Interactive Collaborative Optimization – A ...web.stanford.edu/class/cee320/CEE320C/Flager.pdf · Interactive Collaborative Optimization – A Multidisciplinary Optimization Method

Flager GQE Research Proposal 3/31/2009

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Interactive Collaborative Optimization – A Multidisciplinary Optimization Method Applied to the Design of Steel Building and Civil Structures

By Forest Flager, PhD Student, Center for Integrated Facility Engineering (CIFE), Stanford University; [email protected]

Abstract: Architecture, Engineering and Construction (AEC) professionals are capable of accurately simulating the behavior of complex steel structures using modern Finite Element Analysis (FEA) software. The time required, however, to model and run such simulations using conventional processes and technologies has limited the potential of FEA to inform early-stage design decisions. Engineers typically conduct FEA on only a tiny fraction of the design space or range of options under consideration. Consequently, AEC professionals usually make design decisions with little or no information about either the performance of the chosen design with respect to alternatives or the implications of a particular design decision on downstream choices.

The focus of my doctoral research is the development and application of a new Multidisciplinary Optimization (MDO) method to the design of structures in the AEC industry, including the determination of structure topology, geometry and the sizing of individual structural steel members. The method, called Interactive Collaborative Optimization (ICO), differs from existing structural optimization approaches in that (1) it is multi-level, i.e. it uses multiple optimizers, and (2) it allows the designer to concurrently consider objective and subjective criteria in choosing the best design. ICO is based upon Collaborative Optimization, a formulation developed by Braun and Kroo in the mid-1990s, which the aerospace industry now routinely uses to design aircraft. It is a bi-level hierarchical scheme, with the top level consisting of a system optimizer that operates on variables that affect multiple disciplines (e.g. topology and geometry). At the lower level, subspace optimizers operate on discipline-specific design variables (e.g. member sizes) to satisfy design constraints within each specific discipline. To ensure that the decision variables are compatible and converge to an optimal design, the designer interactively manipulates variable sets at each level based on objective and subjective performance criteria – hence the name, Interactive Collaborative Optimization.

My hypothesis is that the ICO methodology is better suited to AEC organizations than the existing single-level MDO formulations. Single-level formulations require centralized decision-making at the system-level, which can lead to bottlenecks if the number of decision variables is large. ICO allows for decisions to be distributed between project manager at the system level, but also at the subspace level by group leaders and experts in specific disciplines. Allowing experts and group leaders to make local (subspace) decisions more closely replicates existing organizational structures. Also, ICO’s potential computational advantages include a reduction in communication requirements, since local design variables no longer must be passed to the system optimizer, and the capacity to employ specialized optimizers to make local design decisions.

I have already applied the member sizing subspace formulation of ICO to the design of a large stadium roof, significantly reducing design-cycle time as well as cutting steel costs by over 15% when compared to traditional methods. My future research will involve applying the complete ICO formulation, involving topology, geometry, and member sizing, to several academic and industry case-study projects. I will compare ICO to conventional practice and also to equivalent single-level formulations, on the basis of (1) process efficiency, including design cycle time and number of cycles; (2) design knowledge at key decision points; and (3) resulting product performance.


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1. INTRODUCTION

In the past decade, the widespread availability of affordable high-performance personal computers, coupled with advancements in computer-aided design and engineering (CAD/CAE) software, have had a significant impact on the Architecture, Engineering and Construction (AEC) industry as a whole and structural design in particular. Until very recently, computers in structural design were used primarily for analytical purposes during the detailed design phases. They are now being applied to all phases of the design process, from the generation of design concepts thru preliminary and detailed design [2]. This technology aids in the generation, analysis, and optimization of design solutions, but it will not replace designers. On the contrary, the decision-making abilities of designers will be even more crucial because of large number of design alternatives it will be possible to generate, and also because of the need to coordinate many specialists now required in modern multidisciplinary design projects [3]. New design methods and computational environments are required to fully benefit from this progress in information technology.

Researchers in AEC as well as a variety of other industries (e.g. aerospace, automotive) have developed a class of formal methods for the design of complex products, referred to as Multidisciplinary Design Optimization (MDO). The AIAA MDO Technical Committee [4] defines MDO as a new engineering discipline concerned with the formalization of iteration and coordination between groups working on the design of complex engineering systems and sub-systems and with creating an environment conducive to these formal methods. In this context, the term ‘complex’ merits precise definition: an engineering system is ‘complex’ if one individual cannot completely understand the details and interactions between all system components. For example, buildings historically did not qualify as complex systems since a single master designer was capable of comprehending and directing the entire building design process. Modern buildings, however, are complex systems because several interacting, specialized teams are required in the design process.

MDO fundamentally consists of a method of analysis and a method for generating improved designs. One major approach MDO uses is decomposing a large system into smaller subsystems, connected by information flows from the output of one subsystem into the inputs of another [5-7]. Two subsystems connected by information flows are said to be ‘coupled’. Once the method of analysis is determined, the spectrum of available optimization procedures that can be used to generate improved designs ranges from an iterative trial-and-error process to formal algorithms that efficiently guide the design process to an ‘optimal’ solution. The development of appropriate analytic and optimization methods is highly dependent of the needs of the particular industry and/or product. The needs of different industries are diverse, leading to the use of methodologies in each industry that have distinctly different objectives and processes [8].

Section 2 provides an overview of the structural design process and defines requirements for MDO that have been derived from general and case specific observations.

Section 3 describes related research in the fields of design management, MDO, and structural optimization precedents in the AEC industry. These methods are then compared to requirements developed in the previous section in order to highlight certain organizational and computational limitations associated with existing MDO formulations.


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Section 4 introduces a new MDO method called Interactive Collaborative Optimization (ICO). It is the author’s hypothesis that this method will better address the needs of designers in the AEC industry and enable these professionals to compress design cycle times and evaluate many more design alternatves, yielding substantive gains in product quality and performance.

