Signature redacted - Massachusetts Institute of Technology

Visualizing Variable Sensitivity in Structural Design

by

Anthony Benjamin McHugh

B.S., Massachusetts Institute of Technology (2016)

Submitted to the Department of Civil and Environmental Engineeringin partial fulfillment of the requirements for the degree of

Master of Engineering as recommended by the Department of Civil andEnvironmental Engineering

at the

MASSACHUSETTS INSTITUTE OF TECHNOLOGY

June 2017

@ 2017 Anthony McHugh. All rights reserved.

The author hereby grants to MIT permission to reproduce and todistribute publicly paper and electronic copies of this thesis document

in whole or in part in any medium now known or hereafter created.

Author .......................... Signature redactedDepartment of Civil aKEnvironmental Engineering

May 12, 2017

Certified by.......... Signature redacted ......Caitlin T. Mueller

Assistant Professor of Architecture andCivil and Environmental Engineering

//I /I Thsis Supervisor

Accepted by ....... Signature redacted .............Jesse R. Kroll

MASSACHUSETTS INSTITUTE Professor of Civil and Environmental EngineeringOF TECHNOLOGYChair, Graduate Program Committee

JUN 14 2017

LIBRARIESARCHIVES

Visualizing Variable Sensitivity in Structural Design

by

Anthony Benjamin McHugh

Submitted to the Department of Civil and Environmental Engineeringon May 12, 2017, in partial fulfillment of the

requirements for the degree ofMaster of Engineering as recommended by the Department of Civil and

Environmental Engineering

Abstract

Computational tools allow designers to consider vast amounts of information whendesigning structures; however, without intuitive ways to visualize and model this datait is of little use in the creative process. In this thesis, the context for the use of compu-tational design tools is established through a brief review of methods of incorporatingstructural optimization into conceptual design. Then, a novel method of visualizingvariable sensitivity is presented in a way that complements established methods ofinteractive optimization. The technique depends upon local sampling of the designspace, which reveals the behavior of quantitative structural and architectural objec-tives to variations in geometric parameters. Two case studies are given to demonstratethe different forms the visualizations may take and how a designer might choose tointerpret those forms. The visualization technique and design approach contributeto modern practices in high-performance structural design by revealing significantbehaviors of structures during the conceptual design stage.

Thesis Supervisor: Caitlin T. MuellerTitle: Assistant Professor of Architecture and Civil and Environmental Engineering

2

Acknowledgments

Thank you to Caitlin Mueller, Gordana Herning, and John Ochsendorf for teach-

ing me how to think like a structural engineer. Thank you to Rodd Merchant for

consistently sharing with me a passionate, progressive vision of the AEC industry.

Thank you to Nate Brown for introducing me to the world of parametric modeling

and multi-objective optimization while I was still an undergraduate. Thank you to

the many engineers, Carlos Arriagada, Andr6 Cote, Bill Dowd, Jim Fortinski, Emily

Guglielmo,Mike McAffrey, Dezi Mackey, Brent Hanlon, Grant Iwamoto, Nick Murray,

Kieran Kelly-Sneed, Stephen Chen, and Allen Rejaie, with whom I have worked and

from whom I have gathered invaluable insight during my internships at Sirve, S.A.,

the GSA, Martin/Martin, and HNTB. Finally, thank you to my peers in the MEng

program with whom I have both gladly collaborated and commiserated during the

past eight months.

3

Contents

1 Introduction 11

1.1 Effective Structural Design Tools . . . . . . . . . . . . . . . . . . . . 11

1.1.1 Graphic Statics . . . . . . . . . . . . . . . . . . . . . . . . . . 12

1.1.2 Strut-and-Tie Models . . . . . . . . . . . . . . . . . . . . . . . 12

1.1.3 Concerns about Computational Tools in Structural Design . . 13

1.2 Typical Design Process . . . . . . . . . . . . . . . . . . . . . . . . . . 14

1.2.1 Closed-Loop Optimization in Design . . . . . . . . . . . . . . 14

1.2.2 Goals of Interactive Optimization . . . . . . . . . . . . . . . . 15

1.2.3 Interactive Optimization in Design . . . . . . . . . . . . . . . 16

1.2.4 Modification for Human Experts . . . . . . . . . . . . . . . . 16

1.3 Summary and Scope . . . . . . . . . . . . . . . . . . . . . . . . . . . 17

2 Literature Review 19

2.1 Structural Design Models . . . . . . . . . . . . . . . . . . . . . . . . . 19

2.1.1 Features of a Model . . . . . . . . . . . . . . . . . . . . . . . . 19

2.1.2 Examples of Structural Modeling Techniques . . . . . . . . . . 20

2.2 Optimization in Design . . . . . . . . . . . . . . . . . . . . . . . . . . 20

2.2.1 Structural Synthesis . . . . . . . . . . . . . . . . . . . . . . . 21

2.2.2 Multi-Objective Optimization (MOO) . . . . . . . . . . . . . . 21

2.2.3 Variable Sensitivity . . . . . . . . . . . . . . . . . . . . . . . . 22

2.3 Design Space Visualization Tools . . . . . . . . . . . . . . . . . . . . 22

2.3.1 State of the Art . . . . . . . . . . . . . . . . . . . . . . . . . . 22

2.3.2 Lim itations . . . . . . . . . . . . . . . . . . . . . . . . . . . . 23

4

2.4 Open Questions .....................................

3 Methodology 26

3.1 Design Process Overview . . . . . . . . . . . . . . . . . . . . . . . . . 26

3.1.1 Extension of Interactive Optimization . . . . . . . . . . . . . . 27

3.1.2 The Role of Variable Sensitivity Visualizations . . . . . . . . . 27

3.2 User Interaction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 28

3.2.1 Setup of Graphs and Dashboard . . . . . . . . . . . . . . . . . 28

3.2.2 Visualization Techniques . . . . . . . . . . . . . . . . . . . . . 29

3.3 Implementation Details . . . . . . . . . . . . . . . . . . . . . . . . . . 30

3.3.1 Sampling and Evaluating Variables . . . . . . . . . . . . . . . 30

3.3.2 Formatting and Plotting Variable Sensitivity . . . . . . . . . . 31

4 Results 32

4.1 Cable-Supported Canopy . . . . . . . . . . . . . . . . . . . . . . . . . 32

4.1.1 Introductory Example . . . . . . . . . . . . . . . . . . . . . . 34

4.1.2 Experiment Setup. . . . . . . . . . . . . . . . . . . . . . . . . 35

4.1.3 Sampling Investigation . . . . . . . . . . . . . . . . . . . . . . 35

4.1.4 MOO Investigation . . . . . . . . . . . . . . . . . . . . . . . . 39

4.2 Bus Station Canopy . . . . . . . . . . . . . . . . . . . . . . . . . . . 44

4.2.1 Design Priorities for Free Exploration . . . . . . . . . . . . . . 45

4.2.2 Annotated Free Exploration . . . . . . . . . . . . . . . . . . . 46

4.3 D iscussion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 49

5 Conclusion 50

5.1 Summary of Contributions . . . . . . . . . . . . . . . . . . . . . . . . 50

5.2 Potential Impact . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 51

5.3 Future Work . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 51

5.4 Concluding Remarks . . . . . . . . . . . . . . . . . . . . . . . . . . . 52

A Canopy Implementation 53

5

25

B Station Implementation 57

6

List of Figures

1-1 The form diagram on the left corresponds to the force diagram on the

right [M ueller et al., 2015]. . . . . . . . . . . . . . . . . . . . . . . . . 12

