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Modeling Error (modeling + error)

Distribution by Scientific Domains

Engineering	90%

Selected Abstracts

Significance of Modeling Error in Structural Parameter Estimation

COMPUTER-AIDED CIVIL AND INFRASTRUCTURE ENGINEERING, Issue 1 2001
Masoud Sanayei
Structural health monitoring systems rely on algorithms to detect potential changes in structural parameters that may be indicative of damage. Parameter-estimation algorithms seek to identify changes in structural parameters by adjusting parameters of an a priori finite-element model of a structure to reconcile its response with a set of measured test data. Modeling error, represented as uncertainty in the parameters of a finite-element model of the structure, curtail capability of parameter estimation to capture the physical behavior of the structure. The performance of four error functions, two stiffness-based and two flexibility-based, is compared in the presence of modeling error in terms of the propagation rate of the modeling error and the quality of the final parameter estimates. Three different types of parameters are used in the parameter estimation procedure: (1) unknown parameters that are to be estimated, (2) known parameters assumed to be accurate, and (3) uncertain parameters that manifest the modeling error and are assumed known and not to be estimated. The significance of modeling error is investigated with respect to excitation and measurement type and locations, the type of error function, location of the uncertain parameter, and the selection of unknown parameters to be estimated. It is illustrated in two examples that the stiffness-based error functions perform significantly better than the corresponding flexibility-based error functions in the presence of modeling error. Additionally, the topology of the structure, excitation and measurement type and locations, and location of the uncertain parameters with respect to the unknown parameters can have a significant impact on the quality of the parameter estimates. Insight into the significance of modeling error and its potential impact on the resulting parameter estimates is presented through analytical and numerical examples using static and modal data. [source]

Uncertainty and Sensitivity Analysis of Damage Identification Results Obtained Using Finite Element Model Updating

COMPUTER-AIDED CIVIL AND INFRASTRUCTURE ENGINEERING, Issue 5 2009
Babak Moaveni
The shake table tests were designed so as to damage the building progressively through several historical seismic motions reproduced on the shake table. A sensitivity-based finite element (FE) model updating method was used to identify damage in the building. The estimation uncertainty in the damage identification results was observed to be significant, which motivated the authors to perform, through numerical simulation, an uncertainty analysis on a set of damage identification results. This study investigates systematically the performance of FE model updating for damage identification. The damaged structure is simulated numerically through a change in stiffness in selected regions of a FE model of the shear wall test structure. The uncertainty of the identified damage (location and extent) due to variability of five input factors is quantified through analysis-of-variance (ANOVA) and meta-modeling. These five input factors are: (1,3) level of uncertainty in the (identified) modal parameters of each of the first three longitudinal modes, (4) spatial density of measurements (number of sensors), and (5) mesh size in the FE model used in the FE model updating procedure (a type of modeling error). A full factorial design of experiments is considered for these five input factors. In addition to ANOVA and meta-modeling, this study investigates the one-at-a-time sensitivity analysis of the identified damage to the level of uncertainty in the identified modal parameters of the first three longitudinal modes. The results of this investigation demonstrate that the level of confidence in the damage identification results obtained through FE model updating, is a function of not only the level of uncertainty in the identified modal parameters, but also choices made in the design of experiments (e.g., spatial density of measurements) and modeling errors (e.g., mesh size). Therefore, the experiments can be designed so that the more influential input factors (to the total uncertainty/variability of the damage identification results) are set at optimum levels so as to yield more accurate damage identification results. [source]

Significance of Modeling Error in Structural Parameter Estimation

A simple LMS-based approach to the structural health monitoring benchmark problem

EARTHQUAKE ENGINEERING AND STRUCTURAL DYNAMICS, Issue 6 2005
J. Geoffrey Chase
Abstract A structure's health or level of damage can be monitored by identifying changes in structural or modal parameters. However, the fundamental modal frequencies can sometimes be less sensitive to (localized) damage in large civil structures, although there are developing algorithms that seek to reduce this difficulty. This research directly identifies changes in structural stiffness due to modeling error or damage using a structural health monitoring method based on adaptive least mean square (LMS) filtering theory. The focus is on computational simplicity to enable real-time implementation. Several adaptive LMS filtering based approaches are used to analyze the data from the IASC,ASCE Structural Health Monitoring Task Group Benchmark problem. Results are compared with those from the task group and other published results. The proposed methods are shown to be very effective, accurately identifying damage to within 1%, with convergence times of 0.4,13.0 s for the twelve different 4 and 12 degree of freedom benchmark problems. The resulting modal parameters match to within 1% those from the benchmark problem definition. Finally, the methods developed require 1.4,14.0 Mcycles of computation and therefore could easily be implemented in real time. Copyright © 2004 John Wiley & Sons, Ltd. [source]

Nonlinear Laguerre,Volterra observer-controller and its application to process control

INTERNATIONAL JOURNAL OF ROBUST AND NONLINEAR CONTROL, Issue 4 2010
Hai-Tao Zhang
Abstract By expanding each kernel using the orthonormal Laguerre series, a Volterra functional series is used to represent the input/output relation of a nonlinear dynamic system. With the feedback of the modeling error, we design a novel nonlinear state observer, based on which an output feedback controller is derived for both the stabilization and tracking problems. The stability of the closed-loop system is analyzed theoretically. The algorithm is effectively applied on the continuous stirring tank reactor and chemical reactor temperature control system. Copyright © 2009 John Wiley & Sons, Ltd. [source]