Section 5 describes the research methodology proposed for testing the foregoing hypothesis. This involves applying ICO to several academic and industry case-study projects. ICO will be compared to conventional practice, as well as to other MDO formulations, on the basis of process efficiency, design knowledge and product performance.

Finally, Section 6 describes the specific contributions to knowledge that are expected to result from this research. The author also speculates on the broader impact this work may have on future research and industry practice.

2. OVERVIEW OF STRUCTURAL DESIGN

The structural design of buildings and civil structures requires specifying the material(s) to be used (e.g. steel, concrete), determining the overall dimensions of the supporting framework, and selecting the cross sections of individual members. The primary design and engineering considerations during this process are [9]:

• Safety: Ensure that the structure does not collapse under the applied loading or otherwise cause damage to persons or property.

• Serviceability: Confirm the structure meets deflection and acceleration requirements.

• Economy: Make efficient use of materials and construction labor. Although this objective usually can be accomplished by a design that requires a minimum amount of material, savings can also be realized by using more material if it results in a simpler, more easily constructed project.

• Aesthetics: Create a pleasing visual appearance.

Each designer has a different style that is based on their knowledge of functional forms and their viewpoint of the importance of functional efficiency, economy and beauty as well as the relation among them [10]. A civil engineer creates structural form to control physical effects, or forces, while an architect seeks to control space. Following from the civil engineers’ quest to control forces, they are primarily focused on functional efficiency and clarity as well as construction costs, or economy, resulting in preferences for conventional, uniform structural forms without ornamentation, which adds non-functional material. Conversely, an architect’s attempt to control space results in primary design goals of artistic expression and visual impact with only a secondary goal of functional efficiency. Architects tend to have more variation in their aesthetic values since they are not always based on considerations of functional efficiency alone, which allows for greater latitude in the structural forms that are considered in the design process [11].

The design problem can be decomposed into three main categories (Figure 1):


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• Topology involves determining material layout, including the number and connectivity of members

• Shape involves deciding the contour, or form, of a structural system whose topology is fixed

• Member sizing involves defining cross-sections, or dimensions, of a structural system whose topology and shape is fixed

The three design problem categories are closely related to three major stages of the engineering design process as defined by Pahl and Beitz [3]: conceptual, embodiment (design development), and detail. Typically, during the conceptual design phase, the architect and engineer work together closely to identify a structural system, material and topology that satisfy the design program, the functional requirements, and the architectural aesthetic. The shape of the structural system is then determined during the embodiment or design development phase. This includes determining the overall dimensions of the structural system. Design decisions at this stage are made based on both quantitative (e.g. efficiency) as well as qualitative (e.g. aesthetics) criteria [12]. Finally during the detailed design phase, the architect and engineer typically work somewhat independently of each other on discipline-specific problems. At this stage, decisions tend to be quantitative in nature since the first priority of the engineer during this phase is to ensure that the structure meets the design requirements for safety and serviceability.

The people involved, the software tools used, and the design decision variables are different for each type of design problem. To better understand the process by problem type and phase, we will use a recently observed industry project as an example of a typical structural design process.

z

ANALYSIS LAYERElement list: "upper plane"

Scale: 1:992.5

ANALYSIS LElement list:

Scale: 1:7.0

A NA LYS IS LA YE RE lem ent li st: 1939 1940

S cal e: 1:17. 88

x

y

z

Universal Beam (UB) Section

Rectangular HollowSection (RHS)

Circular HollowSection (CHS)

Figure 1: Example of topology, shape, and sizing for a discrete structural design problem


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2.1. Project Example: A Stadium Roof Structure

The project example involves the design of a large steel frame roof for a 65,000 seat athletic stadium, as shown in Figure 2 above. The design process is represented in Figure 3 below; it is based on the Design Structure Matrix (DSM) matrix notation [13], which is discussed further in Section 2.1. The three primary design problems, including topology design, shape design and member sizing, are represented along the downward diagonal of the diagram, going from left to right. Horizontal arcs represent the outputs from tasks, while vertical arcs represent inputs to the tasks. The connectivity between the output from one module and the input of another model is shown by a filleted rectangle that represents the coupling between modules and provides a brief description of the information exchanged. Couplings above the diagonal of the DSM are feed forward couplings, representing sequential execution. Couplings below the diagonal of the DSM are feedback couplings, representing iterations.

MEMBER SIZING

SE

SHAPE DESIGN

A + SE + ME

TOPOLOGY DESIGN

A + SE + ME + FE

N-S BaysE-W Bays

N-S BaysE-W Bays

Arch HeightFrame Depth

AestheticsSteel WeightMember Util

AestheticsSteel WeightMember Util

Each design task is described in more detail below:

2.1.1. TOPOLOGY DESIGN

Number of Iterations Completed Iteration

Type Feasible Infeasible Total

Avg. Time Per Iteration (man hours)

Topology 1 1 2 30 Shape 1 0 1 24

Member Sizing 4 35 39 6

Figure 2: Project example – a steel frame roof structure for an athletics stadium.

Figure 3: LEFT - Process diagram showing coupling between design tasks. RIGHT -Process metrics including the total number and time required for design


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The architectural design for the roof of the stadium was conceived as an arched form that would be continuously supported by the reinforced concrete of the stadium spectator bowl. During the conceptual design, the structural engineer decided that a steel space frame would be the most efficient structural system to achieve the desired form. Once the general system had been decided, the structural engineer identified a number of topology variables that he was interested in studying to create the most efficient design: 1) the number of bays in the structure, 2) the number and position of lateral bracing members. This design decision affected the architectural aesthetic as well as the work of the façade engineer in determining the size and arrangement of cladding panels, and the work mechanical engineer in determining the position of lighting needed to illuminate the athletic field. Because of time restrictions, the design team was able to investigate only two bracing configurations and was not able to vary the number of bays before making a final decision. The topology was determined before an FEA model of the structure was made.