1-2 The four examples here are different structural systems that can be

accurately modeled with similar load paths [Schlaich et al., 19871. 13

1-3 A typical iterative design process without explicit optimization. . . 14

1-4 A design process that incorporates closed-loop optimization. . . . . . 15

1-5 A design process that incorporates interactive optimization. . . . . . 16

2-1 A review of the most relevant structural design tools. . . . . . . . . . 24

3-1 The proposed design process for incorporating guidance from variable

sensitivity visualizations into an interactive optimization design ap-

proach.......... .................................... 27

3-2 The proposed format for visualizing variable sensitivity of multi-objective

design spaces. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 29

4-1 The design variables are shown on the left. A representative design in

the perspective view is on the right. The objective values are displayed

below the image [Brown and Mueller, 2016a] .. . . . . . . . . . . . . . 33

7

4-2 The image on the left is the initial design. The images on the top

are the sampled designs where the variable height of canopy tip is

augmented by -10% and 10%, respectively. The sensitivity of the height

of the canopy tip is captured by the line with squares in the objective

plots and by the bottom left variable plot. The images on the bottom

are the sampled designs for the variable, canopy length. The sensitivity

of the canopy length is captured by the lines with diamonds in the

objective plots and by the bottom right variable plot. . . . . . . . . . 34

4-3 Plots of the variable sensitivity for three objectives of the same design

using four distinct series for sampling . . . . . . . . . . . . . . . . . . 37

4-4 Plots of the variable sensitivity for seven variables of the same design

using four distinct series for sampling . . . . . . . . . . . . . . . . . . 38

4-5 The design shown here was generated by applying an evolutionary

optimization method where the objective function is the sum of each

of the normalized objectives. . . . . . . . . . . . . . . . . . . . . . . . 41

4-6 The purpose of this design is to observe more closely the most inter-

esting variables from the previous design. The series used for sampling

steps by 0.5% from -50% to 50%. A value near the middle of each

variable's range was chosen for convenience. . . . . . . . . . . . . . . 42

4-7 The design shown here is adjusted from the design in figure 4-5 based

on the information presented in figure 4-6. . . . . . . . . . . . . . . . 43

4-8 The bus station in Hamburg that inspired the design problem is shown

on the left [Temme Obermeier, 2012]. The analytical model for struc-

tural modeling is shown in the center. The perspective view of the 3D

model is on the right. . . . . . . . . . . . . . . . . . . . . . . . . . . . 44

4-9 A symmetric design [left], its variable sensitivity plots, and another

design iteration [right] based on the interpretation of the plots. ..... 46

4-10 An arbitrary asymmetric design [left], its variable sensitivity plots, and

another design iteration [right] based on the interpretation of the plots. 48

8

A-1 The grasshopper and Python code used to sample the variables. . . . 54

A-2 The grasshopper and Python code used to format the objective scores

for each design, serialize and stream them in the .csv format. . . . . . 55

A-3 The Matlab code used to read the .csv files and create the objective

and variable plots. . . . . . . . . . . . . . . . . . . . . . . . . . . . . 56

B-1 The grasshopper and Python code used to sample the variables. . . . 58

B-2 The grasshopper and Python code used to format the objective scores

for each design, serialize and stream them in the .csv format. . . . . . 59

B-3 The Matlab code used to read the .csv files and create the objective

and variable plots. . . . . . . . . . . . . . . . . . . . . . . . . . . . . 60

9

List of Tables

4.1 The variables, variable bounds, and objectives for the structural design

of the cable-supported canopy. . . . . . . . . . . . . . . . . . . . . . . 33

4.2 The variables, variable bounds, and objectives for the structural design

of a bus station. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 45

4.3 Comparison of the designs shown in figure 4-9. . . . . . . . . . . . . . 47

4.4 Comparison of the designs shown in figure 4-10. . . . . . . . . . . . . 48

10

Chapter 1

Introduction

The analysis tools available to the modern structural engineer have almost limitless

precision and accuracy to evaluate a finalized concept; however, if most design deci-

sions have been made before the performance of structural system can be analyzed,

then the information provided can have little impact. In order for performance in-

formation in terms of weight, cost and embodied energy to be fully considered, new

techniques and tools are required that generate creative design concepts informed by

light-weight performance simulations early on in the process of design. The follow-

ing work suggests a novel method of incorporating performance information into the

conceptual design of structures. This introduction identifies the characteristics of ef-

fective structural design tools and describes the aspects of design theory of particular

relevance in conceptual structural design problems.

1.1 Effective Structural Design Tools

In order to understand what makes a tool effective in helping a designer incorpo-

rate information about structural performance in the design process, it is valuable

to look at historical examples. Within the history of structural engineering, two ex-

ceptional examples of design tools are graphic statics and the strut-and-tie model.

These tools go beyond determining the forces and deflections in a specific structure

by also suggesting to the designer how subtle changes in its geometry may impact its

11

Figure 1-1: The form diagram on the left corresponds to the force diagram on the

right [Mueller et al., 2015].

performance.

1.1.1 Graphic Statics

In the 1870's, graphic statics was introduced as a visual method of calculating struc-

tural equilibrium. The process involves drawing a series of arrows of relative mag-

nitude to create what is known as a force polygon, see figure 1-1. When complete,

the force polygon represents a potential equilibrium state for the structure. By il-

lustrating the forces in the structure in a visual manner the designer can interpret

how changes in the magnitude and direction of one force impact the magnitude and

direction of the other forces [Mueller et al., 2015].

1.1.2 Strut-and-Tie Models

In the introduction to his original publication of the strut-and-tie model, Schlaich

critiques the truss model of cracked reinforce concrete as being inconsistent when

addressing discontinuities such as point loads and frame corners. Schlaich continues

by asserting that all parts of a structure are of similar importance; therefore, a tool is

only useful for a designer when it leads to design concepts that are demonstrably valid

for all parts of the structure. Similar to graphic statics, the strut-and-tie provides

a rational method of describing the flow of forces through the structure. After pre-

senting the method in detail with several examples, Schlaich goes on to describe the

pedagogical value of the strut-and-tie model. Figure 1-2 depicts four common struc-

tures that reveal similar strut-and-tie models. Making the connection between the

behavior of these distinct applications allows a structural designer to quickly generate

performance information for a large range of design concepts [Schlaich et al., 1987].

12

b)

Figure 1-2: The four examples here are different structural systems that can be

accurately modeled with similar load paths [Schlaich et al., 1987].

1.1.3 Concerns about Computational Tools in Structural De-

sign

The use of computation in structural engineering has expanded the possibility for

structural designers to create predictable high-performance designs. However, over

the decades since the introduction of computer-aided finite element analysis and nu-

merical optimization methods, experts in the field have consistently expressed con-

cerns that reliance on such tools obscure the uncertainty generated by modeling as-

sumptions and inhibit the designer's ability to generate innovative solutions. Typi-

cally, the precision of the output of a computational tools does not reflect the precision

of the input. For example, the moment of inertia of a complex geometric shape can

be calculated to tens of significant digits, but that level of precision would not be

matched by the support conditions unless there was extensive testing to calculate the

spring constant of the points at which the structure is anchored. Concerning creativ-

ity, the computational tools often function as black boxes where the user receives no

information at the end of the process about the relationship between the input and

the output. Understanding these relationships is the basis of the structural intuition

that allows designers to quickly and consistently arrive at valid design concepts. The

13

historical examples of analog structural design tools provide a good baseline compar-

ison when determining whether or not a computational tool is an effective addition

to the design process.

1.2 Typical Design Process

In order to understand how a computation tool benefits the design process, the follow-

ing section addresses the context of designing within the modern practice of structural

engineering. There are a wide variety of design processes that have been applied to

engineering problems. Rather than enumerating all suggested design processes, the

following section combines concepts from design theory and optimization to build

up an algorithmic description of interactive optimization within design. The design

process proposed in Chapter 3 is a revision and extension of the process presented

here.

Ideate Down-Select fromAlternatives

EvaluateDesigns

Typical Design Process

Figure 1-3: A typical iterative design process without explicit optimization.

1.2.1 Closed-Loop Optimization in Design

The typical design process involves ideation, evaluation, down-selection, and, often,

iteration of those three steps until a single design is chosen. When using optimization

14

in design, there is an additional step added to the beginning. Defining the problem

statement, more specifically the variables, variable bounds, and objective function,

comes before the ideation step. Within optimization there is often an assumption of

automated iteration.

DefineK Problem

Statement

End

Design with Optimization

Figure 1-4: A design process that incorporates closed-loop optimization.

1.2.2 Goals of Interactive Optimization

Human-in-the-loop, or interactive, optimization methods for design are proposed for

problems that are difficult to define numerically, that are too large to solve in a rea-

sonable amount of time, or that are intended to develop intuition on the part of the

designer. Aesthetic criteria in architectural design are an example of objectives that

are difficult to quantify. If the initially defined design space is too large, or the eval-

uation process too slow, human interaction can help to avoid time spent evaluating

non-viable solutions reducing the time and computational resources necessary to com-

plete the optimization. The assumption that human interaction is more effective at

avoiding non-viable areas of the design space depends on the designer's understand-

ing of the behavior of the design problem. The development of this understanding

depends on the designer's experience engaging with similar problems. Interaction

requires increased engagement on the part of the designer, which in theory should

15

Down-Select fromAlternatives

OptimizationLoop

Ideate EvaluateDesigns

improve the educational value of experiencing the design process.

i Down-Select from End

Probemn AfternativesStatement

SuggestDesigns?

Interactive FavorZ"" Optimization Designs?

Loop

Ideate Eliminate EvaluateDesigns? Designs

Design with Interactive Optimization

Figure 1-5: A design process that incorporates interactive optimization.

1.2.3 Interactive Optimization in Design

Interactive optimization approaches specify that at one or more of the steps within

the iterative loop there is the opportunity for the human designer to influence the

results of the optimization algorithm. The StructureFit/Stormcloud tool, described

in detail in Chapter 2, achieves interactivity by allowing the designer to adjust the

evaluation step by selecting preferable designs, effectively updating their objective

score to increase the likelihood that similar solutions will appear in later iterations.

A neat way to consider this addition to the process is by adding a decision to interact

or not at each step within the iteration loop. As the described workflow becomes

more complex, the context of the design problem becomes increasingly important.

1.2.4 Modification for Human Experts

Design for engineers necessarily includes an assumption of domain expertise on the

part of the designer [Yang, 2005]. Creative design experts have been found to demon-

strate specific behaviors that need to be taken into account when proposing a design

16

Am

tool or method. In particular, there are two features that have an extensive impact

on the design process proposed in Chapter 3. Creative designer's frequently iden-

tify a "problem frame" and propose a "solution conjecture" [Cross, 2004j. Problem

framing consists of gathering information about a problem and prioritizing criteria.

A solution conjecture is an early hunch about features of the final design, which the

expert develops in parallel with the problem frame.

In terms of the conceptual design process, the solution conjecture might come

before the ideation process. In this case, the ideation process would focus on coming

up with novel alternatives to the typical design solution.The advantage of the solution

conjecture is that the designer explores the edges of a known design space, which is

more likely to yield acceptable results in a timely manner.

