A digital twin-based multidisciplinary collaborative design approach for complex engineering product development

With the ever-increasing demand for personalized product functions, product structure becomes more and more complex. To design a complex engineering product, it involves mechanical, electrical, automation and other relevant fields, which requires a closer multidisciplinary collaborative design (MCD) and integration. However, the traditional design method lacks multidisciplinary coordination, which leads to interaction barriers between design stages and disconnection between product design and prototype manufacturing. To bridge the gap, a novel digital twin-enabled MCD approach is proposed. Firstly, the paper explores how to converge the MCD into the digital design process of complex engineering products in a cyber-physical system manner. The multidisciplinary collaborative design is divided into three parts: multidisciplinary knowledge collaboration, multidisciplinary collaborative modeling and multidisciplinary collaborative simulation, and the realization methods are proposed for each part. To be able to describe the complex product in a virtual environment, a systematic MCD framework based on the digital twin is further constructed. Integrate multidisciplinary collaboration into three stages: conceptual design, detailed design and virtual verification. The ability to verify and revise problems arising from multidisciplinary fusions in real-time minimizes the number of iterations and costs in the design process. Meanwhile, it provides a reference value for complex product design. Finally, a design case of an automatic cutting machine is conducted to reveal the feasibility and effectiveness of the proposed approach.     

Concurrent treatment of parametric uncertainty and metamodeling uncertainty in robust design

Robust design is an effective approach to design under uncertainty. Many works exist on mitigating the influence of parametric uncertainty associated with design or noise variables. However, simulation models are often computationally expensive and need to be replaced by metamodels created using limited samples. This introduces the so-called metamodeling uncertainty. Previous metamodel-based robust designs often treat a metamodel as the real model and ignore the influence of metamodeling uncertainty. In this study, we introduce a new uncertainty quantification method to evaluate the compound effect of both parametric uncertainty and metamodeling uncertainty. Then the new uncertainty quantification method is used for robust design. Simplified expressions of the response mean and variance is derived for a Kriging metamodel. Furthermore, the concept of robust design is extended for metamodel-based robust design accounting for both sources of uncertainty. To validate the benefits of our method, two mathematical examples without constraints are first illustrated. Results show that a robust design solution can be misleading without considering the metamodeling uncertainty. The proposed uncertainty quantification method for robust design is shown to be effective in mitigating the effect of metamodeling uncertainty, and the obtained solution is found to be more “robust” compared to the conventional approach. An automotive crashworthiness example, a highly expensive and non-linear problem, is used to illustrate the benefits of considering both sources of uncertainty in robust design with constraints. Results indicate that the proposed method can reduce the risk of constraint violation due to metamodel uncertainty and results in a “safer” robust solution.     

Maximum variation analysis based analytical target cascading for multidisciplinary robust design optimization under interval uncertainty

Analytical target cascading (ATC) is a generally used hierarchical method for deterministic multidisciplinary design optimization (MDO). However, uncertainty is almost inevitable in the lifecycle of a complex system. In engineering practical design, the interval information of uncertainty can be more easily obtained compared to probability information. In this paper, a maximum variation analysis based ATC (MVA-ATC) approach is developed. In this approach, all subsystems are autonomously optimized under the interval uncertainty. MVA is used to establish an outer-inner framework which is employed to find the optimal scheme of system and subsystems. All subsystems are coordinated at the system level to search the system robust optimal solution. The accuracy and validation of the presented approach are tested using a classical mathematical example, a heart dipole optimization problem, and a battery thermal management system (BTMS) design problem.     

A reliability-based multidisciplinary design optimization procedure based on combined probability and evidence theory

To address the reliability-based multidisciplinary design optimization (RBMDO) problem under mixed aleatory and epistemic uncertainties, an RBMDO procedure is proposed in this paper based on combined probability and evidence theory. The existing deterministic multistage-multilevel multidisciplinary design optimization (MDO) procedure MDF-CSSO, which combines the multiple discipline feasible (MDF) procedure and the concurrent subspace optimization (CSSO) procedure to mimic the general conceptual design process, is used as the basic framework. In the first stage, the surrogate based MDF is used to quickly identify the promising reliable regions. In the second stage, the surrogate based CSSO is used to organize the disciplinary optimization and system coordination, which allows the disciplinary specialists to investigate and optimize the design with the corresponding high-fidelity models independently and concurrently. In these two stages, the reliability-based optimization both in the system level and the disciplinary level are computationally expensive as it entails nested optimization and uncertainty analysis. To alleviate the computational burden, the sequential optimization and mixed uncertainty analysis (SOMUA) method is used to decompose the traditional double-level reliability-based optimization problem into separate deterministic optimization and mixed uncertainty analysis sub-problems, which are solved sequentially and iteratively until convergence is achieved. By integrating SOMUA into MDF-CSSO, the Mixed Uncertainty based RBMDO procedure MUMDF-CSSO is developed. The effectiveness of the proposed procedure is testified with one simple numerical example and one MDO benchmark test problem, followed by some conclusion remarks.     

