基于性能稳健偏差的区间型参数稳健设计优化

提出了基于系统性能稳健偏差的稳健设计优化方法。该方法针对区间型参数非梯度性能函数的稳健设计问题，应用性能稳健偏差概念评估目标性能函数和约束性能函数的稳健性，形成了三层次稳健设计优化模型：①搜索优化设计点；②迭代策略搜索设计点的目标函数和约束函数的稳健偏差；③优化寻求给定性能偏差所对应的稳健性指数。该方法可获得同时满足约束条件和目标值稳健性要求的优化设计，并输出目标值及其稳健偏差。用三杆桁架结构稳健设计优化说明了该方法的用法和特点。     

A novel non-probabilistic approach using interval analysis for robust design optimization

A technique for formulation of the objective and constraint functions with uncertainty plays a crucial role in robust design optimization. This paper presents the first application of interval methods for reformulating the robust optimization problem. Based on interval mathematics, the original real-valued objective and constraint functions are replaced with the interval-valued functions, which directly represent the upper and lower bounds of the new functions under uncertainty. The single objective function is converted into two objective functions for minimizing the mean value and the variation, and the constraint functions are reformulated with the acceptable robustness level, resulting in a bi-level mathematical model. Compared with other methods, this method is efficient and does not require presumed probability distribution of uncertain factors or gradient or continuous information of constraints. Two numerical examples are used to illustrate the validity and feasibility of the presented method.     

具有随机型和区间型干扰因素的产品健壮设计研究

针对随机型和区间型干扰因素共同作用条件下的产品健壮设计问题，在同时考虑设计目标健壮性和设计约束可行健壮性的基础上，提出了健壮设计的分位数型设计准则；在该设计准则的基础上，建立了产品健壮设计的分位数优化模型，保证了所设计产品的抗干扰能力和可靠度。通过汽车离合器膜片弹簧的健壮设计实例，验证了该方法的有效性和实用性。     

并联机构敏感性分析和多目标优化设计方法

为了解决并联机构全局性能指标高计算成本引起的敏感性分析和多目标优化设计困难,提出了一种结合多项式响应面模型、基于方差的敏感性分析方法和智能优化算法的高效计算方法。首先,确定并联机构的目标函数和设计参数,增加节点密度以提高目标函数的计算精度,基于拉丁超立方体抽样方法和最小二乘多项式拟合技术建立全局目标函数与设计参数之间的响应面解析映射模型,并结合基于方差的Sobol’敏感性分析方法得到对目标函数有重要影响的设计参数。然后,结合敏感性分析结果简化设计参数并建立并联机构的多目标优化设计模型,包括目标函数、约束函数和设计参数,结合响应面模型与智能优化算法开展并联机构多目标优化设计。最后,考虑规则工作空间体积、运动学性能和动力学性能指标为目标函数,以DELTA并联机构为例实现了本文提出的方法。优化前后的结果对比证明了算法的有效性。     

Non-probabilistic Robust Optimal Design Method

For the purpose of dealing with uncertainty factors in engineering optimization problems, this paper presents a new non-probabilistic robust optimal design method based on maximum variation estimation. The method analyzes the effect of uncertain factors to objective and constraints functions, and then the maximal variations to a solution are calculated. In order to guarantee robust feasibility the maximal variations of constraints are added to original constraints as penalty term; the maximal variation of objective function is taken as a robust index to a solution; linear physical programming is used to adjust the values of quality characteristic and quality variation, and then a bi-level mathematical robust optimal model is coustructed. The method does not require presumed probability distribution of uncertain factors or continuous and differentiable of objective and constraints functions. To demonstrate the proposed method, the design of the two-bar structure acted by concentrated load is presented. In the example the robustness of the normal stress, feasibility of the total volume and the buckling stress are studied. The robust optimal design results show that in the condition of maintaining feasibility robustness, the proposed approach can obtain a robust solution which the designer is satisfied with the value of objective function and its variation.     

非稳态罚函数遗传算法及其用于机械/结构系统的健壮性设计

在机械 /结构的优化设计中 ,普遍存在约束的作用 ,且最优解往往位于可行域的边界上。由于外界环境的变化或人为因素造成设计变量扰动 ,可能使设计成为不可行。本文提出了一种基于设计变量敏感性的健壮性设计方法 ,并用非稳态罚函数遗传算法来实现多目标优化设计。     

基于分位数数学模型的参数设计新方法

参数设计是产品健壮设计中的重要阶段.为了减少产品的质量波动,提高产品质量的抗干扰能力,在同时考虑设计目标健壮性和设计约束健壮性的基础上,提出了新的基于分位数的参数设计优化模型,并采用理想点法和基于最大可能点的分位数求解算法,构成了该模型的求解框架,保证了该模型求解的效率和灵活性.通过汽车离合器膜片弹簧的参数设计实例,验证了该方法的有效性和实用性.     

