Multidisciplinary optimization design of a new underwater vehicle with highly efficient gradient calculation

Model-Based Systems Engineering (MBSE) supports the system-level design of complex products effectively. Currently, system design and optimization for complex products are two distinct processes that must be executed using different software or platforms, involving intricate data conversion processes. Applying multidisciplinary optimization to validate system optimization often necessitates remodeling the optimization objects, which is time-consuming, labor-intensive, and highly error-prone. A critical activity in systems engineering is identifying the optimal design solution for the entire system. Multidisciplinary Design Optimization (MDO) and reliability analysis are essential methods for achieving this. This paper proposes a SysML-based multidisciplinary reliability design optimization modeling method. First, by analyzing the definitions and mathematical models of multidisciplinary reliability design optimization, the SysML extension mechanism is employed to represent the optimization model based on SysML. Next, model transformation techniques are used to convert the SysML optimization model generated in the first stage into an XML description model readable by optimization solvers. Finally, the proposed method’s effectiveness is validated through an engineering case study of an in-vehicle environmental control integration system. The results demonstrate that this method fully utilizes SysML to express MDO problems, enhancing the efficiency of design optimization for complex systems. Engineers and system designers working on complex, multidisciplinary projects can particularly benefit from these advancements, as they simplify the integration of design and optimization processes, facilitating more reliable and efficient product development.

The design of complex aerospace systems is a multidisciplinary design optimization (MDO) problem involving the interaction of multiple disciplines. However, because of the necessity of evaluating expensive black-box simulations, the enormous computational cost of solving MDO problems in aerospace systems has also become a problem in practice. To resolve this, metamodel-based design optimization techniques have been applied to MDO. With these methods, system models can be rapidly predicted using approximate metamodels to improve the optimization efficiency. This paper presents an overall survey of metamodel-based MDO for aerospace systems. From the perspective of aerospace system design, this paper introduces the fundamental methodology and technology of metamodel-based MDO, including aerospace system MDO problem formulation, metamodeling techniques, state-of-the-art metamodel-based multidisciplinary optimization strategies, and expensive black-box constraint-handling mechanisms. Moreover, various aerospace system examples are presented to illustrate the application of metamodel-based MDOs to practical engineering. The conclusions derived from this work are summarized in the final section of the paper. The survey results are expected to serve as guide and reference for designers involved in metamodel-based MDO in the field of aerospace engineering.

Design engineers and decision-makers across various fields are constantly working to make optimal design decisions for multidisciplinary engineering systems in an effort to improve performance and reduce costs. The multiple disciplines that decision-makers are forced to consider can range from different physical components of a system, to competing physical phenomena influencing a component (e.g. flow forces and structural strength), to completely separate models of interest to a system (e.g. engineering performance and lifecycle cost). The common element that all these decision-making scenarios share is the presence of couplings between the considered disciplines (or subsystems). How the values for these coupling parameters are determined within a decision-making or optimization framework is the subject of countless research efforts. At present the multidisciplinary design optimization (MDO) community has settled on a few proven techniques such Collaborative Optimization (CO) and Analytic Target Cascading (ATC). However, current MDO techniques have issues that limit their effectiveness in solving various MDO problems. Many of these strategies require close coordination between subsystem optimization solvers, require significant effort by decision-makers to pose their problems in a suitable format, and/or can have large computational efficiency problems due to the fact that they involve solving nested optimization problems. In an effort to alleviate some of these issues and make MDO easier to implement and more computationally efficient, a new sequential MDO algorithm called Cooperative Design Optimization (CDO) is proposed. The CDO approach functions through a series of subsystem optimizations using a successively smaller cooperation space. The cooperation space is analogous to the design space of a traditional optimization problem, but includes only the coupling parameters that are a factor in multiple subsystems. A single iteration of the approach can be thought of as a negotiation between all of the subsystems regarding the boundaries of the cooperation space. To facilitate this cooperation, each subsystem optimization problem is restructured as a multi-objective optimization problem so that a Pareto set of optimal solutions, or agreeable design alternatives, are produced. As a result, after all subsystem optimizations are accomplished, each subsystem’s obtained Pareto optimal solution sets are compared with respect to the coupling parameters and new bounds in the cooperation space are determined for the next iteration. This process allows each subsystem to be optimized completely independently within the boundaries of the agreed upon cooperation space while coordination is achieved through an analysis of obtained optimal solutions for each subsystem. Iterations, or negotiations, are repeated until an acceptable solution or set of solutions is obtained for all included subsystems through this cooperative process.