Problem framing, on the other hand, might come after the evaluation of alterna-

tives where the design process iterates. If all of the alternative designs seem inad-

equate to the designer, it is within the designer's power to switch cognitive modes

and decide to reevaluate the basic assumptions of the model, the choice of criteria,

the relative weight of criteria, and the type of changes being made to the design.

Situations of refraining may occur when desirable criteria are found to be directly

incompatible, when the the assumptions of the model are insensitive or overly sensi-

tive to the criteria, or when there is minimal diversity among the alternatives. It is

necessary to not only acknowledge, but to embrace these aspects of human expertise

in design when developing a software tool to aid in the design process.

1.3 Summary and Scope

The example set by exemplary analog design tools informs the concerns that modern

day experts in the practice of structural engineering express about the adoption of

computational tools in the engineering design process. Common practice in engineer-

ing design demonstrates the great attention that has been paid to the complementary

roles of human expertise and computational techniques. The following work reviews

computational design tools within structural engineering in Chapter 2, presents a

17

novel design process within the field of interactive optimization in Chapter 3, and

demonstrates through case studies a novel method of visualizing performance infor-

mation in Chapter 4.

18

Chapter 2

Literature Review

The literature review places in the context of structural engineering the use of com-

putational design tools. The topics flow from a discussion of the general features

of design models to a brief history of modeling techniques in structural design to

the most recent tools specifically intended for visualizing design spaces in structural

optimization.

2.1 Structural Design Models

Information about complex systems is frequently collected and applied to decision-

making through the use of models. Design is a specific type of decision-making

process.

2.1.1 Features of a Model

The three essential characteristics of a model are its resolution, its abstraction, and

its representation. The representations addressed here are visual and numerical. The

level of abstraction is determined by the assumptions necessary to judge structural

performance. The resolution will be determined by the speed at which the perfor-

mance information can be obtained and the flow of the resulting user experience

[Gero, 1990]. The following is a review of the types and features of models commonly

19

used in structural design.

2.1.2 Examples of Structural Modeling Techniques

Three-dimensional physical models have been used in increasingly nuanced ways over

time. There are two types of physical models that are particularly important, scale

structural models and component models for load testing. A particularly famous ex-

ample of effective scale modeling is the work of Antoni Gaudi who built high resolution

hanging string models of La Sagrada Familia to better understand the distribution of

forces [Lirola et al., 20171.

Sketches are useful for both engineering and architectural design of structures;

however, the essential qualities of each sketch are distinct. An engineer might sketch

the flow of forces and magnified deflection of structural elements on a low resolution

model of the geometry. An architect typically would create a higher resolution of the

structure's geometry as well as the site on which it is located [Suwa and Tversky, 1997J,

[Goldschmidt, 1994].

Similar distinctions can be seen in 3D renderings and BIM. BIM contains a sig-

nificant amount of information about the details and function of the building, while

a 3D rendering of the same model would ignore most of the functional details of the

structure in favor of displaying the aesthetic impact [Oxman, 2008].

Computers also made parametric design relevant for both architects and engi-

neers. The first CAD program, Sketchpad, developed by Sutherland at MIT actually

incorporated parametric features [Sutherland, 19641. A recent revival of interest in

parametric design has led to the development of the open-source, visual programming

interfaces, Dynamo and Grasshopper [Arnaud, 2013].

2.2 Optimization in Design

The rise of computers brought about a series of numerical approaches to both struc-

tural analysis and optimization. In structural analysis, finite element modeling proved

to be a far more efficient method than hand calculations for modeling complex struc-

20

tural systems. In the field of optimization, numerical approaches allowed for the

optimization of objective functions for which there was no analytical form.

2.2.1 Structural Synthesis

Schmit introduced the concept of structural synthesis in the 1960s for applications in

aircraft design [Schmit, 1981]. Van der Plaat's review 16 years later, gives a sense of

how the field developed from the early introduction of computers to the modern age

as computational speed changed drastically [Vanderplaats and Vanderplaats, 1997].

Later, stochastic optimization strategies served to address non-convex objective func-

tions with an acceptable level of accuracy [Xie and Steven, 1997].

2.2.2 Multi-Objective Optimization (MOO)

The field of multi-objective optimization contains another set of terminology impor-

tant for understanding objective spaces with more than one dimension. Objective

weights are numerical values that quantify the designer's preference of criteria. The

use of objective weights is an a priori articulation of preferences. Two methods that

are better suited for qualitative preferences are a posteriori articulation and progres-

sive articulation. The former involves looking at a set of alternatives selected by the

algorithm. The concept of Pareto fronts become relevant when telling the algorithm

how to select alternatives. Pareto fronts are sets of designs in which there is no

way to change any of the variables that will not worsen its performance in at least

one objective [Marler and Arora, 2004]. The final approach to MOO, is progressive

articulation. Progressive articulation is the type of optimization best suited for inter-

active approaches. Two approaches to progressive articulation are the isoperformance

method [de Weck and Jones, 2006] and the use of interactive evolutionary optimiza-

tion [Turrin et al., 2011], [Mueller and Ochsendorf, 2015], [Danhaive, 2015] both of

which are described in detail in the next section.

21

2.2.3 Variable Sensitivity

Another essential concept in practical applications of optimization methods is that of

variable sensitivity. Variable sensitivity refers to the partial derivative of an objective

function. Sensitivity determines the relevance of the optimization problem to the

overarching design goal. If sensitivity is close to zero then a suboptimal value for the

variable may be selected without having a significant impact on the performance of

the final design. If a variable's sensitivity nears infinity then the distance between its

actual value and its optimal value is effectively equivalent to the performance of the

design.

The closest existing tools to the method proposed here are StructureFit/Stormcloud,

Design Explorer, Tacit.Blue, and the Isoperformance Method.

2.3 Design Space Visualization Tools

The most effective structural design tools combine visual models with numerical sim-

ulations to encourage creativity within performance-based design.

2.3.1 State of the Art

StructureFit/Stormcloud and Design Explorer have two distinct approaches to the

task of revealing the significant features of the design space.

StructureFit is a user-friendly implementation of a topological and geometric opti-

mization using an interactive evolutionary solver produced by Caitlin Mueller at MIT

[Mueller and Ochsendorf, 20131. Stormeloud, developed as part of a Master's Thesis

by Renaud Danhaive, a student of Prof. Mueller, brings the StructureFit functional-

ity into the generic, parametric environment of Grasshopper [Danhaive, 20151. Both

tools use designer interaction with the evolutionary solver to create catalogues of

diverse, high-performance designs

Design Explorer was developed by Thornton Tomasetti's CORE studio as an

attempt to encourage the consideration of multi-objective optimization approaches

22

within structural design practice [Howe, 2016]. Design explorer uses a sampling tech-

nique to reveal an increasingly selective set of designs as the designer progressively

constrains the variables and objectives.

Tacit.Blue developed by Ned Burnell is an alternative to deterministic optimiza-

tion that encourages interactivity by visualizing the gradient information as arrows

[Burnell, 2014]. The gradient connects the location of each node to the objective

function. The size of the arrow indicates how steep the objective function is at that

specific variable value. The direction of the arrow indicates where the node should

move to minimize the objective. The set of plots in the bottom right corner of figure

2-1 that represent single variable sampling in MOO provide very similar information

to the arrows in Tacit.Blue, but in a denser format. Each line represents an objective

function, while each plot represents a different variable. In this case, the plots include

more information about the objective functions than the gradient. The most salient

feature is the relative sensitivity of each objective to the same change in the variable

value. The relative sensitivity presented in this way is valuable for understanding

trade-offs along a Pareto front [Brown and Mueller, 2016b].

De Weck recommends another approach to understanding multi-objective opti-

mization problems, which he calls the isoperformance method [de Weck and Jones, 20061.

In isoperformance, the designer generates alternatives that lie along contours of the

design space. The contours represent designs that have equivalent objective scores.

De Weck uses the term slack to describe the designer's freedom to choose between

alternatives that the isoperformance method has identified.

2.3.2 Limitations

An important distinction that becomes apparent when considering the information

given by Tacit.Blue and Design Explorer is the difference between global and local

inspection of the design space. Tacit.Blue's gradient-based guidance depends strongly

on a good solution conjecture, while Design Explorer depends on a well-framed prob-

lem and sufficient computational power. Although there is an element of interactivity

within Design Explorer, there is a fundamental difference between the use of surrogate

23

CORE SO IThornton Tomasett

2016

StrucueF & SormcloudMueller 2014 & Danhalve 2016

wd~so - -*.-.. ---- - -

Slngle varable Sampling in MuII-Obtiectve OpmizaionBrOwn 2016

TacitlueBUMelI 2014

Figure 2-1: A review of the most relevant structural design tools.

modeling and the use of an interactive evolutionary algorithm. The term generative

design captures this difference. Design Explorer would not be considered genera-

tive design because the evaluated alternatives are fully determined by the choice of

variable bounds and sampling method. Interactive optimization strategies have the

advantage that they can be stopped and redefined frequently during the time inten-

sive process of evaluating alternatives. A surrogate model that is stopped partway

through this time intensive process can provide incomplete or misleading answers.

None of these methods for visualizing structural design spaces explicitly describe the

contours produced by the isoperformance method described. The single-variable sam-

pling visualization technique, proposed by Brown, is the most applicable, but has not

yet made its way into the interactive user interface of a structural design tool.

