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Sensitivity-Based Finite Element Model Updating Methods with Application to Electronic Equipments

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Sensitivity-Based Finite Element Model Updating Methods with Application to Electronic Equipments FACULTE POLYTECHNIQUE DE MONS SENSITIVITY-BASED FINITE ELEMENT MODEL UPDATING METHODS WITH APPLICATION TO ELECTRONIC EQUIPMENTS Dissertation submitted to the Faculte´ Polytechnique de Mons, Belgium in Partial Fulfillment of the Requirements for the Degree of Doctor in Applied Sciences by Yun-Xin WU Accepted by the jury committee the 12th of July 1999 Jury Committee: Prof. D. LAMBLIN, President of the committee Prof. Y. BAUDOIN, Royal Military School, Brussels Ir. E. FILIPPI, Alcatel-ETCA Prof. S. BOUCHER, Rector Prof. C. CONTI, Dean, Thesis advisor Dr. P. DEHOMBREUX, Co-advisor Abstract When electronic devices are introduced into astronautic structures such as rockets or satellites, the reliability becomes extremely important. Their vibration behaviour should be thoroughly investigated. Finite element analysis is the most powerful tool to predict the behaviour of the structure in the design process. Because of their complexity, the initial finite element models must be validated with experimental data. This dissertation investigates some important aspects of sensitivity-based finite element model updating procedures, and applies them to electronic structures. The existing updating methods are shortly reviewed. The numerical correlation tech- niques, MAC, COMAC, FRAC, FDAC, are first summarised. The mode shape smoothing technique is extended to FRF smoothing. Sensitivity-based finite element model updating equations are expressed in a generic form that is suitable for both modal and impedance updating methods. A new modal updating method, namely quasi-modeshape (QMS) updating approach, is proposed. In the proposed method, the SVD technique is employed to transform the FBM residual force vectors into quasi-modeshapes. Simulation results obtained for a wide range of structures showed that when noise is present, QMS method can produce much better results. A TLS/QR-F model error localization method is proposed. Four steps are included in this method, which are (1) regularising the updating equations in Total-Least-Square sense with SVD technique; (2) performing a QR F forward subset selection where the pivoting i criterion is a cos2 θ property; (3) backward excluding parameters based on their residue de- scending ratios computed via QR decomposition; (4) excluding parameters based on the subset solution. To evaluate the proposed method, a success ratio of parameter error local- ization is also proposed. This success ratio is designed to have the capability of assessing the error localization methods with statistic sense. Numerous simulations showed the advantage of the proposed TLS/QR-F method. Perturbed Boundary Condition test technique can enrich experimental data with few extra effort. In this thesis, PBC model updating is implemented for both modal and impedance methods. The simulations showed that, besides other advantages, PBC technique can also help TLS/QR-F method to augment its error localization success ratio. The proposed techniques are applied to validate finite element models of electronic structures, including a PCB with components, “wedge-lock” slides and a shell box. Practical considerations, such as equivalent thickness of SMT components, Bayesian estimation, are also addressed. ii ACKNOWLEDGMENTS First and foremost I would like to thank my advisor, Prof. C. Conti, for his continuous encouragement, stimulus and guidance throughout the preparation of my dissertation. I would like also take this opportunity to thank Dr. P. Dehombreux, for his assistance during experimental work, and especially for his meticulous reading of the thesis draft and many recomposing suggestions. I wish to express my gratitude to Mr. H. Algrain, for his patience to verify simulation results. Thanks also to Dr. O. Verlinden, Dr. S. Datoussaid, Mr. R. Hadjit, Mr. M. Fontaine, Mr. J-P Devos. They have given me many helps during my study in FPMs. Special thanks are due to my wife and my daughter. Without their emotional support I would not have had the courage to complete this thesis. My study in FPMs was made possible by a cooperation project between la Facult´e Polytechnique de Mons and Central South University of Technology, for which I am very grateful. iii iv Contents ACKNOWLEDGMENTS iii Nomenclature xi 1 Introduction 1 1.1Overview................................... 1 1.2 Review on Electronic Equipment Modelling . ................ 3 1.3ReviewonFiniteElementModelUpdating................. 7 1.3.1 The origin and the philosophy of finite element model updating . 7 1.3.2 Uniqueness aspects of finite element model updating . ..... 8 1.3.3 Matchbetweentestandanalyticalmodels.............. 9 1.3.4 Correlation between measured data and analytical predictions . 10 1.3.5 Modeltuning............................. 11 Global methods . ....................... 12 Local methods . ....................... 12 Error localization and parameter subset selection . ......... 14 1.4 Outline of the text . .............................. 15 1.5 Research contributions and originalities . ................ 17 2 Correlation and model match 19 2.1 Correlation techniques . ....................... 19 2.1.1 Visual comparisons . ....................... 20 2.1.2 Numericalcomparison........................ 21 ModalAssuranceCriterion...................... 21 CoordinateModalAssuranceCriterion............... 22 FRACandFDAC........................... 23 2.1.3 Other comparisons . ....................... 24 2.1.4 Remarks............................... 25 2.2Modelmatchtechniques........................... 26 2.2.1 System-matrix-basedreduction/expansion.............. 27 Guyanstaticreduction/expansion[23]................ 28 Kidder dynamic reduction/expansion ................ 29 2.2.2 Modeshape-basedexpansionprocedures............... 32 v EigenvectorMixingMethod..................... 32 MACexpansion........................... 33 ModalCoordinateMethod...................... 33 System Equivalent Reduction Expansion Process (SEREP) . 34 2.2.3 FRFsmoothing............................ 36 2.2.4 Remarks............................... 37 3 Sensitivity-Based FE Model Updating Equations 39 3.1 Introduction . ................................. 39 3.2 Eigenvalue-based updating equations . ............... 41 3.3 Modal updating equations . ...................... 46 3.3.1 FBM updating equations . ...................... 46 3.3.2 Quasi-modeshape (QMS) updating equations . ........ 47 3.4 Impedance updating equations . ...................... 50 3.5Summary................................... 53 4 SVD, regularization, weighting, constraints and iterations 55 4.1 Introduction . ................................. 55 4.2 SVD, rank-deficiency and matrix condition number . ........ 57 4.3 Least-squares estimation . ...................... 59 4.4 Chi-squares estimation [58] . ...................... 63 4.5 Total Least-squares estimation . ...................... 65 4.6Bayesianestimationtechnique........................ 69 4.7 Weighting updating equations . ...................... 70 4.8Quadraticprogramming(QP)approach................... 72 4.9 Iterative model updating . ...................... 73 4.10Summary................................... 74 5 Error localization 77 5.1 Introduction . ................................. 77 5.2Errorlocalizationprinciples......................... 78 5.2.1 Global error localization . ...................... 78 FBM error localization . ...................... 78 EMM error localization . ...................... 81 5.2.2 Local error localization methods . ............... 86 Introduction . ............................. 86 QR basic solution for rank-deficient updating equations . 87 SVD/QR subset selection . ...................... 92 5.2.3 TLS-based error localization technique ............... 94 TLS-based regularising and condensing ............... 95 QR F forward subset selection . ............... 99 Backward excluding updating parameters . ........ 103 Parameter exclusion based on the subset solution . ........ 107 vi 5.3 Approach of evaluating the efficiency of error localization methods ..... 108 5.3.1 Success ratio of parameter error localization . ......... 108 5.3.2 Measurement noise influence on error localization ......... 110 5.3.3 Simulatednoisepatternincasestudies................ 111 5.3.4 POMUS and success ratio computation . ......... 113 5.4Casestudies.................................. 117 5.4.1 Case Study 1: A Cantilever beam . ................ 117 Using resonance-frequency-based updating equations . ..... 117 Using modeshape-based updating equations . ......... 122 Using FRF-based updating equations ................ 126 5.4.2 Case study 2: A 10-DOF stiffness-mass system . ......... 128 Using modeshape-based updating equations . ......... 129 Using FRF-based updating equations ................ 132 5.4.3 Casestudy3:Threedimensionbaystructure............ 134 Using modeshape-based updating equations . ......... 135 Using FRF-based updating equations ................ 137 5.4.4 Case study 4: A plate structure with components . ......... 141 Using modeshape-based updating equations . ......... 142 Using FRF-based updating equations ................ 145 5.5Summary................................... 149 6 Perturbed Boundary Condition Model Updating 153 6.1 Introduction . .............................. 153 6.2 PBC Testing and Total Message Amount . ................ 154 6.3PBCModelUpdating............................. 156 6.4Examples................................... 159 6.4.1 ExampleI............................... 159 6.4.2 ExampleII.............................. 161 6.5Summary..................................
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