Huanwei Xu

Interaction balance optimization in multidisciplinary design optimization problems

As a bi-level optimization method, collaborative optimization can solve multidisciplinary design optimization problems in practical engineering effectively. However, if there are high-dimensional couplings in a multidisciplinary design optimization problem, a large number of compatibility constraints will be required in collaborative optimization. In this situation, collaborative optimization will not be suitable to be utilized because of low computational efficiency or divergence issue. To solve this problem, an efficient interaction balance optimization method is proposed in this article. In interaction balance optimization method, the simple coordination strategy of interaction balance principle and the distributed optimization strategy of collaborative optimization can be integrated effectively. Lagrange multipliers are used instead of compatibility constraints to maintain the consistency between any two coupled disciplines. Two examples are given to show the effectiveness of the proposed method.

Interaction prediction optimization in multidisciplinary design optimization problems.

The distributed strategy of Collaborative Optimization (CO) is suitable for large-scale engineering systems. However, it is hard for CO to converge when there is a high level coupled dimension. Furthermore, the discipline objectives cannot be considered in each discipline optimization problem. In this paper, one large-scale systems control strategy, the interaction prediction method (IPM), is introduced to enhance CO. IPM is utilized for controlling subsystems and coordinating the produce process in large-scale systems originally. We combine the strategy of IPM with CO and propose the Interaction Prediction Optimization (IPO) method to solve MDO problems. As a hierarchical strategy, there are a system level and a subsystem level in IPO. The interaction design variables (including shared design variables and linking design variables) are operated at the system level and assigned to the subsystem level as design parameters. Each discipline objective is considered and optimized at the subsystem level simultaneously. The values of design variables are transported between system level and subsystem level. The compatibility constraints are replaced with the enhanced compatibility constraints to reduce the dimension of design variables in compatibility constraints. Two examples are presented to show the potential application of IPO for MDO.

A New Method for Achieving Flexibility in Hierarchical Multilevel System Design

Analytical target cascading (ATC) method has been widely applied to solve multilevel decomposed system design optimization problems. In the ATC method, concurrent design is achieved by target cascading. However, due to the complexity and the presence of uncertainty, it is a challenging task to set proper targets. In this article, instead of using point value targets, interval targets are analyzed and propagated through the multilevel system with the goal of reducing the effects of uncertainty while providing more flexibility to a design process. In the proposed method, the design of a hierarchical system at each level is taken as a single-objective optimization problem, by minimizing the degree of deviation between the target response interval and the achievable response interval. Not only the optimal design performance is considered in this method, but also the acceptable variation range of the performance is analyzed. When the present target for a lower level system and the achievable response from a lower level system are not point values, but rather intervals, their probability distributions are not available. Therefore, these variables are treated as interval variables. When the random and interval variables are present, the most probable point-based first-order reliability and the interval analysis methods are used to calculate the reliability bounds. The proposed method for flexibility under uncertainty provides more degree of freedom to the design of lower level systems, while also keeping the performance of the upper systems stable within a tolerable range. The accuracy of the proposed method is demonstrated via comparing results from both the proposed and traditional methods.

A multi-team competitive optimization algorithm for bearing fault diagnosis

To recognize different bearing fault patterns under different operating conditions, a novel multi-team competitive optimization (MTCO) algorithm is proposed. The algorithm is inspired by the competitive behaviors among multiple teams. In the structure, it consists of a three-level optimization organization structure, so that the more potential optimal areas can be searched. Meanwhile, some new strategies imitating human thinking mode are proposed to increase the diversity and guide the members jumping out of location optimal areas, which include acceptable vector designed for imitating some uncertain or random events influencing the decision-making, betrayal mechanism and replacement mechanism designed for ensuring the reasonable turnover of staffs and leaders. Moreover, to reduce fault pattern recognition errors caused by inseparability of data with nonlinear distribution, a kernel function is introduced to increase the separability of data and improve recognition accuracies. Finally, the MTCO algorithm has been applied to diagnose real-world bearings faults. In this case, the MTCO algorithm has proved to have better recognition accuracies and to be effective.

