Structural modal parameter identification with the Power-Exponential window function

Modal parameter identification is an important content for the research on dynamic behavior of civil engineering structures. For the conventional modal parameter identification techniques, excitation signal and response signal are necessary. But excitations can not be measured for structures under natural loading conditions, or excited by random forces. So, the operational modal parameter identification approaches are developing to identify structural modal parameters by using vibration response signal directly. In this paper, a new method for modal parameter identification depending on ambient excitation response signal is proposed based on independent component analysis (ICA). For modal coordinates independent of each other, ICA can extract modal coordinates of structure and estimate mode shape matrix using vibration response signal directly. The free vibration responses can be obtained by random decrement technique (RDT) from modal coordinates which are random processes, and then the natural frequencies and damping ratios are calculated by Hilbert transform. Numerical simulation results indicate that this method is effective and suitable for output-only structural modal parameter identification.

Based on the structure modal parameter identification method, the free vibration signal is first extracted using random decrement technique, and then the cross-correlations of different respond points obtained through NExT method are taken as the inputs of the modal time domain identification, and parameter identification is obtained by means of complex exponential method .. The local damage diagnosis is achieved according to the modal frequency movement. In order to ensure the accuracy of identification, the method of reference points selection is analyzed. The experiment shows that, the reference points selection method discussed here is valid in improving the accuracy of modal parameter identification, and the modal frequency could be used to judge the occurrence of damage.

Modal parameter identification via ambient vibration is popular but faces challenges from uncertainties due to unknown inputs and low signal‐to‐noise ratio. Bayesian methods are gaining increasing attention for operational modal identification due to their ability to quantify uncertainties. However, improvements in computational efficiency are needed, particularly when addressing numerous modes and degrees of freedom. To address this challenge, this study proposes an innovative approach, termed the “Bayesian spectral decomposition” method (BSD), employing the decompose‐and‐conquer strategy. This novel method, operating within the frequency domain, identifies each mode individually by exploiting their inherent separated modal characteristics. For each mode, the response spectrum matrix undergoes an eigenvalue decomposition, yielding crucial eigenvalues (incorporating frequency and damping information) and eigenvectors (containing mode shape information). Subsequently, statistical properties of the eigenvalues and eigenvectors are utilized to establish likelihood functions for Bayesian parameter identification. By combining prior information, the posterior probability distribution functions of modal parameters are derived. The optimal solution is then obtained by resolving the maximum posterior probability distribution function problem. To further quantify the uncertainty of modal parameters, Gaussian distributions are employed to approximate the posterior probability distribution functions. The adoption of the decomposition approach circumvents the joint identification of all modal parameters, substantially reducing the parameter dimensions for optimization. Consequently, this strategy leads to decreased computational complexity and significantly improved computational stability. The effectiveness of the BSD is confirmed through simulated data generated from an 8‐story shear building as well as measured data collected from both an experimental shear frame and the Canton Tower. The results demonstrate that the proposed method achieves high accuracy in identifying modal parameters, greatly improves computational efficiency, and effectively quantifies the uncertainties in modal parameters.

The primary objective of this paper is to develop output only modal identification and structural damage detection. Identification of multi-degree of freedom (MDOF) linear time invariant (LTI) and linear time variant (LTV—due to damage) systems based on Time-frequency (TF) techniques—such as short-time Fourier transform (STFT), empirical mode decomposition (EMD), and wavelets—is proposed. STFT, EMD, and wavelet methods developed to date are reviewed in detail. In addition a Hilbert transform (HT) approach to determine frequency and damping is also presented. In this paper, STFT, EMD, HT and wavelet techniques are developed for decomposition of free vibration response of MDOF systems into their modal components. Once the modal components are obtained, each one is processed using Hilbert transform to obtain the modal frequency and damping ratios. In addition, the ratio of modal components at different degrees of freedom facilitate determination of mode shape. In cases with output only modal identification using ambient/random response, the random decrement technique is used to obtain free vibration response. The advantage of TF techniques is that they are signal based; hence, can be used for output only modal identification. A three degree of freedom 1:10 scale model test structure is used to validate the proposed output only modal identification techniques based on STFT, EMD, HT, wavelets. Both measured free vibration and forced vibration (white noise) response are considered. The secondary objective of this paper is to show the relative ease with which the TF techniques can be used for modal identification and their potential for real world applications where output only identification is essential. Recorded ambient vibration data processed using techniques such as the random decrement technique can be used to obtain the free vibration response, so that further processing using TF based modal identification can be performed.