Multiobjective optimization of injection molding parameters based on soft computing and variable complexity method

The objective of this study is to propose an intelligent methodology for efficiently optimizing the injection molding parameters when multiple constraints and multiple objectives are involved. Multiple objective functions reflecting the product quality, manufacturing cost and molding efficiency were constructed for the optimization model of injection molding parameters while multiple constraint functions reflecting the requirements of clients and the restrictions in the capacity of injection molding machines were established as well. A novel methodology integrating variable complexity methods (VCMs), constrained non-dominated sorted genetic algorithm (CNSGA), back propagation neural networks (BPNNs) and Moldflow analyses was put forward to locate the Pareto optimal solutions to the constrained multiobjective optimization problem. The VCMs enabled both the knowledge-based simplification of the optimization model and the variable-precision flow analyses of different injection molding parameter schemes. The Moldflow analyses were applied to collect the precise sample data for developing BPNNs and to fine-tune the Pareto-optimal solutions after the CNSGA-based optimization while the approximate BPNNs were utilized to efficiently compute the fitness of every individual during the evolution of CNSGA. The case study of optimizing the mold and process parameters for manufacturing mice with a compound-cavity mold demonstrated the feasibility and intelligence of proposed methodology.     

基于灵敏度分析的稳健可靠性优化设计模型及MATLAB实现

在机械零件的可靠性优化设计中,普遍存在约束的作用,且最优解往往位子可行域的边界上。由于外界环境的变化或人为因素造成设计变量扰动,可能使设计成为不可行。本文提出了一种基于设计变量敏感度的稳键性设计方法,建立了基于灵敏度分析产生附加目标函数的两种稳健可靠性优化设计模型,并用 ＭＡＴＬＡＢ语言的优化工具箱和符号工具箱来实现机械零件的稳健可靠性优化设计,计算实例说明所述模型的可行性与实用性。     

A Study for robustness of objective function and constraints in robust design optimization

Since randomness and uncertainties of design parameters are inherent, the robust design has gained an ever increasing importance in mechanical engineering. The robustness is assessed by the measure of performance variability around mean value, which is called as standard deviation. Hence, constraints in robust optimization problem can be approached as probability constraints in reliability based optimization. Then, the FOSM (first order second moment) method or the AFOSM (advanced first order second moment) method can be used to calculate the mean values and the standard deviations of functions describing constraints and object. Among two methods, AFOSM method has some advantage over FOSM method in evaluation of probability. Nevertheless, it is difficult to obtain the mean value and the standard deviation of objective function using AFOSM method, because it requires that the mean value of function is always positive. This paper presented a special technique to overcome this weakness of AFOSM method. The mean value and the standard deviation of objective function by the proposed method are reliable as shown in examples compared with results by FOSM method.     

基于分位数型设计准则的模糊健壮设计新方法

在模糊目标和模糊设计约束的条件下,同时考虑了质量特性的健壮性和设计约束的可行健壮性,提出望目特性、望大特性和望小特性模糊健壮设计的分位数型设计准则。在该设计准则的基础上,建立不同类型质量特性的模糊健壮设计优化模型,并将常规优化算法和基于最大可能点的分位数求解算法相结合构成该模型的求解框架。最后通过实例验证了该方法的有效性。     

Robust fault detection for nonlinear networked systems with stochastic interval delay characteristics

In this paper, the problem of observer-based robust fault detection (RFD) for nonlinear networked systems with stochastic interval delay is investigated. By employing the information of probabilistic distribution of networked-induced time-varying delay, the observer-based fault detection filter as residual generator and a proposed performance index as objective function, the RFD of nonlinear networked systems is formulated as an optimization problem. The desired fault detection filter is constructed in terms of certain linear matrix inequalities, which depend on not only delay-interval but also delay-interval-occurrence-rate. Especially, the sub-optimal trade-off of strong robustness from residual signal to disturbance and parameter uncertainty, as well as high sensitivity to fault is obtained by a repeated application of a two-objective optimization algorithm. Numerical simulations are given to illustrate the effectiveness of proposed techniques.     

