Parameter Identification for Nonlinear Dynamic Systems Using Optimization Techniques

1991 ◽  
Author(s):  
Yih-Charng Deng ◽  
Robert V. Lust
Keyword(s):  
Nonlinear Systems ◽  
Objective Function ◽  
Test Data ◽  
Simulation Models ◽  
Optimization Techniques ◽  
Test Cases ◽  
Unknown Parameters ◽  
Model Response ◽  
Complex Nonlinear Systems ◽  
Order Polytope

Abstract Models of mechanical systems often contain unknown system parameters which cannot be determined directly from component tests. System identification techniques are methods which determine the unknown parameters based on the overall system behavior under prescribed dynamic loading. In this work a methodology was developed for identifying the unknown parameters in a nonlinear mechanical system model which produces a high degree of correlation between the model response and the test data. This technique uses numerical optimization algorithms to minimize differences between the model response and the test data. Two algorithms are used: the BFGS quasi-Newton method and the zero-th order POLYTOPE method. Several example problems are solved which demonstrate our methodology. Both methods accurately identify the unknown parameters in simple mass-spring-damper systems. For more complex nonlinear systems, such as the occupant simulation models, the gradient-based BFGS method is unable to identify the correct parameters in two test cases. This is due to the fact that the objective function contains many local minima for these systems. The POLYTOPE method gives satisfactory results for identifying complex nonlinear systems in all three test cases investigated in this study. For complex nonlinear systems the form of the objective function can affect the final solution. Best results will be achieved when the objective function is highly sensitive to the changes of the unknown parameters.

scholarly journals Identification study of solar cell/module using recent optimization techniques

2022 ◽  
Vol 12 (2) ◽  
pp. 1189
Author(s):  
Mahmoud Abbas El-Dabah ◽  
Ragab Abdelaziz El-Sehiemy ◽  
Mohamed Ahmed Ebrahim ◽  
Zuhair Alaas ◽  
Mohamed Mostafa Ramadan
Keyword(s):  
Experimental Data ◽  
Solar Cell ◽  
Power Systems ◽  
Objective Function ◽  
Optimization Problems ◽  
Parameter Extraction ◽  
Primary Objective ◽  
Optimization Techniques ◽  
Generic Model ◽  
Unknown Parameters

This paper proposes the application of a novel metaphor-free population optimization based on the mathematics of the Runge Kutta method (RUN) for parameter extraction of a double-diode model of the unknown solar cell and photovoltaic (PV) module parameters. The RUN optimizer is employed to determine the seven unknown parameters of the two-diode model. Fitting the experimental data is the main objective of the extracted unknown parameters to develop a generic PV model. Consequently, the root means squared error (RMSE) between the measured and estimated data is considered as the primary objective function. The suggested objective function achieves the closeness degree between the estimated and experimental data. For getting the generic model, applications of the proposed RUN are carried out on two different commercial PV cells. To assess the proposed algorithm, a comprehensive comparison study is employed and compared with several well-matured optimization algorithms reported in the literature. Numerical simulations prove the high precision and fast response of the proposed RUN algorithm for solving multiple PV models. Added to that, the RUN can be considered as a good alternative optimization method for solving power systems optimization problems.

Grey wolf optimizer algorithm for the performance predetermination of variable speed self-excited induction generators

2021 ◽  
Vol ahead-of-print (ahead-of-print) ◽  
Author(s):  
Essaki Raj R. ◽  
Sundaramoorthy Sridhar
Keyword(s):  
Objective Function ◽  
Core Loss ◽  
Optimization Techniques ◽  
Grey Wolf Optimizer ◽  
Grey Wolf ◽  
Unknown Parameters ◽  
Content Type ◽  
Induction Generators ◽  
Loss Resistance ◽  
The Given