An out-put only modal parameter identification method based on variational mode decomposition (VMD) is developed for civil structure identifications. The recently developed VMD technique is utilized to decompose the free decay response (FDR) of a structure into to modal responses. A novel procedure is developed to calculate the instantaneous modal frequencies and instantaneous modal damping ratios. The proposed identification method can straightforwardly extract the mode shape vectors using the modal responses extracted from the FDRs at all available sensors on the structure. A series of numerical and experimental case studies are conducted to demonstrate the efficiency and highlight the superiority of the proposed method in modal parameter identification using both free vibration and ambient vibration data. The results of the present method are compared with those of the empirical mode decomposition-based method, and the superiorities of the present method are verified. The proposed method is proved to be efficient and accurate in modal parameter identification for both linear and nonlinear civil structures, including structures with closely spaced modes, sudden modal parameter variation, and amplitude-dependent modal parameters, etc.

This paper investigates the possibility of utilizing response from natural ice loading for modal parameter identification of real offshore platforms. The test platform is the JZ20-2MUQ jacket platform located in the Liaodong Bay, China. A field experiment is carried out in winter season, as the platform is excited by floating ices. The feasibility is demonstrated by the acceleration response of two different segments. By the SSI-data method, the modal frequencies and damping ratios of four structural modes can be successfully identified from both segments. The estimated information from both segments is almost identical, which demonstrates that the modal identification is trustworthy. Furthermore, by taking the Jacket platform as a benchmark, the numerical performance of five popular time-domain EMA methods is systematically compared from different viewpoints. The comparisons are categorized as: (1) stochastic methods versus deterministic methods; (2) high-order methods versus low-order methods; (3) data-driven versus covariance-driven stochastic subspace identification methods.

In order to select the window function and window size adaptively before getting the results, we proposed adaptive moving window principle component analysis (AMWPCA) based OMA method to identify modal shapes and modal natural frequencies of slow LTV structures with weekly damped only from non-stationary vibration response signal online. The adaptive is achieved in two ways: change the window function or window size. We develop an adaptive indicator as the basis for window function and window size changes. Our adaptive approach is to make the difference between adjacent eigenvalues not too small. The operational modal parameter identification results in non-stationarity response signal dataset of a three-degree-of-freedom structure with slow time-varying mass show that comparing with fixed size moving window principle component analysis, our AMWPCA method can identify the modal shapes and modal frequencies better.

An accurate prediction for the response of civil and mechanical engineering structures subject to ambient excitation requires the information of dynamic properties of these structures including natural frequencies, damping ratios and mode shapes. Since the excitation force is not available as a measured signal, we need to develop techniques which are capable of accurately extracting the modal parameters from output-only data. This article presents the results of modal parameter identification using two time-domain methods as follows: the autoregressive moving average vector (ARMAV) method and the state–space method. These methods directly work with the recorded time signals and allow the analysis of structures where only the output is measured, while the input is unmeasured and unknown. The equivalence between ARMAV and state–space approaches for the problem of modal parameter identification of vibrating systems is shown in the article. Using only the singular value decomposition of a block Hankel matrix of sample covariances, it is shown that these two approaches give identical modal parameters in the case where the block Hankel matrix has full row rank. The time-domain modal identification algorithms have a serious problem of model order determination: when extracting structural modes these algorithms always generate spurious modes. A modal indicator to differentiate spurious and structural modes is presented. Numerical and experimental examples are given to show the effectiveness of the ARMAV or state–space approaches in modal parameter identification using response data only.

The characteristics of oscillation modes, such as interarea, regional, and subsynchronous modes, can vary during a power system fault, which can cause switching and control actions in the power system. Transient data of the modal response due to such a fault can be acquired through phasor measurement units (PMUs). When the transient data have a long duration, it is desirable to perform modal identification separately on each segment of the transient data, so as to reflect the varying characteristics of oscillation modes. A conventional discrete Fourier transform (DFT)-based method for parametric modal identification cannot be efficiently applied to such a segment dataset. In this paper, a DFT-based method with an exponential window function is proposed to identify oscillation modes from each segment of transient data in PMUs. This window function allows the application of the least squares method (LSM) for modal identification in the same manner as the conventional method. The accuracy of identification of the proposed method is compared with those of the conventional method and a Prony method through synthetic data of transient responses. Its feasibility is also verified by identifying real-world oscillation modes from transient data in PMUs.

Interference reduction of high-energy noise for modal parameter identification of offshore wind turbines based on iterative signal extraction

Traditional modal parameter identification methods have many disadvantages, especially when used for processing nonlinear and non-stationary signals. In addition, they are usually not able to accurately identify the damping ratio and damage. In this study, methods based on the Hilbert-Huang transform (HHT) are investigated for structural modal parameter identification and damage diagnosis. First, mirror extension and prediction via a radial basis function (RBF) neural network are used to restrain the troublesome end-effect issue in empirical mode decomposition (EMD), which is a crucial part of HHT. Then, the approaches based on HHT combined with other techniques, such as the random decrement technique (RDT), natural excitation technique (NExT) and stochastic subspace identification (SSI), are proposed to identify modal parameters of structures. Furthermore, a damage diagnosis method based on the HHT is also proposed. Time-varying instantaneous frequency and instantaneous energy are used to identify the damage evolution of the structure. The relative amplitude of the Hilbert marginal spectrum is used to identify the damage location of the structure. Finally, acceleration records at gauge points from shaking table testing of a 12-story reinforced concrete frame model are taken to validate the proposed approaches. The results show that the proposed approaches based on HHT for modal parameter identification and damage diagnosis are reliable and practical.

