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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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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 eigensystem realization-algorithm FOR MODAL PARAMETER-IDENTIFICATION AND MODEL-REDUCTION

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JOURNAL OF GUIDANCE CONTROL AND DYNAMICS 1985年第5期8卷 620-627页

作者： JUANG, JN PAPPA, RS NASA Langley Research Center Hampton Virginia

A method called the eigensystem realization algorithm is developed for modal parameter identification and model reduction of dynamic systems from test data. A new approach is introduced in conjunction with the singular-value decomposition technique to derive the basic formulation of minimum order realization which is an extended version of the Ho-Kalman algorithm. The basic formulation is then transformed into modal space for modal parameter identification. Two accuracy indicators are developed to quantitatively identify the system and noise modes. For illustration of the algorithm, an example is shown using experimental data from the Galileo spacecraft.

关键词： eigensystem realization algorithm Singular Value Decomposition Galileo Spacecraft Finite Element Modeling State Space Representation Flexible Structures Structural Dynamics Data Acquisition Data Analysis Techniques Accelerometer

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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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On-line version of the eigensystem realization algorithm using data correlations

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JOURNAL OF GUIDANCE CONTROL AND DYNAMICS 1997年第1期20卷 137-142页

作者： Cooper, JE University of Manchester Manchester M13 9PL England United Kingdom

An on-line (recursive) version of the eigensystem realization algorithm using data correlations is developed based on the QR decomposition. The method can be used to estimate a theoretically unbiased minimum-order realization from decay response data. The proposed method is an improvement on other on-line time domain identification techniques in that the minimum-order realization permits overspecification of the mathematical model, removing simultaneously the problems of a priori model order selection and possible computational difficulties with identified spurious modes. Time varying modal parameters can also be tracked through the use of a forgetting factor to weight the most recent points. The method is demonstrated on a number of simulated data sets corrupted with measurement noise.

关键词： eigensystem realization algorithm Data Correlation Damping Ratio Single Input Single Output Mathematical Models

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CONSTRAINED eigensystem realization-algorithm FOR LIGHTLY DAMPED DISTRIBUTED STRUCTURES

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JOURNAL OF GUIDANCE CONTROL AND DYNAMICS 1991年第5期14卷 1014-1020页

作者： NORRIS, MA VIRGINIA POLYTECH INST & STATE UNIV ENGN SCI & MECHBLACKSBURGVA 24061

The temporal correlation method for modal identification of lightly damped distributed structures is extended to include system realization and is shown to be a constrained version of the eigensystem realization algorithm. The method relies on the temporal and spatial orthogonality of the modes of vibration, which are properties of lightly damped or nearly self-adjoint distributed systems. Using these properties, the system realization and modal identification can be performed in the configuration space, as opposed to the state space. In this manner, the computational requirements of the eigensystem realization algorithm are decreased, in addition to constraining the algorithm to take advantage of the lightly damped behavior of the system so that the technique may be less sensitive to sensor noise in the system measurements and provide improved realization capabilities. Analytical and experimental examples illustrate and verify the method. The results are compared with the standard version of the eigensystem realization algorithm.

关键词： eigensystem realization algorithm Sensors Lightly Damped Structures Singular Value Decomposition Accelerometer Stiffness Matrices Logarithmic Decrement State Space Representation NASA Langley Research Center Frequency Response Functions

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Random Matrix-Based Approach for Uncertainty Analysis of the eigensystem realization algorithm

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JOURNAL OF GUIDANCE CONTROL AND DYNAMICS 2017年第8期40卷 1877-1891页

作者： Vishwajeet, Kumar Singla, Puneet Majji, Manoranjan Univ Buffalo Dept Mech & Aerosp Engn Buffalo NY 14260 USA

In this paper, uncertainty in the state space matrices in a linear stochastic time-invariant discrete time system is presented by performing uncertainty analysis of the eigensystem realization algorithm (ERA). An analytical expression for the calculation of the singular values of Hankel matrix is developed. The expression for the joint distribution of the singular values is used to estimate the rank of the Hankel matrix. The distribution of singular values is also used to find the distribution on the bound of norm of system matrix.