Purpose This paper aims to apply grey wolf optimizer (GWO) algorithm for steady state analysis of self-excited induction generators (SEIGs) supplying isolated loads. Design/methodology/approach Taking the equivalent circuit of SEIG, the impedances representing the stator, rotor and the connected load are reduced to a single loop impedance in terms of the unknown frequency, magnetizing reactance and core loss resistance for the given rotor speed. This loop impedance is taken as the objective function and minimized using GWO to solve for the unknown parameters. By including the value of the desired voltage as a constraint, the formulated objective function is also extended for estimating the required excitation capacitance. Findings The experimental results obtained on a three phase 415 V, 3.5 kW SEIG and the corresponding predetermined performance characteristics agree closely, thereby validating the proposed GWO method. Moreover, a comparative study of GWO with genetic algorithm and particle swarm optimization techniques reveals that GWO exhibits much quicker convergence of the objective function. Originality/value The important contributions of this paper are as follows: for the first time, GWO has been introduced for the SEIG performance predetermination and computation of the excitation capacitance for attaining the desired terminal voltage for the given load and speed; the predicted performance accuracy is improved by considering the variable core loss of the SEIG; and GWO does not require derivations of lengthy equations for calculating the SEIG performance.

scholarly journals Searching for Analytical Solutions of the (2+1)-Dimensional KP Equation by Two Different Systematic Methods

Complexity ◽  
2019 ◽  
Vol 2019 ◽  
pp. 1-11 ◽  
Author(s):  
Yongyi Gu ◽  
Fanning Meng
Keyword(s):  
Nonlinear Systems ◽  
Exact Solutions ◽  
Rational Function ◽  
Analytical Solutions ◽  
Direct Methods ◽  
Expansion Method ◽  
Complex Method ◽  
Kp Equation ◽  
Extended Complex ◽  
Complex Nonlinear Systems

In this paper, we derive analytical solutions of the (2+1)-dimensional Kadomtsev-Petviashvili (KP) equation by two different systematic methods. Using the exp⁡(-ψ(z))-expansion method, exact solutions of the mentioned equation including hyperbolic, exponential, trigonometric, and rational function solutions have been obtained. Based on the work of Yuan et al., we proposed the extended complex method to seek exact solutions of the (2+1)-dimensional KP equation. The results demonstrate that the applied methods are efficient and direct methods to solve the complex nonlinear systems.

scholarly journals Online Health Management for Complex Nonlinear Systems Based on Hidden Semi-Markov Model Using Sequential Monte Carlo Methods

2012 ◽  
Vol 2012 ◽  
pp. 1-22
Author(s):  
Qinming Liu ◽  
Ming Dong
Keyword(s):  
Monte Carlo ◽  
Nonlinear System ◽  
Nonlinear Systems ◽  
Markov Model ◽  
Sequential Monte Carlo ◽  
Health Management ◽  
Health State ◽  
Health States ◽  
Complex Nonlinear System ◽  
Complex Nonlinear Systems

Health management for a complex nonlinear system is becoming more important for condition-based maintenance and minimizing the related risks and costs over its entire life. However, a complex nonlinear system often operates under dynamically operational and environmental conditions, and it subjects to high levels of uncertainty and unpredictability so that effective methods for online health management are still few now. This paper combines hidden semi-Markov model (HSMM) with sequential Monte Carlo (SMC) methods. HSMM is used to obtain the transition probabilities among health states and health state durations of a complex nonlinear system, while the SMC method is adopted to decrease the computational and space complexity, and describe the probability relationships between multiple health states and monitored observations of a complex nonlinear system. This paper proposes a novel method of multisteps ahead health recognition based on joint probability distribution for health management of a complex nonlinear system. Moreover, a new online health prognostic method is developed. A real case study is used to demonstrate the implementation and potential applications of the proposed methods for online health management of complex nonlinear systems.

scholarly journals Exponential Estimates of a Class of Time–Delay Nonlinear Systems with Convex Representations

2015 ◽  
Vol 25 (4) ◽  
pp. 815-826 ◽  
Author(s):  
Máximo Ramírez ◽  
Raúl Villafuerte ◽  
Temoatzin González ◽  
Miguel Bernal
Keyword(s):  
Nonlinear Systems ◽  
Mimo System ◽  
Sufficient Conditions ◽  
Optimization Techniques ◽  
Linear Matrix ◽  
Exponential Estimates ◽  
Novel Approach ◽  
Guaranteed Cost ◽  
Stability And Stabilization ◽  
Twin Rotor Mimo System

Abstract This work introduces a novel approach to stability and stabilization of nonlinear systems with delayed multivariable inputs; it provides exponential estimates as well as a guaranteed cost of the system solutions. The result is based on an exact convex representation of the nonlinear system which allows a Lyapunov–Krasovskii functional to be applied in order to obtain sufficient conditions in the form of linear matrix inequalities. These are efficiently solved via convex optimization techniques. A real-time implementation of the developed approach on the twin rotor MIMO system is included.