In order to design a vehicle body with high strength and high stiffness, a multi-disciplinary design process should include careful consideration of multi-disciplinary design constraints to properly account for vehicle static stiffness (bending/torsional), durability, Noise/Vibration/Harshness (NVH), crash worthiness, light weight vehicle structure during the early stage of vehicle design process. With this approach, fast development of new vehicle body structures can be achieved with minimal number of iterations to match the conflicting design goals from each discipline. In the current research, a multi-disciplinary design optimization (MDO) based on a meta model is developed and refined to apply for the design of body structure. In an effort to apply the MDO for vehicle body structure, 4 phase procedures were established in the current research. In Phase I, a base model is created. In Phase II, an effect analysis is carried out. In Phase III, a meta model is created. Finally in Phase IV, using the optimization algorithm, the meta model created in Phase III is eventually refined through the process of optimization. In this research, static stiffness (bending / torsional), dynamic stiffness (1st torsion mode) were used for constrained conditions and the mass minimization was the object function for optimization.

Multidisciplinary design optimization of long-range slender guided rockets considering aeroelasticity and subsidiary loads

Multidisciplinary design optimization (MDO) problems are engineering design problems that require the consideration of the interaction between several design disciplines. Due to the organizational aspects of MDO problems, decomposition algorithms are often the only feasible solution approach. Decomposition algorithms reformulate the MDO problem as a set of independent subproblems, one per discipline, and a coordinating master problem. A popular approach to MDO problems is bilevel decomposition algorithms. These algorithms use nonlinear optimization techniques to solve both the master problem and the subproblems. In this paper, we propose two new bilevel decomposition algorithms and analyze their properties. In particular, we show that the proposed problem formulations are mathematically equivalent to the original problem and that the proposed algorithms converge locally at a superlinear rate. Our computational experiments illustrate the numerical performance of the algorithms.

<div class="section abstract"><div class="htmlview paragraph">The design of drive units in electric vehicles (EVs) presents challenges due to the need to pass multiple linear and non-linear load cases. This can result in inefficient design. Therefore, optimization plays a critical role in improving the design efficiency. However, setting up the optimization process itself can be challenging, especially when dealing with complex design variables and different load cases that require the use of various computer-aided engineering (CAE) solvers. The drive unit, being a casting component, presents additional challenges in setting up Multidisciplinary Design Optimization (MDO) process. This paper introduces an efficient process for addressing these challenges by presenting a sample Multidisciplinary Design Optimization (MDO) problem. The problem involves the manipulation of discrete design variables, such as the number of ribs, and incorporates five different load cases that require the utilization of different CAE solvers. The proposed process demonstrates a streamlined approach that can be completed in less than one week. It showcases the steps involved in setting up the optimization process, including defining the design variables, selecting appropriate load cases, and integrating different CAE solvers. By following this process, engineers can effectively optimize the design of drive units in EVs, leading to improved mass efficiency. Overall, this paper highlights the importance of optimization in addressing the challenges associated with the design of drive units in EVs. It presents a practical and efficient process that can be implemented within a short timeframe, allowing engineers to achieve optimal design solutions. By leveraging this approach, manufacturers can enhance the performance and efficiency of EV drive units, contributing to the advancement of electric mobility.</div></div>

With the increasing design dimensionality, it is more difficult to solve multidisciplinary design optimization (MDO) problems. Many MDO decomposition strategies have been developed to reduce the dimensionality. Those strategies consider the design problem as a black-box function. However, practitioners usually have certain knowledge of their problem. In this paper, a method leveraging causal graph and qualitative analysis is developed to reduce the dimensionality of the MDO problem by systematically modeling and incorporating the knowledge about the design problem into optimization. Causal graph is created to show the input–output relationships between variables. A qualitative analysis algorithm using design structure matrix (DSM) is developed to automatically find the variables whose values can be determined without resorting to optimization. According to the impact of variables, an MDO problem is divided into two subproblems, the optimization problem with respect to the most important variables, and the other with variables of lower importance. The novel method is used to solve a power converter design problem and an aircraft concept design problem, and the results show that by incorporating knowledge in form of causal relationship, the optimization efficiency is significantly improved.

