes can be estimated from the Moore–Penrose matrix inverse of the low-dimensional embedding matrix. We also discuss the effects of different parameters (i.e., number of neighbors and matrix assembly) on the results of modal parameter identification. The modal identification results from numerical simulations of the vibration response signals of a cylindrical shell under white noise excitation demonstrate that the proposed method can identify the modal shapes, natural frequencies, and ratios of three-dimensional structures in operational conditions only from the vibration response signals.

A new operational modal analysis (OMA) method is developed for estimation of modal parameters (MPs) of a rotating structure (RS) subject to random excitation using a nonuniform rotating beam model, an image processing method, and an improved demodulation method. The solution to the governing equation of a nonuniform rotating beam is derived, which can be considered as the response of the beam measured by a continuously scanning laser Doppler vibrometer (CSLDV) system. A recently developed tracking CSLDV system can track and scan the RS. The image processing method determines the angular position of the RS so that the tracking CSLDV system can sweep its laser spot along a time-varying path on it. The improved demodulation method obtains undamped mode shapes (UMSs) of the RS by multiplying its measured response by sinusoids whose frequencies are its damped natural frequencies (DNFs) that are obtained from the fast Fourier transform of the measured response. Experimental investigation of the OMA method using the tracking CSLDV system is conducted, and MPs of a rotating fan blade (RFB), including DNFs and UMSs, with different constant speeds and its instantaneous MPs with a non-constant speed are estimated. Estimated first DNFs and UMSs of the stationary fan blade and RFB are compared with those from the lifting method that was previously developed by the authors.

Safety assessment of structures for near-field blast-induced ground excitations using operational modal analysis

This paper investigates the use of conventional operational modal analysis (OMA) techniques for modal parameters identification of a rotating system supported by roller bearings. Although largely applied in civil engineering, in-depth studies on different types of systems are still limited in the literature. The novel of the paper is to address such issue by applying conventional OMA methods, such as enhanced frequency domain decomposition (EFDD) and stochastic subspace identification (SSI-data), to identify the modal parameters of a rotating machine, investigating the challenging particularities of these systems due to their inherent operating conditions, especially regarding the presence of harmonic forces, eventually closed-spaced modes, and non-proportional damping due to the bearings. The results presented in the experimental tests showed that, with the use of specific tools, in comparison with traditional experimental modal analysis (EMA), the used OMA methods have managed to successfully identify the modal parameters of a roller bearing supported rotor.

Abstract. In the present study we investigate development of operational modal analysis (OMA), different OMA techniques as well as relevant issues and experimental studies. Furthermore, we classify previously performed studies have been conducted so far and consider the most important one. So, first we review the fundamental concepts. Then, the history and application of the OMA method will be examined comprehensively to observe their role in the development of the technique. Three basic methods of FDD, SSI, and Next will be discussed and the research works associated to them will be analyzed.

Operational modal analysis (OMA) enables the identification of modal characteristics under operational loads and conditions. Traditional frequency-domain methods cannot directly capture modal changes over time, while existing time-frequency representations are not sufficiently interpretable due to spurious modes and implicit parameter design. This paper develops a new OMA method in time-frequency representation based on frequency-domain decomposition (FDD). Short-time FDD and a convolution-based strategy are proposed to obtain singular values and local mode shape similarity, respectively, which are further fused into mode indicators by a fuzzy-based strategy mimicking the modal assurance criterion. The method provides not only a global view of the modal characteristics over time and frequency but also estimates of the modal parameters. It is applicable to strongly nonstationary responses under time-varying loads and conditions. All the parameters explicitly affect the time-frequency representation, and the interpretability is enhanced by including physical information from the user’s prior knowledge in selecting parameters and peak bands. The proposed method is validated based on a study of railway sleepers under train passage. The rigid-body motions and bending modes are identified at frequencies up to 6,500 Hz in laboratory tests and 4,500 Hz in field tests at speeds up to 200 km/h. The identified natural frequencies and mode shapes agree with experimental modal analysis (EMA). The proposed method outperforms EMA in terms of broad frequency range and low measurement cost and can be potentially applied to structural health monitoring under operational conditions.

