Minimizing energy loss and improving system load capacity and compactness are important objective... more Minimizing energy loss and improving system load capacity and compactness are important objectives for fluid power systems. Recent studies reveal that microtextured surfaces can reduce friction in full-film lubrication, and that asymmetric textures can reduce friction and increase normal force simultaneously. As an extension of these previous discoveries , we explore how enhanced texture design can maximize these objectives together. We design surface texture using a set of distinct parameterizations, ranging from simple to complex, to improve performance beyond what is possible for previously investigated texture geometries. Here, we consider a rotational tribo-rheometer configuration with a fixed textured bottom disk and a rotating top flat disk with controlled separation gap. To model Newtonian fluid flow, the Reynolds equation is formulated in cylindrical coordinates and solved using a pseudospectral method. Model assumptions include incompres-sibility, steady flow, constant viscosity, and a small gap height to disk radius ratio. Multi-objective optimization problems are solved using the epsilon-constraint method along with an interior-point (IP) nonlinear programming algorithm. The trade-off between competing objectives is quantified, revealing mechanisms of performance enhancement. Various geometries are explored and optimized, including symmetric and asymmetric circular dimples, and novel arbitrary continuous texture geometries represented using two-dimensional cubic spline interpolation. Shifting from simple dimpled textures to more general texture geometries resulted in significant simultaneous improvement in both performance metrics for full-film lubrication texture design. An important qualitative result is that textures resembling a spiral blade tend to improve performance for rotating contacts.
Modifying the design of an existing system to meet the needs of a new task is a common activity i... more Modifying the design of an existing system to meet the needs of a new task is a common activity in mechatronic system development. Often engineers seek to meet requirements for the new task via control design changes alone, but in many cases new requirements are impossible to meet using control design only; physical system design modifications must be considered. Plant-Limited Co-Design (PLCD) is a design methodology for meeting new requirements at minimum cost through limited physical system (plant) design changes in concert with control system redesign. The most influential plant changes are identified to narrow the set of candidate plant changes. PLCD provides quantitative evidence to support strategic plant design modification decisions, including tradeoff analyses of redesign cost and requirement violation. In this article the design of a counterbalanced robotic manipulator is used to illustrate successful PLCD application. A baseline system design is obtained that exploits synergy between manipulator passive dynamics and control to minimize energy consumption for a specific pick-and-place task. The baseline design cannot meet requirements for a second pickand-place task through control design changes alone. A limited set of plant design changes is identified using sensitivity analysis, and the PLCD result meets the new requirements at a cost significantly less than complete system redesign.
Customer preferences for sustainable products are dependent upon the context in which the custome... more Customer preferences for sustainable products are dependent upon the context in which the customer makes a purchase decision. This paper investigates a case study in which fifty-five percent of survey customers say they prefer recycled paper towels, but do not purchase them. These customers represent a profit opportunity for a firm. This paper explores the impact of investing capital in activating pro-environmental preferences on a firm's profitability and greenhouse gas (GHG) emissions through a multi-objective optimization study. A product optimization is designed to include models of carbon dioxide emissions, manufacturing costs, customer preference, and technical performance. Because the optimization includes a tradeoff between recycled paper and performance, a model of customer preferences, and a market of competing products, the maximum GHG reduction occurs at less than 100% recycled paper. Also, the tradeoff between GHG reductions and profit is not dictated by the configuration of the product, but instead by its price. These results demonstrate the importance of including customer preferences with engineering performance in design optimization. Investment in the activation of pro-environmental preferences is high at all points on the Pareto optimal frontier, suggesting that further engineering design research into the activation of pro-environmental product preferences is warranted.
Wave energy converters (WECs) extract energy from the motion of ocean waves. A variety of differe... more Wave energy converters (WECs) extract energy from the motion of ocean waves. A variety of different WEC devices have been studied over the past several decades, with emphasis on cost-effective energy extraction. Active control has been shown to improve energy production significantly. Here we investigate energy extraction potential of a tethered heaving cylinder WEC using direct transcription (DT), an open-loop optimal control strategy. This enables direct inclusion of asymmetric constraints on power and tether force, practical considerations not considered in previous studies, and opens the door to WEC optimal control problems with more realistic nonlinear models and integration of control design with physical system design.