2.1.2. SHAPE DESIGN

During the embodiment, or design development, phase of the project, the overall dimensions of the structure were determined. The engineering team was interested in varying both the overall height of the arch at the leading edge of the roof, as well as the depth of the roof frame at key locations. This decision again had an impact on the architecture, as well as the façade and lighting systems. An FEA model was constructed at this stage, however, because it required approximately 24 man-hours to create the FEA model using the architect’s 3-D CAD model (Figure 3), the engineering team concluded that it required too much effort to investigate any further shape configurations after a feasible design was found.

2.1.3. MEMBER SIZING

Finally during the detailed design phase, the cross sections of individual steel members were determined. The goal of this process was to minimize the weight of the structure while satisfying aesthetic criteria and safety and serviceability requirements.

Designers selected from a wide range of standard steel sections to determine the appropriate profile, size and weight of the member. The member sizing process involved first building a detailed FEA model of the structure, including a number of design loading combinations and an initial design (i.e. configuration of member sizes) based on rules of thumb and past experience. For each load case, the FEA results are used to calculate a utilization ratio for each member in the structure based on the applicable engineering code of practice. A utilization ratio of less than unity indicates that the strength of the member is adequate in consideration of the interaction of axial, bending and torsion forces. Based on these results, designers then manually modify the sizes of the members in the structure until all strength and deflection constraints are satisfied.

The FEA model of the stadium roof shown in Figure 2 had 1955 members and 150 load combinations to consider. The number of feasible steel sections for each member ranged from 10-30 different choices. Thus, the number of unique design configurations (i.e., the size of the design space) was approximately 201955! Because design iteration took approximately 4 hours to complete, the design team was only able to evaluate 4 feasible design (39 total designs) as shown in Figure 3 before selecting the final design.

2.2. The Need for Formal Structural Design Methods


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As demonstrated by the stadium roof case study described above, architects and engineers using FEA complete very few design iterations before making final design decisions. The design team considered only three design alternatives for structural topology and geometry and 39 out of a possible 201955 member sizing configurations. These results are consistent with a survey of AEC design firms that found that designers evaluate less than three design alternatives on a typical project using model-based simulation methods such as FEA [14]. The majority of engineers surveyed indicated that they used simulation tools primarily to validate a chosen design option, not to explore multiple alternatives.

AEC professionals’ narrow exploration of the design space results from a number of tool and process limitations. One limitation is that the designers’ tools usually generate static design options and are not intended to help define and explore solution spaces [15]. A second limitation is that these tools do not produce information that is represented in a form that facilitates multidisciplinary analysis. Many in the field have written about the inability of tools used by the different disciplines to share data effectively [16-18] – such data sharing being prerequisite to an effective multidisciplinary analysis. As a result of these limitations, the survey shows that design professionals are now spending less than half of their time doing ‘value-added’ design and analytic work. The majority of their time now is spent in managing design information, including manually integrating and coordinating discipline-specific design and analytical representations. We need to overcome these limitations before we will be able to explore design space on a more thorough and systematic basis.

MDO methods leverage computers’ processing power to enable AEC professionals to explore design spaces and do design work that is well beyond unaided human capabilities [19]. A design methodology is a prerequisite to harnessing this computer power and must provide for flexible and continuous computer support of the design process. Without such a methodology, it is not possible to link separate programs, especially geometric modelers with analytic programs, to ensure a continuous flow of data. Systematic procedures also make it easier to divide work between designers and computers in a meaningful way [3] [20].

The goal of MDO and other formal design methods is to:

• Compress design cycle time

• Increase design knowledge to support more informed decision making

• Yield substantive product quality and performance gains

• Reduce time to market

By increasing design knowledge early in the design process and by maintaining design freedom (Figure 4) , a method such as MDO enables better decisions in the early stages of the design process, well before the freedom to make these decisions is eliminated [1].

Figure 4: Reducing time-to-market by increasing design knowledge and maintaining design freedom [1]


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Using such methods, designers can avoid unanticipated changes which often occur in the later design stages, thereby also achieving significant time savings.

2.3. MDO Requirements for Structural Steel Design

The primary obstacles to implementing MDO in the AEC design process are computational expense and organizational complexity [21]. Successful implementation of MDO methods, therefore, requires careful attention to process, organization and product requirements [22]. These requirements, summarized below, are based upon the general and case-specific observations described above. A successful MDO implementation should:

• Function within the existing organizational structure: AEC design teams typically are led by (1) a project manager and (2) by group leaders and experts in various disciplines. Design decisions are typically distributed between these two management levels. The MDO formulation should leverage these existing resources.

• Allow for the use of heterogeneous software and computer platforms: Project teams use a variety of software and computational platforms to support their respective analyses. An MDO formulation should be able to integrate these technologies effectively.

• Be Scalable: The structural design problems encountered in the AEC industry are complex; they involve many variables, computationally intensive simulations and vast design spaces to explore. An MDO formulation must be able to manage large problems of this nature.

• Be Multi-objective: Each design discipline has separate objectives and constraints which must be satisfied together with the system-level goals and constraints. Goals of individual subsystems may be contradictory, and goal metrics may involve both subjective and objective criteria. An MDO formulation must allow stakeholders to consider and decide between multiple objectives.

3. RELATED RESEARCH

This section describes related research in the fields of design management, MDO, and structural optimization precedents in the AEC industry.

