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As an advanced calculation methodology, reliability-based multidisciplinary design optimization (RBMDO) has been widely acknowledged for the design problems of modern complex engineering systems, not only because of the accurate evaluation of the impact of uncertain factors but also the relatively good balance between economy and safety of performance. However, with the increasing complexity of engineering technology, the proposed RBMDO method gradually cannot effectively solve the higher nonlinear coupled multidisciplinary uncertainty design optimization problems, which limits the engineering application of RBMDO. Many valuable works have been done in the RBMDO field in recent decades to tackle the above challenges. This study is to review these studies systematically, highlight the research opportunities and challenges, and attempt to guide future research efforts.

This study presents a comprehensive review of the RBMDO theory, mainly including the reliability analysis methods of different uncertainties and the decoupling strategies of RBMDO.

First, the multidisciplinary design optimization (MDO) preliminaries are given. The basic MDO concepts and the corresponding mathematical formulas are illustrated. Then, the procedures of three RBMDO methods with different reliability analysis strategies are introduced in detail. These RBMDO methods were proposed for the design optimization problems under different uncertainty types. Furtherly, an optimization problem for a certain operating condition of a turbine runner blade is introduced to illustrate the engineering application of the above method. Finally, three aspects of future challenges for RBMDO, namely, time-varying uncertainty analysis; high-precision surrogate models, and verification, validation and accreditation (VVA) for the model, are discussed followed by the conclusion.

The scope of this study is to introduce the RBMDO theory systematically. Three commonly used RBMDO-SORA methods are reviewed comprehensively, including the methods' general procedures and mathematical models.

Within the current industrial context, companies aim to decrease the design process time and cost. The multidisciplinary design optimization (MDO) appears as a solution to accelerate the process and support designers in different stages of the design cycle. However, this relatively new concept needs to be integrated efficiently in the industrial environment and issues related to collaboration, data management, traceability and reuse need to be overcome.

The aim of this work is to efficiently integrate the MDO in the industrial design cycle by means of knowledge management (KM) techniques. To take into account the industrial environment, the methodology was applied in a collaborative software.

An example of collaborative design and optimization of an electronic throttle body (ETB) controller is presented with industrial requirements. The design problem was solved successfully and demonstrates the efficiency of the methodology in collaborative environments.

The contributions of this work lie in the structuration of the knowledge to support MDO and the definition of a general way to connect the existent MDO tools to the knowledge base. This methodology will enable to freely link different steps of the design process and reduce considerably the setting time of MDO in industries.

In this paper, a turbine blade was optimized by multidisciplinary design optimization (MDO) method. This turbine blade optimization is based on the optimization frame software iSIGHT, in which four disciplines (aerodynamics, thermal dynamics, structural mechanics and structural dynamics) have been integrated. Two commercial discipline analysis soft wares, NUMECA and ANSYS, are coupled in the platform iSIGHT. The three dimensional (3‐D) model of a blade was firstly parameterized. And then a set of parameters are chosen to optimize the blade to obtain the better overall properties. The result shows that the overall performances of the turbine blade have been improved remarkably after it is optimized by using the MDO method.

For complex engineering problems, multidisciplinary design optimization (MDO) techniques use some disciplines that need to be run several times in different modules. In addition, mathematical modeling of a discipline can be improved for each module. The purpose of this paper is to show that multi-modular design optimization (MMO) improves the design performances in comparison with MDO technique for complex systems.

MDO framework and MMO framework are developed to optimum design of a complex system. The nonlinear equality and inequality constrains are considered. The system optimizers included Genetic Algorithm and Sequential Quadratic Programming.

As shown, fewer design variables (optimization variables) are needed at the system level for MMO. Unshared variables are optimized in the related module when shared variables are optimized at the system level. The results of this research show that MMO has lower elapsed times (14 percent) with lower F-count (16 percent).

The monopropellant propulsion upper-stage is selected as a case study. In this paper, the efficient model of the monopropellant propulsion system is proposed. According to the results, the proposed model has acceptable accuracy in mass model (error < 2 percent), performance estimation (error < 6 percent) and geometry estimation (error < 10 percent).

