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.

scholarly journals Suitability of Several Statistical Models to Simulate Observed Distribution of Sample Test Results in Inspections of Aflatoxin-Contaminated Peanut Lots

1996 ◽  
Vol 79 (4) ◽  
pp. 981-988 ◽  
Author(s):  
Thomas Whitaker ◽  
Francis Giesbrecht ◽  
Jeremy Wu
Keyword(s):  
Parameter Estimation ◽  
Negative Binomial Distribution ◽  
Binomial Distribution ◽  
Statistical Models ◽  
Negative Binomial ◽  
Estimation Method ◽  
Likelihood Method ◽  
Model Parameters ◽  
Test Results ◽  
Parameter Estimation Method

Abstract The acceptability of 10 theoretical distributions to simulate observed distribution of sample aflatoxin test results was evaluated by using 2 parameter estimation methods and 3 goodness of fit (GOF) tests. All theoretical distributions were compared with 120 observed distributions of aflatoxin test results of farmers' stock peanuts. For a given parameter estimation method and GOF test, the negative binomial distribution had the highest percentage of statistically acceptable fits. The log normal and Poisson-gamma (gamma shape parameter = 0.5) distributions had slightly fewer but an almost equal percentage of acceptable fits. For the 3 most acceptable statistical models, the negative binomial had the greatest percentage of best or closest fits. Both the parameter estimation method and the GOF test had an influence on which theoretical distribution had the largest number of acceptable fits. All theoretical distributions, except the negative binomial distribution, had more acceptable fits when model parameters were determined by the maximum likelihood method. The negative binomial had slightly more acceptable fits when model parameters were estimated by the method of moments. The results also demonstrated the importance of using the same GOF test for comparing the acceptability of several theoretical distributions.

Hybrid Genetic Algorithm: A Robust Parameter Estimation Technique and Its Application to Heavy Duty Vehicles

2003 ◽  
Author(s):  
Jie Xiao ◽  
Bohdan Kulakowski
Keyword(s):  
Parameter Estimation ◽  
Maximum Likelihood ◽  
Maximum Likelihood Estimation ◽  
Hybrid Genetic Algorithm ◽  
Estimation Method ◽  
Likelihood Estimation ◽  
Optimization Techniques ◽  
Estimation Technique ◽  
Estimation Strategy ◽  
Analysis Experiment

This study aims at establishing an accurate yet efficient parameter estimation strategy for developing dynamic vehicle models that can be easily implemented for simulation and controller design purposes. Generally, conventional techniques such as Least Square Estimation (LSE), Maximum Likelihood Estimation (MLE), and Instrumental Variable Methods (IVM), can deliver sufficient estimation results for given models that are linear-in-the-parameter. However, many identification problems in the engineering world are very complex in nature and are quite difficult to solve by those techniques. For the nonlinear-in-the-parameter models, it is almost impossible to find an analytical solution. As a result, numerical algorithms have to be used in calculating the estimates. In the area of model parameter estimation for motor vehicles, most studies performed so far have been limited either to the linear-in-the-parameter models, or in their ability to handle multi-modal error surfaces. For models with nondifferentiable cost functions, the conventional methods will not be able to locate the optimal estimates of the unknown parameters. This concern naturally leads to the exploration of other search techniques. In particular, Genetic Algorithms (GAs), as population-based global optimization techniques that emulate natural genetic operators, have been introduced into the field of parameter estimation. In this paper, hybrid parameter estimation technique is developed to improve computational efficiency and accuracy of pure GA-based estimation. The proposed strategy integrates a GA and the Maximum Likelihood Estimation. Choices of input signals and estimation criterion are discussed involving an extensive sensitivity analysis. Experiment-related aspects, such as imperfection of data acquisition, are also considered. Computer simulation results reveal that the hybrid parameter estimation method proposed in this study shows great potential to outperform conventional techniques and pure GAs in accuracy, efficiency, as well as robustness with respect to the initial guesses and measurement uncertainty. Primary experimental validation is also implemented including interpretation and processing of field test data, as well as analysis of errors associated with aspects of experiment design. To provide more guidelines for implementing the hybrid GA approach, some practical guidelines on application of the proposed parameter estimation strategy are discussed.

scholarly journals Parameter Estimation for Composite Dynamical Systems Based on Sequential Order Statistics from Burr Type XII Mixture Distribution