3.1. Design Process Management

Design process management pertains to the interaction of a designer with the progress of the solution of a design problem. The roots of this process lie in graph theory [23] [24]. The expansion of graph theory to project management resulted in the development of the Program Evaluation and Review Technique (PERT) and the Critical Path Method (CPM) [25] in the 1950s. These provide important information for tracking the progress of well-defined design and production tasks. An important limitation of PERT and CPM is that iteration is not incorporated into these methods. A variation of PERT, the General Evaluation Review Technique


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(GERT) [26], can handle cycles effectively when they involve simple networks but, this approach has encountered difficulties in representing complex, iterative processes in an easily accessible manner [27].

3.1.1. DESIGN STRUCTURE MATRIX (DSM)

The Design Structure Matrix (DSM), also referred to as the Dependency Structure Matrix, was developed by Steward in 1981 as an alternative to the process flow chart [28]. A sample DSM diagram is shown in Figure 4. The tasks or subsystems are represented as numbered boxes along the downward diagonal of the DSM. As noted previously, horizontal arcs represent the outputs from tasks, while vertical arcs represent the inputs to the tasks. The connectivity from the output of one module into the input of another can be represented by a black or circular or square symbol, which signifies the coupling between modules. Couplings above the diagonal of the DSM represent feed forward couplings, implying sequential execution. Couplings in the lower diagonal of the DSM represent feedback couplings, implying iteration. This cyclic behavior is clear when using the DSM. Additionally, the DSM may be used to group iterative sub cycles that may appear in a design process (termed circuits), thereby making the DSM scalable to larger design processes.

DSM has been used as the basis for a variety of design management tools as reviewed by Smith and Eppinger [29] and Rogers [30]. Two of the most popular DSM-based tools are the Work Transformation Matrix (WTM), which was developed at the Sloan School at MIT [31], and the Design Manager’s Aide for Intelligent Decomposition (DeMAID), which was developed at the NASA-Langley Research Center [32]. These tools provide information on task duration, the probability of iteration, as well as the resulting iterative effort. They are designed to support managers interested in understanding where iteration is likely to occur in a design process and how process tasks can be reorganized to accelerate the process by executing either faster and/or fewer iterations [33].

Rather than using DSM for management purposes, my research uses DSM in an engineering application to support MDO. In an MDO environment, DSM is used to represent a number of linked analysis and optimization codes, where each module often requires full execution, even if the change to the input module is small [27]. This characteristic drives the importance of representing the transfer of specific information and the semantics of the coupling between modules.

3.1.2. MULTIDISCIPLINARY DESIGN NARRATIVES

The narratives developed by Haymaker are formal, visual descriptions of the design process consisting of a directed acyclic graph of task-specific views and dependencies [34, 35]. Haymaker’s representation does not capture design iteration as clearly or compactly as DSM, but it does provide semantics for the coupling between modules as well as an explicit description of the information being exchanged. Each task includes a representation of the information (“perspective”) and the reasoning (“perspector”). The perspector component includes information about (1) the actor, or person(s) responsible for completing the task; and (2) the tool, a description of the technology used to complete the work. This information is useful in describing the nature of a coupling between process tasks.

Figure 4: Sample Design Strucuture Matrix (DSM) Process Representation


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My research will draw upon both methods to represent and decompose MDO problems as shown in Figure 6.

3.2. Multidisciplinary Design Optimization (MDO)

MDO consists fundamentally of an analytic method and a method for generating improved designs. One major approach MDO utilizes is decomposing or partitioning a large system into smaller subsystems. Wagner identifies four types of decomposition strategies that are commonly found in the systems design literature [7]:

• Object decomposition divides a system by physical components or functions such as by thermal zone, room, or structural component.

• Aspect decomposition divides the system according to different specialties or disciplines and is relevant when multiple performance aspects are evaluated for a physical component (e.g. structural cost and energy efficiency).

• Sequential decomposition applies when sub-problems are organized by workflow or process logic (e.g. chemical processes).

• Matrix partitioning is applied to large systems of mathematical equations.

Wagner also explains that in a mathematical programming context, decomposition involves both partitioning and applying a coordination strategy. The main requirement of a coordination strategy is that it converge to the same solution set as that of an unpartitioned problem [36].

Once the analysis method is determined, the spectrum of available optimization procedures to generate improved designs varies from an iterative trial-and-error process to formal algorithms to efficiently guide the design process to an ‘optimal’ solution. MDO strategies can be generally categorized into two types based upon their optimization strategies: single-level and multi-level.

3.2.1. SINGLE-LEVEL FORMULATIONS

System-level Optimizer

Analysis Analysis Analysis

System-level Optimizer

SubspaceOptimizer

Analysis

SubspaceOptimizer

Analysis

SubspaceOptimizer

Analysis

Figure 5: LEFT – A generic single-level MDO formulation RIGHT – A generic multi-level formulation


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The first formulations discussed are considered single-level approaches because an optimizer is only employed at one level – the system level. The analysis may be distributed via partitioning [8], but design is not distributed. All decisions are made at the level of the single system-level optimizer. Three fundamental single-level approaches are discussed here and in more detail by Cramer [22]: Multidisciplinary Feasible (MDF), Individual Disciplinary Feasible (IDF), and All At Once (AAO).

In the MDF approach, a complete system analysis is performed for all optimization iteration. The analyses are performed sequentially and depend upon the previous analysis resulting in a feasible design. In a computational context, this approach is desirable where the analyses are weakly coupled (fast analysis convergence) and computation is not expensive.

To address of the limitations of the MDF formulation, the Individual Disciplinary Feasible (IDF) approach was developed. The key difference is that the optimizer coordinates interactions between the subspaces, rather than relying on a simple iterative scheme, as is the case with MDF. This improves convergence properties and drives the design toward better solutions if multiple analytic solutions exist.

