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Enhancing reliability in estimating modal parameters for automotive disk Brakes: A comprehensive approach using the eigensystem realization algorithm and additional criteria

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MECHANICAL SYSTEMS AND SIGNAL PROCESSING 2025年 224卷

作者： Uradnicek, Juraj Musil, Milos Gasparovic, L'ubos Palenik, Marek Bachraty, Michal Slovak Univ Technol Bratislava Inst Appl Mech & Mechatron Fac Mech Engn Nam Slobody 17 Bratislava 81231 Slovakia Slovak Univ Technol Bratislava Fac Mech Engn Inst Mfg Syst Environm Technol & Qual Management Nam Slobody 17 Bratislava 81231 Slovakia

This paper investigates the challenges in accurately identifying and assessing vibration characteristics in automotive disk brakes, which, due to their geometric symmetry, exhibit closely spaced vibration modes. Understanding the damping characteristics is crucial due to their significant impact on dynamic stability and the potential onset of brake squeal, as damping directly influences the stability threshold and its uneven distribution can destabilize the system. Therefore, this study primarily focuses on the identification of modal parameters with an emphasis on the damping of disk brakes. Traditional Experimental Modal Analysis (EMA) techniques, which rely heavily on Frequency Response Function (FRF) measurements, encounter challenges in distinguishing closely spaced modes, thereby affecting the reliability of parameter estimation, particularly damping. These algorithms are primarily based on FRF measurements and are of multi-input - single-output type (MISO). In comparison to Operational Modal Analyses (OMA) algorithms, which are widely used in civil engineering and are of the multi-input - multi-output type and contain statistical tools for assessing the uncertainty of the estimate, EMA provides limited possibilities to assess the quality of estimating parameters. The primary contribution of this work is demonstrating that the eigensystem realization algorithm (ERA), supplemented with indicators such as Extended Modal Amplitude Coherence (EMAC), Modal Phase Collinearity (MPC), and the Consistent Mode Indicator (CMI), offers a robust tool for accurate damping estimation. Additionally, the application of ERA to data originally acquired for frequency-based methods, specifically the Rational Fraction Polynomial (RFP) method, allows for a direct comparison of these two EMA algorithms using the same dataset. The results demonstrate that the proposed identification process effectively distinguishes system modes from those influenced by noise, providing a pathway to o

关键词： Experimental modal analysis Modal damping estimation Close modes eigensystem realization algorithm Rational fraction polynomial method Disk brake damping

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Improved Subsynchronous Oscillation Parameter Identification Based on eigensystem realization algorithm

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APPLIED SCIENCES-BASEL 2024年第17期14卷 7841页

作者： Chen, Gang Zeng, Xueyang Liu, Yilin Zhang, Fang Shi, Huabo State Grid Sichuan Elect Power Res Inst Chengdu 610041 Peoples R China Power Internet Things Key Lab Sichuan Prov Chengdu 610041 Peoples R China Beijing Jiaotong Univ Sch Elect Engn Beijing 100044 Peoples R China

Subsynchronous oscillation (SSO) is the resonance between a new energy generator set and a weak power grid, and the resonance frequency is usually the sub-/super-synchronous frequency. The eigensystem realization algorithm (ERA) is a classic algorithm for extracting modal parameters based on matrix decomposition. By leveraging the ERA's simplicity and low computational cost, an enhanced methodology for identifying the key parameters of SSO is introduced. The enhanced algorithm realizes SSO angular frequency extraction by constructing an angular frequency fitting equation, enabling efficient identification of SSO parameters using only a 200 ms synchrophasor sequence. In the process of identification, the fitting-based ERA effectively addresses the limitation of the existing ERA. The accuracy of SSO parameter identification is improved, thereby realizing that SSO parameter identification can be carried out using a 200 ms data window. The fitting-based ERA is verified using synthetic and actual data from synchrophasor measurement terminals. The research results show that the proposed algorithm can accurately extract fundamental and subsynchronous or supersynchronous oscillation parameters, effectively realizing dynamic real-time monitoring of subsynchronous oscillations.