Mathematics ◽  
2021 ◽  
Vol 9 (8) ◽  
pp. 810
Author(s):  
Tzong-Ru Tsai ◽  
Yuhlong Lio ◽  
Hua Xin ◽  
Hoang Pham
Keyword(s):  
Monte Carlo ◽  
Parameter Estimation ◽  
Maximum Likelihood ◽  
Maximum Likelihood Estimation ◽  
Survival Function ◽  
Estimation Method ◽  
Mixture Distribution ◽  
Likelihood Estimation ◽  
Model Parameters ◽  
Burr Type Xii

Considering the impact of the heterogeneous conditions of the mixture baseline distribution on the parameter estimation of a composite dynamical system (CDS), we propose an approach to infer the model parameters and baseline survival function of CDS using the maximum likelihood estimation and Bayesian estimation methods. The power-trend hazard rate function and Burr type XII mixture distribution as the baseline distribution are used to characterize the changes of the residual lifetime distribution of surviving components. The Markov chain Monte Carlo approach via using a new Metropolis–Hastings within the Gibbs sampling algorithm is proposed to overcome the computation complexity when obtaining the Bayes estimates of model parameters. A numerical example is generated from the proposed CDS to analyze the proposed procedure. Monte Carlo simulations are conducted to investigate the performance of the proposed methods, and results show that the proposed Bayesian estimation method outperforms the maximum likelihood estimation method to obtain reliable estimates of the model parameters and baseline survival function in terms of the bias and mean square error.

scholarly journals Selection of Efficient Parameter Estimation Method for Two-Parameter Weibull Distribution

2021 ◽  
Vol 2021 ◽  
pp. 1-8
Author(s):  
Mohammed M. A. Almazah ◽  
Muhammad Ismail
Keyword(s):  
Parameter Estimation ◽  
Maximum Likelihood ◽  
Weibull Distribution ◽  
Mean Square Error ◽  
Estimation Method ◽  
Likelihood Method ◽  
Estimation Methods ◽  
Model Parameters ◽  
Mean Square ◽  
Two Parameter

Several studies have considered various scheduling methods and reliability functions to determine the optimum maintenance time. These methods and functions correspond to the lowest cost by using the maximum likelihood estimator to evaluate the model parameters. However, this paper aims to estimate the parameters of the two-parameter Weibull distribution (α, β). The maximum likelihood estimation method, modified linear exponential loss function, and Wyatt-based regression method are used for the estimation of the parameters. Minimum mean square error (MSE) criterion is used to evaluate the relative efficiency of the estimators. The comparison of the different parameter estimation methods is conducted, and the efficiency of these methods is observed, both mathematically and experimentally. The simulation study is conducted for comparison of samples sizes (10, 50, 100, 150) based on the mean square error (MSE). It is concluded that the maximum likelihood method was found to be the most efficient method for all sample sizes used in the research because it achieved the least MSE compared with other methods.

scholarly journals Modeling and Fault Diagnosis of Interturn Short Circuit for Five-Phase Permanent Magnet Synchronous Motor

2015 ◽  
Vol 2015 ◽  
pp. 1-9 ◽  
Author(s):  
Jian-wei Yang ◽  
Man-feng Dou ◽  
Zhi-yong Dai
Keyword(s):  
Parameter Estimation ◽  
Fault Diagnosis ◽  
Permanent Magnet ◽  
Fault Tolerant ◽  
Short Circuit ◽  
Estimation Method ◽  
Trust Region ◽  
Fault Tolerant Control ◽  
Trust Region Algorithm ◽  
Parameter Estimation Method

Taking advantage of the high reliability, multiphase permanent magnet synchronous motors (PMSMs), such as five-phase PMSM and six-phase PMSM, are widely used in fault-tolerant control applications. And one of the important fault-tolerant control problems is fault diagnosis. In most existing literatures, the fault diagnosis problem focuses on the three-phase PMSM. In this paper, compared to the most existing fault diagnosis approaches, a fault diagnosis method for Interturn short circuit (ITSC) fault of five-phase PMSM based on the trust region algorithm is presented. This paper has two contributions. (1) Analyzing the physical parameters of the motor, such as resistances and inductances, a novel mathematic model for ITSC fault of five-phase PMSM is established. (2) Introducing an object function related to the Interturn short circuit ratio, the fault parameters identification problem is reformulated as the extreme seeking problem. A trust region algorithm based parameter estimation method is proposed for tracking the actual Interturn short circuit ratio. The simulation and experimental results have validated the effectiveness of the proposed parameter estimation method.

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