An efficient metamodel-based multi-objective multidisciplinary design optimization framework

This paper presents an efficient metamodel-based multi-objective multidisciplinary design optimization (MDO) architecture for solving multi-objective high fidelity MDO problems. One of the important features of the proposed method is the development of an efficient surrogate model-based multi-objective particle swarm optimization (EMOPSO) algorithm, which is integrated with a computationally efficient metamodel-based MDO architecture. The proposed EMOPSO algorithm is based on sorted Pareto front crowding distance, utilizing star topology. In addition, a constraint-handling mechanism in non-domination appointment and fuzzy logic is also introduced to overcome feasibility complexity and rapid identification of optimum design point on the Pareto front. The proposed algorithm is implemented on a metamodel-based collaborative optimization architecture. The proposed method is evaluated and compared with existing multi-objective optimization algorithms such as multi-objective particle swarm optimization (MOPSO) and non-dominated sorting genetic algorithm II (NSGA-II), using a number of well-known benchmark problems. One of the important results observed is that the proposed EMOPSO algorithm provides high diversity with fast convergence speed as compared to other algorithms. The proposed method is also applied to a multi-objective collaborative optimization of unmanned aerial vehicle wing based on high fidelity models involving structures and aerodynamics disciplines. The results obtained show that the proposed method provides an effective way of solving multi-objective multidisciplinary design optimization problem using high fidelity models.     

An efficient strategy for reliability-based multidisciplinary design optimization using BLISS

This paper presents an efficient reliability-based multidisciplinary design optimization (RBMDO) strategy. The conventional RBMDO has tri-level loops: the first level is an optimization in the deterministic space, the second one is a reliability analysis in the probabilistic space, and the third one is the multidisciplinary analysis. Since it is computationally inefficient when high-fidelity simulation methods are involved, an efficient strategy is proposed. The strategy [named probabilistic bi-level integrated system synthesis (ProBLISS)] utilizes a single-level reliability-based design optimization (RBDO) approach, in which the reliability analysis and optimization are conducted in a sequential manner by approximating limit state functions. The single-level RBDO is associated with the BLISS formulation to solve RBMDO problems. Since both the single-level RBDO and BLISS are mainly driven by approximate models, the accuracy of models can be a critical issue for convergence. The convergence of the strategy is guaranteed by employing the trust region–sequential quadratic programming framework, which validates approximation models in the trust region radius. Two multidisciplinary problems are tested to verify the strategy. ProBLISS significantly reduces the computational cost and shows stable convergence while maintaining accuracy.     

An efficient heuristic for reliability design optimization problems

This paper develops an efficient heuristic to solve two typical combinatorial optimization problems frequently met when designing highly reliable systems. The first one is the redundancy allocation problem (RAP) of series-parallel binary-state systems. The design goal of the RAP is to select the optimal combination of elements and redundancy levels to maximize system reliability subject to the system budget and to the system weight. The second problem is the expansion-scheduling problem (ESP) of multi-state series-parallel systems. In this problem, the study period is divided into several stages. At each stage, the demand is represented as a piecewise cumulative load curve. During the system lifetime, the demand can increase and the total productivity may become insufficient to assume the demand. To increase the total system productivity, elements are added to the existing system. The objective in the ESP is to minimize the sum of costs of the investments over the study period while satisfying availability constraints at each stage. The heuristic approach developed to solve the RAP and the ESP is based on a combination of space partitioning, genetic algorithms (GA) and tabu search (TS). After dividing the search space into a set of disjoint subsets, this approach uses GA to select the subspaces, and applies TS to each selected subspace. Numerical results for the test problems from previous research are reported and compared. The results show the advantages of the proposed approach for solving both problems.     

Sequential optimization and reliability assessment for multidisciplinary systems design

With higher reliability and safety requirements, reliability-based design has been increasingly applied in multidisciplinary design optimization (MDO). A direct integration of reliability-based design and MDO may present tremendous implementation and numerical difficulties. In this work, a methodology of sequential optimization and reliability assessment for MDO is proposed to improve the efficiency of reliability-based MDO. The central idea is to decouple the reliability analysis from MDO with sequential cycles of reliability analysis and deterministic MDO. The reliability analysis is based on the first-order reliability method (FORM). In the proposed method, the reliability analysis and the deterministic MDO use two MDO strategies, the multidisciplinary feasible approach and the individual disciplinary feasible approach. The effectiveness of the proposed method is illustrated with two example problems.     