A method for selecting surrogate models in crashworthiness optimization

Surrogate model or response surface based design optimization has been widely adopted as a common process in automotive industry, as large-scale, high fidelity models are often required. However, most surrogate models are built by using a limited number of design points without considering data uncertainty. In addition, the selection of surrogate model in the literature is often arbitrary. This paper presents a Bayesian metric to complement root mean square error for selecting the best surrogate model among several candidates in a library under data uncertainty. A strategy for automatically selecting the best surrogate model and determining a reasonable sample size was proposed for design optimization of large-scale complex problems. Lastly, a vehicle example with full-frontal and offset-frontal impacts was presented to demonstrate the proposed methodology.     

面向组件的分布式零件优化设计和数据管理系统

采用分布式三层网络模型,构建了分布式的基于UG外部开发的零件参数化设计组件及基于Fortran语言的优化设计组件．利用VC 6．0和UG二次开发接口,以面向组件的系统开发方法和COM／DCOM编程方式进行了组件拼装,开发了一套集零件数据管理、参数化设计、优化设计和有限元分析等功能于一体的分布式零件优化设计与数据管理系统(D3MS)．     

Nonlinear robust H-infinity filtering for a class of uncertain systems via convex optimization

A new approach for robust H-infinity filtering for a class of Lipschitz nonlinear systems with time-varying uncertainties both in the linear and nonlinear parts of the system is proposed in an LMI framework. The admissible Lipschitz constant of the system and the disturbance attenuation level are maximized simultaneously through convex multi-objective optimization. The resulting H-infinity filter guarantees asymptotic stability of the estimation error dynamics with exponential convergence and is robust against nonlinear additive uncertainty and time-varying parametric uncertainties. Explicit bounds on the nonlinear uncertainty are derived based on norm-wise and element-wise robustness analysis.     

Structural design under bounded uncertainty—Optimization with anti-optimization

In many cases precise probabilistic data are not available on uncertainty in loads, but the magnitude of the uncertainty can be bound. This paper proposes a design approach for structural optimization with uncertain but bounded loads. The problem of identifying critical loads is formulated mathematically as an optimization problem in itself (called anti-optimization), so that the design problem is formulated as a two-level optimization. For linear structural analysis it is shown that the antioptimization part is limited to consideration of the vertices of the load-uncertainty domain. An example of a ten-bar truss is used to demonstrate that we cannot replace the anti-optimization process by considering the largest possible loads.     

基于Taguchi-BPNN-SEDEA的精密产品多元质量非参数稳健优化

针对设计参数不确定性和模型结构未知情形下精密产品多元质量波动问题,同时兼顾主体结构对轻量化设计要求,提出一种基于Taguchi-BPNN-SEDEA的多元质量非参数稳健优化方法.首先,通过正交试验设计和有限元分析获取多元质量数值,运用Taguchi方法将多元质量数值转化为信噪比来衡量精密产品稳健性;其次,运用BPNN非参数模型构建多元质量信噪比预测模型,以避免由参数模型设定导致的误差;在此基础上,提出改进的DEA基本模型,采用SEDEA非参数稳健优化方法,将设计参数不确定性下BPNN非参数模型求解问题转化为不确定性条件下复杂多属性决策问题;最后,通过实例表明,所提出的方法能够有效处理设计参数不确定性和模型结构未知并存情况下的多元质量稳健优化问题,从而验证该方法的可行性.     

