Structural topology optimization under harmonic base acceleration excitations

This work is focused on the structural topology optimization methods related to dynamic responses under harmonic base acceleration excitations. The uniform acceleration input model is chosen to be the input form of base excitations. In the dynamic response analysis, we propose using the large mass method (LMM) in which artificial large mass values are attributed to each driven nodal degree of freedom (DOF), which can thus transform the base acceleration excitations into force excitations. Mode displacement method (MDM) and mode acceleration method (MAM) are then used to calculate the harmonic responses and the design sensitivities due to their balances between computing efficiency and accuracy especially when frequency bands are taken into account. A density based topology optimization method of minimizing dynamic responses is then formulated based on the integration of LMM and MDM or MAM. Moreover, some particular appearances such as the precision of response analysis using MDM or MAM, and the duplicated frequencies are briefly discussed. Numerical examples are finally tested to verify the accuracy of the proposed schemes in dynamic response analysis and the quality of the optimized design in improving dynamic performances.     

Dynamic response topology optimization in the time domain using model reduction method

The dynamic response topology optimization problems are usually computationally expensive, so it is necessary to employ the model reduction methods to reduce computational cost. This work will investigate the effectiveness of the mode displacement method(MDM) and mode acceleration method(MAM) for time-domain response problems within the framework of density-based topology optimization. Three objective functions, the mean dynamic compliance, mean strain energy and mean squared displacement are considered. It is found that, in general cases, MDM is not suitable for time-domain response topology optimization problems due to its low accuracy of approximation, while MAM works well for problems of a wide range, and when there are many time steps, the MAM based topology optimization approach is more efficient than the direct integration based approach. So for practical applications, when the problem needs many time steps, the MAM based approach is preferred and otherwise, the direct integration based approach is suggested.     

基于差分进化的因子分解机算法

因子分解机(Factorization Machine,FM) 算法是一种基于矩阵分解的机器学习算法,可用于求解回归、分类和排序等问题。FM模型中的参数求解使用的是基于梯度的优化方法,然而在样本较少的情况下,该优化方法收敛速度慢,且易陷入局部最优。差分进化算法(Differential Evolution,DE)是一种启发式的全局优化算法,具有收敛速度快等特性。为提高FM模型的训练速度,利用DE计算FM模型参数,提出了DE-FM算法。在数据集Diabetes、HorseColic以及音乐分类数据集Music上的实验结果表明,改进后的基于差分进化的因子分解机算法DE-FM在训练速度和准确性上均有所提高。     

Structural topology optimization for frequency response problem using model reduction schemes

This study uses model reduction (MR) schemes such as the mode superposition (MS), Ritz vector (RV), and quasi-static Ritz vector (QSRV) methods, which reduce the size of the dynamic stiffness matrix of dynamic structures, to calculate dynamic responses and sensitivity values with adequate efficiency and accuracy for topology optimization in the frequency domain. The calculation of structural responses to dynamic excitation using the framework of the finite element (FE) procedure usually requires a significant amount of computation time; that is mainly attributable to repeated inversions of dynamic stiffness matrices depending on time or frequency intervals, which hastens the dissemination of the MR schemes in the analysis. However, using well-established MR schemes in topology optimization has not been prevalent. Therefore, this study conducted a comprehensive investigation to highlight the drawbacks and advantages of these MR schemes for topology optimization. In the results, the MS method, which generates reduction bases by considering some of the lowest eigenmodes, can lose the accuracy in both approximated structural responses and sensitivity values due to locally vibrating eigenmodes and higher mode truncation in the solid isotropic material with penalization (SIMP) approach. In addition, the RV and QSRV methods, which generate reduction bases by considering the external force, mass, and stiffness matrices of a structure, can be used as alterative model reduction schemes for stable optimization. Through several analysis and design examples, the efficiency and reliability of the model reduction schemes for topology optimization are compared and validated.     

基础简谐激励下的结构动响应拓扑优化

针对关于结构动响应拓扑优化问题的研究较少、有限元分析软件的拓扑优化模块无法实现的问题,采用变密度法研究连续体结构在基础简谐激励下的动响应拓扑优化.将基础简谐激励下的响应控制问题归结为结构在体积约束下目标点响应幅值最小化的优化模型;推导有阻尼结构在基础简谐激励下目标点响应幅值的灵敏度公式;采用变密度法求解该优化问题.采用多项式惩罚模型解决带惩罚的各向同性固体微结构（Solid Isotropic Microstructure with Penalization,SIMP）模型带来的附属效应现象;采用灰度过滤方法改善经典变密度法在优化过程中灰度单元收敛过慢的问题,从而减少变密度法优化的迭代步数并且使优化结果更清晰.以平面悬臂板模型为例,验证该优化方法对目标点响应幅值的优化以及灰度过滤函数对优化迭代的改善.     