Based on a recently developed stochastic subspace identification methodology equipped with an alternative stabilization diagram and a hierarchical sifting process, this research aims to improve this approach for more efficiently identifying the modal parameters of civil structures with closely spaced modes. The concept of a doubly folded stabilization diagram is proposed to combine the advantages of both the conventional and alternative stabilization diagrams for achieving better computational efficiency. In addition, the hierarchical sifting process is further refined to more properly handle closely spaced modes. The investigated cases for the occurrence of extremely close modes in civil engineering structures include axially symmetric stay cables, a symmetric cable-stayed bridge with respect to the pylon, and a uniformly arranged office building. Applying the upgraded SSI methodology established in this study, it is demonstrated that the modal parameter identification of civil engineering structures with extremely close modes can be elevated to an advanced level with a frequency space index at the order of 0.1%. Such an accurate identification and distinction is particularly important in the practical applications of structural health monitoring to prevent the false alarms resulting from the confusion of two extremely close modes. Furthermore, this approach also performs well in the determination of mode shape vectors for closely spaced modes to provide an excellent tool for observing their corresponding orthogonality property and high sensitivity.

Large-scale bridge projects are an vital part of national infrastructure, and are directly related to the safety of people's lives and properties. The identification of modal parameters of bridge structures under working conditions is an vital part of bridge damage identification. Considering the practicability of bridge detection, bridge detection should generally be based on environmental excitation. The existing means of modal parameter identification under environmental excitation are not suitable for The identification accuracy of the modal frequency is high, while the identification of the displacement mode has a large error. The existing means of modal parameter identification under environmental excitation have relatively high identification accuracy for the modal frequency, while the identification of the displacement mode has a large error. Due to the complexity and large-scale bridge structure, the importance and necessity of bridge structure health monitoring are more and more recognized by people. The means used in this paper is to improve the genetic algorithm to simulate the phenomena of reproduction, crossover and gene mutation that occur in the spontaneous selection and spontaneous heredity process. Genetic algorithm is a global optimization adaptive probabilistic search algorithm, which has the advantages of intelligent optimization and robustness.

Accurate and timely identification of modal parameters of long-span bridges is important for bridge health monitoring and wind tunnel tests. Wavelet analysis is one of the most advantageous methods for identification because of its good localization characteristics in both time and frequency domain. In recent years, the wavelet method has been applied more frequently in parameter identification of linear and nonlinear systems. In this article, based on wavelet ridges and wavelet skeleton, the improved modal parameter identification method was studied. To find the appropriate time-frequency resolution, an optimal wavelet basis design principle based on minimum Shannon entropy was proposed. Aiming at endpoint effect in wavelet transform, a prediction continuation method based on support vector machine (SVM) was proposed, which can effectively suppress the endpoint effect of the extended samples. In view of the fact that the ridges of metric matrices obtained by the traditional crazy climber algorithm cannot fully reflect the distribution of ridges of modulus value matrices of wavelet coefficients, an improved high-precision crazy climber algorithm was put forward to accurately identify the position of the ridge of wavelet coefficients. Finally, taking a long-span cable-stayed bridge and a long-span suspension bridge as the engineering background, improved continuous wavelet transform (CWT) was applied to modal parameter identification of bridge under ambient excitation. The modal parameters such as modal frequency, damping ratio, and mode shape were obtained. Compared with the calculation value of the numerical simulation of long-span cable-stayed bridge and wind tunnel test of long-span suspension bridge, the reliability of CWT for modal parameter identification of long-span bridges under ambient excitation was verified.

The coupling of various modes in centrifugal pumps renders the process of modal parameter identification through frequency response functions both time-consuming and labour-intensive. To accurately identify modal parameters, current modal testing typically requires the deployment of numerous measurements or excitation points. However, certain modal parameters may suffer from low SNR, leading to distorted modal shapes that deviate from reality. This study employs a semi-empirical approach to ingeniously design the excitation vector by leveraging the relationships among the centre of mass, inertial axes, and excitation points. During modal testing experiments, specific modes of the centrifugal pump are decoupled, significantly improving the SNR for the targeted modes. Experimental validation demonstrates that the proposed method markedly enhances the accuracy of modal parameters identification, thereby facilitating the analysis of its vibration characteristics. The findings enable rapid identification of modal parameters related to vibration issues in engineering applications, contributing to the swift localization and resolution of vibration problems.