Sequential optimization and reliability assessment for multidisciplinary design optimization under aleatory and epistemic uncertainties

In engineering design, to achieve high reliability and safety in complex and coupled systems (e.g., Multidisciplinary Systems), Reliability Based Multidisciplinary Design Optimization (RBMDO) has been received increasing attention. If there are sufficient data of uncertainties to construct the probability distribution of each input variable, the RBMDO can efficiently deal with the problem. However there are both Aleatory Uncertainty (AU) and Epistemic Uncertainty (EU) in most Multidisciplinary Systems (MS). In this situation, the results of the RBMDO will be unreliable or risky because there are insufficient data to precisely construct the probability distribution about EU due to time, money, etc. This paper proposes formulations of Mixed Variables (random and fuzzy variables) Multidisciplinary Design Optimization (MVMDO) and a method of MVMDO within the framework of Sequential Optimization and Reliability Assessment (MVMDO-SORA). The MVMDO overcomes difficulties caused by insufficient information for uncertainty. The proposed method enables designers to solve MDO problems in the presence of both AU and EU. Besides, the proposed method can efficiently reduce the computational demand. Examples are used to demonstrate the proposed formulations and the efficiency of MVMDO-SORA.     

A surrogate based multistage-multilevel optimization procedure for multidisciplinary design optimization

Optimization procedure is one of the key techniques to address the computational and organizational complexities of multidisciplinary design optimization (MDO). Motivated by the idea of synthetically exploiting the advantage of multiple existing optimization procedures and meanwhile complying with the general process of satellite system design optimization in conceptual design phase, a multistage-multilevel MDO procedure is proposed in this paper by integrating multiple-discipline-feasible (MDF) and concurrent subspace optimization (CSSO), termed as MDF-CSSO. In the first stage, the approximation surrogates of high-fidelity disciplinary models are built by disciplinary specialists independently, based on which the single level optimization procedure MDF is used to quickly identify the promising region and roughly locate the optimum of the MDO problem. In the second stage, the disciplinary specialists are employed to further investigate and improve the baseline design obtained in the first stage with high-fidelity disciplinary models. CSSO is used to organize the concurrent disciplinary optimization and system coordination so as to allow disciplinary autonomy. To enhance the reliability and robustness of the design under uncertainties, the probabilistic version of MDF-CSSO (PMDF-CSSO) is developed to solve uncertainty-based optimization problems. The effectiveness of the proposed methods is verified with one MDO benchmark test and one practical satellite conceptual design optimization problem, followed by conclusion remarks and future research prospects.     

An efficient lightweight design strategy for body-in-white based on implicit parameterization technique

Structural and Multidisciplinary Optimization - In the early design phase of vehicles, performing lightweight design of body-in-white (BIW) using shape, size and topology optimization is a...     

OpenMDAO: an open-source framework for multidisciplinary design,analysis, and optimization

Structural and Multidisciplinary Optimization - Multidisciplinary design optimization (MDO) is concerned with solving design problems involving coupled numerical models of complex engineering...     

A web services-based multidisciplinary design optimization framework for complex engineering systems with uncertainties

With the increased complexity of complex engineering systems (CES), more and more disciplines, coupled relationships, work processes, design data, design knowledge and uncertainties are involved. Currently, the MDO is facing unprecedented challenges especially in dealing with the CES by different specialists dispersed geographically on heterogeneous platforms with different analysis tools. The product design data integration and data sharing among the participants and the workflow optimization hamper the development and applications of MDO in enterprises seriously. Therefore, a multi-hierarchical integrated product design data model (MiPDM) supporting the MDO in web environment and a web services-based MDO framework considering aleatory and epistemic uncertainties are proposed in this paper. With the enabling technologies including web services, ontology, workflow, agent, XML, and evidence theory, the proposed framework enables the designers geographically dispersed to work collaboratively in the MDO environment. The ontology-based workflow enables the logical reasoning of MDO to be processed dynamically. Finally, a proof-of-concept prototype system is developed based on Java 2 Platform Enterprise Edition (J2EE) and an example of supersonic business jet is demonstrated to verify the web services-based MDO framework.     

Extending SORA method for reliability-based design optimization using probability and convex set mixed models

Structural and Multidisciplinary Optimization - In many practical applications, probabilistic and bounded uncertainties often arise simultaneously, and these uncertainties can be described by using...     