Bacterial foraging optimization and adaptive version for economically optimum sitting,sizing and harmonic tuning orders setting of LC harmonic passive power filters in radial distribution systems with linear and nonlinear loads

This paper presents bacterial foraging optimization (BFO) algorithm and its adaptive version to optimize the planning of passive harmonic filters (PHFs).The important problem of using PHFs is determining location, size and harmonic tuning orders of them, which is reach standard levels of harmonic distortion with applying minimum cost of passive filters.In this study to optimize the PHFs location, size and setting the harmonic tuning orders in the distribution system, considered objective function includes the reduction of power loss and investment cost of PHFs. At the same time, constraints include voltage limits, number/size of installed PHFs, limit candidate buses for PHFs installation and the voltage total harmonic distortion (THDv) in all buses. The harmonic levels of system are obtained by current injections method and the load flow is solved by the iterative method of power sum, which is suitable for the accuracy requirements of this type of study. It is shown that through an economical placement and sizing of PHFs the total voltage harmonic distortion and active power loss could be minimized simultaneously.The considered objective function is of highly non-convex manner, and also has several constraints. On the other hand due to significant computational time reduction and faster convergence of BFO in comparison with other intelligent optimization approach such as genetic algorithm (GA), particle swarm optimization (PSO) and artificial bee colony (ABC) the simple version of BFO has been implemented. Of course other versions of BFO such as Adaptive BFO and combination of BFO with other method due to complexity of harmonic optimization problem have not considered in this research.The simulation results for small scale test system with 10 buses, showed the significant computational time reduction and faster convergence of BFO in comparison with GA, PSO and ABC. Therefore in large scale radial system with 34 buses, the proposed method is solved using BFO.The simulation results for a 10-bus system as a small scale and 34-bus radial system as a large scale show that the proposed method is efficient for solving the presented problem.     

因子分解机模型研究综述

传统矩阵分解方法因其算法的高可扩展性和较好的性能等特点,在预测、推荐等领域有着广泛的应用.然而大数据环境下,更多上下文因素的获取变得可能,传统矩阵分解方法缺乏对上下文信息的有效利用.在此背景下,因子分解机模型提出并流行.为了更好地把握因子分解机模型的发展脉络,促进因子分解机模型与应用相结合,针对因子分解机模型及其算法进行了综述.首先,对因子分解机模型的提出进行了溯源,介绍了从传统矩阵分解到因子分解机模型的演化过程;其次,从模型准确率和效率两方面对因子分解机模型存在的基本问题和近年来的研究进展进行了总结,然后综述了适用于因子分解机模型求解的4种代表性优化算法;最后分析了因子分解机模型目前仍存在的问题,提出了可能的解决思路,并对未来的研究方向进行了展望.     

The approximate reanalysis method for topology optimization under harmonic force excitations with multiple frequencies

In mode acceleration method for topology optimization related harmonic response with multiple frequencies, most of the computation effort is invested in the solution of the eigen-problem. This paper is focused on reduction of the computational effort in repeated solution of the eigen-problem involved in mode acceleration method. The block combined approximation with shifting method is adopted for eigen-problem reanalysis, which simultaneously calculates some eigenpairs of modified structures. The triangular factorizations of shifted stiffness matrices generated within a certain number of design iterations are utilized to calculate the modes. For improving computational efficiency, Basic Linear Algebra Subprograms (BLAS) are utilized. The reanalysis method is based on matrix-matrix operations with Level-3 BLAS and can provide very fast development of approximate solutions of high quality for frequencies and associated mode shapes of the modified structure. Numerical examples are given to demonstrate the efficiency of the proposed topology optimization procedure and the accuracy of the approximate solutions.     

Mid-range metamodel assembly building based on linear regression for large scale optimization problems

In this work an approach to building a high accuracy approximation valid in a larger range of design variables is investigated. The approach is based on an assembly of multiple surrogates into a single surrogate using linear regression. The coefficients of the model assembly are not weights of the individual models but tuning parameters determined by the least squares method. The approach was utilized in the Multipoint Approximation Method (MAM) method within the mid-range approximation framework. The developed technique has been tested on several benchmark problems with up to 1000 design variables and constraints. The obtained results show a high degree of accuracy of the built approximations and the efficiency of the technique when applied to large-scale optimization problems.     

一种用Powell方法局部优化的人工萤火虫算法

针对人工萤火虫算法在寻找函数全局最优值时,存在着收敛速度慢、易陷入局部最优、收敛成功率和求解精度低等不足,利用Powell方法强大的局部优化能力,将其作为一局部搜索算子嵌入到人工萤火虫算法,提出一种用Powell方法局部优化的人工萤火虫算法。最后,8个标准函数测试结果表明,改进后人工萤火虫算法在收敛速度、精度和稳定性方面都优于人工萤火虫算法。