Previous research presents both sensitivity-based and principal component-based techniques for im... more Previous research presents both sensitivity-based and principal component-based techniques for improving the tractability of system identification. Both have proven viable, but the former may be computationally inefficient for large problems, and the latter require a change of realization that may compromise the physical meaning of the parameters to be identified. This paper proposes for the first time the use of activity analysis, an efficient and realization-preserving model reduction technique, for identification space reduction. Theoretical and numerical studies highlighting the viability of activity analysis versus the previous two methods are presented.
Effective powertrain design for the emerging electric vehicle market is a complex, multidisciplin... more Effective powertrain design for the emerging electric vehicle market is a complex, multidisciplinary problem. As such, engineers may often use formal decomposition-based optimisation strategies to partition the problem into more manageable subproblems and then integrate their solutions to obtain an optimal system design. Sometimes, these strategies yield decision variables that consist of highly-discretised functional data which must be reduced to enable efficient, practical optimisation. Reduced representation methods such as Proper Orthogonal Decomposition (POD) can help achieve this goal, but the effectiveness of POD in terms of design solution accuracy and optimisation efficiency is dependent on its interaction with the optimisation strategy. Therefore, this paper investigates the impact of a tuning parameter within POD on solution accuracy and optimisation efficiency in the context of decomposition-based electric vehicle powertrain design. is responsible for the research, design and initial development of novel hybrid powertrain architectures. He graduated Summa Cum Laude with a BS in Mechanical Engineering at the University of Cincinnati and continued his studies in Mechanical Engineering by earning his MSE (2008) and PhD (2011) at the University of Michigan. His general research interests include multidisciplinary design optimisation, hybrid-electric/electric vehicle design, functional data approximation and metamodelling.
Modern engineering systems often are impractical to design from the ground up. New designs typica... more Modern engineering systems often are impractical to design from the ground up. New designs typically are modifications of earlier systems (and frequently only small perturbations of them). This limited redesign approach is becoming increasingly important as the scale and complexity of engineering systems increases. One significant application of limited redesign is the repurposing of mechatronic systems. Often engineers seek to meet the needs of a new application by redesigning only the control system for a mechatronic device. While in many cases this approach is successful, control design changes alone may not always be sufficient. If control redesign alone is inadequate, physical system (plant) design changes should be investigated. Complete plant redesign cost may be prohibitive, and usually is unnecessary. A limited set of plant design changes should be identified that enable system requirement satisfaction at the lowest cost. Here we present a formal integrated approach for limited redesign of mechatronic systems. Candidate plant modifications are identified using sensitivity analysis, and then an optimization problem is solved that minimizes the cost of system redesign while satisfying requirements. This formal methodology for plant limited co-design (PLCD) is demonstrated using a robotic manipulator design problem. First the manipulator is designed in a way that exploits passive dynamics to minimize energy consumption for a specific task. Afterward a new task is introduced that cannot be performed successfully through control changes alone. Limited plant changes are identified, and the PLCD result for this new task is compared to a full system redesign. The PLCD result costs significantly less than the full redesign with a small performance penalty. Parametric studies illustrate the tradeoff between redesign cost and performance, and it is shown that the proposed sensitivity analysis results in the lowest cost limited redesign.
Design of physical systems and associated control systems are coupled tasks; design methods that ... more Design of physical systems and associated control systems are coupled tasks; design methods that manage this interaction explicitly can produce system-optimal designs, whereas conventional sequential processes may not. Here we explore a new technique for combined physical system and control design (co-design) based on a simultaneous dynamic optimization approach known as direct transcription, which transforms infinitedimensional control design problems into finite dimensional nonlinear programming problems. While direct transcription problem dimension is often large, sparse problem structures and finegrained parallelism (among other advantageous properties) can be exploited to yield computationally efficient implementations. Extension of direct transcription to co-design gives rise to a new problem structures and new challenges. Here we illustrate direct transcription for co-design using a new automotive active suspension design example developed specifically for testing codesign methods. This example builds on prior active suspension problems by incorporating a more realistic physical design component that includes independent design variables and a broad set of physical design constraints, while maintaining linearity of the associated differential equations.
