复杂系统的多学科设计优化综述

从设计和分析的本质出发,结合复杂系统的特点,通过分析传统设计优化流程在面对复杂系统时存在的困难和缺陷,指出多学科设计优化(multidisciplinary design optimization,MDO)方法是解决复杂系统设计优化问题的一种有效措施.在此基础上,介绍了多学科优化方法的基本思想,总结了子系统耦合方式及MDO在处理耦合时的基本方法,归纳了MDO的知识框架和主要研究内容.最后在现有研究成果的基础上,对MDO今后的研究提出了几点参考意见.     

Reliability analysis for multidisciplinary systems with the mixture of epistemic and aleatory uncertainties

Epistemic and aleatory uncertain variables always exist in multidisciplinary system simultaneously and can be modeled by probability and evidence theories, respectively. The propagation of uncertainty through coupled subsystem and the strong nonlinearity of the multidisciplinary system make the reliability analysis difficult and computational cost expensive. In this paper, a novel reliability analysis procedure is proposed for multidisciplinary system with epistemic and aleatory uncertain variables. First, the probability density function of the aleatory variables is assumed piecewise uniform distribution based on Bayes method, and approximate most probability point is solved by equivalent normalization method. Then, important sampling method is used to calculate failure probability and its variance and variation coefficient. The effectiveness of the procedure is demonstrated by two numerical examples. Copyright © 2013 John Wiley & Sons, Ltd.     

Reliability based design optimization using response surfaces in application to multidisciplinary systems

Traditionally, reliability based design optimization (RBDO) is formulated as a nested optimization problem. For these problems the objective is to minimize a cost function while satisfying the reliability constraints. The reliability constraints are usually formulated as constraints on the probability of failure corresponding to each of the failure modes or a single constraint on the system probability of failure. The probability of failure is usually estimated by performing a reliability analysis. The difficulty in evaluating reliability constraints comes from the fact that modern reliability analysis methods are themselves formulated as an optimization problem. Solving such nested optimization problems is extremely expensive for large scale multidisciplinary systems which are likewise computationally intensive. In this research, a framework for performing reliability based multidisciplinary design optimization using approximations is developed. Response surface approximations (RSA) of the limit state functions are used to estimate the probability of failure. An outer loop is incorporated to ensure that the approximate RBDO converges to the actual most probable point of failure. The framework is compared with the exact RBDO procedure. In the proposed methodology, RSAs are employed to significantly reduce the computational expense associated with traditional RBDO. The proposed approach is implemented in application to multidisciplinary test problems, and the computational savings and benefits are discussed.     

Collaborative optimization with inverse reliability for multidisciplinary systems uncertainty analysis

This article introduces a method which combines the collaborative optimization framework and the inverse reliability strategy to assess the uncertainty encountered in the multidisciplinary design process. This method conducts the sub-system analysis and optimization concurrently and then improves the process of searching for the most probable point (MPP). It reduces the load of the system-level optimizer significantly. This advantage is specifically more prominent for large-scale engineering system design. Meanwhile, because the disciplinary analyses are treated as the equality constraints in the disciplinary optimization, the computation load can be further reduced. Examples are used to illustrate the accuracy and efficiency of the proposed method.     

Cost minimization of repairable systems subject to availability constraints using efficient cuckoo optimization algorithm

System availability is a key element for any industry. System designers and operators try to do their best to maintain the required availability of the systems to avoid production stoppages. They set up and undertake different maintenances, and these interventions imply cost. Therefore, the goal is to minimize the cost, but considering the constraint of the availability requirement. The problem involves three main aspects: redundancy allocation, component failure rates, and repair rates. In this paper, a novel solution approach is proposed based on an efficient cuckoo optimization algorithm (EF-COA). Two numerical case studies are solved, and the results confirm the effectiveness of the approach proposed.     

Riemannian optimization and multidisciplinary design optimization

Riemannian Optimization (RO) generalizes standard optimization methods from Euclidean spaces to Riemannian manifolds. Multidisciplinary Design Optimization (MDO) problems exist on Riemannian manifolds, and with the differential geometry framework which we have previously developed, we can now apply RO techniques to MDO. Here, we provide background theory and a literature review for RO and give the necessary formulae to implement the Steepest Descent Method (SDM), Newton’s Method (NM), and the Conjugate Gradient Method (CGM), in Riemannian form, on MDO problems. We then compare the performance of the Riemannian and Euclidean SDM, NM, and CGM algorithms on several test problems (including a satellite design problem from the MDO literature); we use a calculated step size, line search, and geodesic search in our comparisons. With the framework’s induced metric, the RO algorithms are generally not as effective as their Euclidean counterparts, and line search is consistently better than geodesic search. In our post-experimental analysis, we also show how the optimization trajectories for the Riemannian SDM and CGM relate to design coupling and thereby provide some explanation for the observed optimization behaviour. This work is only a first step in applying RO to MDO, however, and the use of quasi-Newton methods and different metrics should be explored in future research.     