The last of the three basic, single-level strategies is the highly centralized All-At-Once (AAO) strategy. Instead of utilizing analyzers to complete the analysis for each subspace, evaluators are used that compute only the residuals of the governing equations. The system optimizer is now saddled with three sets of decision variables: the original design variables, the coupling variables, and the state variables. AAO centralizes both design and analysis, but still distributes evaluation of governing equations. This high degree of centralization offers impressive computational efficiency in some situations, but because of AAO’s centralization and specialized structure, it can be is difficult to map to organizational structures [8].

3.2.2. MULTI-LEVEL FORMULATIONS

In many cases, single-level formulations perform well. However, there are several reasons for adopting multi-level approaches. The complete design centralization of single-level approaches may not map well to existing organizational structures. Many design teams are lead by a project manager at the system level but also by a group leaders or disciplinary experts at the subspace levels. Allowing experts or group leaders to make local decisions uses existing resources more efficiently. Local decision making is represented by subspace optimizers in multi-level architectures, providing the subspace autonomy that is frequently required to map a formulation to an existing organizational structure [37]. In addition, multi-level strategies allow designers to utilize specialized optimizers to make local design decisions, instead of separating the analysis and forcing it to work with a system optimizer. Finally, multi-level formulations can reduce communication requirements, since local design variables no longer must be passed to the system optimizer. The system optimizer is limited to coordinating the subspace interactions and guiding the entire process to a system-optimal design.

Several variations of multi-level strategies have been developed. One class of these formulations is the Disciplinary Constraint Feasible (DCF) architecture. An optimizer is associated with each subspace and is charged with ensuring local design constraints are satisfied and minimizing applicable objective functions (which may be modified from the original design problem) with respect to subspace level variables. The system optimizer is responsible for ensuring system consistency, and minimizing the system objective function, with respect to system level variables. The term DCF arises from the fact that


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each subspace optimizer is required to return a local design that is a consistent at the system-level and satisfies local discipline design constraints. Three popular formulations that employ the basic DCF architecture are discussed below and surveyed in detail by Kodiyalam [38].

Collaborative Optimization (CO) [39-41] is a bi-level hierarchical scheme, with the top level consisting of the system optimizer that operates on multidisciplinary variables to satisfy interdisciplinary compatibility constraints. These subspace optimizer(s) are permitted to vary local parameters to ensure subspace feasibility. Since there may not exist sufficient local degrees of freedom to satisfy all of the constraints, subspaces are permitted to depart from the values of interdisciplinary parameters established as targets by the system-level coordination method, although these departures are to be minimized. Thus, it is the job of the subspaces to satisfy constraints while working to define a design that everyone can agree on.

Concurrent Subspace Optimization (CSSO) [5] is a non-hierarchic scheme that optimizes decomposed subspaces concurrently. This is followed by a coordination procedure for directing system problem convergence and resolving subspace conflicts. This corresponds to common design practice where individual design teams optimize their local component designs and compromises are made at the integrated product team or system level. In CSSO, each subspace optimization problem is a system level problem formulated with respect to a subset of the total system design vector. Within the subspace optimization, the non-local states that are required to evaluate the objective and constraint functions are approximated using the Global Sensitivity Equations (GSE) [5]. The CSSO method provides for multidisciplinary analysis feasibility at each cycle but deals with all the design variables simultaneously at the system level.

The recently introduced Bi-Level Integrated System Synthesis (BLISS) [42] method uses a gradient-guided path to reach an improved system design, alternating between the set of design subspaces (discipline-specific problems) and the system level design space. BLISS is an AAO-like method in that at the beginning of each cycle of the path it performs a complete system analysis to maintain multidisciplinary feasibility. With BLISS, the general system optimization problem is decomposed into a set of local optimizations that deal with a large number of detailed local design variables and a system level optimization that deals with a relatively small number of global variables.

3.3. Structural Optimization in the Architecture, Engineering and Construction Industry (AEC)

The early work of Maxwell [43] in the nineteenth century, and the subsequent development by Michell [44], provided the basic theory for the optimal layout of idealized two-dimensional truss structures to achieve minimum weight designs under a single load condition and subject only to stress constraints. Confidence in our ability to predict the behavior of complex structures grew significantly in the 1950s and 1960s with the development of reliable FEA methods. These advancements, coupled with the continuing growth in digital computing power, led to the first application of computational optimization methods to structural design. Formal optimization methods based on the assumption of continuity, such as mathematical programming [45] and optimality criteria [46], worked well on member sizing problems that usually were well-defined in terms of mathematical models. Haftka [47] provides a good overview of techniques of this type.

The generalization of the problem to include topology and shape design increased the complexity of the optimization task greatly and rendered many traditional methods inadequate. This issue became a starting


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point for the development of enhanced formal and heuristic methods dating back to the mid-1970s, including simulated annealing and evolutionary algorithms (EAs). These methods generally perform well when applied to global optimization problems with non-linear, stochastic, or chaotic components, where traditional gradient techniques and purely random search are unsatisfactory. There has been subsequent research into heuristic methods, as surveyed by Kicinger [2]. These methods can be categorized into single-level and multi-level formulations based on their optimization strategies, as defined in Section 3.2 above.

3.3.1. SINGLE-LEVEL FORMULATIONS

The vast majority of existing methods are ‘single-level’, meaning that a single optimizer is employed to generate better designs. Within this category of approaches, researchers have been primarily focused on managing (1) larger, more complex problems, (2) problems with multiple objectives, and (3) heterogeneous software requirements.

To address large, complex problems involving topology, shape and member sizing, researchers have experimented with various types of representations for structural systems using EAs, including Voronoi-based [48], integer-based [49], and cellular automata [50] representations. Researchers also have focused on tuning genetic algorithm (GA) operators to particular problems, e.g. by adapting mutation and crossover rates for a particular class of member sizing problems [51-57]. In addition, researchers have explored algorithms other than GAs, including genetic programming [58-61] and simulated annealing [62]. These advances have enabled designers to optimize fairly large, complex problems, including electric transmission towers [63] and bracing topologies for tall building structures [64].