The method proposed here presents local information that complements global

approaches by refocusing computational energy into the most interesting areas of the

design space. These interesting areas can be considered synonymous with Cross's

solution conjectures. Although both isoperformance and single-variable sampling

visualization techniques are promising, the single-variable sampling method is pursued

in this work for reasons of computational efficiency, intuitive designer interactions and

readability.

24

I---

.0

2.4 Open Questions

Considering the limitations mentioned previously the most pressing questions that

remain open are as follows: How can we provide visual information to designers to

give them more performance-based guidance in the conceptual design process? How

can a designer use variable sensitivity of parametrically-defined alternatives to revise

the definition of the design problem? What type of visualizations clearly display the

sensitivity of variables within the design space?

25

Chapter 3

Methodology

The proposed contributions are a design process, a set of visualization techniques

to support the design process, a description of the intended workflow, and example

implementations through two case studies. The case studies will be fully discussed in

Chapter 4.

3.1 Design Process Overview

This section provides a conceptual overview of the proposed process for performing

structural design tasks while making the most effective use of variable sensitivity

information.

26

Define Redefine VisualizeProblem Variables/ Procee Sensitivity of

Statement Objectives Design Space

Interactto ProduceAlternative

Optimize Visualizeto Produce Design

Design Performance

Conceptual Design with Guidance

EvaluateDesign

End

Figure 3-1: The proposed design process for incorporating guidance from variablesensitivity visualizations into an interactive optimization design approach.

3.1.1 Extension of Interactive Optimization

Following the same motivation that fueled the development of interactive optimization

approaches, designing with guidance applies to design problems for which the opti-

mization problem is poorly defined. Typically, the problem definition is not within

the iteration loop. The proposed design process involves bringing the problem defi-

nition into the iteration loop of an interactive optimization approach to design. The

critical assumption behind the additional layer of complexity to the process is that

information generated during the design process teaches the designer how to improve

the problem definition, and sometimes even the algorithm definition.

3.1.2 The Role of Variable Sensitivity Visualizations

The critical information produced is the variable sensitivity, described in detail in

Chapter 2. The relative relationship of the variables with the objective values provides

the designer with the ability to infer whether or not further iteration will converge

to a meaningful result. In interactive optimization, the designer's direction towards

more viable areas of the design space can greatly improve the speed and final result of

27

the design process. In design with guidance, the designer can choose to redirect the

optimization, adjusting the precision of the optimization, or redefine the design space

entirely to achieve the same objective of exploring a more viable set of alternative

designs. Redirecting the optimization involves changing the objective function in

order to improve the down-selection step. Adjusting the precision of the optimization

involves changing how the algorithm uses the objective function in order to improve

the ideation, generative design, step. In multi-objective optimization problems, the

down-selection process frequently involves weighting each of the objectives. Changing

the relative weight of the objectives would be considered adjusting the precision of the

optimization and not a change to the objective function according to these definitions.

Redefining the design space involves changing which parameters are design variables

and/or changing the bounds of the design variables.

3.2 User Interaction

The following section describes how to setup a software workflow that allows the user

to follow the design process described above.

3.2.1 Setup of Graphs and Dashboard

The first step is to come up with the best tool for creating the necessary graphs. One

alternative using Google Sheets and Charts is used in figure 3-2. A second method

that relies on Matlab is used for both of the case studies in Chapter 4. Grasshopper

provides an exceptional environment for incorporating interactivity within a struc-

tural modeling environment. The dashboard for this example is entirely within

grasshopper. The values for the design variables are set through the use of slider

components. The matrix displays output of raw objective scores as well as the sam-

pled and normalized objective scores. The baseline for the most recently evaluated

design is displayed directly below a record of the best performance score so far. The

text information is then streamed to a directory, which is read into Matlab to generate

the sensitivity plots.

28

3.2.2 Visualization Techniques

Objective N

P

0

10 00%

SM

a0 0-5.00%

-~I ~--w0.00%

Change in Variable / Variable

Variable M1000%

I0a)

0

5.00%

-0.00%-5 .-10 .0%-.00% 0

Change in Variae M/ Variable M

Figure 3-2: The proposed format for visualizing variable sensitivity of multi-objectivedesign spaces.

29

-W Vanable 1

-0- Variable M

5.00% 10.00%

-0- Objective 1-0- Objective N

5.00% 10.00%

0000

)0%

The clear presentation of design sensitivity information affects the designer's ability

to improve the optimization process. The suggested visualization method is shown

in 3-2. The top left graph depicts the sensitivity of a single variable to every ob-

jective. The bottom right graph depicts the sensitivity of each variable to a single

objective. In single objective optimization problems only the bottom right graph

is necessary; however, in multi-objective optimization problems the graphs are best

presented together. The objective graphs illustrate the relative importance of each

variable, allowing the designer to infer whether some variables are unnecessary or too

tightly constrained. The variable graphs emphasize the objective trade-offs, allow-

ing the designer to infer whether the problem will converge to an optimal design or

generate a set of Pareto optimal designs. The specific behavior demonstrated on the

objective graph at the bottom of figure 3-2 can be interpreted as a Pareto optimal

design with linear and non-linear behaviors. The specific behavior demonstrated on

the variable graph at the top of figure 3-2 can be interpreted as an optima where the

shallower curvature of variable m indicates a lower sensitivity than variable one.

3.3 Implementation Details

The process of creating the graph and dashboard can be split into two pieces. The first

piece is the creation and evaluation of a series of design vectors. The second piece is

the formatting and plotting of the sensitivity of each variable. The full documentation

for the case studies in Chapter 4 is provided in the appendix.

3.3.1 Sampling and Evaluating Variables

Similar to the creation of populations in an evolutionary algorithm, the idea behind

the sampling is to create a series of alternatives to be evaluated simultaneously. The

sampling resolution and extents are set by a series of steps. Each step is defined as

the percentage change in the variable. A two variable example of the sampling can be

seen in 3-2. The variables are sampled independently (i.e. the second variable is held

constant while the first variable steps and vice-versa). For a 2 variable example with

30

11 sampling steps, there will be a population of 22 design vectors to be evaluated.

The objective functions are all produced numerically, not analytically, within the

Grasshopper environment using Karamba Structural Analysis. Within Grasshopper,

the Hoopsnake component keeps track of the objective scores of each design vector

as Karamba evaluates them one by one.

3.3.2 Formatting and Plotting Variable Sensitivity

Once every design vector has been evaluated, the objective values saved within the

Hoopsnake component are converted from raw scores into percentage change from

the objective value of the initial design. For readability, the percentage change values

are truncated to the 0.01%. The percentage change values are serialized as .csv files,

which can be read into Matlab to create the objective and variable plots. There will

be a separate plot for each variable and each objective. As a result, each data point

actually appears twice within the final set of graphs. For the code needed to replicate

the implementation described, refer to the appendices.

31

Chapter 4

Results

The two case studies presented in this chapter are realistic conceptual design problems

for architects and structural engineers. The first case focuses on reading the variable

sensitivity visualizations and investigates the effect of different sampling approaches.

The second case emphasizes the use of the visualizations within a design process by

iterating based on the guidance of the variable graphs.

4.1 Cable-Supported Canopy

The task given in this study was the design of a canopy structure for the outdoor

seating area of the restaurant figure 4-1. Due to the desire for a free edge and the

ability to anchor into the wall above, the hypothetical client asked for a cable-stayed

structure. The main topology of the structure is formed by beams that cantilever

out from the wall and are supported by a series of cables, which also anchor into

the wall. Within this main geometry, participants were allowed to adjust the anchor

point spread, height of cable and beam connections, height and horizontal distance

to the canopy tip, number of cables, and the curvature of the canopy.

32

Anchor Point Spread0 4

Height of Cable Anchor Point1 *15 P

Height of Canopy Anchor Point

Length of Canopy*19

Height of Canopy Tip100

Nwber of Cabs

Canopy Curvature Maximum Deflection [in]: 0.125 norm 7.35 lwwm&rCarbon Emissions [kg]: 1061.7 norm: 2.41Shaded Area (ft^2]: 127.31 norm: 3.37 L

Figure 4-1: The design variables are shown on the left. A representative design in theperspective view is on the right. The objective values are displayed below the image[Brown and Mueller, 2016a].

Variable Units Min Max

Anchor Point Spread 0.0 1.0

Height of (Top) Cable Anchor Point ft 8 30

Height of Canopy Anchor Point ft 5 25

Length of Canopy ft 5 40

Height of Canopy Tip ft 5 15

Number of Cables 1 10

Curvature 0.5 1.5

Objective Units Direction Evaluation Method

Shaded Area ft2 Maximize 50' sun angle

Embodied Carbon kg C02 Minimize FEM + Sizer

Maximum Deflection in Minimize FEM

Table 4.1: The variables, variable bounds, and objectives for the structural design of

the cable-supported canopy.