An often cited motivation for using decomposition-based optimization methods to solve engineering... more An often cited motivation for using decomposition-based optimization methods to solve engineering system design problems is the ability to apply discipline-specific optimization techniques. For example, structural optimization methods have been employed within a more general system design optimization framework. We propose an extension of this principle to a new domain: control design. The simultaneous design of a physical system and its controller is addressed here using a decompositionbased approach. An optimization subproblem is defined for both the physical system (i.e., plant) design and the control system design. The plant subproblem is solved using a general optimization algorithm, while the controls subproblem is solved using a new approach based on optimal control theory. The optimal control solution, which is derived using the the Minimum Principle of Pontryagin (PMP), accounts for coupling between plant and controller design by managing additional variables and penalty terms required for system coordination. Augmented Lagrangian Coordination is used to solve the system design problem, and is demonstrated using a circuit design problem.
In decomposition-based design optimization strategies, such as Analytical Target Cascading (ATC),... more In decomposition-based design optimization strategies, such as Analytical Target Cascading (ATC), it is sometimes necessary to use reduced dimensionality representations to approximate functions of large dimensionality whose values need to be exchanged among subproblems. The reduced representation variables may not be physically meaningful, and it can become challenging to constrain them properly and define the model validity region. For example, in coordination strategies like ATC, representing vector-valued coupling variables with improperly constrained reduced representation variables can lead to poor performance or convergence failure. This paper examines two approaches for constraining effectively the model validity region of reduced representation variables based on proper orthogonal decomposition: a penalty value-based heuristic and a support vector domain description. An ATC application on electric vehicle design helps to illustrate the concepts discussed.
Many engineering systems are too complex to design as a single entity. Decompositionbased design ... more Many engineering systems are too complex to design as a single entity. Decompositionbased design optimization methods partition a system design problem into subproblems, and coordinate subproblem solutions toward an optimal system design. Recent work has addressed formal methods for determining an ideal system partition and coordination strategy, but coordination decisions have been limited to subproblem sequencing. An additional element in a coordination strategy is the linking structure of the partitioned problem, i.e., the allocation of constraints that guarantee that the linking variables among subproblems are consistent. There may exist many alternative linking structures for a decomposition-based strategy that can be selected for a given partition, and this selection should be part of an optimal simultaneous partitioning and coordination scheme. This article develops a linking structure theory for a particular class of decomposition-based optimization algorithms, augmented Lagrangian coordination (ALC). A new formulation and coordination technique for parallel ALC implementations is introduced along with a specific linking structure theory, yielding a partitioning and coordination selection method for ALC that includes consistency constraint allocation. This method is demonstrated using an electric water pump design problem.
Your article is protected by copyright and all rights are held exclusively by Springer-Verlag. Th... more Your article is protected by copyright and all rights are held exclusively by Springer-Verlag. This e-offprint is for personal use only and shall not be self-archived in electronic repositories. If you wish to self-archive your work, please use the accepted author's version for posting to your own website or your institution's repository. You may further deposit the accepted author's version on a funder's repository at a funder's request, provided it is not made publicly available until 12 months after publication.
Use of decomposition-based design optimization methods requires a priori selection of system part... more Use of decomposition-based design optimization methods requires a priori selection of system partitioning and of the corresponding coordination strategy. Typically, partitioning systems into smaller, easier to solve subproblems leads to more complicated, computationally expensive coordination strategies. Previous optimal partitioning techniques have not addressed the coordination issue explicitly. A Pareto-optimal problem formulation was proposed recently to address simultaneous partitioning and coordination decisions. Due to the combinatorial nature of this problem, exhaustive enumeration was used to demonstrate the approach to small system examples. This article presents and demonstrates an evolutionary algorithm that can solve this problem for systems of moderate size. A readily partitioned truss design formulation is introduced on which design problems with a wide variety of interaction patterns and system sizes can be based. An eight-bar truss problem is used to demonstrate the effectiveness of the proposed evolutionary algorithm.
Previous research presents both sensitivity-based and principal component-based techniques for im... more Previous research presents both sensitivity-based and principal component-based techniques for improving the tractability of system identification. Both have proven viable, but the former may be computationally inefficient for large problems, and the latter require a change of realization that may compromise the physical meaning of the parameters to be identified. This paper proposes for the first time the use of activity analysis, an efficient and realization-preserving model reduction technique, for identification space reduction. Theoretical and numerical studies highlighting the viability of activity analysis versus the previous two methods are presented.