关键词： eigensystem realization algorithm Finite Element Modeling Controllability Gramian Singular Value Decomposition Model Order Reduction Mathematical Models Computing Frequency Response Functions Euler Bernoulli Beam Theory Observer Kalman Filter Identification

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RECURSIVE FORM OF THE eigensystem realization-algorithm FOR SYSTEM-IDENTIFICATION

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JOURNAL OF GUIDANCE CONTROL AND DYNAMICS 1989年第5期12卷 647-652页

作者： LONGMAN, RW JUANG, JN NASA LANGLEY RES CTRHAMPTONVA 23665

An algorithm is developed for recursively calculating the minimum realization of a linear system from sampled impulse response data. The Gram-Schmidt orthonormalization technique is used to generate an orthonormal basis for factorization of the data matrix. The system matrix thus identified is in upper Hessenberg form, which has advantages for the identification of modal parameters including damping coefficients, frequencies, mode shapes, and modal participation factors. It also has the property that once an element of the system matrix is computed, it is never altered as the dimension of the model is increased in the recursive process. Numerical examples are presented for comparison of the recursive and nonrecursive forms of the eigensystem realization algorithm.

关键词： eigensystem realization algorithm Linear Time Invariant System Damping Coefficient Singular Value Decomposition Flexible Structures Frequency Domain Ofeq

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CONSISTENT-MODE INDICATOR FOR THE eigensystem realization-algorithm

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JOURNAL OF GUIDANCE CONTROL AND DYNAMICS 1993年第5期16卷 852-858页

作者： PAPPA, RS ELLIOTT, KB NASA LANGLEY RES CTRSPACECRAFT CONTROLS BRANCHHAMPTONVA 23681 GERMAN AEROSP RES ESTAB INST AEROELAST DLRW-3400 GOTTINGENGERMANY

A new method is described for assessing the consistency of structural modal parameters identified with the eigensystem realization algorithm. Identification results show varying consistency in practice due to many sources including high modal density, nonlinearity, and inadequate excitation. Consistency is considered to be a reliable indicator of accuracy. The new method is the culmination of many years of experience in developing a practical implementation of the eigensystem realization algorithm. The effectiveness of the method is illustrated using data from NASA Langley's controls-structures-interaction evolutionary model.

关键词： eigensystem realization algorithm NASA Langley Research Center Data Analysis Accelerometer Trusses Singular Value Decomposition Finite Element Analysis Nastran Frequency Response Functions Structural Modeling

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Reduced-order models for control of fluids using the eigensystem realization algorithm

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THEORETICAL AND COMPUTATIONAL FLUID DYNAMICS 2011年第1-4期25卷 233-247页

作者： Ma, Zhanhua Ahuja, Sunil Rowley, Clarence W. Princeton Univ Dept Mech & Aerosp Engn Princeton NJ 08544 USA

As sensors and flow control actuators become smaller, cheaper, and more pervasive, the use of feedback control to manipulate the details of fluid flows becomes increasingly attractive. One of the challenges is to develop mathematical models that describe the fluid physics relevant to the task at hand, while neglecting irrelevant details of the flow in order to remain computationally tractable. A number of techniques are presently used to develop such reduced-order models, such as proper orthogonal decomposition (POD), and approximate snapshot-based balanced truncation, also known as balanced POD. Each method has its strengths and weaknesses: for instance, POD models can behave unpredictably and perform poorly, but they can be computed directly from experimental data;approximate balanced truncation often produces vastly superior models to POD, but requires data from adjoint simulations, and thus cannot be applied to experimental data. In this article, we show that using the eigensystem realization algorithm (ERA) (Juang and Pappa, J Guid Control Dyn 8(5):620-627, 1985) one can theoretically obtain exactly the same reduced-order models as by balanced POD. Moreover, the models can be obtained directly from experimental data, without the use of adjoint information. The algorithm can also substantially improve computational efficiency when forming reduced-order models from simulation data. If adjoint information is available, then balanced POD has some advantages over ERA: for instance, it produces modes that are useful for multiple purposes, and the method has been generalized to unstable systems. We also present a modified ERA procedure that produces modes without adjoint information, but for this procedure, the resulting models are not balanced, and do not perform as well in examples. We present a detailed comparison of the methods, and illustrate them on an example of the flow past an inclined flat plate at a low Reynolds number.

关键词： Flow control Model reduction eigensystem realization algorithm Balanced truncation

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