33

A

4.1.1 Introductory Example

CanopyTip Height

Aa

CanopLength

Sampin of Structural Weight (Emissionat

30

20

0

0

-10

-20

-30-10 -5 0 5 10

Change in Variable / Variable (%)

30

20

10

0o -10

-20

-30

-40_I

y

AI * |

Sampling of Deflection 4Sampling of Length of Canopy

-A- Length of Canopy-0- Helght of Canopy Tip 30

- 20

10

0

o-10 -

-20

-30'

-400 -5 0 5 10 -10 -5 0 5 'O

Change in Variable / Variable (%) Change in Variable / Variable (%)

ASampling of Height of Canopy Tip

-- Structural Weight (Emissions)

6 -0Deflection

4

20

o -2

c-4

-6

-8-10 -5 0 5 10

Change in Variable / Variable (%)

Figure 4-2: The image on the left is the initial design. The images on the top arethe sampled designs where the variable height of canopy tip is augmented by -10%and 10%, respectively. The sensitivity of the height of the canopy tip is capturedby the line with squares in the objective plots and by the bottom left variable plot.The images on the bottom are the sampled designs for the variable, canopy length.The sensitivity of the canopy length is captured by the lines with diamonds in theobjective plots and by the bottom right variable plot.

A simple example to explain the interpretation of the variable sensitivity graphs is

shown in figure 4-2. The example depicts two variables, height of canopy tip and

canopy length, being stepped once in the positive direction and once in the negative

direction. Each of the five designs is evaluated for two objectives, structural weight

and shading area. The first objective graph shows that structural weight increases

34

Aa

a

with both tip height and canopy length; however, the canopy length has a much

greater impact as seen by its steeper slope. The designer interprets this behavior

as having greater flexibility to vary the height of the canopy tip in order to meet

qualitative aesthetic or constructability criteria. The first variable graph shows that

increasing canopy length has a similar impact, percentage-wise, on shading area and

structural weight. The designer interprets this behavior as an even trade-off where one

objective has to be sacrificed, decreasing shading area, in order to improve another

objective, making a lighter structure.

4.1.2 Experiment Setup

The following section presents two investigations into the behavior of the variable sen-

sitivity visualizations for the cable-supported canopy. The first investigation adjusts

the number, spacing, and extents of the sampling steps. The second investigation

begins with an "optimized" design and densely samples select variables to make in-

formed objective trade-offs.

4.1.3 Sampling Investigation

There are four separate series of sampling steps used to evaluate the same design.

Each series of sampling steps is defined as the percentage by which the initial value is

changed. The general would be xo+6* (xmax - Xmin) where x, is the initial value of

the variable, Xinax and xmi,, are the variable bounds, and 6 is the sampling step. The

first series steps in 11 uniform, linear increments from -10% to 10%. The second series

steps in 6 uniform, linear increments from -10% to 0 and 5 uniform, linear increments

from 1% to 9%. The intention of the second series is to see whether asymmetry

obscures or reveals different behaviors from symmetric sampling. The third series

steps from -1 to - in seven logarithmic steps of base two. The purpose of the third

series is to slightly expand the breadth of the design being explored while reducing

the resolution. The fourth series steps from -100% to 100% in seven logarithmic steps

of base ten. Effectively, the fourth series looks at the variable minimum bound, the

35

variable maximum bound, at a 10% change in each direction, and at a 1% change

in each direction. in figure 4-3 each line of plots corresponds to a different sampling

method of the same design, shown in the top right. In figure 4-4, each two line set of

seven plots corresponds to a different sampling method of the same design, which is

identical to the design shown in figure 4-3.

36

C A fvh-eM.20 0 '3 o3. m

100

002502

50

a

III

Sermpling at ObiedW.e1200 Sirw-I Weight (Emigaiont)

100

-5g I I

-10 -5 0 S 10Change in Varibl / V401 Mbe()

S00 p00g at Obodim2M(00SIruietheri Weight (Eislns)

20

110[0

Change In Vaiabls / Varb0 I%)

5 -10 4 0 00 20 . 'Cha ng Variabl e IVL M

0000022000 0002gh0 (EoMleoo)

- .. o. ---- O

Ch02g200000r00000/ 00dao000(%)

Ownph.g .1 Obifoctive'40- Sthscharal Weight (Ewln-)

1200

100 -

200

.100 -5 1Chopg In Varibe /VSd&l (%M

so

40

0 -

-20 -

40.10 t 0

Change in Vernable 1 Varftbe N%)

Sacpting of ObfelooW0.11.01-on

1~0

-to

Charge In Varb0 I Varble (%)

Sanplin; at Oblilve

0

-Q -

-20

-15 -1. -5 0 1 1. 5

Change 1. Variable / VarWbM (%6)

ao.00

2100

. n.. I0/002202 V000 0o.. (00)

SampiNg of Obieth eShaded AMe

0b

.- 2.gha C"nsiinp-4-- unpy C."Mnui

.... k I ' l l-10 -5 0 10

Change In Venable / Van"bl (%)

swmpikig of ObjcthveShaded Aree

Mi-nseC-- .1- c -sp TIPlu

-1 s 0 1 10Change M Variable I Virlable %)

Samplin of 0cctiShaded Arm

20

010 02

40Heighte Calenan -n- a n . -b-eien

-15 -10 -5 e ' 0 isChange in Varlable VaAeb 1%)

S-ipling if Cat#"She" Anea

- - e iO 'lCle!Ac, ran

-10 0 - 5 o 0

Change In Variable I Variable (%)

Figure 4-3: Plots of the variable sensitivity for three objectives of the same design

using four distinct series for sampling.

37

Steeping of Stemp0ng of Samplng at Steep"ng .Anchor Point pead 2 Haight of Cable A hor Point In 0gho Canopy Anchor Point LmnM of Compy

0.6 150- - e e-- - -- 0- - 0 0 00

0.0.1040 0.,90-,4. S 0 0 -o f e.

0 IN.-1 0 -4---.- - my / - 5

.10 5 10 10 4 0 5 10 -10 .5 0 5 10 .10 - 0 5 10

S pngOf Somp*0n of Sampling of10 Holght of Canopy Tlp 5 Numrbar of Capt. s Canopy Connemara

. -10 -5 0-n -5 It s 1 -1. -0 5s 10 100 -5 Va /V0 0 0 )

C rrft Em49n Chang. In5. Varbr I0 Vaialshad..A= tes "1 19 n _w i iiiiiiii

-1 pingtif 1ampin of Sanplng of Swemplng ot0.5 2no.9oint PMd H00MO OHOC AoogPhtM 04I of Canopy Anchor Point 6 Lngth of Canopy

. 0 .5 0 -- 1- o - PU ooO-20

4.5 ()t 0 .4'et0000at tear.0

0 -+ 0--- 0--00.0

-10 - 0 5 10 -10 0 0 5 10 -10 -t 0 ; 10 -10 5 0 5 10

So"pIngl" -1 B.mpbn of Saeoport .f10 H191ght fCanopy"Tip nembe, ar Cal" s Ctanpy C -ralr

5 4o

o - tK 0 eo e 20|"

-10 -A 0 5 1 -10 .5 a 10 .10 It 5 10Change in Variable / Variabe (%)

"llp"n Of Smpling .1 S.mpIng of Uaing ofAnh.r Point Spread 30Hifight al Cobb Arethor Point "eight of Coapy Andhw Point to LaogOh of Canopy

0.5 200 0 0--- -005-00--9

-0.5

01 000N 0-r0.0A

00 -0.5

20 -10 0 10 20 -20 -10 0 10 20 -M -10 0 10 20 20 10 0 10 2

SoMphIg of Sarnpling at Seping4 ofo Haight Canopy TIP 5 W00

- O 50 -O-~~~Shuland ih(miea

5 V

-2V -10 0 10 20 420 -10 0 10 20 -0 -10 0 10 20Change in Var t i e i Variable (%)

usgpif o Sadpcg of Sfeoping Of Seapning4 Anchor Point Spread H2igh of Cobb Anchor Point Ieg of Canopy Anchor Point 100 Longth CH Canopy

2 SDO800.5--M r e e 400

-)AS 0"/.100 -50 0 so 1IN -100 0 N -IN0 -50 0 so 1;0 Ib -50 0 5W IN

S.mplhg of Seampani of seempitg of40 "ig"I of Can"p TIP 1ISM letmber of Cablew coy C-rvture

20 ON0 00

.20 0 -'de A.. ----- - - -

-IN.5 5 0 -1oo 40 0 so 1001 -100 -50 0 50 100Change In Variable I Variable (%)

Figure 4-4: Plots of the variable sensitivity for seven variables of the same designusing four distinct series for sampling.

38

The most significant visual impact of the different variable sampling method comes

from the number of sampling points. The fourth method, the five point sampling,

shown at the bottom of both figures 4-3 and 4-4, does not have enough degrees

of freedom to capture behavior other than smooth exponential or linear behavior.

Furthermore, many non-linear behaviors are inaccurately presented as identical to

smoothly exponential and linear behaviors, which makes the five point sampling in-

effective at identifying the variables that need to be sampled more thoroughly. The

anchor point spread variable also demonstrates the weakness of symmetric and low

resolution sampling. Its behavior is distinct with each sampling method. The sym-

metric and asymmetric linear sampling capture similar global behavior, but the local

variations from the 3% to 6% range differ significantly in magnitude and the local

variations from the 7% to 10% range differ in the direction of the slope. These dif-

ferences indicate a need for more precise sampling of that variable. The variables

with smooth exponential or linear behavior are meaningfully displayed by all sam-

pling methods. Discrete variables such as the number of cables are clearly displayed

by the first three sampling methods, but not by the five point sampling. There does

not seem to be any significant visual advantage to the third method, seven points of

logarithmic sampling of base two, in either the objective or the variable graphs.

