Being nowadays possible to develop alternative approaches,such as inverse methodologies, in solving complex problems. In the presentpaper, two types of inverse approaches will be discussed, namely the parameteridentification and optimization problems. A method for load parameter identification and optimization basedon integral calculation is presented. Mathematicalanalyses of using integral equations are presented for parameter identificationand optimization. The aim of the former is to evaluate the input parameters for materialconstitutive models that would lead to the most accurate set of resultsrespecting physical experiments. The second category involves determining theinitial foundation of a given specimen leading to a desired final result afterthe forming process. The purpose of the present work is then to formulate theseinverse problems as optimization problems, introducing a straightforwardmethodology of process optimization in engineering applications such as metalforming and structural analysis. To reach this goal, an integrated optimizationapproach, using a finite element code together with a numerical optimizationprogram, was employed.

Consideringthe practice of Civil Structure under earthquake loading using parameter identification.Thecivil engineering practice needs correct information about actual condition ofbuilding structures after earthquake. The objective is to find and analyze thedamaged parts of the structure. If the records of the earthquake excitation andresponse of the building structure are available, the numerical model of thestructure can be created. The modal analysis of inelastic structures is appliedfor detecting structural failures in buildings during earthquake. To define thereal condition of the structure the parameter identification of the numericalmodel is applied. The modal decomposition of the dynamic response is applied.The reason is that mode shapes describe the expected dynamic displacements ofthe structure. This is the advantage of modal decomposition compared withFourier decomposition based on the harmonic functions. The modal analysis isderived from elastic behavior. The mathematical advantage is in uncoupling ofequations of motion into independent equation for each degree of freedom.Displacements of a nonlinear system can be mathematically expressed also as acombination of the natural modes of the undamped system vibrating within therange of its linear behavior. Equations in this case are not more uncoupled.Civil structures under earthquake loading after yielding are composed of linearsubsystems connected through nonlinear elements.

This paper provides an overview of the generalprocedure and concepts related to identification of parameters or optimizationby using integral equation method. A discussion of errors and their implicationfor an appropriate function for minimization in inverse procedures ispresented, and two methods for achieving this minimization are discussed. Somesequential concepts for parameter identification and optimization arepresented, along with a discussion of residuals and confidence intervals.Experiment design and optimization are reviewed, and a discussion of residualsand their relation to model building is presented. Load parameter identification using a gradient‐based numerical optimization procedure is assessed withrespect to stability by using pseudo‐experimentalindentation curves, obtained from modelling with known material parameters, andsuperposed with artificial noise. The effect of the load history on parameteridentification is investigated.

In the existing on-line measurement methods such as incrementalmethod, differential equation method and integral equation method, parametersare all worked out by solving the over-determined equations acquired indifferent tests.

The complex, nonlinearand stochastic characteristics of load increase the difficulty of modelling. Inthis paper, a new approach of ambient signal based load model parameteridentification method is proposed to solve this problem. With the proposedmethod, load model parameter can be identified in any time regardless of theexistence of fault.

2. 研究的基本内容与方案

1. Introduction

As we known,load model is an important part of power system simulation. While it has alsobeen recognized that the proper parameters for the load model is significant torepresent a load accurately. Parameter identification is the essence of anumerical optimization process, namely seeking a set of parameters that makethe error between the estimated value and actual value as small as possible byusing the appropriate optimization algorithm under the condition of certainconstraints. Recently years, some parameter identification strategies have beenproposed to the parameter identification. At present, the modern optimizationalgorithm is the more effective algorithm in the aspect of comprehensive loadparameter identification. Modern optimization method belongs to the stochasticglobal optimization algorithm in mechanism, it is basically no initial valuerequirement, which is expected to obtain better recognition results than traditionaloptimization algorithm.

Numericalsimulations in demanding applications such as metal forming processes areusually carried out within a direct engineering procedure, that is, given theinput data available, to try to simulate the overall adopted process towardsthe achievement of a final part. Being a well-established procedure, with rootsback to the 70’s, the finite element method (FEM) is the procedure of choice onthe overall majority of metal forming numerical simulations, mainly whenrelated to sheet metal forming products. Within this dominant approach, anddealing with the need to obtain new products, designers are still faced with akind of “trial-and-error” approach, in the sense that generally several runsare needed to achieve the desired component, free from defects such aswrinkling, splitting or springback, to name the most common of them. In thissense, it can be said that the majority of FEM applications are still groundedon a deep knowledge of the process to be simulated, along with a comprehensiveinput data base including tools geometry, constitutive material laws orparameters, loading cases, friction laws, etc. Proceeding in this way, thenumerical simulation process can then be defined as a direct problem (Ponthotand Kleinermann 2006). Focusing on sheet metal forming applications of the FEM,for instance, mostly the problems that are posed on the development of a newcomponent are the determination of the proper shape of the initial metallicsheet, the proper geometrical (and number) of forming tools and, in some cases,the decision about the need (or not) of including multiple stage formingoperations and, if so, proper number of such operations (Marciniak et al. 2002;Wagoner and Chenot 2001; Tang and Pan 2007). Within this context, the presentwork attempts to provide a reliable and straightforward methodology on thegeometrical/shape optimization for tools and initial blank involved in metalforming applications. The same methodology can also be used in general structuralproblems, as will be shown. Focusing on sheet metal forming applications,however, and respective to the geometrical optimization of tools and initialblank shape, eventually (and mostly grounded on the background experience), itis possible to infer about the sensitivity of the initial design to some chosenparameters by, for instance, varying some of them and rerunning thesimulations. It is clear, however, that such a procedure can be very timeconsuming and, in complex stamped products, provides a reduced efficiency.Eventually, this kind of trial-and-error numerical procedure can lead to abetter understood of the influence of the selected design parameters.Nevertheless, the number of parameters involved, along with their variationwindow, must remain necessarily small (Ponthot and Kleinermann 2006; Jansson2005).

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