Parameter Adaptation by Parameter Signature Isolation in the Time-Scale Domain

2008 ◽  
Author(s):  
Kourosh Danai ◽  
James R. McCusker
Keyword(s):  
Error Estimates ◽  
Time Scale ◽  
Prediction Error ◽  
Dynamic Models ◽  
Noise Suppression ◽  
Model Parameters ◽  
Isolation Method ◽  
Parameter Adaptation ◽  
Single Output ◽  
Parameter Error

It is shown that delineation of output sensitivities with respect to model parameters in dynamic models can be enhanced in the time-scale domain. This enhanced differentiation of output sensitivities then provides the capacity to isolate regions of the time-scale plane wherein a single output sensitivity dominates the others. Due to this dominance, the prediction error can be attributed to the error of a single parameter at these regions so as to estimate each model parameter error separately. The proposed Parameter Signature Isolation Method (PARSIM) that uses these parameter error estimates for parameter adaptation has been found to have an adaptation precision comparable to that of the Gauss-Newton method for noise-free cases. PARSIM, however, appears to be less sensitive to input conditions, while offering the promise of more effective noise suppression by the capabilities available in the time-scale domain.

Parameter Estimation by Parameter Signature Isolation in the Time-Scale Domain

2009 ◽  
Vol 131 (4) ◽  
Author(s):  
Kourosh Danai ◽  
James R. McCusker
Keyword(s):  
Parameter Estimation ◽  
Error Estimates ◽  
Time Scale ◽  
Prediction Error ◽  
Dynamic Models ◽  
Noise Suppression ◽  
Isolation Method ◽  
Estimation Precision ◽  
Parameter Error

It is shown that output sensitivities of dynamic models can be better delineated in the time-scale domain. This enhanced delineation provides the capacity to isolate regions of the time-scale plane, coined as parameter signatures, wherein individual output sensitivities dominate the others. Due to this dominance, the prediction error can be attributed to the error of a single parameter at each parameter signature so as to enable estimation of each model parameter error separately. As a test of fidelity, the estimated parameter errors are evaluated in iterative parameter estimation in this paper. The proposed parameter signature isolation method (PARSIM) that uses the parameter error estimates for parameter estimation is shown to have an estimation precision comparable to that of the Gauss–Newton method. The transparency afforded by the parameter signatures, however, extends PARSIM’s features beyond rudimentary parameter estimation. One such potential feature is noise suppression by discounting the parameter error estimates obtained in the finer-scale (higher-frequency) regions of the time-scale plane. Another is the capacity to assess the observability of each output through the quality of parameter signatures it provides.

Improved Parameter Estimation by Noise Compensation in the Time-Scale Domain

2009 ◽  
Author(s):  
James R. McCusker ◽  
Todd Currier ◽  
Kourosh Danai
Keyword(s):  
Parameter Estimation ◽  
Dynamic Model ◽  
Time Scale ◽  
Prediction Error ◽  
Noise Suppression ◽  
Model Parameters ◽  
Individual Parameter ◽  
Noise Compensation ◽  
Confidence Factor ◽  
Estimated Parameters

It was shown recently that parameter estimation can be performed directly in the time-scale domain by isolating regions wherein the prediction error can be attributed to the error of individual dynamic model parameters [1]. Based on these single-parameter attributions of the prediction error, individual parameter errors can be estimated for iterative parameter estimation. A benefit of relying entirely on the time-scale domain for parameter estimation is the added capacity for noise suppression. This paper explores this benefit by introducing a noise compensation method that estimates the distortion by noise of the prediction error in the time-scale domain and incorporates it as a confidence factor when estimating individual parameter errors. This method is shown to further improve the estimated parameters beyond the time-filtering and denoising techniques developed for time-based estimation.

Mutual Identifiability Analysis for Parameter Signature Isolation in the Time-Scale Plane

2008 ◽  
Author(s):  
Kourosh Danai ◽  
James R. McCusker ◽  
C. V. Hollot
Keyword(s):  
Time Scale ◽  
Prediction Error ◽  
Linear Models ◽  
Necessary Condition ◽  
Model Parameters ◽  
Identifiability Analysis ◽  
Individual Model ◽  
Model Parameter

It was shown recently that regions in the time-scale plane can be isolated wherein the prediction error can be attributed to the error of an individual model parameter. A necessary condition for this isolation capacity is the mutual (pairwise) identifiability of the model parameters. This paper presents conditions for mutual identifiability of parameters of linear models and refines these conditions for models that exhibit rank-1 dependency on the parameters.

Integrating Parameter Estimation Solutions From the Time and Time-Scale Domains

2009 ◽  
Author(s):  
James R. McCusker ◽  
Kourosh Danai
Keyword(s):  
Parameter Estimation ◽  
Least Squares ◽  
Time Scale ◽  
Prediction Error ◽  
Nonlinear Least Squares ◽  
Integrated Approach ◽  
Parameter Estimates ◽  
Model Parameters ◽  
Single Model ◽  
Iterative Estimation

A method of parameter estimation was recently introduced that separately estimates each parameter of the dynamic model [1]. In this method, regions coined as parameter signatures, are identified in the time-scale domain wherein the prediction error can be attributed to the error of a single model parameter. Based on these single-parameter associations, individual model parameters can then be estimated for iterative estimation. Relative to nonlinear least squares, the proposed Parameter Signature Isolation Method (PARSIM) has two distinct attributes. One attribute of PARSIM is to leave the estimation of a parameter dormant when a parameter signature cannot be extracted for it. Another attribute is independence from the contour of the prediction error. The first attribute could cause erroneous parameter estimates, when the parameters are not adapted continually. The second attribute, on the other hand, can provide a safeguard against local minima entrapments. These attributes motivate integrating PARSIM with a method, like nonlinear least-squares, that is less prone to dormancy of parameter estimates. The paper demonstrates the merit of the proposed integrated approach in application to a difficult estimation problem.