4.1.4 MOO Investigation

The example shown here a possible method of applying variable sensitivity to make

more informed objective trade-offs. The initial design in figure 4-5 is generated by

a single-variable optimization of the sum of the three normalized objectives. Each

objective was normalized by dividing its value for this specific design by the minimum

possible value for the design space. Ideally, this means the design is on a Pareto front.

The variables that demonstrate significant objective trade-offs are the length of the

canopy, the height of the tip of the canopy, the number of cables, and the height of

the cable anchor point. The design and graphs shown in figure 4-6 are generated by

setting the selected variables to a value in the middle of their range and sampling them

densely across their entire range. The final design, shown in figure 4-7 is a modified

39

version of the design in figure 4-5 based on the variable behavior demonstrated in

figure 4-6. The canopy length is selected to be at the point where the sensitivity to

shaded area and structural weight have equivalent slopes. This value can be found by

plotting the slope of both functions and finding where they intersect. Following the

same method the canopy tip height is selected to be at intersection of the shaded area

and deflection sensitivity slopes. The canopy anchor point height is at its maximum

value and the number of cables was held at its mid-range value. The sensitivity results

for the final design demonstrate that some of the information gathered by sampling

variables individually does not hold true when multiple values change. Of particular

note is the height of the cable anchor point. In figure 4-6 the optimal value is at

the extrema, while in figure 4-7 its behavior has changed. One conclusion is that the

behavior of the cable anchor point is highly correlated to one of the other variables

and in order to appropriately predicts its behavior it must be sampled simultaneously

with the correlated variable.

40

Sampling OfDeflection

60

20

40 - -

_ 0 11-10 i 0 5 10

Chcnge in Variable / Varncbie (%)

1k

I'

~ x

Madurn Odeiton lN: 0301 wam: 2.67Camon 1mAssaimn Jiig 391.3 nom: 1.50 MShded Arnn t^2: 105.6 norn: 4.01

Sampling ofStructural Weight

30

10

0 -10

Samping ofShading Area

30

20

10 .

SAhoPoit -pr- - d.10

-20 - -n-Higt I Cable Anchor PoaHghi of Canopy Anchor

-+- Length of Canopy- - Height of Canopy To

-30 Ncmnber of Cablea-4-Canopy C-rvalrn

-10 -0 0 0 10Change In Variable / Variable (%)

8

--tO -5 0 0 10Change in Variable / Variable (%)

Sampling iof

20 Anchor Point Spread

15

10

-10 -5 0 5 10Change in Variable / Variable (%I

Sampling ofOf low0gi CopyTip

-.2

-4

-6

-10(.10 -5 0 5 10

Change In Variable / Variable (%)

Sampling of Samplng Of., Height of Cable Anchor Point Height of Canopy Anchor Point

10.0.5

c -0.5-5

-10 -- 0 --0 -10 -0 5 10

Change in Variable V atiable %) Change in Variable /Variable(%

Samnplng 06 Sampling of

50 lumher ot Cables 2V Canopy Curvature

830 4

ric -0 -1 - '- 'i -

110

-10 302.10 -5 0 5 10 -10 -5 0 5 10Change in Variable / Variable (%) Change in Variable / Variable (%)

Sampling ofs Length of Canopy

60

84020

0

-10 -5 0 5 10

Change in Variable I Variable (%)

- n-- r nal WeIght

+Shadig Ania

Figure 4-5: The design shown here was generated by applying an evolutionary opti-mization method where the objective function is the sum of each of the normalizedobjectives.

41

0

IndPoil

Samplng ofDeflection

250

200

8150

0-5

-40 -20 0 20 40

Change In Variable / Variable (%)

hMtumDSllCan [ht: 43612 rane: 3M .95

Carbon Emissions Mho: 3236.5 non: 240 mShaded Ame W2 169.31 nom: 2.54

Sampling ofStructaral Weight

40 -20 0 20 40

Change In Variable /Variable I%)

Samping ofShading Area

I-O- ght of Cable Anchor Point-O-Lngt of Campy

ght of CanoTip

100

8

C 04

-10

- 0 0 50Change in Variable /Variable I%)

Samping of1110ht of Cable Anchor Point

16 r 0

L)

-50 0 50Change in Variable / Variable (%)

Samping ofLength of Canopy

Sampling ofHeight of Canopy Tip

250

400 -20

200

300 10

200 0

0 -20 - 0

-50 0 50 -50 0 00Change in Variable / Variable (%) Change In Variable/ Variable (%)

Sampling ofNumber of Cables

-- SKWANcMal WeightSheding Area

0 0 aChange in Variable / Variable (%)

Figure 4-6: The purpose of this design is to observe more closely the most interest-ing variables from the previous design. The series used for sampling steps by 0.5%from -50% to 50%. A value near the middle of each variable's range was chosen forconvenience.

42

500

400

00

200

100

8

8

14

12

1U

4

2n

0

-100

I

Sampling ofDeflection50 -

40 ...

30

~20

.10 -

- 20 -

-36-10 -5 0 5 10Change in Variable / Variable (%)

Samping ofAnchor Point Spread

20

810.1' .e 4004 -4--a--.10

-10 -5 0 5 10Change in Variable I Variable (%)

Sampng tOfHeight of Canopy Tip

5

0

c 51

10 -5 0 0 10Change in Variable I Variable (%)

MaIft eOvmamWni 0.PO - ra :."mcssEdsama 1g 631.2 'arn: 2A4

9.060b A-e MM2 157 32 -on 2.3

Sampling ofStructural Weight

20

15

10

5

301

20

10

-20

- 0 5

-201

-10 - 0 0 10Change in Variable / Variable I%)

Sampang of

0 - raC r A orr

2

..5-to -z 0 5 10Change in Variable I Variable (%)

Sampang ofluber of Cables

30

20

.10

.-20.10 -5 0 5 10Change in Variable Y Variable (%)

Samping OfShaded Area

-G-Andla Palnt peead

Hgh 0f Cable Anhr PaintHeight f Copy AnChr Point

-A- Length of CanOPYHeghlf Canpy Tip-- Cabem Cablet

+-CanoIpy CUrVatue

-30 1 a a-10 -4 0 5 10

Change in Variable / Variable (%)

Samplng of Sampling ofS leight of Canopy Anchor Point Length of Canopy

13

-20

0-10 .50 100 -10 .5 0 5 10Change in Variable / Variable (%) Change in Variable/ Variable (%)

Swnpling ofZZ3 Canopy Curvabur23

1 -

0 -10 -0 0 5 10Change in Variable / Variable (.)

Figure 4-7: The design shown here is adjusted from the design in figure 4-5 based onthe information presented in figure 4-6.

43

4.2 Bus Station Canopy

The task given in this study is a canopy for a bus station, based off of an actual

structure built in Hamburg, and recreated as a design problem by Caitlin Mueller

and Renaud Danhaive for a course taught at MIT in the fall of 2016. The basic

requirements of the design are to provide commuters with shelter from the rain and to

serve as an artistic piece celebrating engineering. The main topology of the structure

is a series of columns that branch at the top to support the mid span of transversal

beams that meet at the structure's spine. Longitudinal beams connect the tips of

the transversal beams and run parallel to the spine. See figure 4-8 for an example

design. The design performance objectives under consideration are the area covered

by structure, strain energy, maximum deflection, and structural weight.

Spine

Beam 2 Beam I

Node

Module

Span

Figure 4-8: The bus station in Hamburg that inspired the design problem is shownon the left [Temme Obermeier, 2012]. The analytical model for structural modelingis shown in the center. The perspective view of the 3D model is on the right.

44

Variable Units Min Max

Node Height ft 0.0 12.0

Spine Height ft 6.0 12.0

Overhang Width 1 ft 1.0 10.0

Vertical Translation 1 ft 1.0 10.0

Overhang Width 2 ft 1.0 10.0

Vertical Translation 2 ft 1.0 10.0

Node Location on Beam 1 0.0 1.0

Node Location on Beam 2 0.0 1.0

Number of Modules 1 10

Span Between Columns ft 1 10

Number of Subs 1 10

Objective Units Direction Evaluation Method

Projected Area ft2 Maximize Geometric

Embodied Carbon kg C02 Minimize FEM + Sizer

Maximum Deflection in Minimize FEM

Strain Energy lb - ft Minimize FEM

Table 4.2: The variables, variable bounds, and objectives for the structural design ofa bus station.

4.2.1 Design Priorities for Free Exploration

The intention of this case study is to explore the impact that performance information

has on free exploration of the design space. The results will be a record of the

designs evaluated for variable sensitivity, the designer's interpretation of the variable

sensitivity visuals and an explanation of intended changes for the next iteration.

45

4.2.2 Annotated Free Exploration

A design setting all variables to the middle of their range and then iterated once is

shown in figure 4-9. The variable sensitivity visualizations demonstrated local optima

for most variables. The node height was raised to produce a more visually interesting

effect. The spine height was lowered and the number of subdivisions was decreased to

reduce embodied carbon without sacrificing projected area. As seen in table 4.3, the

resulting structure decreased in embodied carbon and maximum deflection without a

change in projected area.

I Node Height 5 Spine Height ( 00 Overhang Width I 00 Verical translation I

500 -Y0

0 ti0 410 0 a11 0 0 5001.