The monopropellant propulsion system is broken down into the three important modules including propellant tank (tank and propellant), pressurized feeding (tank and gas) and thruster (catalyst, nozzle and catalysts bed) when chemical decomposition, aerothermodynamics, mass and configuration, catalyst and structure have been considered as the disciplines. The both MMO and MDO frameworks are developed for the monopropellant propulsion system.

The purpose of this paper is to present a modified bi-level integrated system collaborative optimization (BLISCO) to avoid the non-separability of the original BLISCO. Besides, to mitigate the computational burden caused by expensive simulation codes and employ both efficiently simplified and expensively detailed information in multidisciplinary design optimization (MDO), an effective framework combining variable fidelity metamodels (VFM) and modified BLISCO (MBLISCO) (VFM-MBLISCO) is proposed.

The concept of the quasi-separable MDO problems is introduced to limit range of applicability about the BLISCO method and then based on the quasi-separable MDO form, the modification of BLISCO method without any derivatives is presented to solve the problems of BLISCO. Besides, an effective framework combining VFM-MBLISCO is presented.

One mathematical problem conforms to the quasi-separable MDO form is tested and the overall results illustrate the feasibility and robustness of the MBLISCO. The design of a Small Waterplane Area Twin Hull catamaran demonstrates that the proposed VFM-MBLISCO framework is a feasible and efficient design methodology in support of design of engineering products.

The proposed approach exhibits great capability for MDO problems with tremendous computational costs.

A MBLISCO is proposed which can avoid the non-separability of the original BLISCO and an effective framework combining VFM-MBLISCO is presented to efficiently integrate the different fidelities information in MDO.

The purpose of this paper is to study the consideration of uncertainty from analysis modules for aircraft conceptual design by implementing uncertainty-based design optimization methods. Reliability-Based Design Optimization (RBDO), Possibility-Based Design Optimization (PBDO) and Robust Design Optimization (RDO) methods were developed to handle uncertainties of design optimization. The RBDO method is found suitable for uncertain parameters when sufficient information is available. On the other hand, the PBDO method is proposed when uncertain parameters have insufficient information. The RDO method can apply to both cases. The RBDO, PBDO and RDO methods were considered with the Multidisciplinary Design Optimization (MDO) method to generate conservative design results when low fidelity analysis tools are used.

Methods combining MDO with RBDO, PBDO and RDO were developed and have been applied to a numerical analysis and an aircraft conceptual design. This research evaluates and compares the characteristics of each method in both cases.

The RBDO result can be improved when the amount of data concerning uncertain parameters is increased. Conversely, increasing information regarding uncertain parameters does not improve the PBDO result. The PBDO provides a conservative result when less information about uncertain parameters is available.

The formulation of RDO is more complex than other methods. If the uncertainty information is increased in aircraft conceptual design case, the accuracy of RBDO will be enhanced.

This research increases the probability of a feasible design when it considers the uncertainty. This result gives more practical optimization results on a conceptual design level for fabrication.

It is RBDO, PBDO and RDO methods combined with MDO that satisfy the target probability when the uncertainties of low fidelity analysis models are considered.

The purpose of this paper is to investigate the use of multidisciplinary optimization (MDO) formulations within space‐mapping techniques in order to reduce their computing time.

The aim of this work is to quantify the interest of using MDO formulations within space mapping techniques. A comparison of three MDO formulations is carried out in a short time by using an analytical model of a safety transformer. This comparison reveals the advantage of two formulations in terms of robustness and computing time among the three MDO formulations. Then, the best formulations are investigated within output space mapping, using both analytical and FE models of the transformer.

A major computing time gain equal to 5.5 is achieved using the Individual Disciplinary Feasibility formulation within the output space‐mapping technique in the case of the safety transformer.

The MultiDisciplinary Feasibility formulation is the common formulation used within space‐mapping technique because it is the most conventional way to perform MDO. The originality of this paper is to investigate the Individual Disciplinary Feasibility formulation within output space‐mapping technique in order to allow the parallelization of calculation and to achieve a major reduction of computing time.