An efficient strategy for multidisciplinary reliability design and optimization based on CSSO and PMA in SORA framework

The conventional reliability-based multidisciplinary design optimization (RBMDO) integrates the reliability-based design optimization and multidisciplinary design optimization (MDO) directly, which leads to a triple-level nested optimization loop. Especially, the multidisciplinary reliability analysis in the middle layer dominates the whole efficiency of RBMDO. To tackle this problem, first of all, a sequential multidisciplinary reliability analysis (SMRA) approach that integrates the concurrent subspace optimization (CSSO) strategy and the performance measure approach is proposed, in which the multidisciplinary analysis, system sensitivity analysis and reliability analysis are decoupled and arranged sequentially, making a recursive loop. The multidisciplinary analysis and system sensitivity analysis provide the value and gradient information of limit-state function for reliability analysis respectively. As a result, a great number of repeated iterations of the whole reliability analysis are eliminated. Secondly, the CSSO has been integrated with the sequential optimization and reliability assessment (SORA) to decouple the triple-level nested RBMDO procedures into a sequence of cycles of deterministic MDO and multidisciplinary reliability analysis. Therefore, the expensive computation of the whole reliability analysis model in each iteration of RBMDO is avoided. And also, the CSSO is adopted in the deterministic MDO to deal with medium-scale and coupled multidisciplinary systems. The procedures of the proposed approaches are presented in detail. The effectiveness of the proposed strategies is demonstrated and verified with two design examples.     

Probabilistic analysis and control of systems with uncertain parameters over non-hypercube domain

Generalized polynomial chaos expansion provides a computationally efficient way of quantifying the influence of stochastic parametric uncertainty on the states and outputs of a system. In this study, a polynomial chaos-based method was proposed for an analysis and design of control systems with parametric uncertainty over a non-hypercube support domain. In the proposed method, the polynomial chaos for the hypercube domain was extended to non-hypercube domains through proper parameterization to transform the non-hypercube domains to hypercube domains. Based on the proposed polynomial chaos framework, a constrained optimization problem minimizing the mean under the maximum allowable variance was formulated for a robust controller design of dynamic systems with the parametric uncertainties of the non-hypercube domain. Several numerical examples ranging from integer to fractional order systems were considered to validate the proposed method. The proposed method provided superior control performance by avoiding the over-bounds from a hypercube assumption in a computationally efficient manner. From the simulation examples, the computation time by gPC analysis was approximately 10–100 times lower than the traditional approach.     

支持多学科设计优化的集成产品过程建模方法

针对当前主要的设计过程建模方法缺乏表达复杂产品多学科设计过程中资源的组织调用和协作方式等信息,提出一种支持复杂产品多学科设计优化的设计路线图框架过程建模方法.从全面表达设计过程信息的角度出发,描述产品多学科设计优化过程中的主要活动及其协同关系,建立支持多学科设计优化的过程模型;在此基础上,给出了多学科设计优化的过程规划方法,以降低产品设计过程中的迭代,通过构建支持多学科设计优化的集成产品设计过程结构框架,实现产品多学科设计优化的过程集成.最后通过已开发的多学科系统集成平台,应用具体设计实例验证了整套方法的有效性.     

卫星有效载荷的多目标多学科设计优化研究

在卫星有效载荷系统研究中,实施多目标多学科优化的可行性设计。首先,分析了开展卫星有效载荷多学科设计优化的关键技术。建立了包含天线、转发器、数据传输、可靠性、成本和质量的多学科分析模型。然后,应用多目标遗传算法对某卫星有效载荷的可靠性和成本进行多目标设计优化,获得最优解集。最后,运用多学科协同优化结合遗传算法进行可靠性单目标设计优化。研究结果表明:有效载荷的多目标多学科设计优化全面考虑了多个学科之间的关系,设计人员可按需选择其满意的优化结果,大幅提高设计效率;协同优化方法有助于实现学科自治、并行设计,提高设计的灵活性和缩短设计周期。     

Likelihood-based representation of epistemic uncertainty and its application in robustness-based design optimization

In this paper, we propose a new likelihood-based methodology to represent epistemic uncertainty described by sparse point and/or interval data for input variables in uncertainty analysis and design optimization problems. A worst-case maximum likelihood-based approach is developed for the representation of epistemic uncertainty, which is able to estimate the distribution parameters of a random variable described by sparse point and/or interval data. This likelihood-based approach is general and is able to estimate the parameters of any known probability distributions. The likelihood-based representation of epistemic uncertainty is then used in the existing framework for robustness-based design optimization to achieve computational efficiency. The proposed uncertainty representation and design optimization methodologies are illustrated with two numerical examples including a mathematical problem and a real engineering problem.     