Sequential optimization and fuzzy reliability analysis for multidisciplinary systems

Structural and Multidisciplinary Optimization - To meet the rising demand for high reliability in complex multidisciplinary engineering systems, more attention has been paid to reliability-based...     

An approximate sequential optimization and reliability assessment method for reliability-based design optimization

Sequential optimization and reliability assessment (SORA) is one of the most popular decoupled approaches to solve reliability-based design optimization (RBDO) problem because of its efficiency and robustness. In SORA, the double loop structure is decoupled through a serial of cycles of deterministic optimization and reliability assessment. In each cycle, the deterministic optimization and reliability assessment are performed sequentially and the boundaries of violated constraints are shifted to the feasible direction according to the reliability information obtained in the previous cycle. In this paper, based on the concept of SORA, approximate most probable target point (MPTP) and approximate probabilistic performance measure (PPM) are adopted in reliability assessment. In each cycle, the approximate MPTP needs to be reserved, which will be used to obtain new approximate MPTP in the next cycle. There is no need to evaluate the performance function in the deterministic optimization since the approximate PPM and its sensitivity are used to formulate the linear Taylor expansion of the constraint function. One example is used to illustrate that the approximate MPTP will approach the accurate MPTP with the iteration. The design variables and the approximate MPTP converge simultaneously. Numerical results of several examples indicate the proposed method is robust and more efficient than SORA and other common RBDO methods.     

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.     

Component-oriented decomposition for multidisciplinary design optimization in building design

The potential of Multidisciplinary Design Optimization (MDO) is not sufficiently exploited in current building design practice. I argue that this field of engineering requires a special setup of the optimization model that considers the uniqueness of buildings, and allows the designer to interact with the optimization in order to assess qualities of aesthetics, expression, and building function. For this reason, the approach applies a performance optimization based on resource consumption extended by preference criteria. Furthermore, building design-specific components serve for the decomposition and an interactive way of working. The component scheme follows the Industry Foundation Classes (IFC) as a common Building Information Model (BIM) standard in order to allow a seamless integration into an interactive CAD working process in the future. A representative case study dealing with a frame-based hall design serves to illustrate these considerations. An N-Square diagram or Design Structure Matrix (DSM) represents the system of components with the disciplinary dependencies and workflow of the analysis. The application of a Multiobjective Genetic Algorithm (MOGA) leads to demonstrable results.     

An efficient query optimization strategy for spatio-temporal queries in video databases

The interest for multimedia database management systems has grown rapidly due to the need for the storage of huge volumes of multimedia data in computer systems. An important building block of a multimedia database system is the query processor, and a query optimizer embedded to the query processor is needed to answer user queries efficiently. Query optimization problem has been widely studied for conventional database systems; however it is a new research area for multimedia database systems. Due to the differences in query processing strategies, query optimization techniques used in multimedia database systems are different from those used in traditional databases. In this paper, a query optimization strategy is proposed for processing spatio-temporal queries in video database systems. The proposed strategy includes reordering algorithms to be applied on query execution tree. The performance results obtained by testing the reordering algorithms on different query sets are also presented.     

An efficient procedure for structural reliability-based robust design optimization

This paper focuses on the development of an optimization tool with the aim to obtain robust and reliable designs in short computational time. The robustness measures considered here are the expected value and standard deviation of the performance function involved in the optimization problem. When using these robustness measures combined, the search of optimal design appears as a robust multiobjective optimization (RMO) problem. Reliable design addresses uncertainties to restrict the structural probability of failure. The mathematical formulation for the reliability based robust design optimization (RBRDO) problem is obtained by adding a reliability based constraint into the RMO problem. As both, statistics calculations and the reliability analysis could be very costly, approximation technique based on reduced-order modeling (ROM) is also incorporated in our procedure. The selected ROM is the proper orthogonal decomposition (POD) method, with the aim to produce fast outputs considering structural non-linear behavior. Moreover, to obtain RBRDO designs with reduced CPU time we propose others developments to be added in the integrated tool. They are: Probabilistic Collocation Method (PCM) to evaluate the statistics of the structural responses and, also, an approximated reliability constraints procedure based on the Performance Measure Approach (PMA) for reliability constraint assessment. Finally, Normal-Boundary Intersection (NBI) or Normalized Normal-Constraint (NNC) multiobjective optimization techniques are employed to obtain fast and even spread Pareto robust designs. To illustrate the application of the proposed tool, optimization studies are conducted for a linear (benchmark) and nonlinear trusses problems. The nonlinear example consider different loads level, exploring the material plasticity. The integrated tool prove to be very effective reducing the computational time by up to five orders of magnitude, when compared to the solutions obtained via classical standard approaches.     