Design of modern engineering products requires complexity management. Several methodologies for c... more Design of modern engineering products requires complexity management. Several methodologies for complex system optimization have been developed in response. Single-level strategies centralize decision-making authority, while multi-level strategies distribute the decision-making process. This article studies the impact of coupling strength on single-level Multidisciplinary Design Optimization formulations, particularly the Multidisciplinary Feasible (MDF) and Individual Disciplinary Feasible (IDF) formulations. The Fixed Point Iteration solution strategy is used to motivate the analysis. A new example problem with variable coupling strength is introduced, involving the design of a turbine blade and a fully analytic mathematical model. The example facilitates a clear illustration of MDF and IDF and provides an insightful comparison between these two formulations. Specifically, it is shown that MDF is sensitive to variations in coupling strength, while IDF is not.
Analytical Target Cascading (ATC) is a product development tool that computes component design sp... more Analytical Target Cascading (ATC) is a product development tool that computes component design specifications such that the final system design is consistent and meets design targets. ATC is useful for complex product design that must be approached by decomposition, and facilitates concurrent design activities. While ATC has been applied successfully to automotive design, this article introduces the application of ATC to aircraft design, and discusses how it can be congruent with current design practice. ATC is used to solve an aircraft design problem where several flight regimes are considered separately. ATC can be used to balance low-fidelity system analysis and component-level multidisciplinary design optimization (MDO) activities. Finally, ATC may be used to coordinate overall aircraft design, with MDO employed to solve tightly coupled disciplinary problems that exist within ATC elements.
Design of complex products with several interacting subsystems or disciplinary analyses poses sub... more Design of complex products with several interacting subsystems or disciplinary analyses poses substantive challenges to both analysis and optimization, necessitating specialized solution techniques. A product or system may qualify as complex due to large scale or due to strong interactions. Single-level strategies for complex system optimization centralize decision-making authority, while multilevel strategies distribute the decisionmaking process. This article studies important differences between two popular singlelevel formulations: multidisciplinary feasible (MDF) and individual disciplinary feasible (IDF). Results presented aim at aiding practitioners in selecting between formulations. Specifically, while IDF incurs some computational overhead, it may find optima hidden to MDF and is more efficient computationally for strongly coupled problems; further, MDF is sensitive to variations in coupling strength, while IDF is not. Conditions that lead to failure of MDF are described. Two new reproducible design examples are introduced to illustrate these findings and to provide test problems for other investigations.
Minimizing energy loss and improving system load capacity and compactness are important objective... more Minimizing energy loss and improving system load capacity and compactness are important objectives for fluid power systems. Recent studies reveal that microtextured surfaces can reduce friction in full-film lubrication, and that asymmetric textures can reduce friction and increase normal force simultaneously. As an extension of these previous discoveries , we explore how enhanced texture design can maximize these objectives together. We design surface texture using a set of distinct parameterizations, ranging from simple to complex, to improve performance beyond what is possible for previously investigated texture geometries. Here, we consider a rotational tribo-rheometer configuration with a fixed textured bottom disk and a rotating top flat disk with controlled separation gap. To model Newtonian fluid flow, the Reynolds equation is formulated in cylindrical coordinates and solved using a pseudospectral method. Model assumptions include incompres-sibility, steady flow, constant viscosity, and a small gap height to disk radius ratio. Multi-objective optimization problems are solved using the epsilon-constraint method along with an interior-point (IP) nonlinear programming algorithm. The trade-off between competing objectives is quantified, revealing mechanisms of performance enhancement. Various geometries are explored and optimized, including symmetric and asymmetric circular dimples, and novel arbitrary continuous texture geometries represented using two-dimensional cubic spline interpolation. Shifting from simple dimpled textures to more general texture geometries resulted in significant simultaneous improvement in both performance metrics for full-film lubrication texture design. An important qualitative result is that textures resembling a spiral blade tend to improve performance for rotating contacts.
Modifying the design of an existing system to meet the needs of a new task is a common activity i... more Modifying the design of an existing system to meet the needs of a new task is a common activity in mechatronic system development. Often engineers seek to meet requirements for the new task via control design changes alone, but in many cases new requirements are impossible to meet using control design only; physical system design modifications must be considered. Plant-Limited Co-Design (PLCD) is a design methodology for meeting new requirements at minimum cost through limited physical system (plant) design changes in concert with control system redesign. The most influential plant changes are identified to narrow the set of candidate plant changes. PLCD provides quantitative evidence to support strategic plant design modification decisions, including tradeoff analyses of redesign cost and requirement violation. In this article the design of a counterbalanced robotic manipulator is used to illustrate successful PLCD application. A baseline system design is obtained that exploits synergy between manipulator passive dynamics and control to minimize energy consumption for a specific pick-and-place task. The baseline design cannot meet requirements for a second pickand-place task through control design changes alone. A limited set of plant design changes is identified using sensitivity analysis, and the PLCD result meets the new requirements at a cost significantly less than complete system redesign.