Decoupled approach to multidisciplinary design optimization under uncertainty

We propose solution methods for multidisciplinary design optimization (MDO) under uncertainty. This is a class of stochastic optimization problems that engineers are often faced with in a realistic design process of complex systems. Our approach integrates solution methods for reliability-based design optimization (RBDO) with solution methods for deterministic MDO problems. The integration is enabled by the use of a deterministic equivalent formulation and the first order Taylor’s approximation in these RBDO methods. We discuss three specific combinations: the RBDO methods with the multidisciplinary feasibility method, the all-at-once method, and the individual disciplinary feasibility method. Numerical examples are provided to demonstrate the procedure. Anukal Chiralaksanakul is currently a full-time lecturer in the Graduate School of Business Administration at National Institute of Development Administration (NIDA), Bangkok, Thailand.     

Benchmarking multidisciplinary design optimization algorithms

A comparison of algorithms for multidisciplinary design optimization (MDO) is performed with the aid of a new software framework. This framework, pyMDO, was developed in Python and is shown to be an excellent platform for comparing the performance of the various MDO methods. pyMDO eliminates the need for reformulation when solving a given problem using different MDO methods: once a problem has been described, it can automatically be cast into any method. In addition, the modular design of pyMDO allows rapid development and benchmarking of new methods. Results generated from this study provide a strong foundation for identifying the performance trends of various methods with several types of problems.     

Multi-objective optimization by a new hybridized method: applications to random mechanical systems

In this article two linear problems with random Gaussian loading are transformed into multi-objective optimization problems. The first problem is the design of a pillar geometry with respect to a compressive random load process. The second problem is the design of a truss structure with respect to a vertical random load process for several frequency bands. A new algorithm, motivated by the Pincus representation formula hybridized with the Nelder–Mead algorithm, is proposed to solve the two multi-objective optimization problems. To generate the Pareto curve, the normal boundary intersection method is used to produce a series of constrained single-objective optimizations. The second problem, depending on the frequency band of excitation, can have as Pareto curve a single point, a standard Pareto curve, or a discontinuous Pareto curve, a fact that has been reported here for the first time in the literature, to the best of the authors’ knowledge.     

基于可靠性的复合材料结构稳定性约束优化设计

基于结构的可靠性, 研究了复合材料结构的稳定性约束优化设计方法。考虑材料及载荷的不确定性, 通过结构可靠性分析的响应面法和有限元法的结合, 对复合材料结构稳定性进行可靠性分析; 利用优化软件iSIGHT集成可靠性分析程序, 实现了以铺层层数及铺层角度为设计变量的复合材料结构稳定性约束问题的可靠性优化方法。对层合板及层合圆柱进行算例分析, 验证了本文中可靠性优化方法的有效性, 为工程实际中的复合材料结构稳定性约束优化设计问题提供借鉴。      

Topology optimization of continuum structures subjected to uncertainties in material properties

This work addresses the use of the topology optimization approach to the design of robust continuum structures under the hypothesis of uncertainties with known second‐order statistics. To this end, the second‐order perturbation approach is used to model the response of the structure, and the midpoint discretization technique is used to discretize the random field. The objective function is a weighted sum of the expected compliance and its standard deviation. The optimization problem is solved using a traditional optimality criteria method. It is shown that the correlation length plays an important role in the obtained topology and statistical moments when only the minimization of the standard deviation is considered, resulting in more and thinner reinforcements as the correlation length decreases. It is also shown that the minimization of the expected value is close to the minimization of the deterministic compliance for small variations of Young's modulus. Copyright © 2016 John Wiley & Sons, Ltd.     

