Deterministic Multidisciplinary Design Optimization Research Articles

Multidisciplinary design optimization of an autonomous underwater vehicles based on random uncertainty

Herein, discipline decomposition was performed for an autonomous underwater vehicle (AUV) based on multidisciplinary design optimization (MDO), and its design parameters were determined. Parameterized analysis of the hull-form and structure disciplines was performed, and an approximate model of these disciplines was established with a high fitting accuracy. An analysis model of propulsion, energy, and system disciplines was developed based on the formula method. Based on collaborative optimization as well as discipline and system level models, a deterministic MDO framework for AUVs was established. Subsequently, an optimized solution was obtained. By considering the random uncertainty of design variables, an MDO framework for the uncertainty of AUVs was established and optimized solutions were obtained. The distribution of solutions obtained from uncertainty optimization was more concentrated and the distribution range was smaller than that obtained using deterministic optimization. Robustness analysis was performed on the initial scheme, typical deterministic optimization schemes, and typical uncertainty optimization schemes. Results showed that fluctuations in design variables may lead to constraints that exceed boundary conditions in the deterministic optimization design scheme. Using uncertainty and objective function optimization, the robustness of the overall scheme of AUVs was improved.

EVTOL Tilt-Wing Aircraft Design under Uncertainty Using a Multidisciplinary Possibilistic Approach

Recent development in Electric Vertical Take-off and Landing (eVTOL) aircraft makes it a popular design approach for urban air mobility (UAM). When designing these configurations, due to the uncertainty present in semi-empirical estimations, often used for aerodynamic characteristics during the conceptual design phase, results can only be trusted to approximately 80% accuracy. Accordingly, an optimized aircraft using semi-empirical estimations and deterministic multi-disciplinary design optimization (MDO) approaches can be at risk of not being certifiable in the detailed design phase of the life cycle. The focus of this study was to implement a robust and efficient possibility-based design optimization (PBDO) method for the MDO of an eVTOL tilt-wing aircraft in the conceptual design phase, using existing conventional designs as an initial configuration. As implemented, the optimization framework utilizes a deterministic gradient-based optimizer, run sequentially with a possibility assessment algorithm, to select an optimal design. To achieve this, the uncertainties which arise from multi-fidelity calculations, such as semi-empirical methods, are considered and used to modify the final design such that its viability is guaranteed in the detailed design phase. With respect to various requirements, including trim, stability, and control behaviors, the optimized eVTOL tilt-wing aircraft design offers the preferred results which ensure that airworthiness criteria are met whilst complying with predefined constraints. The proposed approach may be used to revise currently available light aircraft and develop eVTOL versions from the original light aircraft. The resulting aircraft is not only an optimized layout but one where the stability of the eVTOL tilt-wing aircraft has been guaranteed.

Uncertainty analysis and design optimization of solid rocket motors with finocyl grain

The traditional multidisciplinary design optimization (MDO) method for the conceptual design of the solid rocket motor (SRM) is usually deterministic and seldom focuses on systematic design optimization. This paper develops a systematic design model of the SRM with a finocyl grain and proposes an approach for uncertainty analysis and design optimization of SRM. The mean value and standard deviation of the target function, as well as the probability that the constraints can be met, are calculated using Monte Carlo simulation (MCS) analysis. The uncertainty-based multidisciplinary design optimization (UMDO), together with the deterministic multidisciplinary design optimization (DMDO), is applied to the conceptual design of SRM based on the third-stage engine ZEFIRO9 of the Vega launch vehicle. By main effect diagrams and Pareto diagrams, the most influential design variables and standard deviation of uncertain parameters are obtained, which can help designers understand more of the uncertainty relationships between parameters and system performance.

A novel methodology of sequential optimization and non-probabilistic time-dependent reliability analysis for multidisciplinary systems

Abstract Various uncertainties, which are usually time-dependent, affect the reliability of complicated engineering systems seriously. Considering the fact that only limited sample data of the uncertain variables can be obtained in engineering practice during the whole in-service time of multidisciplinary systems, the interval process model is introduced to model the time-dependent uncertain variables, and a non-probabilistic time-dependent reliability estimation model is proposed. In addition, a sequential multidisciplinary optimization and non-probabilistic time-dependent reliability assessment (SMO_NTRA) approach is developed to decouple the time-dependent reliability analysis from the multidisciplinary design optimization (MDO). In the framework of SMO_NTRA, the deterministic MDO and non-probabilistic time-dependent reliability analysis are executed in a sequential manner. Thus the computationally expensive double level optimization problem can be avoided and the efficiency can be greatly improved. Furthermore, the shifting distance of the constraint is calculated by bi-section method. Both numerical and engineering examples are employed to demonstrate the validity of the proposed method.

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.