One of the most active research fields in recent years has been the development of optimization methods that are able to deal with multiple, conflicting objectives. There are two primary goals of multi-objective optimization. The first is to find a large number of Pareto-optimal [65] solutions to a given problem. The second is to find solutions that are widely differentiated [66]. Khajepour and Grierson have developed methods involving multi-objective genetic algorithms (MOGAs) and Pareto optimization to investigate trade-offs for high-rise structures [67, 68]. Grierson subsequently has developed a multi-criteria decision making (MCDM) strategy that employs a trade-off analytic technique to identify compromise designs in which competing criteria are mutually satisfied in a Pareto-optimal sense [69, 70]. In related work, Parmee and Machwe have led efforts to incorporate aesthetic criteria into the decision-making process through the use of interactive methods and machine learning that incorporate designer preferences into the computational optimization process [71, 72].

Finally, Shea and Holzer have created integrated, performance-driven, generative design tools by creating a level of interoperability between computer-aided design (CAD) software, finite element analysis (FEA), and optimization software. CAD tools with parametric or associative geometry capabilities are now able to parametrically vary design concepts in step with the designer’s intent [73]. To guide this generative method, Shea incorporated an optimization process called structural topology and shape annealing (STSA), which combines structural grammars; performance evaluation, including structural analysis and performance metrics; and stochastic optimization via simulated annealing [15]. Similarly, Holzer used a parametric CAD tool linked with a proprietary optimization algorithm to optimize the shape of a stadium roof structure [74]. This work has demonstrated the value of incorporating analysis models to guide


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computational generation of design alternatives. It also has shown the potential of software integration to improve collaboration among multiple disciplines (i.e. architects and structural engineers).

3.3.2. MULTI-LEVEL FORMULATIONS

Multi-level formulations have an optimizer at the top, or system, level and also at each subspace level. A few common multi-level MDO formulations were discussed above in Section 3.2.2. In contrast to single-level approaches, there have been only a few applications of multi-level MDO methods to structural design.

The first such application was a Disciplinary Constraint Feasible (DCF) approach developed by Sobieszczanski-Sobieski [75]. The DCF approach was bi-level, with decomposition by object (physical components), that sought to minimize the mass of a structure while satisfying strength and deflection constraints. The system optimizer controlled variables relating to the stiffness and mass distribution along the finite elements of the structure. The subspace level optimizers controlled variables relating to the physical cross sections of the elements. This method was applied to the structural design of an aerospace vehicle, and it allowed engineers to work concurrently on the same, large problem. Bloebaum and Sobieszczanski-Sobieski also have applied Concurrent Subspace Optimization (CSSO), a multi-level, non-hierarchic scheme discussed in Section 3.2.2, to the design of simple truss structures [76]. These methods, however, have not yet been applied to complex, multi-objective structural design problems nor have they been implemented within AEC organizations.

The only known application of a multi-level MDO method to a structural design problem in AEC was Balling’s use of Collaborative Optimization (CO) to decompose a bridge design problem between two groups of designers – a superstructure design group and a deck design group [77]. In that example, each group was allowed to search for different design concepts and to formulate the design variables and constraints for each concept. The autonomy of the two groups was managed by a system-level gradient-based optimizer, which insured that overall system objectives were met and that coupling was accounted for properly. Simplified analytic methods not involving FEA were used to reduce the complexity of the problem.

4. THE INTERACTIVE COLLABORATIVE OPTIMIZATION APPROACH

4.1. Observed Limitations of Existing Methods

Although a significant amount of research has been devoted to the application of MDO methods to building and civil structures in the AEC industry, a large gap exists between theory and practice. There have been few industry applications of the structural optimization methods discussed above [78]. Single-level methods discussed in Section 3.3.1 have addressed many of the requirements for successful implementation of MDO methods in structural design, namely:

• Computational scalability to large, complex problems


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• Ability to handle multiple, competing objectives with objective and subjective criteria

• Use of heterogeneous software, including CAD and FEA tools.

However, these formulations require centralized design decision-making, which does not map well to the structure of AEC design teams where decisions are typically distributed between 1) project managers on the one hand and 2) group leaders and experts in various disciplines on the other. In addition, as the number of decision variables and design trade-offs grows, single-level formulations can overwhelm human decision-makers’ data processing capabilities [79].

Multi-level formulations attempt to address this concern, but little research has been conducted on the application of these methods to problems in the AEC industry’s domain. The only known application of such a method was Balling’s application of CO to a simple conceptual bridge design problem. While this work discussed in Section 2.3.2 showed promise, further research is required to determine how multi-level methods such as CO perform, given 1) larger, more complex problems involving model-based FEA analysis; 2) multi-objective problems involving both subjective and objective criteria; and 3) decomposition of the problem by aspect (discipline) rather than by object (physical component).

4.2. Hypothesis

My hypothesis is that an MDO method, which is (1) multi-level, i.e. uses multiple optimizers and (2) allows the designer to concurrently consider multiple-objectives with subjective and objective criteria, is better suited than other known methods to the organizational structures and the types of problems faced by structural designers in the AEC industry. My research question is:

What is an effective decomposition and coordination method for multidisciplinary optimization of building and civil structures that can be used in the AEC industry?

To address this question, I propose in the following sections a new MDO method that I plan to compare in my research both to conventional practice and to equivalent single-level methods.