关键词： subsynchronous oscillations parameter identification fitting equation eigensystem realization algorithm

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Tube MPC for a two-tank system based on eigensystem realization algorithm

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JOURNAL OF PROCESS CONTROL 2025年 151卷

作者： Dyvik, Mathias Rotondo, Damiano Univ Stavanger UiS Dept Elect & Comp Engn IDE N-4009 Stavanger Norway

This paper presents the design of a linear, data-driven, tube-based robust model predictive control (MPC) for level control in a coupled nonlinear two-tank system. Two state-space models are identified from step responses using the eigensystem realization algorithm (ERA): one from a high-fidelity nonlinear process simulator and the other using data from the physical plant. The obtained models have states that lack physical meaning, necessitating a state observer to estimate the states from the level sensor measurements. The paper shows that a proportional-integral Kalman filter provides more robust state estimates than a standard Kalman filter and is thus used for controller implementation. The proposed ERA-based tube MPC demonstrated robust performance and constraint satisfaction compared to a conventional MPC in both simulation and experimental settings. However, it violated constraints under certain disturbances within the predefined bounds because of modeling mismatches caused by applying a linear control strategy to a nonlinear system. Addressing these violations by incorporating parametric uncertainty in the disturbance bounds and using more aggressive tuning mitigates the issue but increases conservatism and control effort. These findings offer insights into the tuning of Tube MPC for desired trade-offs in industrial applications.

关键词： Tube MPC eigensystem realization algorithm Kalman filter Liquid level control Water tank system

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An evaluation of the influence of eigensystem realization algorithm settings on multiple input multiple output system identification

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JOURNAL OF VIBRATION AND CONTROL 2022年第21-22期28卷 3286-3301页

作者： Soares Jr, Dirceu Serpa, Alberto Luiz Univ Estadual Campinas UNICAMP Campinas Brazil Fed Inst Espirito Santo IFES Vitoria Spain

One characteristic of the eigensystem realization algorithm method for system identification concerns about the difficulty of finding more appropriate parameters to run the algorithm. One of this work's purposes is to tackle the cumbersome task of achieving the ideal algorithm settings, providing additional knowledge about algorithm parameters' influence, and searching to improve results with quicker settings of the algorithm's parameters, especially for Multiple Input Multiple Output (MIMO) systems. The application of a Fit Rate indicator to evaluate the identified system arises as a novelty in the eigensystem realization algorithm applications, aiming to assess the system identification performance and drive the algorithm to better adjustments. Another objective of this article regards the application of a Pseudo Random Binary Sequence as excitation signals, which has not been used until now with the eigensystem realization algorithm, despite being successfully applied in the system identification process. The proposed approach is verified and analyzed with numerical simulations for a mass-spring-damper model of 5 degrees of freedom. The results reported in time response analysis and frequency response analysis allow us to realize the effect of settings accordingly for the system identification improvement. The results analysis was extended to simulate and compare the Pseudo Random Binary Sequence with Gaussian white noise excitation, and the system was also submitted to the presence of measurement noise.

关键词： System identification eigensystem realization algorithm Multiple Input Multiple Output systems Pseudo Random Binary Sequence Hankel matrix

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Comparative Assessment of Prony Analysis and eigensystem realization algorithm for Forced Oscillation Detection and Mode Estimation Considering PMU Noise 3

Comparative Assessment of Prony Analysis and Eigensystem Rea...

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3rd IEEE International Conference on Smart Technologies for Power, Energy and Control, STPEC 2023

作者： Abhinav, Kumar Rai, Piyush Prakash, Abhineet Parida, S.K. Indian Institute of Technology Department of Electrical Engineering Patna801103 India

ISBN: (纸本)9798350304732

In this study, Prony and eigensystem realization algorithm (ERA) are compared for identifying electromechanical and forced oscillation modes. The varying number of excited modes in practical power systems makes the process of determining model order challenging. Prony requires an iterative procedure, while ERA utilizes Singular Value Decomposition (SVD) for direct model order determination. Comparitive studies shows that ERA accurately estimates the signal, and generates fewer insignificant modes compared to Prony. Identified modes are used to design a filter, which estimates desired signal frequency. The filtered signal's periodogram is then compared with detection threshold to detect Forced oscillation (FO) at specific frequencies. © 2023 IEEE.