Model-based synthesis of nonlinear PI and PID controllers

AICHE JOURNAL, Issue 8 2001
Raymond A. Wright
PI and PID controllers continue to be popular methods in industrial applications. It is well known that linear PI and PID controllers result from the application of model-based controller design methods to linear first- and second-order systems. It is shown that nonlinear PI and PID controllers result from the application of nonlinear controller design methods to nonlinear first- and second-order systems. As a result, the controllers resulting from nonlinear model-based control theory are put in a convenient form, more amenable to industrial implementation. Additionally, the quantities used in the controller are useful for monitoring the process and quantifying modeling error. Chemical engineering examples are used to illustrate the resulting control laws. A simulation example further demonstrates the performance of the nonlinear controllers, as well as their useful process monitoring quantities. [source]

Recursive Back-Stepping Design of An Adaptive Fuzzy Controller for Strict Output Feedback Nonlinear Systems

ASIAN JOURNAL OF CONTROL, Issue 3 2002
Wei-Yen Wang
ABSTRACT In this paper, a back-stepping adaptive fuzzy controller is proposed for strict output feedback nonlinear systems. The unknown nonlinearity and external disturbances of such systems are considered. We assume that only the output of the system is available for measurement. As a result, two filters are constructed to estimate the states of strict output feedback systems. Since fuzzy systems can uniformly approximate nonlinear continuous functions to arbitrary accuracy, the adaptive fuzzy control theory combined with a tuning function scheme is developed to derive the control laws of strict output feedback systems that possess unknown functions. Moreover, the H, performance condition is introduced to attenuate the effect of the modeling error and external disturbances. Finally, an example is simulated in order to confirm the applicability of the proposed method. [source]

Uncertainty and Sensitivity Analysis of Damage Identification Results Obtained Using Finite Element Model Updating

Generalized probabilistic approach of uncertainties in computational dynamics using random matrices and polynomial chaos decompositions

INTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN ENGINEERING, Issue 8 2010
Christian Soize
Abstract A new generalized probabilistic approach of uncertainties is proposed for computational model in structural linear dynamics and can be extended without difficulty to computational linear vibroacoustics and to computational non-linear structural dynamics. This method allows the prior probability model of each type of uncertainties (model-parameter uncertainties and modeling errors) to be separately constructed and identified. The modeling errors are not taken into account with the usual output-prediction-error method, but with the nonparametric probabilistic approach of modeling errors recently introduced and based on the use of the random matrix theory. The theory, an identification procedure and a numerical validation are presented. Then a chaos decomposition with random coefficients is proposed to represent the prior probabilistic model of random responses. The random germ is related to the prior probability model of model-parameter uncertainties. The random coefficients are related to the prior probability model of modeling errors and then depends on the random matrices introduced by the nonparametric probabilistic approach of modeling errors. A validation is presented. Finally, a future perspective is introduced when experimental data are available. The prior probability model of the random coefficients can be improved in constructing a posterior probability model using the Bayesian approach. Copyright © 2009 John Wiley & Sons, Ltd. [source]

Robust fault estimation of uncertain systems using an LMI-based approach

INTERNATIONAL JOURNAL OF ROBUST AND NONLINEAR CONTROL, Issue 18 2008
Euripedes G. Nobrega
Abstract General recent techniques in fault detection and isolation (FDI) are based on H, optimization methods to address the issue of robustness in the presence of disturbances, uncertainties and modeling errors. Recently developed linear matrix inequality (LMI) optimization methods are currently used to design controllers and filters, which present several advantages over the Riccati equation-based design methods. This article presents an LMI formulation to design full-order and reduced-order robust H, FDI filters to estimate the faulty input signals in the presence of uncertainty and model errors. Several cases are examined for nominal and uncertain plants, which consider a weight function for the disturbance and a reference model for the faults. The FDI LMI synthesis conditions are obtained based on the bounded real lemma for the nominal case and on a sufficient extension for the uncertain case. The conditions for the existence of a feasible solution form a convex problem for the full-order filter, which may be solved via recently developed LMI optimization techniques. For the reduced-order FDI filter, the inequalities include a non-convex constraint, and an alternating projections method is presented to address this case. The examples presented in this paper compare the simulated results of a structural model for the nominal and uncertain cases and show that a degree of conservatism exists in the robust fault estimation; however, more reliable solutions are achieved than the nominal design. Copyright © 2008 John Wiley & Sons, Ltd. [source]

Constrained PID tracking control for output PDFs of non-gaussian stochastic system based on LMIs,

ASIAN JOURNAL OF CONTROL, Issue 5 2009
Yang Yi
Abstract This paper presents a new PID tracking control strategy for general non-Gaussian stochastic systems based on a square root B-spline model for the output probability density functions (PDFs). Using the B-spline expansion with modeling errors and the nonlinear weight model with exogenous disturbances, the PDF tracking is transformed to a constrained dynamical tracking control problem for weight vectors. Instead of the non-convex design algorithms, the generalized PID controller structure and the improved convex linear matrix inequality (LMI) algorithms are proposed to fulfil the PDF tracking problem. Meanwhile, in order to enhance robustness, the robust peak-to-peak measure is applied to optimize the tracking performance. Copyright © 2009 John Wiley and Sons Asia Pte Ltd and Chinese Automatic Control Society [source]