一种多学科设计优化工作流验证方法

在多学科设计优化集成系统中,设计过程和优化求解算法均通过可视化工作流实现,工作流有效性验证对提高设计效率和提高系统的用户体验具有重要意义。当前验证方法主要针对办公自动和企业管理系统中的工作流验证问题,多学科设计优化集成系统中的工作流验证问题研究较少。在分析前期工作验证技术的基础上,针对以循环结构为特征的优化环,提出一种基于图论方法的,名为浓缩环(concentration-loop)的验证算法。结合发射平台数字化设计系统的设计与实现,对该算法进行了验证。     

An efficient optimization method for periodic lattice cellular structure design based on the K-fold SVR model

The design optimization of periodic lattice cellular structure relying exclusively on the computational simulation model is a time-consuming, even computationally prohibitive process. To relieve the computational burden, an efficient optimization method for periodic lattice cellular structure design based on the K-fold support vector regression model (K-SVR) is proposed in this paper. First, based on the loading experiments, the most promising unit cell of periodic lattice cellular structure is selected from five typical unit cells. Second, an initial SVR model is constructed to replace the simulation model of the periodic lattice cellular structure, and the K-fold cross-validation approach is used to extract the error information from the SVR model at the sample points. According to the error information, the sample points are sorted and classified into several sub-sets. Then, a global K-SVR model is re-constructed by aggregating each SVR model under each sub-set. Third, considering that there exists prediction errors between the K-SVR model and the simulation model, which may lead to infeasible optimal solutions, an uncertainty quantification approach is developed to ensure the feasibility of the optimal solution for the periodic lattice cellular structure design. Finally, the effectiveness and merits of the proposed approach are demonstrated on the design optimization of the A-pillar and seat-bottom frame.

     

A duality based framework for integrating reliability and precision for sensor network design

In sensor network design literature, requirements such as maximization of the network reliability [Y. Ali, S. Narasimhan, Sensor network design for maximizing reliability of linear processes, AIChE J. 39 (1993) 820–828; Y. Ali, S. Narasimhan, Redundant sensor network design for linear processes, AIChE J. 41 (1995) 2237–2249] and minimization of cost subject to precision constraints [M. Bagajewicz, Design and retrofit of sensor networks in process plants, AIChE J. 43 (1997) 2300–2306; M. Bagajewicz, E. Cabrera, New MILP formulation for instrumentation network design and upgrade, AIChE J. 48 (2002) 2271–2282] have been proposed as a criteria for optimally locating sensors. In this article, we show that the problems of maximizing reliability and maximizing precision (or minimizing variance) for linear processes are dual of each other. To achieve this duality, we propose transformations which can be used to convert sensor failure probabilities into equivalent sensor variances and vice versa. Thus, the duality enables working in a single framework with specified criteria on reliability as well as precision. As an application of this duality, we propose two formulations for the sensor network design problem viz., maximization of the network reliability subject to precision constraints and minimization of the network variance subject to reliability constraints. We also show the utility of these formulations to determine the pareto-front for the combinatorial sensor network design problem. Hydrodealkylation and steam-metering case studies are used to illustrate the proposed ideas.     

Implementation of set-based design in multidisciplinary design optimization

Set-based design is a design approach where feasible regions for the design variables are determined from different disciplines, with the goal of locating and working with the areas of feasible overlap. During the process the constraints are adjusted in order to accommodate conflicting requirements between disciplines. The main objective of set-based design is to narrow the design space, while delaying the pursuit of a single point design as much as possible. This process avoids finalizing decisions early and allows for flexibility in dealing with requirement creep. This paper presents the development and application of a new multidisciplinary design optimization (MDO) algorithm inspired by the principles of set-based design. The new MDO algorithm was developed with the core concept of describing the design using sets to incorporate features of set-based design and achieve greater flexibility than with a single-point optimization. The MDO algorithm was applied to a ship design problem and the ship design application demonstrated the value of utilizing set-based design as a space-reducing technique before approaching the problem with a point-based optimization. Furthermore, incorporating flexibility in the constraints allowed the optimization to handle a problem with very strict constraints in a rational manner and minimize the necessary constraint violation.