基于约束关系网的膜片离合器装配设计缺陷辨识与最优修正

提出了机械产品装配设计参数与其约束判定函数的关联方法,研究了装配约束关系网中节点的数据结构,给出了装配约束关系网的构建方法,描述了装配约束关系网的禁忌表访问方式,在此基础上提出了基于装配约束关系网的装配设计缺陷的辨识模型与方法。从装配约束关系网中的设计缺陷节点出发,以约束路径的权值之和为目标函数,采用蚁群算法对装配设计缺陷的修正路径进行了优化。以膜片离合器的装配设计为实例进行了装配设计缺陷的辨识与修正,结果表明,提出的装配设计缺陷辨识模型与修正方法不仅能够快速辨识出装配设计缺陷,而且能够有效地提高装配设计缺陷的修正质量和效率。     

结合机械设计约束处理的差分进化算法

针对机械设计中的约束优化问题,提出了改进约束处理的自适应罚函数法。结合一般机械约束优化问题维数不高和差分进化算法简单、高效的特点,应用差分进化算法容易求得机械约束优化问题的全局最优解。给出了2个机械约束优化的数值实例,与已有的文献结果比较,表明新方法处理机械约束优化问题稳健且有效。     

基于物理规划的起重机主梁稳健优化设计

在机械优化设计中考虑载荷等不确定性因素的影响,用凸集模型描述设计中存在的不确定性,采用物理规划的方法构造不确定性参数的不满意度函数,通过极小化不满意度函数最差值的方法来实现目标函数的稳健性,通过最坏情况分析方法来实现约束函数的稳健性,使目标函数和约束函数都能实现稳健性。建立基于物理规划的稳健可靠性优化模型,这种模型是一种嵌套的优化模型,采用分层方法对其求解。以起重机主梁优化设计为例说明这种模型的合理性。     

工程稳健优化设计

本文从工程设计观点讨论了设计解的稳健性、稳健设计和稳健优化设计的基本概念,提出了一种基于随机优化技术的稳健优化设计的建模原理和求解算法,这一方法将通过调整设计变量的名义值和控制它的容差来考虑可控变量和不可控参数的变差对产品质量的影响,以提高设计解的可行稳健性和质量函数的不灵敏性。     

Study of the fractional order proportional integral controller for the permanent magnet synchronous motor based on the differential evolution algorithm

A tuning method of the fractional order proportional integral speed controller for a permanent magnet synchronous motor is proposed in this paper. Taking the combination of the integral of time and absolute error and the phase margin as the optimization index, the robustness specification as the constraint condition, the differential evolution algorithm is applied to search the optimal controller parameters. The dynamic response performance and robustness of the obtained optimal controller are verified by motor speed-tracking experiments on the motor speed control platform. Experimental results show that the proposed tuning method can enable the obtained control system to achieve both the optimal dynamic response performance and the robustness to gain variations.     

Analytical approach to robust design of nonlinear mechanical systems

The robustness of mechanical systems is influenced by various factors. Their effects must be understood for designing robust systems. This paper proposes a model for describing the relationships among functional requirements, structural characteristics, design parameters and uncontrollable variables of nonlinear systems. With this model, the sensitivity of systems was analyzed to formulate a system sensitivity index and robust sensitivity matrix to determine the importance of the factors in relation to the robustness of systems. Based on the robust design principle, an optimization model was developed. Combining this optimization model and the Taguchi method for robust design, an analysis was carried out to reveal the characteristics of the systems. For a nonlinear mechanical system, relationships among structural characteristics of the system, design parameters, and uncontrollable variables can be formulated as a mathematical function. The characteristics of the system determine how design parameters affect the functional requirements of the system. Consequently, they affect the distribution of system performance functions. Nonlinearity of the system can facilitate the selection of design parameters to achieve the required functional requirements.     

Development of characteristic equations and robust stability analysis for SISO move suppressed and shifted DMC

New controller and closed loop transfer functions for move suppressed and shifted dynamic matrix control were derived in order to compare the controller robustness on several plants as a function of tuning parameters lambda and m. The derivation of these transfer functions are for any order plant requiring its open loop step or impulse response. A generic control design algorithm was developed for selecting the controller tuning parameters using controller robustness as a performance index, in the presence of plant parameter variations and uncertainties. Shifted dynamic matrix control (DMC) was found to be more robust with respect to all plant parameter variations, and therefore more suited than move suppressed DMC to control plants with wide ranging parameters. This result was demonstrated on an experimental direct current servomotor system, and further verified on a plant having a cascade control structure with the (m , m) being the most robust to plant variations.     

基于参数和代理模型不确定性的冲压稳健性设计优化

在传统的基于代理模型的冲压稳健性设计中,由于代理模型与真实模型间存在着误差,必然会导致优化结果存在一定的误差。将实验设计、Kriging模型相结合,综合考虑参数不确定性和代理模型不确定性的影响,提出了一种新的冲压稳健性优化设计方法。通过因素敏感性分析筛选出相应的设计变量和噪声因素,基于Kriging模型构建设计参数和质量指标的代理模型,采用蒙特卡罗分析方法以及遗传算法获得最优工艺解。实例分析结果表明,综合两种不确定因素的稳健设计方法能有效地降低拉裂、起皱约束失效概率,提高冲压件成形质量和工艺稳健性。