Customer preferences for sustainable products are dependent upon the context in which the custome... more Customer preferences for sustainable products are dependent upon the context in which the customer makes a purchase decision. This paper investigates a case study in which fifty-five percent of survey customers say they prefer recycled paper towels, but do not purchase them. These customers represent a profit opportunity for a firm. This paper explores the impact of investing capital in activating pro-environmental preferences on a firm's profitability and greenhouse gas (GHG) emissions through a multi-objective optimization study. A product optimization is designed to include models of carbon dioxide emissions, manufacturing costs, customer preference, and technical performance. Because the optimization includes a tradeoff between recycled paper and performance, a model of customer preferences, and a market of competing products, the maximum GHG reduction occurs at less than 100% recycled paper. Also, the tradeoff between GHG reductions and profit is not dictated by the configuration of the product, but instead by its price. These results demonstrate the importance of including customer preferences with engineering performance in design optimization. Investment in the activation of pro-environmental preferences is high at all points on the Pareto optimal frontier, suggesting that further engineering design research into the activation of pro-environmental product preferences is warranted.
Wave energy converters (WECs) extract energy from the motion of ocean waves. A variety of differe... more Wave energy converters (WECs) extract energy from the motion of ocean waves. A variety of different WEC devices have been studied over the past several decades, with emphasis on cost-effective energy extraction. Active control has been shown to improve energy production significantly. Here we investigate energy extraction potential of a tethered heaving cylinder WEC using direct transcription (DT), an open-loop optimal control strategy. This enables direct inclusion of asymmetric constraints on power and tether force, practical considerations not considered in previous studies, and opens the door to WEC optimal control problems with more realistic nonlinear models and integration of control design with physical system design.
Previous research presents both sensitivity-based and principal component-based techniques for im... more Previous research presents both sensitivity-based and principal component-based techniques for improving the tractability of system identification. Both have proven viable, but the former may be computationally inefficient for large problems, and the latter require a change of realization that may compromise the physical meaning of the parameters to be identified. This paper proposes for the first time the use of activity analysis, an efficient and realization-preserving model reduction technique, for identification space reduction. Theoretical and numerical studies highlighting the viability of activity analysis versus the previous two methods are presented.
Effective powertrain design for the emerging electric vehicle market is a complex, multidisciplin... more Effective powertrain design for the emerging electric vehicle market is a complex, multidisciplinary problem. As such, engineers may often use formal decomposition-based optimisation strategies to partition the problem into more manageable subproblems and then integrate their solutions to obtain an optimal system design. Sometimes, these strategies yield decision variables that consist of highly-discretised functional data which must be reduced to enable efficient, practical optimisation. Reduced representation methods such as Proper Orthogonal Decomposition (POD) can help achieve this goal, but the effectiveness of POD in terms of design solution accuracy and optimisation efficiency is dependent on its interaction with the optimisation strategy. Therefore, this paper investigates the impact of a tuning parameter within POD on solution accuracy and optimisation efficiency in the context of decomposition-based electric vehicle powertrain design. is responsible for the research, design and initial development of novel hybrid powertrain architectures. He graduated Summa Cum Laude with a BS in Mechanical Engineering at the University of Cincinnati and continued his studies in Mechanical Engineering by earning his MSE (2008) and PhD (2011) at the University of Michigan. His general research interests include multidisciplinary design optimisation, hybrid-electric/electric vehicle design, functional data approximation and metamodelling.