4.3. Description of the Interactive Collaborative Optimization (ICO) Method

ICO is based upon Collaborative Optimization, a formulation developed by Braun and Kroo in the mid-1990s, which the aerospace industry now routinely uses to design aircraft [39]. It is a bi-level hierarchical scheme, with the top level consisting of a system optimizer that operates on variables that affect multiple disciplines (e.g. topology and geometry). At the lower level, subspace optimizers operate on discipline-specific design variables (e.g. member sizes) to satisfy design constraints within each specific discipline. To ensure that the decision variables are compatible and converge to an optimal design, the designer interactively manipulates variable sets at each level based on objective and subjective performance criteria – hence the name, Interactive Collaborative Optimization. Figure 6 illustrates the ICO process applied to the stadium roof structure example discussed in Section 2.1. The five steps that are involved in the decomposition and coordination method are described in detail below.


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4.3.1. STEP 1:

IDENTIFY ANALYSIS VARIABLES AND COUPLING

Figure 6: ICO formulation applied to the stadium roof project example

SYSTEMOPTIMIZER

A + SE + ME + FE

SHAPE DESIGN

A + SE + ME

TOPOLOGY DESIGN

A + SE + ME + FE

N-S BaysE-W Bays

Arch HeightFrame Depth

AestheticsSteel Weight


SUBSPACEOPTIMIZER

SE

MEMBERSIZING

SE



Section Sizes


17

First, the analyses required for the MDO must be identified together with the following information about each analysis module as discussed in Section 3.1:

(1) Actor: the person(s) responsible for completing the task; (2) Tool: a description of the technology used to complete the work, and (3) Information: the design variables and other information required for analytic input and output.

Once the analyses are described, the information dependencies, or coupling between analyses, must be identified. As discussed in Section 3.1.1, the Design Structure Matrix (DSM), provides a useful representation to identify coupling between analyses as well as to describe where iteration occurs. Figure 7 above describes the nature of coupling between the various modules in the stadium roof MDO example.

4.3.2. STEP 2: FORMULATIONS CLASSIFY VARIABLES BY SYSTEM AND SUBSYSTEM

The next step is to classify the design variables identified as belonging either at the system level or to a particular subsystem. The classification method is identical to that used in the Collaborative Optimization (CO) method. System-level variables are those that affect multiple design disciplines, that is to say, affect the input to and/or the performance of the analysis models of various disciplines. Subsystem variables are local variables that affect only the discipline in question. As in CO, a system level optimizer manages system-level variables while subspace optimizers manage their respective local or subspace-level variables. In the stadium roof example, topology and geometry are system-level variables, while member sizing involves subspace variables as shown in Figure 6.

4.3.3. STEP 3: SET VARIABLE RANGES

Once the variables are classified, each must be assigned a range of values that will be considered in the optimization process. The range for system variables must be set first since these variables may have a strong impact on subsystem choices as a result of the coupling between the two levels that occurs in the process. Subspace variable ranges can be set independently since, by definition, there is no coupling between modules for these variables. The ranged variable approach is similar to set-based design methods, where designers explicitly communicate and contemplate multiple design alternatives. The sets are gradually narrowed through the elimination of inferior alternatives until the final solution emerges [80-82].

4.3.4. STEP 4: SELECT AND RUN OPTIMIZERS

Once the analyses, variables and respective ranges have been defined, an optimizer must be selected for the system and subspace level(s). The selection of an appropriate optimizer depends upon the formulation of the optimization problem, including objectives, constraints, and variable types (i.e. discrete or continuous). Also, computing resources and time constraints may influence the choice of optimizer used. Once the optimizer has been selected and configured, the MDO can be run to assess the system’s performance.

4.3.5. STEP 5: MODIFY VARIABLE RANGES BASED UPON SYSTEM PERFORMANCE AND

ROBUSTNESS


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Multi-objective design performance is assessed using Pareto optimization methods discussed in Section 3.3.1. To concurrently consider subjective and objective criteria, this methodology employs data visualization techniques to graphically describe a range of choices developed by Stump and others as part of the Advanced Trade Space Visualizer (ATSV) [83]. This technique allows a stakeholder to select a design from a Pareto plot to display both qualitative and quantitative information, such as 3D geometries, images, data tables and other documents as shown in Figure 7.

Robust design is concerned with minimizing the effect of uncertainty or variation in design parameters without eliminating the source of that uncertainty or variation [84]. In a multi-level MDO formulation, decisions made at the system level may have strong influence on subsequent design decisions made at the subspace level. For example in the stadium roof project, decisions relating to geometry and topology variables may make it difficult for the member-sizing specialist to find satisfactory or even feasible designs. Accordingly, it is important that designers are able to assess variable sensitivities and relationships in order to develop robust, top-level specifications.

The parallel coordinate box plot (PCPB) developed by Parmee [85] [12] gives an overall perspective on much of the information relating to variable and objective sensitivities (Figure 7). The length of the vertical axes in the figure represents each decision variable’s range, as well as applicable constraints and objectives. Each colored line corresponds to a design option with darker colored lines corresponding to more efficient designs. This process generates highly visual representations of results in both variable and objective space. Use of this visualization method can assist the designer develop an ‘intuitive map’ of the highly complex relationships between variables and assess the compatibility between variable sets and objectives.

Based on the observed system performance and robustness, designers at the system and subspace level are expected to modify their respective variable ranges as necessary until a satisfactory solution emerges. During this process, it is assumed that subspace designers will react rationally to the design decisions made at the system-level; meaning that they will work to find a satisfactory design given the system-level constraints rather than only considering local objectives and constraints. This reaction is embodied in a construct from game theory called the Rational Reaction Set [86] [87].

Figure 7: LEFT: Parallel Coordinate Plot Box (PCPB) used to assess variable and objective sensitivies. RIGHT: Picking a Pareto optimal point to evaluate the 3d design geometry


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5. RESEARCH METHODS

My research methods include five basic steps discussed in more detail below: 1) benchmarking current practice, 2) process integration design optimization proof of concept, 3) literature review, 4) development of ICO method, and 5) ICO validation.

