Identification Techniques for Operational Modal Analysis – An Overview and Practical Experiences

Operational Modal Analysis, also known as Output Only Modal Analysis, has for several years been used for extracting modal parameters of mechanical structures. In this paper, an overview of the Frequency Domain Decomposition (FDD) technique and the Stochastic Subspace Identification (SSI) technique is given. Use of the recently developed projection channel technique in combination with the SSI technique is described and discussed. Practical experiences in the use of these techniques are illustrated from measurement examples by comparing the results from the different techniques INTRODUCTION Operational Modal Analysis is a technique for extraction of the modal parameters from vibration response signals. A main difference compared to the traditional mobility based modal analysis technique is that measurement of the input forces is not required. This enables testing of structures under operating conditions or in other situations were the input forces are impossible to measure. It is therefore also called Ambient Modal or Output only Modal. The technique has been known for a long time and the method has been used for civil engineering for more than a decade and in recent years within rotating machinery, automotive and aerospace applications. Performing modal test under operating (ambient or natural) conditions means that the structure is subjected to realistic vibration behaviour, which might be difficult to obtain by use of artificial excitation. It also means that the test can be performed simultaneously with other response tests and it provides the possibility for extraction of modal information under conditions where a traditional mobility based modal test is very difficult or impossible to perform. The measured responses are governed by the dynamic characteristics of the system and the forces, which excite the system. The derived model thus contains information of both the system characteristics as well as the excitation signals. This is one of the challenges in Operation Modal Analysis and some understanding of the nature and the characteristics of the excitation forces are therefore very important in order to interpret and understand the results and be able to derive a proper modal model. This paper gives an overview of the practical use of the most commonly used operational modal analysis techniques, the Frequency Domain Decomposition (FDD) technique and the Stochastic Subspace Identification (SSI) techniques and application of the recently developed projection channel technique is covered as well. DATA ACQUISITION AND VALIDATION EQUIPMENT For acquisition and validation of the response data a Brüel & Kjær PULSE multianalyser system is used together with Brüel & Kjær modal accelerometers. For some of the tests the handheld exciter Brüel & Kjær Type 5961 is used. PULSE multianalyser performs analysis and validation of the acquired time data in terms of contour plots of Short Time Fourier Transforms (STFT). This reveals the spectral distribution of the response signals as a function of time and content of sinusoidal frequency components can be detected. The frequencies of the main participating modes can often be identified from these contour plots. Figure (1) shows an example of a contour plot of a STFT of one of the response signals from a test of a plate. Apart from the broadband random content a number of sinusoidal components are clearly seen as well. These components are due to excitation forces from a motor running at almost constant speed. The speed was approximately 5850RPM, corresponding to a fundamental frequency of approximately 97,5Hz. The first harmonic as well as the third and fourth harmonic is present. The responses thus contain stationary operating deflection shapes at these frequencies (spectral ODS), which is very important information for the subsequent operational modal analysis. The geometry and the time data are subsequently transferred into the Brüel & Kjær Operational Modal Analysis software for further signal processing and modal parameter extraction. Figure 1 Example of a contour plot of a STFT of a response signal revealing random as well as sinusoidal content MODAL PARAMETER EXTRACTION METHODS SIGNAL PROCESSING In order to optimize the subsequent modal parameter extraction, by use of the time domain techniques, digital processing in terms of low-pass, high-pass, band-pass, band-rejection filtering and further decimation of the data can be performed. Possible requirement of filtering of the data depends upon the spectral distribution of the response signals. The first step of the analysis is therefore to calculate the Power Spectral Densities of the response signals and validate these together with the Short Time Fourier Transform (STFT) analysis performed earlier in the data acquisition process as described above and exemplified in Figure (1). If for example the response signals have high content at low frequencies, due to high excitation of rigid body modes or measurement noise, a high-pass filtering of the signals can make the identification of the lower elastic modes, using the SSI technique, much easier. The filtering should, however, be made as “gentle” as possible, meaning that the order of the filter (giving the slope of the filter characteristic) should be as low as possible. FREQUENCY DOMAIN DECOMPOSITION THEORY BACKGROUND The Frequency Domain Decomposition (FDD) is an extension of the Basic Frequency Domain (BFD) technique, or more often called the Peak-Picking technique. This approach uses the fact that modes can be estimated from the spectral densities calculated in the condition of a white noise input and a lightly damped structure, Refs. [3,4,8]. The FDD technique estimates the modes using a Singular Value Decomposition (SVD) of each of the Spectral Density matrices. This decomposition corresponds to a Single Degree of Freedom (SDOF) identification of the system for each singular value. In the following the most important relationships for understanding the FDD technique are given. The relationship between the input x(t), and the output y(t) of a linear system can be written in the following form, Refs. [5,6], [ ] [ ] [ ] [ ]T xx yy H G H G ) ( ) ( ) ( ) ( * ω ω ω = ω , (1) where [Gxx(ω)] is the input spectral matrix, [Gyy(ω)] is the output spectrum matrix, and [H(ω)] is the Frequency Response Function (FRF) matrix. Writing the FRF matrix in the typical partial fraction form (used in classical Modal analysis), in terms of poles, λ and residues, R, and assuming that the input is random in both time and space, has a zero mean white noise distribution (i.e. Gxx(ω) = Const. for all the inputs) and that the damping is light, the response spectrum matrix can be written as the following final form, Ref. [3]: