Sparse Sum-of-Squares Optimization for Model Updating Through Minimization of Modal Dynamic Residuals

2019 ◽  
Vol 2 (1) ◽  
Author(s):  
Dan Li ◽  
Yang Wang
Keyword(s):  
Optimization Problem ◽  
Model Updating ◽  
Polynomial Optimization ◽  
Element Model ◽  
Optimization Method ◽  
Sum Of Squares ◽  
Global Optimality ◽  
Polynomial Optimization Problem ◽  
Computation Efficiency ◽  
Dynamic Residuals

This research investigates the application of sum-of-squares (SOS) optimization method on finite element model updating through minimization of modal dynamic residuals. The modal dynamic residual formulation usually leads to a nonconvex polynomial optimization problem, the global optimality of which cannot be guaranteed by most off-the-shelf optimization solvers. The SOS optimization method can recast a nonconvex polynomial optimization problem into a convex semidefinite programming (SDP) problem. However, the size of the SDP problem can grow very large, sometimes with hundreds of thousands of variables. To improve the computation efficiency, this study exploits the sparsity in SOS optimization to significantly reduce the size of the SDP problem. A numerical example is provided to validate the proposed method.

Frequency-based dynamic topology optimization methodology for improved door closing sound quality

2019 ◽  
Vol 234 (7) ◽  
pp. 1311-1322 ◽  
Author(s):  
Gozde Tuncer ◽  
Polat Sendur
Keyword(s):  
Topology Optimization ◽  
Element Model ◽  
Optimization Method ◽  
Sound Quality ◽  
Sum Of Squares ◽  
Design Parameters ◽  
Design Constraint ◽  
Front Door ◽  
Optimization Methodology ◽  
Material Layout

Door closing sound quality of a vehicle has become one of the most important customer-related quality metrics in the recent years. There has been a vast amount of information on the design parameters contributing to this attribute in the literature. Amongst them, damping pad on the door outer panel emerges as one of the most significant factors on the door closing sound quality. In this paper, we apply solid isotropic material with penalization topology optimization method to determine the optimum material layout for within a given volume constraint on a front door of a typical vehicle. The objective function of the topology optimization is chosen as the minimization of residual sum of squares of the accelerance of the door outer panel up to 200 Hz. The optimization problem is subject to design constraint to use a predetermined percentage of the full damping pad. The methodology is demonstrated on the finite element model of front door of a Toyota vehicle. Two optimization case studies using 60% and 45% of the damping pad on the door outer panel are introduced as a result of the application of the proposed topology optimization methodology. In addition, more manufacturable optimization configurations with the same % of the damping pad are suggested as a means for more feasible application by automotive original equipment manufacturers. All the optimization configurations are compared to each other on (i) accelerance spectrum up to 200 Hz, (ii) residual sum of squares of the accelerance, and (iii) weight of the damping pad. The results show that it is possible to improve the aforementioned metrics significantly by the application of topology optimization.

scholarly journals A Shifted Power Method for Homogenous Polynomial Optimization over Unit Spheres

2015 ◽  
Vol 7 (2) ◽  
pp. 175 ◽  
Author(s):  
Shuquan Wang
Keyword(s):  
Global Convergence ◽  
Optimization Problem ◽  
Polynomial Optimization ◽  
Power Method ◽  
Polynomial Optimization Problem

In this paper, we propose a shifted power method for a type of polynomial optimization problem over unit spheres. The global convergence of the proposed method is established and an easily implemented scope of the shifted parameter is provided.

Finite Element Model Updating for Unsymmetrical Damping System with Genetic Algorithm

2012 ◽  
Vol 166-169 ◽  
pp. 2999-3003 ◽  
Author(s):  
Bao Qiang Zhang ◽  
Guo Ping Chen ◽  
Qin Tao Guo
Keyword(s):  
Genetic Algorithm ◽  
Finite Element ◽  
Finite Element Model ◽  
Model Updating ◽  
Element Model ◽  
Maximum Error ◽  
Optimization Method ◽  
Finite Element Model Updating ◽  
Modal Data ◽  
Complex Modal

Finite element model updating using incomplete complex modal data for unsymmetrical damping system with genetic algorithm is presented. The genetic algorithm method and finite element model updating based on optimization method using complex modal eigenvalue are introduced. The updating for simulation example about a flexible rotor system which is a typical unsymmetrical damping system is performed using bearing stiffness, bearing damping and diameter moment of inertia parameters. The results show that the maximum error of updated parameters is 0.15% and the objective function of genetic algorithm is 0.0081. The study demonstrates that the finite element model updating method using incomplete complex modal data with genetic algorithm is feasible and effective for unsymmetrical damping system.

A Multi-Scale Wavelet Finite Element Model for Damage Detection of Beams Under a Moving Load

2018 ◽  
Vol 18 (06) ◽  
pp. 1850078 ◽  
Author(s):  
Wen-Yu He ◽  
Songye Zhu ◽  
Zhi-Wei Chen
Keyword(s):  
Finite Element ◽  
Finite Element Model ◽  
Dynamic Analysis ◽  
Damage Detection ◽  
Model Updating ◽  
Moving Load ◽  
Element Model ◽  
Multi Scale ◽  
Computation Efficiency ◽  
Wavelet Finite Element

The resolution of structural finite element model (FEM) determines the computation cost and accuracy in dynamic analysis. This study proposes a novel wavelet finite element model (WFEM), which facilitates adaptive mesh refinement, for the dynamic analysis and damage detection of beam structures subjected to a moving load (ML). The multi-scale equations of motion for the beam under the ML are derived using the second-generation cubic Hermite multi-wavelets as the shape functions. Then an adaptive-scale analysis strategy is established, in which the scales of the wavelet beam elements are dynamically changed according to the ML position. The performance of the multi-scale WFEM is examined in both dynamic analysis and damage detection problems. It is demonstrated that the multi-scale WFEM with a similar number of degrees of freedom can achieve much higher accuracy than the traditional FEM. In particular, the multi-scale WFEM enables the detection of sub-element damage with a progressive model updating process. The advantage in computation efficiency and accuracy makes the proposed method a promising tool for multi-scale dynamic analysis or damage detection of structures.

scholarly journals Detecting optimality and extracting solutions in polynomial optimization with the truncated GNS construction

2021 ◽  
Author(s):  
María López Quijorna
Keyword(s):  
Optimization Problem ◽  
Polynomial Optimization ◽  
Gaussian Quadrature ◽  
Hankel Matrix ◽  
Optimal Solution ◽  
Quadrature Rule ◽  
Polynomial Optimization Problem ◽  
Optimal Value ◽  
Semialgebraic Subset ◽  
Gns Construction

AbstractA basic closed semialgebraic subset of $${\mathbb {R}}^{n}$$ R n is defined by simultaneous polynomial inequalities $$p_{1}\ge 0,\ldots ,p_{m}\ge 0$$ p 1 ≥ 0 , … , p m ≥ 0 . We consider Lasserre’s relaxation hierarchy to solve the problem of minimizing a polynomial over such a set. These relaxations give an increasing sequence of lower bounds of the infimum. In this paper we provide a new certificate for the optimal value of a Lasserre relaxation to be the optimal value of the polynomial optimization problem. This certificate is to check if a certain matrix has a generalized Hankel form. This certificate is more general than the already known certificate of an optimal solution being flat. In case we have detected optimality we will extract the potential minimizers with a truncated version of the Gelfand–Naimark–Segal construction on the optimal solution of the Lasserre relaxation. We prove also that the operators of this truncated construction commute if and only if the matrix of this modified optimal solution is a generalized Hankel matrix. This generalization of flatness will enable us to prove, with the use of the GNS truncated construction, a result of Curto and Fialkow on the existence of quadrature rule if the optimal solution is flat and a result of Xu and Mysovskikh on the existence of a Gaussian quadrature rule if the modified optimal solution is a generalized Hankel matrix . At the end, we provide a numerical linear algebraic algorithm for detecting optimality and extracting solutions of a polynomial optimization problem.

Updating the Finite Element Model of a Bridge Model Using a Hybrid Optimization Method

2010 ◽  
Vol 456 ◽  
pp. 37-50
Author(s):  
Xiang Wei Hao ◽  
Yang Liu
Keyword(s):  
Finite Element ◽  
Finite Element Model ◽  
Optimization Problem ◽  
Model Updating ◽  
Random Search ◽  
Optimization Technique ◽  
Hybrid Approach ◽  
Element Model ◽  
Search Methods ◽  
Bridge Model

Finite element model updating of structures usually ends up with a nonlinear optimization problem. An efficient optimization technique is proposed firstly, which draws together the global searching capability of chaos-based optimization technique and high searching efficiency of trust-region Newton method. This hybrid approach is demonstrated to be more efficient and prone to global minimum than conventional gradient search methods and random search methods by testifying with three test functions. The optimization problem for model updating using modal frequencies and modal shapes is formulated, and a procedure to update the boundary support parameters is presented. A modal test was conducted on a beam structure, and the identified mode frequencies are employed to formulate the optimization problem with the support parameters as the updating parameters. The discrepancy between the mode frequencies of the finite element models before and after updating is greatly reduced, and the updated support condition meet quite well with the insight to the devices that form the supports.

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