CD-

-10 -5 - 0 5 11 0 0 5 0 5 10 is -10 -5 0 5 10 -10 -5 0 5 1

0 -107 -5 1

Change in Variable /Variable () Change in Variable /Variable (%) Change in Variable /Variable () Change in Variable /Variable (%)1 od. Overhang Width 2 1000 Vertical Translation 2 40 Node Location 1n eem 1 Node Location on Beem 2

SMI 20' 201

500.~00gC - 8 ---". ------1

-- 0 -5 0 5 10 --0 -52 10 -10 -5 0 5 10 -10 -5 0 5 10Change in Variable / Variable (%) Change in Variable / Variable (%) Change in Variable / Variable (%) Change in Variable / Variable (%)

Number of Modules Span between Coamns Nm e Locatio onr M 1Ne a o a20-1- Strain Energy

00 1

- -MaximumDisplacement Embodied Carbon

~-10 -5 0 5 (*0

-) 10 -n 0 a 10 -10 -5 0 5 10Change in Variable / Variable (%) Change in Variable / Variable (%) Change in Variable / Variable (%)

Figure 4-9: A symmetric design [left], its variable sensitivity plots, and another designiteration [right] based on the interpretation of the plots.

46

ll Initial Iteration Comparison Notes

Projected Area (ft2 ) 275 275 100% equal area

Embodied Carbon (kg C02) 348.8 267 77% lower embodied carbon

Deflection (in) 0.303 0.298 98% lower max deflection

Strain Energy (lb - ft) 2.1 2.4 113% greater total deflection

Table 4.3: Comparison of the designs shown in figure 4-9.

A second arbitrarily chosen asymmetric design and its iteration are shown in 4-10.

The node height is raised because the designer sees that it will have minimal impact

on the performance and decided to leave more room for seating beneath the cannopy.

The designer chose to reduce the number of subdivisions while simultaneously increase

the span and number of modules in the hopes that these trade-offs would improve the

ratio of area covered to structural weight. Finally, the designer decided to move the

node locations on beam 1 and 2 in order to minimize all three structural objectives

because they can improve performance without impacting the projected area. The

iteration of the asymmetric design increases in projected area, decreases in embodied

carbon, decreases in maximum deflection and increases in strain energy. The results

shown in table 4.4 show that the changes informed by the sensitivity graphs improve

performance. The most interesting result might be that the strain energy increases

while the material used and maximum deflection are reduced which implies that the

changing geometry offsets the structural impact of the increased load by distributing

deflection more evenly along the structure.

47

Node Height

0 -10 -5 0 5 10

Change in Variable / Variable (%)

3 Overhang Width 2

0

0 10 -5 0 5 10Change in Variable / Variable (%)

Number of Modules40

20 -

20

( -10 -5 0 5 10Change in Variable / Variable (%)

- Spine HeightS15

10,

5

S04. -10 -5 0 5 10

Change in Variable / Variable (%)Vertical Translation 2

0

0,

10 -5 0 5 10Change in Variable / Variable (%)

Span between Columns

40

h20

10 -5 0 5 1

Change in Variable / Variable (%)

2 Overhang Width I20

10

100 -10 -5 0 5 10

Change in Variable / Variable (%)- Node Location on Beam 1

0

-10 -5 0 5 10Change in Variable / Variable (%)

: Number of Subs per Modules

g0

-10 - 0 5 10

Change in Variable Variable (%)

Verical translation 1

5 M~ 0

S-5 *0 -10 -5 0 5 10Change in Variable / Variable (%)

- Nods Location on Seam 26 10

0

o -10 -5 0 5 10Change in Variable / Variable (%)

-9-- Strain Energy+Maron i OplanrnmnnErnaded Cearo

--Proeted Are

Figure 4-10: An arbitrary asymmetric design [left], its variable sensitivity plots, and

another design iteration [right] based on the interpretation of the plots.

Initial Iteration Comparison Notes

Projected Area (ft2) 162.5 234.0 144% greater area

Embodied Carbon (kg C0 2) 283.4 233.8 83% lower embodied carbon

Deflection (in) 0.49 0.46 95% lower maximum deflection

Strain Energy (lb - ft) 2.6 3.9 151% greater total deflection

Table 4.4: Comparison of the designs shown in figure 4-10.

48

L

4.3 Discussion

The first case study demonstrates that the choice of sampling is critical to the read-

ability of the design sensitivity visualizations. The most effective visualizations seem

to balance number of variables with the range and resolution of the sampling. When

beginning a design problem with a large design vector, it may be best to sample with

a large range and a low resolution. After reducing the problem to a smaller set of

variables that demonstrate objective trade-offs, a smaller range and greater resolution

are valuable in fine-tuning geometry.

The second case study demonstrates that the design sensitivity visualizations can

be used to improve arbitrary designs in a manner similar to an interactive optimization

algorithm. Additionally, the impact of the initial design is clearly shown by the

appearance of local optima for the symmetric, but not the asymmetric case. The

arbitrary starting point within the design space of the asymmetric design encourages

the designer to explore different variables than in the symmetric case.

One critical disadvantage demonstrated by both case studies is the embedded as-

sumption of variable independence. By only sampling a single variable at a time,

the interaction of variables remains hidden. The clearest example of this behavior

is noted in the MOO investigation section 4.1.4 where the cable anchor point vari-

able significantly changes its behavior in the second design iteration even though the

anchor point value itself does not change.

Another disadvantage is that it is quite easy for the designer to find a local optima

and disregard a more thorough search for the globally optimal approach. As a result,

the variable sensitivity visualizations should be used in tandem with some form of

global, or stochastic, optimization technique in order to scan the design space and

become aware of diverse designs that may have significantly better performance than

the initial design.

49

Chapter 5

Conclusion

The variable sensitivity visualizations presented here are an important step in making

structural performance a critical, usable criteria in the conceptual design process.

The graphical format of variable sensitivity information along with examples of their

interpretation effectively reveal behavior of realistic design spaces.

5.1 Summary of Contributions

The two contributions presented and demonstrated through case studies are a computer-

aided design process that accommodates the observed behavior of expert structural

designers and a graphical format for visualizing variable sensitivity of multi-objective

design spaces. Although graphs of single-variable sampling have been introduced

previously as a method of understanding MOO problems in structural design, the

workflow incorporating these visualizations within a specific design process is a novel

contribution. Another distinction between the visualizations demonstrated previously

and those shown here is the combination of objective graphs and variable graphs. The

single-variable sampling in previous work has presented a single graph for each vari-

able, while in this work there is a single graph for each variable as well as a single

graph for each objective. The combination allows a designer to switch back and forth

between considering the impact of changing a specific variable and considering which

variable would have the most significant impact on a specific objective. In a simi-

50

lar manner, the additional loop within the novel design process allows the designer

to switch back and forth between deciding which alternatives to generate within a

specific design space and deciding whether or not to reframe the design space itself

by changing variables, variable bounds, or objective functions. The intentional act

of moving between problem framing and analysis of a solution conjecture during the

design process is grounded in the protocol studies of expert designers referenced in

Chapter 1.

5.2 Potential Impact

The incorporation of variable sensitivity considerations in both practical and edu-

cational scenarios will improve the intelligent application of optimization techniques

within the field of structural design. A design process that encourages the designer to

question the design space in which they apply optimization methods should serve to

reduce the misuse of computational design tools, while simultaneously increasing their

adoption and further development. As designers become more comfortable at inte-

grating computational tools in their methods without threatening their own creative

contribution, they will become more effective at integrating the enormous amount of

information produced by increasingly nuanced performance simulations.

5.3 Future Work

The most pressing future work is to create a more seamless transition between inter-

action with the model's variables and visualizing their sensitivity. The simultaneous

development of additional case studies and a catalogue of observed behaviors will

improve the quick interpretation of design guidance provided by the visualizations.

The coupling of variables in the sampling method should improve the reliability of

the design guidance. For example, the cable anchor point issue presented in 4.1.4

could possibly be resolved in three ways. The first would be to create a coupled

sampling approach that steps height of the cable anchor point at the same time as

51

another variable both in the positive direction, then both in the negative and then

a third and fourth time where the variables are stepped in opposing directions. The

second would be to replace the height of the cable anchor point and the height of

the canopy anchor point with a new variable that describes the distance between the

anchor points. If it is the case that these two variables are only correlated with each

other then the behavior of the new variable would appear consistent as the other

variables change. A third, more algorithmic method, might use a statistical test to

check for independence of all of the variables; however, the computational cost would

need to be taken into consideration. If variables prove to be dependent, then the

computational tool may suggest that the designer reframe the problem to separate

those variables.

5.4 Concluding Remarks

The desire to understand the sensitivity of the variables in a structural design problem

is a quality that designers need to develop in order to make the most effective use

of the suite of computational tools available to them. The pursuit of performance

information is a valuable educational experience regardless of the specific method

used to gather such information. As a result, the author hopes to continue to see the

development of innovative approaches to gathering and displaying such information

within the field of structural design.

52

Appendix A

Canopy Implementation

53

N Sw . I C

GrasshopperPythonScptEditor

File Help

varList - [x,z,u,v,w,s,t,xx,xy]a-[x[oJ:b-[z[0o];c-[u[0JJ;d-[v[0;e-w[0J];f-[s[0]];g-(t[o0J:h-[xx[o]J:i-[xy0]J:reaList - [a,b,c,d,e,f,g,h,il

for indVar,var in enumerate (varList):if type(var) - None or len(var) < 3:

-var - [0,0,0]for step in y:

-for IndRes,res in enumerate(resLlst):- initial - varList[indRes] [0]- bound - varList[indRes] (2]-varList[indRles [1]

if indRes - indVar:res. append (initial+step*bound)

- * -else:res .append (initial)

Figure A-1: The grasshopper and Python code used to sample the variables.