关键词： eigensystem realization algorithm Forced Oscillation Periodogram Detector Prony Analysis

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Parameter Identification of Power Grid Subsynchronous Oscillations Based on eigensystem realization algorithm

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ENERGIES 2024年第11期17卷 2575页

作者： Zeng, Xueyang Chen, Gang Liu, Yilin Zhang, Fang Shi, Huabo State Grid Sichuan Elect Power Res Inst Chengdu 610041 Peoples R China Power Internet Things Key Lab Sichuan Prov Chengdu 610041 Peoples R China Beijing Jiaotong Univ Sch Elect Engn Beijing 100044 Peoples R China

The subsynchronous oscillation caused by the resonance between power electronic devices and series compensation devices or weak power grids introduced by large-scale renewable energy generation greatly reduces the transmission capacity of the system and may endanger the safe operation of the power system. It even leads to system oscillation instability. In this paper, based on the advantages of a simple solution, a small amount of calculation and anti-noise of ERA, a method of subsynchronous oscillation parameter identification based on the eigensystem realization algorithm (ERA) is proposed. The Hankel matrix in the improved ERA is obtained by splicing the real part matrix and the imaginary part matrix of the synchrophasor, thus solving the problem of angular frequency conjugate constraints of two fundamental components and two oscillatory components which are not considered in the existing ERA. The solution to this problem is helpful to improve the accurate parameter identification results of ERA under the data window of 200 ms and weaken the limitation caused by the assumption that the synchrophasor model is fixed. The practicability of the improved method based on PMU is verified by the synthesis of ERA and the actual measurement data. Compared with the existing ERA, the improved ERA can accurately identify the parameters of each component under the ultra-short data window and realize the dynamic monitoring of power system subsynchronous oscillation.

关键词： subsynchronous oscillations (SSOs) parameter identification synchrophasor eigensystem realization algorithm

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An eigensystem realization algorithm for Identification of Modal Parameters of Nonviscous Damping Structure System

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INTERNATIONAL JOURNAL OF STRUCTURAL STABILITY AND DYNAMICS 2024年第5期24卷 2450052-2450052页

作者： Shen, Renjie Qian, Xiangdong Zhou, Jianfang Lee, Chin-Long Jiangsu Univ Sci & Technol Sch Naval Architecture & Ocean Engn Dept Engn Mech Zhenjiang 212100 Jiangsu Peoples R China Hohai Univ Coll Mech & Mat 1 Xikang Rd Nanjing 210098 Jiangsu Peoples R China Univ Canterbury Dept Civil & Nat Resources Engn Christchurch 8041 New Zealand

In this paper, a modified eigensystem realization algorithm for modal parameter identification and relaxation parameter is extended from a viscous damping system to a nonviscous damping system. The equation of motion with nonviscous damping in second-order form is expressed in the state space formulation. The eigenvalues of the second-order form equation are proved equal to the state space formulation. The extended method is based on the proposed nonlinear relationship between the eigenvalues and the damping parameters of a nonviscous damping system. The identified procedure of the proposed method is given in detail. Finally, the method is validated using three numerical examples for assessing its accuracy.

关键词： Nonviscous damping eigensystem realization algorithm parameter identification modal parameter relaxation parameter

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Automatic modal identification via eigensystem realization algorithm with improved stabilization diagram technique

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ENGINEERING STRUCTURES 2023年第1期291卷

作者： Feng, Wen -Hai Wu, Chao -Yuan Fu, Ji-Yang Ng, Ching-Tai He, Yun-Cheng Guangzhou Univ Res Ctr Wind Engn & Engn Vibrat Guangdong Peoples R China Univ Adelaide Sch Civil Environm & Min Engn Adelaide SA Australia