多学科设计优化研究及发展趋势分析

多学科设计优化技术属于当前复杂系统设计研究中最新、最活跃的领域,受到越来越广泛的重视。在阐述多学科设计优化技术的定义与内涵的基础上,分析多学科设计优化技术的研究内容,综述了国外的研究现状并对国内外发展状况进行了对比分析,指出了目前多学科设计优化技术研究中存在的问题以及今后的主要发展趋势。     

Performance analysis of BER optimization in WDM systems using EDFA

Wavelength division multiplexing (WDM) systems, which are widely used in telecommunication, have the advantages of huge bandwidth support and reliability. A performance analysis is presented of a WDM system using an erbium-doped fiber amplifier (EDFA), with specific emphasis on bit error rate (BER) optimization. EDFA parameters, including doped fiber length and pump power, are optimized and performance evaluating parameters for different modulation schemes are observed. Simulation results provide optimized BER, noise figure, and gain flatness values. The WDM system is modeled from 1546 nm to 1558 nm bandwidth to obtain maximum gain uniformity, low noise figure, and low BER. This wavelength range is selected to investigate the 1550 nm wavelength commonly used in the telecommunication industry. Also, that we are using a WDM grid, so multiple channels can be accommodated in this range.     

Source/relays/destination combined MMSE-based optimization for AF-MIMO multiple-relay systems with correlated channel uncertainties

In this paper, source/relays-precoders and destination-equalizer combined optimization are proposed as a dual-hop amplify-and-forward (AF) multiple-input multiple-output (MIMO) multiple-relay system with Gaussian random and correlated channel uncertainties in both hops. Taking correlated channel uncertainties into account, a robust transceiver joint optimization design is developed based on the minimum mean-squared error (MMSE) criterion under individual power constraints at the source and the relays. Simulation results illustrate that the robust multiple relays/transceiver joint design architecture for an AF-MIMO system equipped with multiple relays substantially outperforms a nonrobust transceiver design that assumes estimated channels as actual channels.     

Electrical characterization of CMOS transistors subject to externally applied mechanical stress

Hole and electron mobilities in CMOS structures are significantly influenced by a mechanical strain state. In the present work a new experimental device has been designed, able to apply a uniaxial in-plane strain along different crystallographic orientations. A hole mobility enhancement of +10% and an electron mobility decrease of −5% have been demonstrated with the application of a 0.05% compressive 1 1 0 strain; a hole mobility enhancement of +2% and an electron mobility decrease of −3% have been induced into the material with the application of a 0.05% compressive 1 0 0 strain.     

Topology optimization with geometric uncertainties by perturbation techniques

The aim of this paper was to present a topology optimization methodology for obtaining robust designs insensitive to small uncertainties in the geometry. The variations are modeled using a stochastic field. The model can represent spatially varying geometry imperfections in devices produced by etching techniques. Because of under‐etching or over‐etching parts of the structure may become thinner or thicker than a reference design supplied to the manufacturer. The uncertainties are assumed to be small and their influence on the system response is evaluated using perturbation techniques. Under the above assumptions, the proposed algorithm provides a computationally cheap alternative to previously introduced stochastic optimization methods based on Monte Carlo sampling. The method is demonstrated on the design of a minimum compliance cantilever beam and a compliant mechanism. Copyright © 2012 John Wiley & Sons, Ltd.     

Reliability analysis of hierarchical computer-based systems subject to common-cause failures

The results from reliability modeling and analysis are key contributors to design and tuning activities for computer-based systems. Each architecture style, however, poses different challenges for which analytical approaches must be developed or modified. The challenge we address in this paper is the reliability analysis of hierarchical computer-based systems (HS) with common-cause failures (CCF). The dependencies among components introduced by CCF complicate the reliability analysis of HS, especially when components affected by a common cause exist on different hierarchical levels. We propose an efficient decomposition and aggregation (EDA) approach for incorporating CCF into the reliability evaluation of HS. Our approach is to decompose an original HS reliability analysis problem with CCF into a number of reduced reliability problems freed from the CCF concerns. The approach is represented in a dynamic fault tree by a proposed CCF gate modeled after the functional dependency gate. We present the basics of the EDA approach by working through a hypothetical analysis of a HS subject to CCF and show how it can be extended to an analysis of a hierarchical phased-mission system subject to different CCF depending on mission phases.     

Shape optimization based design of arch-type dams under uncertainties

Comparing existing design methodologies for arch-type dams, model-based shape optimization can effectively reduce construction costs and leverage the properties of construction materials. To apply means of shape optimization, suitable variables need to be chosen to formulate the objective function, which is here the volume of the arch dam. A genetic algorithm is adopted as the optimization method, which allows a global search. The reliability index is considered as the main constraint. Its computation is realized by adaptive Kriging Monte Carlo simulation, which visibly increases the analysis efficiency compared with traditional Monte Carlo simulations. Constraints, such as the reliability index and further with respect to the geometry, are taken into consideration by a penalty formulation. By means of this approach, a reliability-based design can be found which ensures both the safety and serviceability of a newly designed arch-type dam.