LOcal Uncertainty Processing (LOUP) method for multidisciplinary robust design optimization

In this paper, the basic concepts and methods of multidisciplinary design optimization, uncertainty analysis and robust design have been introduced. According to the features of a multi-functional open-air hydraulic drill, a new design theory called multidisciplinary robust optimization design was discussed. This theory can undertake uncertainty analysis and robust design in multidisciplinary design optimization. It fully considers both the synergy among each disciplinary or subsystem in the multi-functional open-air hydraulic drill to get the optimal solution to the whole system and the effect of the uncertainty factors upon the drill quality, and adopts the parallel design to improve the quality, robustness and reliability of the drill, to shorten the market cycles of products, to reduce product cost. Finally, the design points were discussed in detail in the paper.

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.

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.

In studying multidisciplinary design optimization method for non-hierarchic system, Multidisciplinary Object Compatibility Design Optimization method based on simulated annealing algorithm is presented. In order to coordinate the independent optimization of subsystems, the compatibility constraint in system level and compatibility objective in subsystem work together. As optimization process continued, the coupling relationship between system level and different subsystems is gradually improved by state accepting function which is embedded in compatibility constraint. In this way, abnormal program termination and premature convergence will be avoided and ideal global optimal solution will be achieved effectually. Then the method is used in the optimization design of TR-B triple-redundancy transmission system. The multidisciplinary object compatibility design optimization model is established and the comprehensive optimal solution is obtained which meets the matching relationship of gear teeth, strength requirement and dynamic requirement, etc

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.

Purpose – 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. Design/methodology/approach – 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 eva...

The implementation of a general and flexible method of formulating problems of mathematical programming in structural and multidisciplinary optimization systems is described. The method, which is based on the so-called bound formulation, enables the formulation and solution of problems involving local, integral, mintmax, maxlmin and possibly non-differentiable user-defined functions in any conceivable mix and using user-defined mathematical functions. The computer implementation involves a parser capable of interpreting and performing symbolic dfierentiation of the user defined functions. A sample problem of thermo-elasticity is given. It is concluded that this approach is well suited for multidisciplinary design optimization systems. 1. Motivation One of the great challenges of research in design automation is the development of practically applicable systems for multidisciplinary design optimization. Such systems will, if they are truly generally applicable, cause a revolution in the way design laboratories work. Several papers with the focus on system design rather than single applications have emerged in recent years. Some examples are Esping (1986), Rasmussen (1989), Papalarnbros & Chirehdast (1990), Choi & Chang (1991), Botlun et. al. (1 992), Rasmussen et. al. (1993), and Cardoso & Santos (1 993). Obtaining the necessary generality, however, is a very difficult task. Designing even simple components involves many different considerations. For the sake of the argument, we may categorize them into groups of increasing complexity: The functional behavior, for instance weight, energy consumption, power output, efficiency, eigenfrequencies, strength, stiffness, pressures, velocities, accelerations, temperatures, electric and magnetic properties, etc. These qualities can often be modeled mathematically and analyzed by means of digital computers. The fabricational behavior, for instance the cost of machining, the necessary production facilities, the necessary manpower, stock and inventory, financial requirements, etc. These properties are usually very difficult to analyze because of the many degrees of freedom in choice of production planning and processes, the dependency of other products manufactured simultaneously, and even the dependence on the economic boundary conditions formed by the outside world. The aesthetic properties that are impossible to evaluate objectively, but are none the less tightly connected with the functional and fabricational properties. For instance, the shape of the hull of a ship determines strength, stiffness and drag properties, but it also forms an important part of the visual impression. In the development of multidisciplinary systems, we have only begun to cover the first category of product properties, so it may be argued that there is still a long way to go. At the Institute of Mechanical Engineering, Aalborg University, Denmark, a system for multidisciplinary design optimization is under development. The system is called 'Associate Professor of Mechanical Engineering '+~esearch Assistant Copyright O 1994 by the American Institute of Aeronautics and Astronautics, Inc. All rights reserved.

It is necessary to employ the Multidisciplinary Design Optimization (MDO) method in the design process of automatic weapon, because the process in itself is related to many disciplines and their couplings. The knowledge structure of MDO is analyzed, which includes mathematic modeling, system decomposition, optimization framework, approximation model, sensitivity analysis, optimization method, software integration, and etc.. The idea of using MDO in the design process of individual soldier automatic weapon is also explored. Based on the software package of iSIGHT, the primary multidisciplinary integration is carried out. Current research work will be helpful for further research on integrating MDO into the design of automatic weapon.

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

Collaborative optimization (CO), a decomposition-based multidisciplinary design optimization (MDO) method, is generally used in aeronautical systems. However, the subsystems optimizations of CO method are nested into system optimization of it in the execution process, numerous subsystem analyses are required to achieve consistency for entire system. For this problem, a nonnested collaborative optimization (NNCO) method is developed, in which system and subsystem optimizations are solved sequentially and repeatedly, and system consistancy is coordinated by a loop process together with the update of penalty parameters. Through test results of common analytical problems, which are generally used in the experiments of CO method, it's shown that the NNCO method requires two third fewer calls of the subsystem analysis than the CO method at least. Further more, CO and NNCO method are used to solve a satellite MDO problem, 0.05 and 8.05 hours are consumed for these two methods respectively. The efficiency of NNCO method in practical engineering design problem is proved.

