基于子集模拟的结构可靠度分析与混合和声优化算法

发布时间：2018-06-20 01:09

本文选题：子集模拟 + 随机结构　；参考：《大连理工大学》2014年硕士论文

【摘要】：结构可靠性分析和优化设计是国内外工程力学界学者研究的两个重要课题。可靠性分析对结构安全评定与服役寿命预测和正常运行至关重要。结构优化设计可以使结构的性能达到最佳,同时使资源得到合理利用,降低工程造价。子集模拟法是一种估计小概率失效问题的可靠性分析方法,后来被推广应用到结构优化领域。本文借鉴子集模拟算法的马尔科夫链概念改进了基本的和声搜索算法,建立了子集模拟和声搜索算法,并研究了子集模拟方法在随机结构可靠性分析和结构动力优化设计两方面的应用。具体内容如下：在工程实际中,外荷载和结构参数通常具有随机性。地震作用是典型的随机荷载,时变随机地震作用下结构动力可靠度的高效分析是一个富有挑战性的问题。子集模拟法作为一种效率较高的数字模拟方法为求解这类问题提供了有效工具。子集模拟法通过引入合理的较大失效概率的中间失效事件,将小失效概率转化为一系列较大失效概率的乘积,对于这些较大失效概率可利用马尔可夫链模拟高效估计条件样本点来得到,从而提高计算效率。由随机结构动力可靠度分析表明,子集模拟法大大减少了结构重分析次数,提高了计算效率。而且,工程结构不可避免地受到外界冲击或振动的干扰,为了确保工程结构在动荷载作用下能够安全可靠地工作,需要进行结构动力优化设计。另一方面,子集模拟优化算法是将优化中的极值问题巧妙地转化为可靠性分析的小失效概率问题。本文基于子集模拟优化算法有效地解决了频率约束下桁架的尺寸优化和尺寸形状优化以及动载荷作用下框架的尺寸优化问题,得到了优化的结构尺寸和形状设计方案。最后,针对基本和声搜索不能获得较高精度的解,易陷入局部最优且效率不高的不足,借鉴了已有的参数和声保留概率、音调调节概率和调节步长的改进措施,并结合子集模拟算法,提出了子集模拟和声搜索混合优化算法。由基准数学算例和桁架结构优化实例表明,子集模拟和声搜索混合算法具有较好的精确寻优能力和鲁棒性,能迅速收敛到最优解,且对于多维优化问题,其计算性能表现良好。
[Abstract]:Structural reliability analysis and optimization design are two important topics studied by domestic and foreign engineering mechanics scholars. Reliability analysis is very important for structural safety assessment, service life prediction and normal operation. The optimum design of the structure can achieve the best performance of the structure, at the same time, the resources can be used reasonably, and the project cost can be reduced. Subset simulation is a reliability analysis method for estimating small probability failure problems, which has been extended to the field of structural optimization. In this paper, the basic harmonic search algorithm is improved by using the Markov chain concept of the subset simulation algorithm, and the subset simulation harmonic search algorithm is established. The application of subset simulation method in reliability analysis and dynamic optimization design of stochastic structures is also studied. The main contents are as follows: in engineering practice, external loads and structural parameters are usually random. Seismic action is a typical random load, and the efficient analysis of structural dynamic reliability under time-varying random earthquake is a challenging problem. As an efficient digital simulation method, subset simulation provides an effective tool for solving this kind of problems. By introducing a reasonable intermediate failure event with a high failure probability, the subset simulation method converts the small failure probability into the product of a series of larger failure probability. For these large failure probabilities, the Markov chain is used to simulate the efficient estimation of conditional sample points, thus improving the computational efficiency. The dynamic reliability analysis of random structures shows that the method of subset simulation greatly reduces the times of structural reanalysis and improves the efficiency of calculation. Moreover, the engineering structure is inevitably disturbed by external shock or vibration. In order to ensure that the engineering structure can work safely and reliably under the dynamic load, it is necessary to carry out structural dynamic optimization design. On the other hand, the subset simulation optimization algorithm is a small failure probability problem which transforms the optimization extremum problem into the reliability analysis problem. Based on the subset simulation optimization algorithm, the optimization of the size and shape of truss under frequency constraints and the optimization of frame size under dynamic load are effectively solved in this paper, and the optimal design scheme of structure size and shape is obtained. Finally, aiming at the deficiency that the basic harmonic search can not get a higher precision solution and is prone to fall into the local optimum and low efficiency, the improved measures of parameter and sound retention probability, tone adjustment probability and adjusting step size are used for reference. Combined with subset simulation algorithm, a subset simulation and acoustic search hybrid optimization algorithm is proposed. The examples of benchmark mathematics and truss structure optimization show that the hybrid algorithm of subset simulation and acoustic search has good accuracy and robustness, and can converge to the optimal solution quickly, and the performance of the hybrid algorithm is good for multidimensional optimization problems.
【学位授予单位】：大连理工大学
【学位级别】：硕士
【学位授予年份】：2014
【分类号】：TB114.3;TB12

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