Multiparametric optimization for multidisciplinary engineering design

The area of Multiparametric Optimization (MPO) solves problems that contain unknown problem data represented by parameters. The solutions map parameter values to optimal design and objective function values. In this paper, for the first time, MPO techniques are applied to improve and advance Multidisciplinary Design Optimization (MDO) to solve engineering problems with parameters. A multiparametric subgradient algorithm is proposed and applied to two MDO methods: Analytical Target Cascading (ATC) and Network Target Coordination (NTC). Numerical results on test problems show the proposed parametric ATC and NTC methods effectively solve parametric MDO problems and provide useful insights to designers. In addition, a novel Two-Stage ATC method is proposed to solve nonparametric MDO problems. In this new approach elements of the subproblems are treated as parameters and optimal design functions are constructed for each one. When the ATC loop is engaged, steps involving the lengthy optimization of subproblems are replaced with simple function evaluations.     

Robust stability considerations in optimal design of dynamic systems under uncertainty

This paper presents a method for the incorporation of robust stability criteria in the design of dynamic systems under uncertainty. Process systems are modelled via dynamic mathematical models, variations include both uncertain parameters and time-varying disturbances, while control structure selection and controller design is considered as part of the design optimization problem. Stability criteria are included, based on the concept of the measure of a matrix, to maintain desired dynamic characteristics, in a multiperiod design formulation. A combined flexibility-stabiluty analysis step is also introduced to ensure feasible and stable operation of the dynamic system in the presence of parametric uncertainties and process disturbances. The potential of the proposed approach is illustrated with a ternary distillation column design and control problem (featuring a rigorous tray-by-tray model).     

Use of measurements for enforcing the necessary conditions of optimality in the presence of constraints and uncertainty

Measurements can be used in an optimization framework to compensate the effects of uncertainty in the form of model mismatch or process disturbances. Among the various options for input adaption, a promising approach consists of directly enforcing the necessary conditions of optimality (NCO) that include two parts, the active constraints and the sensitivities. In this paper, the variations of the NCO due to parametric uncertainty are studied and used to design appropriate adaptation laws. The inputs are separated into constraint-seeking and sensitivity-seeking directions depending on which part of the NCO they enforce. In addition, the directional influence of uncertainty is used to reduce the number of variables to adapt. The theoretical concepts are illustrated in simulation via the run-to-run optimization of a batch emulsion polymerization reactor.     

A graph theoretic approach to problem formulation for multidisciplinary design analysis and optimization

The formulation of multidisciplinary design, analysis, and optimization (MDAO) problems has become increasingly complex as the number of analysis tools and design variables included in typical studies has grown. This growth in the scale and scope of MDAO problems has been motivated by the need to incorporate additional disciplines and to expand the parametric design space to enable the exploration of unconventional design concepts. In this context, given a large set of disciplinary analysis tools, the problem of determining a feasible data flow between tools to produce a specified set of system-level outputs is combinatorially challenging. The difficulty is compounded in multi-fidelity problems, which are of increasing interest to the MDAO community. In this paper, we propose an approach for addressing this problem based on the formalism of graph theory. The approach begins by constructing the maximal connectivity graph (MCG) describing all possible interconnections between a set of analysis tools. Graph operations are then conducted to reduce the MCG to a fundamental problem graph (FPG) that describes the connectivity of analysis tools needed to solve a specified system-level design problem. The FPG does not predispose a particular solution procedure; any relevant MDO solution architecture could be selected to implement the optimization. Finally, the solution architecture can be represented in a problem solution graph (PSG). The graph approach is applied to an example problem based on a commercial aircraft MDAO study.     

A stochastic cross‐efficiency data envelopment analysis approach for supplier selection under uncertainty

This paper addresses one of the key objectives of the supply chain strategic design phase, that is, the optimal selection of suppliers. A methodology for supplier selection under uncertainty is proposed, integrating the cross‐efficiency data envelopment analysis (DEA) and Monte Carlo approach. The combination of these two techniques allows overcoming the deterministic feature of the classical cross‐efficiency DEA approach. Moreover, we define an indicator of the robustness of the determined supplier ranking. The technique is able to manage the supplier selection problem considering nondeterministic input and output data. It allows the evaluation of suppliers under uncertainty, a particularly significant circumstance for the assessment of potential suppliers. The novel approach helps buyers in choosing the right partners under uncertainty and ranking suppliers upon a multiple sourcing strategy, even when considering complex evaluations with a high number of suppliers and many input and output criteria.