A number of game strategies have been developed in past decades and used in the fields of economics, engineering, computer science, and biology due to their efficiency in solving design optimization problems. In addition, research in multiobjective and multidisciplinary design optimization has focused on developing a robust and efficient optimization method so it can produce a set of high quality solutions with less computational time. In this paper, two optimization techniques are considered; the first optimization method uses multifidelity hierarchical Pareto-optimality. The second optimization method uses the combination of game strategies Nash-equilibrium and Pareto-optimality. This paper shows how game strategies can be coupled to multiobjective evolutionary algorithms and robust design techniques to produce a set of high quality solutions. Numerical results obtained from both optimization methods are compared in terms of computational expense and model quality. The benefits of using Hybrid and non-Hybrid-Game strategies are demonstrated.

The design of multidiscipli nary systems (such as aircraft, automobiles, and others) often requires an iterative cycle that includes a design initialization, a system analysis, a sensitivity analysis, and design optimization. This design cycle is standard in the field of Multidisciplinary Optimization (MDO) and has often been referred to in literature as the Multiple Discipline-Feasible (MDF) approach. The name stems from the fact that complete multidisciplinary feasibility is maintained each and every design cycle. The drawback of MDF is that it can be a timely and a costly procedure. Numerous researchers have developed alternate means for posing and subsequently solving the multidisciplinary design problem. One such solution procedure has been referred to both as Simultaneous Analysis and Design (SAND) and All-at-Once (AAO), and treats the entire multidisciplinary design cycle as one large optimization problem. Another alternate solution procedure lias been referred to as Individual-Discipline-Feasible (DDF); this procedure exhibits characteristics which lie in between the two extremes exemplified by MDF and AAO. IDF assures that each individual discipline is feasible on every design cycle, while driving the entire system (all disciplines) towards multidisciplinary feasibility. The present work will present a rigorous numerical comparison of these solution strategies over a wide variety of problem sizes and complexities. The multidisciplinary design test problems that are used for these comparisons are generated by a robust simulation tool called CASCADE. * Research Assistant, Student member, AIAA | Associate Professor, Member AIAA Background and Motivation Concurrent engineering is a systematic approach to the integrated, simultaneous design of products and their related processes. Many of the recently developed capabilities to address concurrent engineering have stemmed from the emerging area of Multidiscipli nary Optimization, or MDO. The origins of MDO can be traced back to the early 1980's, where Sobieski14 used a linear decomposition approach to subdivide the design of a large engineering system into a grouping of related and more manageable subsystems. However, such a decomposition often results in a grouping of subsystems which cannot be placed into a definitive top-down hierarchy. The resultant decomposition grouping is typically hybrid-hierarchic in nature as shown in the example decomposition of Figure 1.

Battery thermal management system (BTMS) is a complex and highly integrated system, which is used to control the battery thermal conditions in electric vehicles (EVs). The BTMS consists of many subsystems that belong to different disciplines, which poses challenges to BTMS optimization using conventional methods. This paper develops a general variable fidelity-based multidisciplinary design optimization (MDO) architecture and optimizes the BTMS by considering different systems/disciplines from the systemic perspective. Four subsystems and/or subdisciplines are modeled, including the battery thermodynamics, fluid dynamics, structure, and lifetime model. To perform the variable fidelity-based MDO of the BTMS, two computational fluid dynamics (CFD) models with different levels of fidelity are developed. A low fidelity surrogate model and a tuned low fidelity model are also developed using an automatic surrogate model selection method, the concurrent surrogate model selection (COSMOS). An adaptive model switching (AMS) method is utilized to realize the adaptive switch between variable-fidelity models. The objectives are to maximize the battery lifetime and to minimize the battery volume, the fan's power, and the temperature difference among different cells. The results show that the variable-fidelity MDO can balance the characteristics of the low fidelity mathematical models and the computationally expensive simulations, and find the optimal solutions efficiently and accurately.

On-orbit applications, such as active debris removal, satellite refueling, maintenance and satellite health diagnosis require the ability for low-cost spacecraft to closely inspect other orbital objects in a non-cooperative manner. During this kind of mission, the relative navigation process becomes of critical importance for guaranteeing safe and collision-free proximity operations and maneuvers. The selection of relative navigation sensors appears being a critical task as it might drive the design choices in other subsystems (e.g., Attitude and orbit control system (AOCS), payload, power supply). This paper aims at studying the application of a Multidisciplinary Design Optimization (MDO) method to the design of AOCS and Navigation subsystems under small satellite constraints. The porposed MDO process is based on the optimization of navigation performance and mass reduction while respecting volume and power constraints for orbital close rendezvous. The navigation chain, including sensor simulation and navigation filter is simulated and integrated into the design cost function. The proposed MDO process based on a Genetic Algorithm (GA) and on an Extended Kalman Filter (EKF) aims at simplifying satellite design by determining a set of optimal admissible sensor combinations despite contradictory objectives on navigation and payload accuracy, mass reduction, power consumption and volume. Possible key advantages of the inclusion of the relative navigation subsystem within MDO process are the reduction of the design process time, the automation and optimization of the navigation architecture while respecting volume and power constraints of small satellites. A demonstration of the effectiveness of the proposed MDO method is provided on the benchmark of AVANTI mission.

5 - Multidisciplinary Design and Optimization Methods