Efficient and automatic identification of modal parameters becomes increasingly important for real-time structural health monitoring (SHM) of civil structures. As spurious modes usually exist as a key problem for most output-based identification methods, great efforts have been made to eliminate them typically via stabilizationdiagram techniques. However, the quality of traditional stabilization diagrams depends on preset parameters whose values usually vary from one case to another, which makes the method to be less objective and low efficient. This article proposes an improved stabilization-diagram technique, through combined usage of MonteCarlo sampling simulation, as well as fuzzy C-means (FCM) clustering and three-stage sifting manipulations. While the Monte-Carlo simulation aims to generate more robust stable-axis, the sifting and clustering manipulations can further remove outliers and discriminate true modal results. The improved stabilization-diagram technique is then applied to two mainstream modal identification methods, i.e., eigensystem realization algorithm (ERA) and stochastic subspace identification (SSI) under the context of both a simulation study on a dynamic system and a field research about a super-tall building. Results through comparison demonstrate that the improved stabilization-diagram technique can facilitate ERA and SSI to identify modal parameters automatically and effectively at a comparably good accuracy. However, ERA outperforms SSI evidently in terms of computational efficiency (upmost 15 times faster), which is attractive for real-time SHM. Parametric analysis has been also conducted to examine detailed performance of ERA aided by the proposed stabilization-diagram technique. Overall, the aforementioned method can be adopted to achieve a good balance between identification effectiveness and computational efficiency in an automatic working pattern, and has application prospect for realtime SHM of civil structures.

关键词： eigensystem realization algorithm Automatic modal identification Stabilization diagram Cluster Time-varying properties identification

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A tutorial on data-driven eigenvalue identification: Prony analysis, matrix pencil, and eigensystem realization algorithm

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INTERNATIONAL TRANSACTIONS ON ELECTRICAL ENERGY SYSTEMS 2020年第4期30卷 1-17页

作者： Almunif, Anas Fan, Lingling Miao, Zhixin Univ S Florida Dept Elect Engn Tampa FL 33620 USA

To identify power system eigenvalues from measurement data, Prony analysis, matrix pencil (MP), and eigensystem realization algorithm (ERA) are three major methods. This paper reviews the three methods and sheds insight on the principles of the three methods: eigenvalue identification through various Hankel matrix formulations. In addition, multiple channel data handling and noise-resilience techniques are investigated. In the literature, singular value decomposition (SVD)-based rank reduction technique has been applied to MP and resulted in a reduced-order system eigenvalue estimation and an excellent noise resilient feature. In this paper, ERA is refined using the SVD-based rank reduction to achieve superior performance. Further, a reduced-order Prony analysis method is proposed. With this technique, Prony analysis can not only give reduced-order system eigenvalues, but also become noise resilient. Four case studies are conducted to demonstrate the effectiveness of the eigenvalue identification methods, including a tutorial example of an RLC circuit resonance, a power grid oscillation case study for a 16-machine 68-bus system, an example of subsynchronous resonance (SSR) of a type-3 wind grid integration system, and real-world oscillation events captured by Independent System Operator-New England (ISO-NE).

关键词： eigensystem realization algorithm Hankel matrix matrix pencil power system oscillations Prony analysis singular value decomposition subsynchronous resonances

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Automated eigensystem realization algorithm for Operational Modal Identification of Bridge Structures

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JOURNAL OF AEROSPACE ENGINEERING 2019年第2期32卷

作者： Yang, Xiao-Mei Yi, Ting-Hua Qu, Chun-Xu Li, Hong-Nan Liu, Hua Dalian Univ Technol Sch Civil Engn Dalian 116023 Peoples R China China Railway Major Bridge Nanjing Bridge & Tunne Nanjing 210061 Jiangsu Peoples R China

The subject of vibration-based structural health monitoring (SHM) has attracted increasing attention, especially in the field of civil engineering. However, the development of these monitoring processes is not a simple task, with user interaction playing a significant role in the extraction of modal characteristics. In this paper, an automated operational modal analysis methodology based on an eigensystem realization algorithm (ERA) and a two-stage clustering strategy is proposed. Three crucial steps are addressed in this study. In the first phase, ERA is adopted to calculate modes from state-space models of different orders. Subsequently, the dissimilarity of modal parameters is employed as the features of fuzzy C-means (FCM) clustering to separate stable modes from unstable ones. The final step consists of grouping stable modes with similar structural properties to select physical modes. No user-specified parameter is required in the clustering procedure to single out physical modes. A practical bridge example is used to verify that the proposed method can estimate modal parameters effectively in real time.

关键词： eigensystem realization algorithm Automated modal identification Clustering

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