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.

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.

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.

scholarly journals Efficient gradient-based parameter estimation for dynamic models using qualitative data

2021 ◽  
Author(s):  
Leonard Schmiester ◽  
Daniel Weindl ◽  
Jan Hasenauer
Keyword(s):  
Parameter Estimation ◽  
Qualitative Data ◽  
Dynamic Models ◽  
Unknown Parameters ◽  
Differential Equation Models ◽  
Gradient Calculation ◽  
Order Of Magnitude ◽  
Gradient Based ◽  
Objective Function Values

AbstractMotivationUnknown parameters of dynamical models are commonly estimated from experimental data. However, while various efficient optimization and uncertainty analysis methods have been proposed for quantitative data, methods for qualitative data are rare and suffer from bad scaling and convergence.ResultsHere, we propose an efficient and reliable framework for estimating the parameters of ordinary differential equation models from qualitative data. In this framework, we derive a semi-analytical algorithm for gradient calculation of the optimal scaling method developed for qualitative data. This enables the use of efficient gradient-based optimization algorithms. We demonstrate that the use of gradient information improves performance of optimization and uncertainty quantification on several application examples. On average, we achieve a speedup of more than one order of magnitude compared to gradient-free optimization. Additionally, in some examples, the gradient-based approach yields substantially improved objective function values and quality of the fits. Accordingly, the proposed framework substantially improves the parameterization of models from qualitative data.AvailabilityThe proposed approach is implemented in the open-source Python Parameter EStimation TOolbox (pyPESTO). All application examples and code to reproduce this study are available at https://doi.org/10.5281/zenodo.4507613.

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.

Methods of parallel computing for multilevel fuzzy Takagi – Sugeno systems

2016 ◽  
pp. 141-149
Author(s):  
S.V. Yershov ◽  
◽  
R.М. Ponomarenko ◽  
Keyword(s):  
Dynamic Models ◽  
Fuzzy Inference ◽  
Knowledge Bases ◽  
Comparative Characteristic ◽  
Software Systems ◽  
Scientific Papers ◽  
Speed Up ◽  
Diagnostic Software ◽  
Takagi Sugeno

Parallel tiered and dynamic models of the fuzzy inference in expert-diagnostic software systems are considered, which knowledge bases are based on fuzzy rules. Tiered parallel and dynamic fuzzy inference procedures are developed that allow speed up of computations in the software system for evaluating the quality of scientific papers. Evaluations of the effectiveness of parallel tiered and dynamic schemes of computations are constructed with complex dependency graph between blocks of fuzzy Takagi – Sugeno rules. Comparative characteristic of the efficacy of parallel-stacked and dynamic models is carried out.

scholarly journals Development of new total RNA isolation method for tissues with rich phenolic compounds

2020 ◽  
Vol 45 (4) ◽  
pp. 343-350
Author(s):  
Zafer Seçgin ◽  
Gökhan Gökdemir ◽  
Elif Seda Atabay ◽  
Aslıhan Kurt Kızıldoğan ◽  
Musa Kavas
Keyword(s):  
Phenolic Compounds ◽  
Rna Sequencing ◽  
Rna Isolation ◽  
Wall Structure ◽  
Isolation Method ◽  
High Quality ◽  
Ctab Method ◽  
Total Rna Isolation

AbstractBackgroundRNAs to be used in transcriptome analysis must be of high quality and pure in order to ensure maximum representation of the expressed genes. RNA isolation is difficult in hazelnut tissues containing large amounts of secondary metabolite, phenolic compounds and the cell wall structure. Commonly used protocols for RNA isolation are those that require a lot of labor and time and also do not allow sufficient RNA isolation when applied to tissues rich in phenolic compounds. This study was aimed to develop an efficient method for isolation of total RNAs from bud of hazelnut to be used in RNA sequencing.Materials and methodsAn optimized new method was successfully applied on three different hazelnuts genotypes (Çakıldak, Palaz, Tombul) and about 25 times higher amount of total RNAs per mg fresh tissues were obtained compared to classical CTAB method. Different methods have been tried for the isolation of RNA from hazelnut tissues and the determination of the quality of the obtained RNAs.ResultsThe quality and quantity of isolalated total RNAs were determined by spectrophotometer, electrophoresis and PCR. This success has been caught without any compromise of purity since A260/A280 ratios ranged from 1.90 to 2.04 and A260/A230 ratios were >2.0 in all purified RNAs.ConclusionThe total RNAs isolated with new protocol was found to be suitable for RNA sequencing and other molecular applications.

Error estimation and bias correction in phase-improvement calculations

1999 ◽  
Vol 55 (9) ◽  
pp. 1555-1567 ◽  
Author(s):  
Kevin Cowtan
Keyword(s):  
Error Estimates ◽  
Error Estimation ◽  
Bayesian Methods ◽  
Bias Correction ◽  
Phase Error ◽  
Acta Cryst

With the rise of Bayesian methods in crystallography, the error estimates attached to estimated phases are becoming as important as the phase estimates themselves. Phase improvement by density modification can cause problems in this environment because the quality of the resulting phases is usually overestimated. This problem is addressed by an extension of the γ correction [Abrahams (1997). Acta Cryst. D53, 371–376] to arbitrary density-modification techniques. The degree to which the improved phases are biased by the features of the initial map is investigated in order to determine the limits of the resulting procedure and the quality of the phase-error estimates.

Parameter Estimation in a Nonlinear Vibrating System Using an Observer for an Extended System

1999 ◽  
Author(s):  
Anindya Chatterjee ◽  
Joseph P. Cusumano
Keyword(s):  
Parameter Estimation ◽  
Time Scale ◽  
Asymptotic Methods ◽  
System Response ◽  
Parameter Estimates ◽  
Fast Time ◽  
State Variables ◽  
Slow Time ◽  
Unknown Parameters ◽  
Lipschitz Continuous

Abstract We present a new observer-based method for parameter estimation for nonlinear oscillatory mechanical systems where the unknown parameters appear linearly (they may each be multiplied by bounded and Lipschitz continuous but otherwise arbitrary, possibly nonlinear, functions of the oscillatory state variables and time). The oscillations in the system may be periodic, quasiperiodic or chaotic. The method is also applicable to systems where the parameters appear nonlinearly, provided a good initial estimate of the parameter is available. The observer requires measurements of displacements. It estimates velocities on a fast time scale, and the unknown parameters on a slow time scale. The fast and slow time scales are governed by a single small parameter ϵ. Using asymptotic methods including the method of averaging, it is shown that the observer’s estimates of the unknown parameters converge like e−ϵt where t is time, provided the system response is such that the coefficient-functions of the unknown parameters are not close to being linearly dependent. It is also shown that the method is robust in that small errors in the model cause small errors in the parameter estimates. A numerical example is provided to demonstrate the effectiveness of the method.

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