The purpose of this paper is a development of a virtual flight test framework with derivative design optimization. Aircraft manufactures and engineers have been putting significant effort into the design process to lower the cost of development and time to a minimum. In terms of flight tests and aircraft certification, implementing simulation and virtual test techniques may be a sufficient method in achieving these goals. In addition to simulation and virtual test, a derivative design can be implemented to satisfy different market demands and technical changes while reducing development cost and time.

In this paper, a derivative design optimization was applied to Expedition 350, a small piston engine powered aircraft developed by Found Aircraft in Canada. A derivative that changes the manned aircraft to an Unmanned Aerial Vehicle for payload delivery was considered. An optimum configuration was obtained while enhancing the endurance of the UAV. The multidisciplinary design optimization module of the framework represents the optimized configuration and additional parameters for the simulator. These values were implemented in the simulator and generated the aircraft model for simulation. Two aircraft models were generated for the flight test.

The optimization process delivered the UAV derivative of Expedition E350, and it had increased endurance up to 21.7 hours. The original and optimized models were implemented into virtual flight test. The cruise performance exhibited less than 10 per cent error on cruise performance between the original model and Pilots Operating Handbook (POH). The dynamic stability of original and optimized models was tested by checking Phugoid, short period, Dutch roll and spiral roll modes. Both models exhibited stable dynamic stability characteristics.

The original Expedition 350 was generated to verify the accuracy of the simulation data by comparing its result with actual flight test data. The optimized model was generated to evaluate the optimization results. Ultimately, the virtual flight test framework with an aircraft derivative design was proposed in this research. The additional module for derivative design optimization was developed and its results were implemented to commercial off-the-shelf simulators.

This paper proposed the application of UAV derivative design optimization for the virtual flight test framework. The methodology included the optimization of UAV derivative utilizing MDO and virtual flight testing of an optimized result with a flight simulator.

In multidisciplinary design optimization (MDO), if the relationships between design variables and some output parameters, which are important performance constraints, are complex implicit problems, plenty of time should be spent on computationally expensive simulations to identify whether the implicit constraints are satisfied with the given design variables during the optimization iteration process. The purpose of this paper is to propose an ensemble of surrogates-based analytical target cascading (ESATC) method to tackle such MDO engineering design problems with reduced computational cost and high optimization accuracy.

Different surrogate models are constructed based on the sample point sets obtained by Latin hypercube sampling (LHS) method. Then, according to the error metric of each surrogate model, the repeated ensemble of surrogates is constructed to approximate the implicit objective functions and constraints. Under the framework of analytical target cascading (ATC), the MDO problem is decomposed into several optimization subproblems and the function of analysis module of each subproblem is simulated by repeated ensemble of surrogates, working together to find the optimum solution.

The proposed method shows better modeling accuracy and robustness than other individual surrogate model-based ATC method. A numerical benchmark problem and an industrial case study of the structural design of a super heavy vertical lathe machine tool are utilized to demonstrate the accuracy and efficiency of the proposed method.

This paper integrates a repeated ensemble method with ATC strategy to construct the ESATC framework which is an effective method to solve MDO problems with implicit constraints and black-box objectives.

To obtain the global optimum of large‐scale complex engineering systems, the paper proposes a decomposition‐coordination method of multidisciplinary design optimization (MDO).

A rational decomposition approach based on artificial neural network (ANN) and genetic algorithms is proposed for partitioning the complex design problem into smaller, more tractable subsystems. Once the problem is decomposed into subsystems, each subsystem may be solved in parallel provided that there is some mechanism to coordinate the solutions in the different subsystems. So the response surface approximation model based on the ANN as a coordination method is described and a MDO framework is presented.

The proposed method was implemented in the design of a tactical missile. Numerical results show the effectiveness of the decomposition‐coordination method, as indicated by both better performance and lower computational requirements.

This paper adopts a novel MDO method to solve complex engineering problem and offers a potential and efficient MDO framework to researchers.