Modern engineering systems often are impractical to design from the ground up. New designs typica... more Modern engineering systems often are impractical to design from the ground up. New designs typically are modifications of earlier systems (and frequently only small perturbations of them). This limited redesign approach is becoming increasingly important as the scale and complexity of engineering systems increases. One significant application of limited redesign is the repurposing of mechatronic systems. Often engineers seek to meet the needs of a new application by redesigning only the control system for a mechatronic device. While in many cases this approach is successful, control design changes alone may not always be sufficient. If control redesign alone is inadequate, physical system (plant) design changes should be investigated. Complete plant redesign cost may be prohibitive, and usually is unnecessary. A limited set of plant design changes should be identified that enable system requirement satisfaction at the lowest cost. Here we present a formal integrated approach for limited redesign of mechatronic systems. Candidate plant modifications are identified using sensitivity analysis, and then an optimization problem is solved that minimizes the cost of system redesign while satisfying requirements. This formal methodology for plant limited co-design (PLCD) is demonstrated using a robotic manipulator design problem. First the manipulator is designed in a way that exploits passive dynamics to minimize energy consumption for a specific task. Afterward a new task is introduced that cannot be performed successfully through control changes alone. Limited plant changes are identified, and the PLCD result for this new task is compared to a full system redesign. The PLCD result costs significantly less than the full redesign with a small performance penalty. Parametric studies illustrate the tradeoff between redesign cost and performance, and it is shown that the proposed sensitivity analysis results in the lowest cost limited redesign.
Design of physical systems and associated control systems are coupled tasks; design methods that ... more Design of physical systems and associated control systems are coupled tasks; design methods that manage this interaction explicitly can produce system-optimal designs, whereas conventional sequential processes may not. Here we explore a new technique for combined physical system and control design (co-design) based on a simultaneous dynamic optimization approach known as direct transcription, which transforms infinitedimensional control design problems into finite dimensional nonlinear programming problems. While direct transcription problem dimension is often large, sparse problem structures and finegrained parallelism (among other advantageous properties) can be exploited to yield computationally efficient implementations. Extension of direct transcription to co-design gives rise to a new problem structures and new challenges. Here we illustrate direct transcription for co-design using a new automotive active suspension design example developed specifically for testing codesign methods. This example builds on prior active suspension problems by incorporating a more realistic physical design component that includes independent design variables and a broad set of physical design constraints, while maintaining linearity of the associated differential equations.
An often cited motivation for using decomposition-based optimization methods to solve engineering... more An often cited motivation for using decomposition-based optimization methods to solve engineering system design problems is the ability to apply discipline-specific optimization techniques. For example, structural optimization methods have been employed within a more general system design optimization framework. We propose an extension of this principle to a new domain: control design. The simultaneous design of a physical system and its controller is addressed here using a decompositionbased approach. An optimization subproblem is defined for both the physical system (i.e., plant) design and the control system design. The plant subproblem is solved using a general optimization algorithm, while the controls subproblem is solved using a new approach based on optimal control theory. The optimal control solution, which is derived using the the Minimum Principle of Pontryagin (PMP), accounts for coupling between plant and controller design by managing additional variables and penalty terms required for system coordination. Augmented Lagrangian Coordination is used to solve the system design problem, and is demonstrated using a circuit design problem.
In decomposition-based design optimization strategies, such as Analytical Target Cascading (ATC),... more In decomposition-based design optimization strategies, such as Analytical Target Cascading (ATC), it is sometimes necessary to use reduced dimensionality representations to approximate functions of large dimensionality whose values need to be exchanged among subproblems. The reduced representation variables may not be physically meaningful, and it can become challenging to constrain them properly and define the model validity region. For example, in coordination strategies like ATC, representing vector-valued coupling variables with improperly constrained reduced representation variables can lead to poor performance or convergence failure. This paper examines two approaches for constraining effectively the model validity region of reduced representation variables based on proper orthogonal decomposition: a penalty value-based heuristic and a support vector domain description. An ATC application on electric vehicle design helps to illustrate the concepts discussed.
Many engineering systems are too complex to design as a single entity. Decompositionbased design ... more Many engineering systems are too complex to design as a single entity. Decompositionbased design optimization methods partition a system design problem into subproblems, and coordinate subproblem solutions toward an optimal system design. Recent work has addressed formal methods for determining an ideal system partition and coordination strategy, but coordination decisions have been limited to subproblem sequencing. An additional element in a coordination strategy is the linking structure of the partitioned problem, i.e., the allocation of constraints that guarantee that the linking variables among subproblems are consistent. There may exist many alternative linking structures for a decomposition-based strategy that can be selected for a given partition, and this selection should be part of an optimal simultaneous partitioning and coordination scheme. This article develops a linking structure theory for a particular class of decomposition-based optimization algorithms, augmented Lagrangian coordination (ALC). A new formulation and coordination technique for parallel ALC implementations is introduced along with a specific linking structure theory, yielding a partitioning and coordination selection method for ALC that includes consistency constraint allocation. This method is demonstrated using an electric water pump design problem.