A novel approach to increase the share of renewable purchase obligation for planning of distribution network including grid scale energy storage

2021 ◽  
Vol 0 (0) ◽  
Author(s):  
Jitendra Singh Bhadoriya ◽  
Atma Ram Gupta
Keyword(s):  
Energy Storage ◽  
Objective Function ◽  
Distributed Generation ◽  
Carbon Emissions ◽  
Distribution Network ◽  
Clean Energy ◽  
Distribution Networks ◽  
Optimization Techniques ◽  
Novel Approach ◽  
Demand Models

Abstract In recent times, producing electricity with lower carbon emissions has resulted in strong clean energy incorporation into the distribution network. The technical development of weather-driven renewable distributed generation units, the global approach to reducing pollution emissions, and the potential for independent power producers to engage in distribution network planning (DNP) based on the participation in the increasing share of renewable purchasing obligation (RPO) are some of the essential reasons for including renewable-based distributed generation (RBDG) as an expansion investment. The Grid-Scale Energy Storage System (GSESS) is proposed as a promising solution in the literature to boost the energy storage accompanied by RBDG and also to increase power generation. In this respect, the technological, economic, and environmental evaluation of the expansion of RBDG concerning the RPO is formulated in the objective function. Therefore, a novel approach to modeling the composite DNP problem in the regulated power system is proposed in this paper. The goal is to increase the allocation of PVDG, WTDG, and GSESS in DNP to improve the quicker retirement of the fossil fuel-based power plant to increase total profits for the distribution network operator (DNO), and improve the voltage deviation, reduce carbon emissions over a defined planning period. The increment in RPO and decrement in the power purchase agreement will help DNO to fulfill round-the-clock supply for all classes of consumers. A recently developed new metaheuristic transient search optimization (TSO) based on electrical storage elements’ stimulation behavior is implemented to find the optimal solution for multi-objective function. The balance between the exploration and exploitation capability makes the TSO suitable for the proposed power flow problem with PVDG, WTDG, and GSESS. For this research, the IEEE-33 and IEEE-69 low and medium bus distribution networks are considered under a defined load growth for planning duration with the distinct load demand models’ aggregation. The findings of the results after comparing with well-known optimization techniques DE and PSO confirm the feasibility of the method suggested.

scholarly journals Evolutionary Algorithms for Constrained Parameter Optimization Problems

1996 ◽  
Vol 4 (1) ◽  
pp. 1-32 ◽  
Author(s):  
Zbigniew Michalewicz ◽  
Marc Schoenauer
Keyword(s):  
Nonlinear Programming ◽  
Evolutionary Algorithms ◽  
Evolutionary Computation ◽  
Numerical Optimization ◽  
Optimization Problems ◽  
Optimization Techniques ◽  
Test Cases ◽  
Nonlinear Constraints ◽  
Nonlinear Programming Problem ◽  
General Nonlinear Programming

Evolutionary computation techniques have received a great deal of attention regarding their potential as optimization techniques for complex numerical functions. However, they have not produced a significant breakthrough in the area of nonlinear programming due to the fact that they have not addressed the issue of constraints in a systematic way. Only recently have several methods been proposed for handling nonlinear constraints by evolutionary algorithms for numerical optimization problems; however, these methods have several drawbacks, and the experimental results on many test cases have been disappointing. In this paper we (1) discuss difficulties connected with solving the general nonlinear programming problem; (2) survey several approaches that have emerged in the evolutionary computation community; and (3) provide a set of 11 interesting test cases that may serve as a handy reference for future methods.

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