Improved collaboration pursuing method for multidisciplinary robust design optimization

The collaboration pursuing method (CPM) is a computationally efficient approach for deterministic multidisciplinary design optimization (MDO). However, it has not been employed to handle problems with uncertainty. Moreover, obtaining actual uncertainty probability distributions is challenging. Compared to probability distributions, the interval information of uncertainties can be more easily obtained. Thus, multidisciplinary robust design optimization (MRDO) under interval uncertainty has been widely investigated. To overcome the inefficiency of existing methods for solving MRDO, this paper proposes an improved collaboration pursuing method (ICPM). In this method, the collaboration model (CM) is utilized to filter the samples that satisfy the coupled state equations in system analysis (SA) or multidisciplinary analysis (MDA). Then, a robustness discrepancy model (RDM) is developed to efficiently select candidate samples that meet the robustness requirements. Next, the mode pursuing sampling (MPS) method is utilized as a global optimizer to drive the optimization process and identify the robust optimum. Finally, a mathematical example and two engineering examples are utilized to evaluate the feasibility and effectiveness of the proposed method.

A novel methodology of reliability-based multidisciplinary design optimization under hybrid interval and fuzzy uncertainties

Various uncertainties exist in engineering practice, which brings adverse effects to the reliability of complicated engineering systems. Considering the case that interval and fuzzy uncertainties exist simultaneously, a new reliability estimation model is proposed based on the level cut strategy and volume ratio theory. The new reliability model is better than the traditional one which is very conservative. Moreover, a sequential optimization and reliability assessment (SORA) approach for multidisciplinary systems under hybrid interval and fuzzy uncertainties is developed to decouple the reliability analysis from the deterministic multidisciplinary design optimization (MDO). In the framework of SORA, the deterministic MDO and reliability analysis are executed sequentially, thus the efficiency can be improved. For the multidisciplinary uncertainty analysis, the first order Taylor expansion method and the interval vertex method are formulated. The calculation of the safety possibility under the volume ratio theory and the calculation of the shifting distance are deduced. Both numerical and engineering examples are employed to demonstrate the validity of the proposed method.

Reliability-Based Multidisciplinary Design Optimization Using Subset Simulation Analysis and Its Application in the Hydraulic Transmission Mechanism Design

The Monte Carlo simulation (MCS) can provide high reliability evaluation accuracy. However, the efficiency of the crude MCS is quite low, in large part because it is computationally expensive to evaluate a very small failure probability. In this paper, a subset simulation-based reliability analysis (SSRA) approach is combined with multidisciplinary design optimization (MDO) to improve the computational efficiency in reliability-based MDO (RBMDO) problems. Furthermore, the sequential optimization and reliability assessment (SORA) approach is utilized to decouple an RBMDO problem into a sequential of deterministic MDO and reliability evaluation problems. The formula of MDO with SSRA within the framework of SORA is proposed to solve a design optimization problem of a hydraulic transmission mechanism.

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.

A Collaborative Approach for Multidisciplinary Systems Reliability Design and Optimization

In order to improve the efficiency and robustness of reliability-based multidisciplinary design optimization (RBMDO), a new collaborative strategy (named C-RBMDO) which integrates performance measure approach (PMA) and concurrent subspace optimization strategy (CSSO) is proposed. Both the mathematical model and optimization procedure are put forward. The traditional triple-level nested flowchart of RBMDO is decoupled with the sequential optimization and reliability assessment (SORA). The deterministic multidisciplinary design optimization and the multidisciplinary reliability analysis are executed by CSSO and PMA respectively. Finally, the proposed method is verified through the design example of gear transmission.

A PMA-Based Collaborative Strategy for Reliability Design and Optimization of Multidisciplinary Systems

To tackle the computing efficiency and robustness problems caused by the reliability index approach (RIA) in reliability-based multidisciplinary design optimization (RBMDO), a new performance measure approach-based method for RBMDO is proposed. Meanwhile, the traditional triple-level nested flowchart of RBMDO is decoupled through the main idea of sequential optimization and reliability assessment (SORA). Both deterministic multidisciplinary design optimization and the multidisciplinary reliability analysis are executed by collaborative optimization (CO). Finally, the proposed method is verified through the design example of gear transmission.

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.

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.

Reliability-based multidisciplinary optimization for aircraft wing design

Aircraft wing design typically involves multiple disciplines such as aerodynamics and structure. Multidisciplinary design optimization (MDO) has been recently used to deal with the multidisciplinary efforts in wing design. When reliability is considered, MDO for the wing design becomes much more computationally intensive. To improve the efficiency, the strategy of using Sequential Optimization and Reliability Assessment (SORA) in MDO is proposed with the application of a simplified wing design problem. The overall reliability-based MDO is decomposed into sequential cycles of deterministic MDO and reliability analysis. The reliability analysis is therefore decoupled from the MDO loop, and the number of reliability analyses is then reduced significantly. It is shown that the use of the SORA method is efficient through the demonstration of a light aircraft wing design problem.