Large scale multidisciplinary design optimization (MDO) problems often involve massive computation over vast data sets; Regardless of the MDO problem solving methodology, advanced computing technologies and architectures are indispensable. The data parallelism inherent in some engineering problems makes massively parallel architectures a natural choice, but efficiently harnessing the power of massive parallelism requires sophisticated algorithms and techniques. This paper presents an effort to apply massively scalable distributed control and dynamic load balancing techniques to the reasonable design space identification phase of a variable complexity approach to the multidisciplinary design optimization of a high speed civil transport (HSCT). The scalability and performance of two dynamic load balancing techniques, random polling and global round robin with message combining, and two termination detection schemes, token passing and global task count, are studied. The extent to which such techniques are applicable to other MDO paradigms, and to the potential for parallel multidisciplinary design with current large-scale disciplinary codes, is of particular interest.

The programming language Java (recently referred to as the computer language of the Web) offers substantial possibilities for the type of complex engineering problems typically encountered in multidisciplinary design optimization (MDO) problems. In order to demonstrate the potential uses of Java for MDO problems, this paper presents the development of the Web Interface for complex engineering design (WICkED) software, which simulates the convergence of a decomposed complex system in a distributed computing environment and computes the sensitivity derivatives of the system with respect to the independent input variables using the GSE method or the finite difference method. In this application, one computer is designated as the server and sends out required inputs to a number of client subsystems over the Internet. A number of client computers can connect to the server and then receive the inputs necessary to calculate the solution to their model. As the code necessary to solve the model already exists at the client, only the inputs have to be sent over the network. When the client has solved the calculation, it returns the results to the server which processes the result to produce new inputs.

Engineering systems have become quite complicated in recent days. The requirements of design are complex and it is hard to meet them by considering only one discipline. In this paper, we suggest a hybrid Multi-objective Genetic Algorithm (MOGA) for a Multidisciplinary Design Optimization (MDO) model in engineering design. In order to get Pareto optimal solutions, we use local search to enhance the efficiency and effectiveness. We solve a problem of airplane wings optimization using MOGA. After compared with other MDO algorithms, we find the result shows that the proposed algorithm’s performance has an advantage over previous work for these MDO problems. As the algorithm is evaluated based on practical data, we show that the approach can be used to solve MDO problems in the real world.

Satellite constellation system design is a challenging and complicated multidisciplinary design optimization (MDO) problem involving a number of computation-intensive multidisciplinary analysis models. In this paper, the MDO problem of a constellation system consisting of small observation satellites is investigated to simultaneously achieve the preliminary design of constellation configuration and the satellite subsystems. The constellation is established based on Walker-? configuration considering the coverage performance. Coupled with the constellation configuration, several disciplines including payload, power, thermal control, and structure are taken into account for satellite subsystems design subject to various constraints (i.e., ground resolution, power usage, natural frequencies, etc.). Considering the mixed-integer and time-consuming behavior of satellite constellation system MDO problem, a novel sequential radial basis function (RBF) method using the support vector machine (SVM) for discrete-continuous mixed variables notated as SRBF-SVM-DC is proposed. In this method, a discrete-continuous variable sampling method is utilized to handle the discrete variables, i.e., the number of orbit planes and number of satellites, in the satellite constellation system MDO problem. RBF surrogates are constructed and gradually refined to represent the time-consuming simulations during optimization, which can efficiently lead the search to the optimum. Finally, the proposed SRBF-SVM-DC utilized to solve the satellite constellation system MDO problem is compared with a conventional integer coding based genetic algorithm (ICGA). The results show that SRBF-SVM-DC significantly decreases the system mass by about 28.63% subject to all the constraints, which greatly reduces the cost of the satellite constellation system. Moreover, the computational budget of SRBF-SVM-DC is saved by over 85% compared with ICGA, which demonstrates the effectiveness and practicality of the proposed surrogate assisted optimization approach for satellite constellation system design.