Validation of Dynamic Models by Image Distances in the Time-Scale Domain

2009 ◽  
Author(s):  
Kourosh Danai ◽  
James R. McCusker ◽  
Todd Currier ◽  
David O. Kazmer
Keyword(s):  
Time Series ◽  
Dynamic Model ◽  
Model Validation ◽  
Time Scale ◽  
Prediction Error ◽  
Dynamic Models ◽  
Traditional Approaches

Model validation is the procedure whereby the fidelity of a model is evaluated. The traditional approaches to dynamic model validation either rely on the magnitude of the prediction error between the process observations and model outputs or consider the observations and model outputs as time series and use their similarity to assess the closeness of the model to the process. Here, we propose transforming these time series into the time-scale domain, to enhance their delineation, and using image distances between these transformed time series to assess the closeness of the model to the process. It is shown that the image distances provide a more consistent measure of model closeness than available from the magnitude of the prediction error.

scholarly journals An Enhanced Intrinsic Time-Scale Decomposition Method Based on Adaptive Lévy Noise and Its Application in Bearing Fault Diagnosis

Symmetry ◽  
2021 ◽  
Vol 13 (4) ◽  
pp. 617
Author(s):  
Jianpeng Ma ◽  
Shi Zhuo ◽  
Chengwei Li ◽  
Liwei Zhan ◽  
Guangzhu Zhang
Keyword(s):  
Fault Diagnosis ◽  
Time Scale ◽  
Lévy Noise ◽  
Model Parameters ◽  
Rolling Bearings ◽  
Intrinsic Time ◽  
Time Scale Decomposition ◽  
Weak Fault ◽  
Levy Noise ◽  
The Impact

When early failures in rolling bearings occur, we need to be able to extract weak fault characteristic frequencies under the influence of strong noise and then perform fault diagnosis. Therefore, a new method is proposed: complete ensemble intrinsic time-scale decomposition with adaptive Lévy noise (CEITDALN). This method solves the problem of the traditional complete ensemble intrinsic time-scale decomposition with adaptive noise (CEITDAN) method not being able to filter nonwhite noise in measured vibration signal noise. Therefore, in the method proposed in this paper, a noise model in the form of parameter-adjusted noise is used to replace traditional white noise. We used an optimization algorithm to adaptively adjust the model parameters, reducing the impact of nonwhite noise on the feature frequency extraction. The experimental results for the simulation and vibration signals of rolling bearings showed that the CEITDALN method could extract weak fault features more effectively than traditional methods.

scholarly journals Modular Dynamic Biomolecular Modelling: The Unification of Stoichiometry, Thermodynamics, Kinetics and Data

2021 ◽  
Author(s):  
Peter J. Gawthrop ◽  
Michael Pan ◽  
Edmund J. Crampin
Keyword(s):  
Dynamic Models ◽  
System Development ◽  
Kinetic Modelling ◽  
Simulation Models ◽  
Bond Graph ◽  
Model Parameters ◽  
Biomolecular Systems ◽  
Genome Wide ◽  
Estimation Of Model Parameters ◽  
Genome Scale

AbstractRenewed interest in dynamic simulation models of biomolecular systems has arisen from advances in genome-wide measurement and applications of such models in biotechnology and synthetic biology. In particular, genome-scale models of cellular metabolism beyond the steady state are required in order to represent transient and dynamic regulatory properties of the system. Development of such whole-cell models requires new modelling approaches. Here we propose the energy-based bond graph methodology, which integrates stoichiometric models with thermo-dynamic principles and kinetic modelling. We demonstrate how the bond graph approach intrinsically enforces thermodynamic constraints, provides a modular approach to modelling, and gives a basis for estimation of model parameters leading to dynamic models of biomolecular systems. The approach is illustrated using a well-established stoichiometric model of E. coli and published experimental data.

Genetic Algorithm-Based Maximum Likelihood Parameter Estimation for Transit Buses

2001 ◽  
Author(s):  
Jie Xiao ◽  
Bohdan T. Kulakowski
Keyword(s):  
Parameter Estimation ◽  
Maximum Likelihood ◽  
Dynamic Models ◽  
Estimation Method ◽  
Optimization Techniques ◽  
Model Parameters ◽  
Parameter Estimation Method ◽  
Transit Buses ◽  
Simulation And Control ◽  
And Control

Abstract Vehicle dynamic models include parameters that qualify the dependence of input forces and moments on state and control variables. The accuracy of the model parameter estimates is important for modeling, simulation, and control. In general, the most accurate method for determining values of model parameters is by direct measurement. However, some parameters of vehicle dynamics, such as suspension damping or moments of inertia, are difficult to measure accurately. This study aims at establishing an efficient and accurate parameter estimation method for developing dynamic models for transit buses, such that this method can be easily implemented for simulation and control design purposes. Based on the analysis of robustness, as well as accuracy and efficiency of optimization techniques, a parameter estimation method that integrates Genetic Algorithms and the Maximum Likelihood Estimation is proposed. Choices of output signals and estimation criterion are discussed involving an extensive sensitivity analysis of the predicted output with respect to model parameters. Other experiment-related aspects, such as imperfection of data acquisition, are also considered. Finally, asymptotic Cramer-Rao lower bounds for the covariance of estimated parameters are obtained. Computer simulation results show that the proposed method is superior to gradient-based methods in accuracy, as well as robustness to the initial guesses and measurement uncertainty.

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