First-Order Second-Moment based multidisciplinary design optimization

Uncertainties in multidisciplinary design optimization (MDO) have a significant influence on the whole design process of the engineering system. If uncertainty in the engineering system is not considered, optimization results may be unreliable. On the basis of the existing methods for uncertainty analysis, a new method for MDO under uncertainty, i.e. First-Order Second-Moment based collaborative optimization (FOSM-CO), is proposed, and its particular computational process is described in detail. The FOSM-CO is an optimization approach that utilizes reliability index to evaluate the probability that the random variables are in the safe region and instead of the original constraints with the probability. The computation results of the example indicate that FOSM-CO is an effective reliability design method for MDO under uncertainty.

Topology optimization considering stress and reliability constraints

In the past two decades, many researches have been carried out to study the structural topology optimization. Most of them focused on minimizing the mean compliance of structures under material volume constraint, but stress constraints are seldom considered in the problem formulations. So, the optimum structure may be not safe because the material failure criterion is not checked during optimization process. Even if stress constraints are considered, the optimum structure still could fail with high probability because the applied forces, material properties and many other design parameters could be random factors in reality. Hence, both stress constraints and random parameters should be considered to design an optimized structure with high reliability. This paper presents a procedure to implement Reliability-based based Topology Optimization (RBTO) considering stress constraints. Numerical examples show the impacts of stress constraint and random factors on the final topology of optimum structure.

Sequential Multidisciplinary Design Optimization and Reliability Analysis Using an Efficient Third-Moment Saddlepoint Approximation Method

In Reliability based Multidisciplinary Design and Optimization (RBMDO), saddlepoint approximation has been utilized to improve reliability evaluation accuracy while sustaining high efficiency. However, it requires that not only involved random variables should be tractable; but also a saddlepoint can be obtained easily by solving the so-called saddlepoint equation. In practical engineering, a random variable may be intractable; or it is difficult to solve a highly nonlinear saddlepoint equation with complicated Cumulant Generating Function (CGF). To deal with these challenges, an efficient RBMDO method using Third-Moment Saddlepoint Approximation (TMSA) is proposed in this study. TMSA can construct a concise CGF using the first three statistical moments of a limit state function easily, and then express the probability density function and cumulative distribution function of the limit state function approximately using this concise CGF. To further improve the efficiency of RBMDO, a sequential optimization and reliability analysis strategy is also utilized and a formula of RBMDO using TMSA within the framework of SORA is proposed. Two examples are given to show the effectiveness of the proposed method.Copyright

Weibull distribution research based on Fourier series

With the development of science and technology, the engineering equipment and products are becoming more and more complicated. So, the system reliability has attracted great attention of Scholars and engineers. Because the system reliability is mainly subjected to Weibull distribution, it is important to improve the Weibull model. A new method is proposed in this paper, which can improve calculation efficiency by using Fourier series to transform the probability density function of Weibull distribution into a periodic function. The proposed method is applied to estimate the reliability of fuel system, and the outcome proves that the method is effective.

Notice of Retraction Multidisciplinary design optimization based on physical programming

Generally, multidisciplinary design optimization (MDO) has a good performance when dealing with the coupled relationship among disciplines. However, the preference of designers could not be reflected in MDO. Therefore, some effective approaches, which can reflect preference of designers, should be proposed to handle the optimization problem with increased complexity. In this paper, an effective optimal approach is proposed based on the combination of collaborative optimization and physical programming. And then, the proposed approach is applied for the optimization of a XX-type missile. By contrast, the proposed approach has a better performance.

Sequential Particle Swarm Optimization and Reliability Assessment of Planar-Type Voice Coil Motor

Planar-type voice coil motor (VCM) is a key component in ultra-precision motion of fine stage of lithography machine. The reliability-based design optimization (RBDO) method given in this work provides a novel criterion to ensure performance of Lorentz motors by evaluating the reliability of force constant. To solve the reliability based design optimization problem in discrete space with the speed of decoupled loop in sequential optimization and reliability assessment (SORA) for global solution, a Sequential Particle Swarm Optimization and Reliability Assessment method is proposed. The reliability boundary shift is put into penalty function for constrained optimization in fitness evaluation of particle swarm optimization (PSO). The presented optimization design model, the geometric parameters of the studied Planar-type VCM in finite element model are treated as design variables whereas the thrust force constant is an output quantity of interests. By using electromagnetic analysis, the desired requirements of Lorentz motors are verified.Copyright