Research on multidisciplinary fatigue optimization design method in structural design of high speed train

The optimal design of multidisciplinary systems under uncertainty involves three types of iterative analyses- multidisciplinary analyses, reliability analyses, and optimization. If these processes are carried out in a nested manner in reliability based multidisciplinary design optimization (RBMDO), the computational expense can be enormous. Computationally efficient simultaneous analysis and design (SAND) or All-AtOnce methods have been developed earlier for deterministic MDO. Single loop RBDO methods have also been developed to integrate reliability analysis and optimization in a single loop. This paper develops a novel formulation of RBMDO problems with both system and component level reliability constraints. The formulation allows for solution with a single design optimization loop by using the KKT optimality conditions of the first-order reliability method (FORM) as constraints in the design optimization along with disciplinary consistency constraints. Alternative solution processes which remove the FORM MPP’s from the decision space and many constraints from the problem are developed. The alternative solution methods are more efficient and more robust than using nonlinear programming to solve the single loop formulation. A numerical example is solved with the two proposed solution algorithms. I. Introduction In the design of multidisciplinary systems it is often necessary to make decisions under uncertainty. This requires that multidisciplinary systems modeling be integrated with uncertainty analysis and optimization. A common example of such an engineering design application would be the design of an aircraft wing under uncertain aerodynamic loading conditions, with multiple structural components with uncertain capacities, such that the entire structural system achieves a prescribed level of reliability. The problem has coupled physics, in that the pressure distribution is dependent upon the deflection, and the deflection is dependent on the pressure distribution. Such designs have been performed using multidisciplinary optimization (MDO). Other examples where MDO may be applied include electronics packaging, in which the disciplines of heat transfer and circuit analysis are coupled, the design of new types of aircraft and integrating them into an existing fleet of aircraft, and even the management of interconnected homeland infrastructures. While MDO has matured with the development of different types of algorithms for various types of problems and design organizations, there has been little work to incorporate reliability analysis into MDO. However, system and component reliabilities are often a major concern in the design of multidisciplinary systems. MDO can be computationally expensive due to the need to achieve consistency across multiple disciplinary analysis codes; each disciplinary analysis code may be computationally expensive to run. Further, the optimal design of multidisciplinary systems under uncertainty involves three types of iterative procedures- multidisciplinary analyses, reliability analyses, and optimization. The integration of these three procedures is referred to in this paper as reliability based multidisciplinary design optimization (RBMDO). If these processes are carried out simultaneously, the computational expense can be enormous. Computational savings can often be achieved with simultaneous analysis and design (SAND) or All-At-Once methods, which allow for the solution of the multidisciplinary analyses and the optimization in one single loop. Single loop RBDO methods allow for the integration of reliability analysis and optimization in a single loop. Applying SAND and single-loop RBDO together may allow for large computational savings when applied to problems in RBMDO. This paper develops a novel formulation of RBMDO problems with both system and component level reliability constraints based on the SAND method for MDO and by use of the KKT conditions of the first order reliability method (FORM). The resulting formulation may be solved as a standard nonlinear programming problem. While the single loop formulation presented in this paper is a solution of the RBMDO problem, robustness and efficiency are improved through two improved algorithms which can remove the MPP’s from the decision space, thereby significantly reducing the optimizer’s workload.

Multidisciplinary design optimization based on independent subspaces (MDOIS), which is a multidisciplinary design optimization (MDO) algorithm, has been recently proposed. Since MDOIS is relatively simple compared with other MDO algorithms, it is easy to apply MDOIS to practical engineering problems. In this research, an MDO problem is defined for the design of a belt-integrated seat (BIS) while considering crashworthiness. The crash model consists of an airbag, a BIS, an energy-absorbing steering system, and a safety belt. It is found that the current design problem has two disciplines - structural non-linear analysis and occupant analysis. The interdisciplinary relationship between the disciplines is identified. Interdisciplinary variables between the two disciplines are stiffness of the seat back frame and the belt load. The interdisciplinary relationship is addressed in the system analysis step in MDOIS. Prior to each independent subspace design, values of interdisciplinary variables at a given design point are determined in the system analysis step. The determined values are passed to corresponding subspaces, and the subspaces treat the received values of the interdisciplinary variables as constant parameters throughout the subspace design. For the present example, the belt load is passed to the structural analysis subspace and the stiffness of the seat back frame is passed to the occupant analysis subspace. Determined design variables in each subspace are passed to the system analysis step. In this way, the design process iterates until the convergence criterion is satisfied. As a result of the design, the weight of the BIS and the head injury criterion (HIC) of an occupant are reduced while the specified constraints are satisfied. Since the system analysis cannot be formulated in an explicit form in the current example, an optimization problem is formulated to solve the system analysis. The results from MDOIS are discussed.