Your article is protected by copyright and all rights are held exclusively by Springer-Verlag. Th... more Your article is protected by copyright and all rights are held exclusively by Springer-Verlag. This e-offprint is for personal use only and shall not be self-archived in electronic repositories. If you wish to self-archive your work, please use the accepted author's version for posting to your own website or your institution's repository. You may further deposit the accepted author's version on a funder's repository at a funder's request, provided it is not made publicly available until 12 months after publication.
Use of decomposition-based design optimization methods requires a priori selection of system part... more Use of decomposition-based design optimization methods requires a priori selection of system partitioning and of the corresponding coordination strategy. Typically, partitioning systems into smaller, easier to solve subproblems leads to more complicated, computationally expensive coordination strategies. Previous optimal partitioning techniques have not addressed the coordination issue explicitly. A Pareto-optimal problem formulation was proposed recently to address simultaneous partitioning and coordination decisions. Due to the combinatorial nature of this problem, exhaustive enumeration was used to demonstrate the approach to small system examples. This article presents and demonstrates an evolutionary algorithm that can solve this problem for systems of moderate size. A readily partitioned truss design formulation is introduced on which design problems with a wide variety of interaction patterns and system sizes can be based. An eight-bar truss problem is used to demonstrate the effectiveness of the proposed evolutionary algorithm.
Previous research presents both sensitivity-based and principal component-based techniques for im... more Previous research presents both sensitivity-based and principal component-based techniques for improving the tractability of system identification. Both have proven viable, but the former may be computationally inefficient for large problems, and the latter require a change of realization that may compromise the physical meaning of the parameters to be identified. This paper proposes for the first time the use of activity analysis, an efficient and realization-preserving model reduction technique, for identification space reduction. Theoretical and numerical studies highlighting the viability of activity analysis versus the previous two methods are presented.
Design of modern engineering products requires complexity management. Several methodologies for c... more Design of modern engineering products requires complexity management. Several methodologies for complex system optimization have been developed in response. Single-level strategies centralize decision-making authority, while multi-level strategies distribute the decision-making process. This article studies the impact of coupling strength on single-level Multidisciplinary Design Optimization formulations, particularly the Multidisciplinary Feasible (MDF) and Individual Disciplinary Feasible (IDF) formulations. The Fixed Point Iteration solution strategy is used to motivate the analysis. A new example problem with variable coupling strength is introduced, involving the design of a turbine blade and a fully analytic mathematical model. The example facilitates a clear illustration of MDF and IDF and provides an insightful comparison between these two formulations. Specifically, it is shown that MDF is sensitive to variations in coupling strength, while IDF is not.
Analytical Target Cascading (ATC) is a product development tool that computes component design sp... more Analytical Target Cascading (ATC) is a product development tool that computes component design specifications such that the final system design is consistent and meets design targets. ATC is useful for complex product design that must be approached by decomposition, and facilitates concurrent design activities. While ATC has been applied successfully to automotive design, this article introduces the application of ATC to aircraft design, and discusses how it can be congruent with current design practice. ATC is used to solve an aircraft design problem where several flight regimes are considered separately. ATC can be used to balance low-fidelity system analysis and component-level multidisciplinary design optimization (MDO) activities. Finally, ATC may be used to coordinate overall aircraft design, with MDO employed to solve tightly coupled disciplinary problems that exist within ATC elements.
Design of complex products with several interacting subsystems or disciplinary analyses poses sub... more Design of complex products with several interacting subsystems or disciplinary analyses poses substantive challenges to both analysis and optimization, necessitating specialized solution techniques. A product or system may qualify as complex due to large scale or due to strong interactions. Single-level strategies for complex system optimization centralize decision-making authority, while multilevel strategies distribute the decisionmaking process. This article studies important differences between two popular singlelevel formulations: multidisciplinary feasible (MDF) and individual disciplinary feasible (IDF). Results presented aim at aiding practitioners in selecting between formulations. Specifically, while IDF incurs some computational overhead, it may find optima hidden to MDF and is more efficient computationally for strongly coupled problems; further, MDF is sensitive to variations in coupling strength, while IDF is not. Conditions that lead to failure of MDF are described. Two new reproducible design examples are introduced to illustrate these findings and to provide test problems for other investigations.
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