54

L

-

Grasshopper Python Script Editor

* Fk Hel

import Grasshopper as G

baseLine - objSet.pop(c0

aeightedDL - (intt(val - bseie .e/boeeL'C , for va o :se:verbose stputList - ["arreeri - format+1,we g e for i rangeen aYerbSeOutut - [-" iOln(vo) for vo in 7erbOutI i s tfdlesnlt - "Change in objective as a percenr "-" -".ioin4v'erbfSeC.tp

diffiree - G.DataTreelfloati I)print IanweightedL)for Ind,nevVal in in~mwat(egtedIZ.)

xndAdi - ind/SmlemdiffTree.osurePath(indAdj)path - difflree.PathfiAndJdjdiffTree.Add(nesVaiparb)

print diffree

x a

I b I;, LHeaders

L L

'aWi

An~cho.r nuir~t

2,Anchor H0ight

4,Tip Height 2,TipHeight T4p

loopi'1: r

Ing Civ

0 .~ f~ ~ NOW ~ oboe

4/27/2017 7:04 AM Microsoft Office E...

4/27/2017 7:04 AM Microsoft Office E...

4/27/2017 7:04 AM Microsoft Office E...

4/27/2017 7:04 AM Microsoft Office E...

1 KB

1 KB

1 KB

6 KB

Figure A-2: The grasshopper and Python code used to format the objective scoresfor each design, serialize and stream them in the .csv format.

55

I~

I

=objSet1

t: objSet2

ISj objSet3

~pramSet

%%Streaming from csv output of GHfileFolder =

'C:\Users\abmchugh\Documents\Streaming

GH\Mar3020l7\';

numObjSets = 3;rSP = ceil(numObjSets/2);

figure; hold on;

markers =

resO = cell(numObjSets,1);for j=l :numObjSets

objNum = char(string(j));

fileName = ['objSet' char(string(j))

'.csv'];filePath = [fileFolder,fileName];resO U} = csvread(filePath);[numVars,~] = size(resO{j});subplot(rSP,2,j); hold on;for i = 2:numVars

marker = markers { i- I};varRes = resO{j}(i,:);steps = resO{j}(1,:);

plot(steps,varRes,marker)

endxlabel('Change in Variable / Variable

ylabel(['Change in Objective'

objNum ' / Objective' objNum'(%)']);title(['Sampling of Objective'

objNum]);end

legend Toggle;

fileFolder =

'C:\Users\abmchugh\Documents\Streaming

GH\Mar3020l7\';

numVars = 7;numObjSets = 3;rSP = ceil(numVars/3);

fig = figure; hold on;

resV = cell(numVars, 1);markers =

for i = 2:numVars+1

subplot(rSP,3,i-1); hold on;

for j= l:numObjSets

.csv'];

marker = markers {jobjNum = char(string(j));

fileName = ['objSet' char(string(j))

filePath = [fileFolder,fileName];

resV{i- } = csvread(filePath);

varRes = resV{i- I}(i,:);

steps = resV{i-1}(1,:);plot(steps,varRes,marker)

endend

for k=2:numVars+1

subplot(rSP,3,k-1);

title(['Sampling of Variable'

char(string(k- 1))]);end

xlabel('Change in Variable / Variable (%)');ylabel('Change in Objective / Objective

legend Toggle;

Figure A-3: The Matlab code used to read the .csv files and create the objective andvariable plots.

56

57

Appendix B

Station Implementation

N

D

af(x<y,iTrue,Fazse) R

if y(vc) R o o

wa = ,0,0

Xbn 1 122

z b

vdwL L

S L L

if tem)-nt

A - -n

k c

-- Grasshopper Python Script Editwr

File Help

Vartst - [xZ ,U, ,s ,xxxa-[X[0] ];b-[Z[0]1;c-[u[0]];d-[v[0]];e-[w[O]];f-[8[0]];g"[t[0]];h-[xx[0]];i-[xy[0]];j=[xzf[0]reaList - (a,b,c,d,e,f,g,h,I,J,k]for indVar, var in enoerate (varList) :

-ftype(var) - None or len(var) < 3:var - [0,0,0]

-or step in y:-or indRes, res in enumerate (resList ):

initial - varList~indRes] [0]-mx - varList [indRes] [2]

mn - varList [indRea] [1]-bound - mx - n

- - -i f indRes -- indVar :steppedRes - initial + step*boundif type(mx) -= Int:

- 2 - -x-teppedRes - round(steppedRes)- u -if steppedRes < mn:

-steppedRes - mn- -if steppedRes > mx:

steppedRes - mx- -res.appmnd(steppedRes)X1 'also:

res.append(initial)

Ia

58

Figure B-1: The grasshopper and Python code used to sample the variables.

File HelpImort Grasshopper as G

baseLine - objSet.pop(O)weightedDL - (for val In objSet

-res - (val - baseLine)/baseLine'truncRes = Int(res*10000)/100.0-weightedDL. wpa4t runcRe4

diffTree - G.DataTree(float] ()print len(weightedDL)for ind,nevVal in eanmerate(weightedDL):

-indAdj = in/Sasmles-diffTree.RnsurmPath (indAdJ)

,path = diffTree .Path (indAdJ).4 - V - A Ab

I'E print diffTree

HeKders i6-Vakies CV Node Height, Spin*

Deliit Itdth I,Wxrical- travolation

3Mm (00) 1, 0verhang Wiidth

stepInput

M-0., .,- .,

objriput dirree

objlcw

dTree

M

driree

stepiput obj3cw

dWreeM

dWrtree

obj2cwararnInput M

0 -.

0{02.,0-0,2-0,4.,6.0

,8.0,10-0

a V a ft'A a C=& M

7_1~ia - [U

for input In ghenv.Camponent. Params. Input:-for source in input.Sources:

-print source. Rickiame-if source.Name - "Number Slider":

a.append(str(source.Nickfame))

Figure B-2: The grasshopper and Python code used to format the objective scoresfor each design, serialize and stream them in the .csv format.

59

)

p

t

1A

%%Streaming from csv output of GH

fileFolder =

'C:\Users\abmchugh\Documents\StreamingGH\StationAprI

72017\FreeExploreShortBackspan\';

numObjSets = 3;

rSP = ceil(numObjSets/2);

figure; hold on;

markers = :resO = cell(numObjSets,I);

for j=l:numObjSets

objNum = char(string(j));

fileName = ['objSet' char(stringtj))'.csv'];

filePath = [fileFolderfileName];

resOij} = csvread(filePath);

[numVars,~] = size(resO Usubplot(rSP,2,j); hold on;

for i = 2:numVars

marker = markers{i-l};

varRes = resO{j}(i,:);

steps = resO U }(1,:);

[culledResculllnd~]= unique(varRes);

[sortedStepssortlnd]= sort(steps(cullind));

sortedRes = culledRes(sortlnd);

plot(stepsvarRes,marker)

end

xlabel('Change in Variable / Variable (%)');

ylabel(['Change in Objective' objNum '

Objective' objNum'(%)']);

title(['Sampling of Objective' objNum]);

end

fileName ='paramSet.csv';

%fileName ='ParamSet3D.csv';

filePath = [fileFolderfileName;

filelD = fopen(filePath);

parse = ";

for k= I:numVars

parse = [parse '%s'];

end

C = textscan(fileID,parse....

'Delimiter',',');

fclose(filelD);

[~,n]= size(C);paramNames = C) (1(1);

for I= 2:n-l

paramNames = [paramNames C{l}(l)J;end

legend(paramNames);

fileFolder =

'C:\Users\abmchugh\Documents\StreamingGH\StationAprl

72017\FreeExploreShortBackspan\';

numVars = 11;numObjSets = 3;rSP = ceil(numVars/3);

fig = figure; hold on;

resV = cell(numVars, I);

markers = {,;for i = 2:numVars+l

subplot(rSP,3,i-l); hold on;

for j=l:numObjSets

marker = markersj };

objNum = char(stringoj));

fileName = ['objSet' char(string(j)) '.csv'];

filePath = [fileFolderfileName];

resV i-l} = esvread(filePath):varRes = resV i- )(i,:);steps= resV{i-l}(l,:);

[culledRes,culllnd,~] = unique(varRes);

[sortedSteps,sortlnd] = sort(steps(culllnd));

sortedRes = culledRes(sortlnd);

%plot(sortedSteps,sortedRes,'o-')

plot(steps,varRes,marker)

%plot(I:length(steps),varRes,'o-') %log plot bad

xlabel

end

end

for k=2:numVars+1

subplot(rSP,3,k-I);

title(['Sampling of' paramNames{k-I }])

%title(['Sampling of Variable'

char(string(k-l))]);

xlabel(['Change in Variable / Variable (%)']);

%xlabel(['Change in Variable' char(string(k- 1))'/ Variable (%)']);

ylabel('Change in Obj / Obj (%)');end

C = {('Embodied Carbon') ['Maximum Displacement')

('Energy');

[~,n] = size(C);

objNames= C{l }(1);

for 1= 2:n

objNames = [objNames C 11 [(1)];

end

legend(paramNames);

legend(objNames);

Figure B-3: The Matlab code used to read the .csv files and create the objective andvariable plots.

60

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