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

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.

The dimensionality and complexity of typical multidisciplinary systems hinders the use of formal optimization techniques in application to this class of problems. The use of approximations to represent the system design metrics and constraints has become vital for achieving good performance in many multidisciplinary design optimization (MDO) algorithms. This paper reports recent research efforts on the use of variable fidelity response surface approximations (RSA) to drive the convergence of MDO problems using a trust region model management algorithm. The present study focuses on a comparative study of different response sampling strategies based on design of experiment (DOE) approaches within the disciplines to generate the zero order data to build the RSAs. Two MDO test problems that have complex coupling between disciplines are used to benchmark the performance of each sampling strategy. The results show that these types of variable fidelity RSAs can be effectively managed by the trust region model management strategy to drive convergence of MDO problems. It is observed that the efficiency of the optimization algorithm depends on the sampling strategy used. A comparison of the DOE approaches with those obtained using a optimization based sampling strategy (i.e. concurrent subspace optimization --- CSSO) shows the DOE methodologies to be competitive with the CSSO based sampling methodology in some cases. However, the CSSO based sampling strategy was found to be, in general, more efficient in driving the optimization.

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.

A blowout preventer (BOP) is a large valve that encases an oil well on the surface. The valve may be closed while drilling if overpressure from a reservoir causes formation fluids such as oil and natural gas to back up within the wellbore and endanger the rig. A pipe ram is one of the critical components in the BOP system, which is designed to seal around a drill pipe, restricting the flow in the annulus between the outside of the drill pipe and the wellbore. The pipe ram design family, which contains hundreds of pipe ram designs, intends to cover different configurations to suit a variety of dill pipe sizes. To assure their structural integrity under service loads, these pipe rams need to be designed to meet the stress requirements per the American Petroleum Institute (API) Specification 16A and ASME (American Society of Mechanical Engineers) Boiler and Pressure Vessel Code Section VIII, Division 2. With a conventional manual design workflow, it would take a significant amount of time and effort to complete all the designs for the product family with code compliance. Therefore, a scalable solution is highly desirable for delivery of customer-needed ram blocks with much shorter lead time. MDO (Multi-Disciplinary Optimization) involves multi-code integration, CAE (Computer-Aided Engineering) workflow automation, design space exploration, and optimization. MDO-enabled, automated design optimization is becoming increasingly popular in both scientific and engineering communities. In this paper, a methodology for integration of CAD (Computer Aided Design), FEA (Finite Element Analysis), cost, and optimization packages to enable FEA automation and design optimization is presented. A BOP pipe ram is adopted as the use case. The ram block geometry was parameterized before being imported into an FEA package. The FEA workflow was automated such that once a set of geometric parameters are given, the preprocessing, solving, and postprocessing steps can be automatically completed. As part of the FEA postprocessing, stress linearization analysis per the API and ASME BPVC codes has also been automated, which had never been done in the past. A manufacturing cost analysis package can also be used to consume the parameterized geometry for automatic manufacturability assessment and cost predictions. The stress analysis and cost analysis workflows are conducted separately but also orchestrated by an MDO package. Reports that contain the analysis results are sequentially generated for various design permutations. The MDO-enabled automated design and cost analysis approach could substantially enhance efficiency and consistency in performing FEA and cost studies and producing analysis reports. It is also the backbone for automated design optimization, which could significantly improve the product performance and reliability and, meanwhile, minimize the development and product cost.

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.

The design of space systems is a complex and multidisciplinary process with multiple conflicting objectives, large number of design variables, and constraints that limits application of the existing multidisciplinary design optimization architectures to this class of design problems. This paper presents an enhanced multidisciplinary design optimization architecture to concurrent holistic design optimization of a satellite system. The proposed multidisciplinary design optimization architecture extends concepts of multidiscipline feasible and bi-level integrated system synthesis into a unified architecture using metamodels. The proposed architecture was evaluated and compared with the existing multidisciplinary design optimization architectures that include all-at-once, bi-level integrated system synthesis, and multidisciplinary design optimization using a remote sensing small satellite in low earth orbit. The satellite design optimization problem deals with the minimization of the total mass of the satellite, involving disciplines of mission analysis, payload, structures, attitude determination and control, communication, command and data handling, power and thermal. The computational performance and accuracy of the proposed architecture were compared with multidisciplinary design optimization benchmark problems. Then the proposed architecture is successfully applied to the satellite system design problem. The results obtained show that metamodel-based bi-level integrated system synthesis-multidisciplinary design optimization architecture presented in this paper provides an effective way of solving large-scale design problems.