Frequency Domain Decomposition (FDD) is an operational modal analysis method by which the dynamic parameters of structures are obtained using response signals recorded on several locations of structures. In recent years, many researchers have employed the method to estimate the modal parameters of several Multi-Degree-of-Freedom (MDOF) mechanical and civil systems. The accuracy of the results depends on recording and signal processing parameters such as sampling frequency, windowing, filtering etc. As a result, investigation on the influence of these parameters on the accuracy of the estimates is a good practice. In this research, the uncertainty of modal frequencies obtained from FDD method is analyzed. In order to achieve this goal, the exact values of modal parameters must be available to be compared with the results from FDD method. For this purpose, synthetic signals with random characteristics the same as the ambient vibrations’ are produced and structures with known dynamic parameters are simulated and loaded. The effect of several parameters are investigated in the accuracy of results and proper values and settings are proposed to minimize the errors.

Rotating machines are key components in energy generation processes, and faults can lead to shutdowns or catastrophes encompassing economic and social losses. Structural Health Monitoring (SHM) of structures in operation is successfully performed via Operational Modal Analysis (OMA), which has advantages over traditional methods. In OMA, white noise inputs lead to the accurate extraction of modal parameters without taking the system out of operation. However, this excitation condition is not easy to attain for rotating machines used in power generation, and OMA can provide inaccurate information. This research investigates the applicability of machine learning as a pre-stage of OMA to differentiate adequate from inadequate excitations and prevent inaccurate extraction of modal parameters. Data from a rotor system was collected under different conditions and OMA was applied. In a training stage, measurements were characterized by statistical features and K-means was used to determine which features provided information about the excitation condition, that is, which excitation was adequate to extract the rotor’s modal parameters via OMA. In a testing stage, data were successfully classified as adequate or not adequate for OMA, achieving 100% accuracy and revealing the technique’s potential to support SHM of rotating machines. The technique is extendable to other monitoring systems based on OMA.

Modal analysis has developed into a major technology for the study of structural dynamics in the past several decades. Through it, complex structural dynamics phenomena can be represented in terms of structural invariants, i.e., the modal parameters: natural frequencies, damping ratios and mode shapes. Operational Modal Analysis (OMA) deals with the estimation of modal parameters on vibration data measured for operational conditions, when the excitation on the structure is not measured. In this work, OMA is performed on a wind turbine blade undergoing wind tunnel testing. These tests included different wind speeds, pitch angles and also different health conditions of the blade, where masses of different magnitude were fixed to the blade on different locations to emulate damage conditions. In order to monitor the modal parameters across multiple days of varied tests in the wind tunnel, the Polymax modal parameter estimator was implemented, coupled with an Automated Modal Analysis methodology. This methodology included an automatic modal parameter selection technique, using a Machine Learning (ML) clustering algorithm, coupled with a modal tracking procedure which applied statistical thresholds on the modal parameters’ values. The tracking procedure searches for modes similar to the ones calculated for healthy conditions. The results show how the modal parameters of the wind turbine blade vary with the different measured conditions in the wind tunnel. Moreover, a damage detection methodology is implemented to differentiate between the healthy and damaged conditions on the blade, by leveraging an anomaly detection algorithm using the Multivariate Gaussian Distribution (MGD). This algorithm takes as input the modal parameters calculated by the previous Automated Modal Analysis methodology and detects statistical deviations among them which could indicate the presence of damage. All steps of this work contribute to developing an automatic framework able to detect damages on a wind turbine blade, and therefore perform Structural Health Monitoring (SHM) for different operational conditions.

This document addresses enduring challenges encountered in modern experimental modal analysis as well as earlier “resonance testing” associated with measured mode orthogonality requirements. To this end, the document’s goals are (1) retirement of false damping and real mode notions (dating back to Lord Rayleigh, 1877), (2) achievement a community consensus on 85+ years of resonance and modal testing, and (3) establishment of an experimental modal analysis process that is independent of a-priori predictive mathematical models. The above goals are satisfied by addressing six key objectives, namely (a) validation of measured complex experimental modes, (b) empirical isolation of experimental modes (the “Holy Grail” of resonance testing), (c) definition of a state-space orthogonality standard, independent of an approximate reduced-order mass matrix, (d) exploitation of state-space, left-hand eigenvectors and their relationship to modal momentum and kinetic energy distributions, (e) establishment of a universal practice for a broad family of modal testing methods, and (f) application of the above six objectives to ambient (operational modal analysis) methods.

Experimental research of cable tension tuning of a scaled model of cable stayed bridge