5.1. Benchmarking Current Practice

The first step in my research was to develop a better understanding of the efficiency and effectiveness of current AEC design processes. To accomplish this objective, I conducted a survey of Arup engineers in their San Francisco, London and Manchester offices to identify 1) the average number of design iterations completed on typical project, and 2) the average time required to complete design iteration. These results where then compared to a similar survey of aerospace engineers at Boeing to assess the appropriateness of adapting methods and technology developed in the aerospace industry to AEC projects.

5.1.1. PAPER REFERENCE

Flager, F. and J. Haymaker (2007). A Comparison of Multidisciplinary Design, Analysis and Optimization Processes in the Building Construction and Aerospace Industries. 24th International Conference on Information Technology in Construction. I. Smith. Maribor, Slovenia: 625-630

5.2. Process Integration Design Optimization (PIDO) Proof of Concept

The aerospace industry has used Process Integration and Design Optimization (PIDO) methods to enable a greater number of design iterations and improved processes and product performance. This research involved a test application of PIDO to an AEC case study: the multidisciplinary design and optimization (MDO) of a classroom building for structural and energy performance. We demonstrated how PIDO can enable orders of magnitude improvement in the number of iterations typically achieved in practice, and assessed the methodology’s potential to improve AEC MDO processes and products.

5.2.1. PAPER REFERENCE

Flager, F., B. Welle, et al. (2009). "Multidisciplinary Process Integration and Design Optimization of a Classroom Building." Information Technology in Construction(accepted with minor revisions).

5.3. Literature Review

We also reviewed relevant literature in the fields of design process management, multidisciplinary design optimization (MDO) and structural optimization in the AEC industry. This research led to development of a set of requirements for the successful implementation of MDO to structural design problems in AEC. In addition, it helped identify the limitations of existing MDO methods when compared to the requirements identified.

5.4. Interactive Collaborative Optimization (ICO) Method Development

A New MDO Method – Interactive Collaborative Optimization – was developed to overcome the observed limitations of existing methods. This method is discussed in detail in Section 3. The


20

development of this method required its implementation within a commercial PIDO platform ModelCenter from Phoenix Integration.

5.5. ICO Validation

In the course of my research, I will apply ICO to several academic and industry case-study projects. I will compare ICO to conventional practice and to equivalent single-level formulations on the basis of (1) process efficiency; (2) design knowledge at key decision points; and (3) improvements in resulting product performance. I will use the following definitions for this purpose:

• Design option: A particular configuration of the following variables: (1) structural topology, (2) geometry, and (3) member sizing. A change to one of more of these variables constitutes a distinct design option.

• Design iteration: The generation and analysis of a single design option using model-based methods

• Design space: The domain of options, both feasible and infeasible, that the design team has an interest in investigating.

5.5.1. PROCESS EFFICIENCY

Process efficiency is measured (1) by the time required to complete single design iteration, and (2) by the time spent on a given iteration.

5.5.2. DESIGN KNOWLEDGE

Design knowledge at a particular point in time as defined by Simpson [1] is the ratio of the number of different options which have been analyzed over the size of the design space.

5.5.3. PRODUCT PERFORMANCE

The effectiveness of the process is measured by the performance of the resulting product. The metrics for product performance are to be determined by the stakeholders in the project (e.g. weight, cost, aesthetics).

5.5.4. PLANNED PAPERS

Three papers are planned to complete my dissertation:

• Single-level, single discipline: Member sizing for a large steel frame stadium roof structure.

• Multi-level, single discipline: Topology, geometry and member sizing for a large steel frame roof structure.

• Multi-level, multidisciplinary: Topology, geometry and member sizing for a building structure along with an additional discipline such as energy analysis.


21

5.6. Schedule

ID Task Name20092008 20102007

Q1 Q3Q4Q1Q2 Q2Q3 Q4 Q3Q1 Q2 Q4Q3 Q1

2 Survey 1: Current Practice Metrics at Arup

9 ICO Methodology Development and Validation

10 Case Study: Single level, single discipline

12 Case Study: Multi-level, single discipline

14 Case Study: Multi-level, multidisciplinary

16 Research Synthesis and Conclusion

17 Synthesis and Conclusions

Paper : Topology , geometry and member sizing for a large steel frame roof structure.13

Paper : Topology , geometry and member sizing for a building structure along with an additional discipline such as energy analysis .15

3 PIDO Proof of Concept

1 Benchmarking Current Practive

5 Research existing PIDO platforms

18 Final Thesis Defense

6 Case Study: Multidisciplinary Optimization of a Classroom Building

7 Paper : “Multidisciplinary Process Integration and Design Optimization of a Classroom Building”

11 Paper : Member sizing for a large steel frame stadium roof structure

Q2

4 Paper : “A Comparision of Multidisciplinary Design , Analysis and Optimization Processes in the Building Construction and Aerospace Industries”

8 Literature Review

Q4

6. CLAIMED CONTRIBUTIONS

6.1. Theoretical

The primary theoretrical contribution is the development of the Interactive Collaborative Method (ICO), a new MDO method that differs from existing structural optimization approaches in that (1) it is multi-level, i.e. it uses multiple optimizers, and (2) it allows the designer to concurrently consider objective and


22

subjective criteria in choosing the best design. In addition to the development of the ICO, I will conduct a scientific assessment of the ICO method on AEC industry projects compared to conventional practice and also to equivalent single-level MDO formulations. I hope that is information will be useful to future research efforts towards the development of new MDO methods for application in the AEC industry.

6.2. Practical

I hope that the ICO method will be applied by AEC professionals to:

• Compress design cycle time

• Increase design knowledge to support more informed decision making

• Yield substantive product quality and performance gains

• Reduce time to market

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