Design of haptic devices requires trade-off between many conflicting requirements, such as high stiffness, large workspace, small inertia, low actuator force/torque, and a small size of the device. With the traditional design and optimization process, it is difficult to effectively fulfill the system requirements by separately treating the different discipline domains. To solve this problem and to avoid sub-optimization, this work proposes a design methodology, based on Multidisciplinary Design Optimization (MDO) methods and tools, for design optimization of six degree-of-freedom (DOF) haptic devices for medical applications, e.g. simulators for surgeon and dentist training or for remote surgery. The proposed model-based and simulation-driven methodology aims to enable different disciplines and subsystems to be included in the haptic device optimization process by using a robust model architecture that integrates discipline-specific models in an optimization framework and thus enables automation of design activities in the concept and detail design phase. Because of the multi-criteria character of the performance requirements, multi-objective optimization is included as part of the proposed methodology. Because of the high-level requirements on haptic devices for medical applications in combination with a complex structure, models such as CAD (Computer Aided Design), CAE (Computer Aided Engineering), and kinematic models are considered to be integrated in the optimization process and presenting a systems view to the design engineers. An integration tool for MDO is used as framework to manage, integrate, and execute the optimization process. A case study of a 6-DOF haptic device based on a TAU structure is used to illustrate the proposed methodology. With this specific case, a Multi-objective Genetic Algorithm (MOGA) with an initial population based on a pseudo random SOBOL sequence and Monte Carlo samplings is used for the optimization.

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.

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.

<div class="htmlview paragraph">In this paper the development of statistical metamodels and statistical fast running models is presented first. They are utilized for propagating uncertainties in a multi-discipline design optimization process. Two main types of uncertainty can be considered in this manner: uncertainty due to variability in design variables or in random parameters; uncertainty due to the utilization of metamodels instead of the actual simulation models during the optimization process. The value of the new developments and their engagement in multi-discipline design optimization is demonstrated through a case study. An underwater vehicle is designed under four different disciplines, namely, noise radiation, self-noise due to TBL excitation, dynamic response due to propulsion impact loads, and response to an underwater detonation. The case study also demonstrates the value of the multi-discipline design optimization in identifying a system level optimum, and it emphasizes the importance of including uncertainties in the design optimization process.</div>

Preliminary designs with deterministic approaches used to solve the uncertainty related information from a ship design results preliminary design of conventional. In order to overcome the imbalance of optimization in the design process, the preliminary design is equipped with a method Collaborative Optimization (CO), which is part of the Multidisciplinary Design Optimization (MDO). Process design optimization in preliminary design with a deterministic approach based on the value subsystem optimization required by the vessel (d). Ship design requirements of this study are deadweigth requirements, volume cargo requirements and speed/resistance requirements. The preliminary design hull form general cargo for shipping Jakarta to Makassar by using deterministic approach is expected to provide an alternative principal dimension and design variations of the optimal hull form based on information dock and owner reqiurement. In addition, this study is also expected to be an alternative method used in the preliminary process design of modern ships because in the preliminary designs have efforts to optimize an element ship design.

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.

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

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.

All engineering design problems can be characterized by the underlying assumptions around which the problem is formulated. The effect of these assumptions - including everything from general assumptions defining an operating environment to detailed assumptions regarding material properties - is variability in system performance, and resulting deviations from expected performance. Assumptions are made to eliminate uncertainties that would prevent the quantification of design performance. Probabilistic methods have been developed in recent decades to convert such deterministic problem formulations into probabilistic formulations to model and assess the effects of these known uncertainties and thus relax restrictive assumptions. Until very recently, however, the computational expense of probabilistic analysis of a single design has made its application impractical for all but very simplistic design problems. Consequently, probabilistic optimization has been considered prohibitively expensive, particularly for complex multidisciplinary systems. Today a number of enabling technologies are available to support probabilistic design analysis and optimization for complex engineering design problems, including: flexible software frameworks that allow integration and automation of a complex multidisciplinary process; probabilistic analysis and optimization tools that allow uncertainty to be modeled and performance variation to be measured and reduced; large scale parallel processing capabilities leading to greatly increased efficiency; and advanced surrogate modeling capabilities to replace complex nonlinear analyses with computationally efficient approximation models. Along with steady increases in computing power, the combination of these enabling technologies can facilitate effective probabilistic analysis and optimization for complex design problems. In this paper we focus primarily on two of these enabling technologies. We present a comprehensive probabilistic design optimization formulation, a six sigma based approach that incorporates variability within all elements of the formulation - input design variable bound formulation, output constraint formulation, and robust objective formulation. We discuss the applicability of kriging, one surrogate modeling approach that supports the approximation of complex nonlinear analyses, for facilitating probabilistic multidisciplinary design optimization. These enabling technologies, as implemented within the commercial software framework provided by iSIGHT, including capability to facilitate parallel processing, are demonstrated for a multidisciplinary conceptual ship design problem.