A conceptual modeling and simulation Framework for

Discrete Simulation and Modeling

A Conceptual Modeling and Simulation Framework for System Design Eric Coatanéa | Tampere University of Technology Ric Roca | Johns Hopkins University Applied Physics Laboratory Hossein Mokhtarian | Tampere University of Technology Faisal Mokammel | Aalto University Kimmo Ikkala | Tampere University of Technology

The dimensional analysis conceptual modeling (DACM) framework is a conceptual modeling mechanism for lifecycle systems engineering. Originally developed for military projects, the DACM framework is now available for other applications, too. This powerful approach handles the specifying, discovering, validating, and reusing of building blocks as well as system behavior analysis in early development stages.

C

omputer modeling and simulation (M&S) techniques and methods are present in many areas, including system engineering, acquisition, training, analysis, experimentation, planning, and testing. But for various reasons, past research and development (R&D) for M&S systems hasn’t produced broad classes of models capable of being used and reused across multiple domains. Factors include (but are not limited to) proprietary architectures, lack of consistent and clearly defined development standards, model fidelity, and scalability issues that computer science and software engineering have yet to overcome. For M&S to mature both as an industry and academic discipline, the M&S community must develop standards and frameworks in the areas of conceptual modeling, because conceptual development stages carry implications for multiple decisions that heavily impact subsequent stages of system development and performance. M&S at the conceptual level is consequently a strategic domain poorly explored at the moment.

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Computing in Science & Engineering

1521-9615/16/$33.00 © 2016 IEEE

Copublished by the IEEE CS and the AIP

July/August 2016

According to leading researchers, the advancement of M&S conceptual modeling best practices, grounded in engineering and scientific formalisms, could have a significant impact on future model development, system quality, and reuse costs for stakeholders in both industry and academia. More research is needed to address M&S at the conceptual level—the effort we describe here attempts to answer this need. Research Method In his topical book summarizing years of research work and discovery associated with behavioral psychology and decision making in economics, Daniel Kahneman analyzed the reasons behind biased and irrational decisions.1 The fundamental highlights of his research are the two modes the human brain uses, System 1 (the automatic and fast-thinking mode) and System 2 (the analytical and slow mode). System 2 consumes a lot of brain power and consequently is hard to use for a long period of time. System 1 is usually more efficient in urgent and dangerous situations, when fast actions or reactions must be taken, thus it’s usually favored by humans, even when a situation’s complexity actually requires System 2. In engineering, early development phases such as requirements elicitation, initial concept developments and strategic decision making belong to the class of activities best handled by System 2. Cause-effect analysis is the other most common mechanism that humans use for action and reaction in the physical world.2 One idea developed in this article is that well-informed causal analysis can efficiently support conceptual modeling and analysis of complex systems and facilitate the use of the reflexive mode. Our dimensional analysis conceptual modeling (DACM) framework thus had to fulfill four important characteristics: ■■

■■

■■

■■

be able to favor the brain’s slow and reflective mode, use the brain’s natural tendency to classify information in the form of cause-effect relationships, offer mechanisms to organize and simplify the complexity in problem representation, and propose a mechanism to simulate behavior using qualitative information.

Dimensional Analysis Theory Dimensional analysis (DA) offers an approach for reducing the complexity of modeling problems to the simplest form before going into more details with any type of qualitative or quantitative modeling or simulation.3 The DA theory has been developed over the years by an active research community

that includes prominent researchers in both physics and engineering.4–6 Essentially, DA aims to deduce from the dimensions of the variables (length, mass, time, and so on) used in models certain constraints on possible relationship among variables. For example, in the most familiar dimensional notation, learned in high school or college physics, force is usually represented as M × L × T –2 , where m is mass, L is length, and t is time. Newton’s law, F = m × a, where F is force, m is mass, and a is acceleration, is constrained by the dimensional homogeneity principle, which can be verified by checking the dimensions on both sides of Newton’s law. Another widely used result in DA is VashyBuckingham’s ∏-theorem, which was stated and proved in 1914.4 This theorem identifies the number of independent dimensionless numbers that can characterize a given physical situation, offering a way to simplify problem complexity by grouping the variables into dimensionless primitives. Every law that takes the form yo = f(x1, x2, x3, …, xn) can take the alternative form, ∏0 = f (∏1 , ∏2 ,..., ∏n ) , (1)

where ∏i are the dimensionless products. This alternative form is the final result of DA and is the consequence of the Vashy-Buckingham theorem. A dimensionless number is a product that takes the following form: α

πk = yi ⋅ x j ij ⋅ xl αil ⋅ xm αml , (2)

where xi are repeating variables, yi are performance variables, and αij are exponents. Equation 2 presents the dimensionless form of the primitive (the reusable modeling primitives) we used to develop the framework presented in this article. Examples of these primitives are present in multiple domains of science, including the efficiency rate, the Reynolds number, and the Froude number. To understand how dimensionless primitives are associated with the causal graphs used in this work, consider the causal relations among energy (En) measured in Joules ( J), power (P) measured in Watts (W), and time (t) in measured seconds (s) (see Figure 1). From the causally oriented graph presented in Figure 1 and presenting causal relationship between En, P, and t, we can use Equation 2 to construct a dimensionless product: π En = En ⋅ t −1 ⋅ P −1 . (3)

www.computer.org/cise

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En

P t Figure 1. A small causal graph showing the relations among energy (E), time (t), and power (P).

En P t

Propagated objective: To minimize

Figure 2. Backward propagation of objectives in a causal graph representing the relations among energy, time, and power.

In this article, we use a mathematical machinery that R. Bhaskar and Anil Nigam7 developed to reason about a system using the type of relationship derived from Equation 2. A dimensionless group initially presented in Equation 2 can be expressed yi = π k ⋅ x j

−αij

⋅ xl

−αil

⋅ xm

−αmi

, (4)

which can be divided by xj to form −αij

xj yi x −αil xm−αmi (5) = πk ⋅ ⋅ l ⋅ . xj xj xj xj

From Equation 4, we can write a partial derivative involving variables yi and xj, taking the form −α

x j ij x l −αil xm−αmi ∂ yi = −πk ⋅ αij ⋅ ⋅ . (6) ∂x j xj xj xj The partial derivative can be reformulated and simplified by replacing Equation 5 with Equation 6: ∂ yi y = −αij i . (7) ∂x j xj

From Equation 7, the sign of the derivative (∂yi)/ (∂xj) can be determined by simply verifying the 4

∂ En En = 1 . (8) ∂P P ∂ En En = 1 . (9) ∂t t

Initial objective: To be minimized

Propagated objective: To minimize

sign of exponent αij. This simple machinery provides a powerful approach for propagating qualitative optimization objectives (maximize, minimize) in a causal network. Let’s take the small example of Figure 1, in which we define the initial objective of minimizing energy (En). What should be the resulting objectives for power (P) and time (t)? By using Equation 3, we can derive two partial derivatives:

From Equations 8 and 9, we can deduce that both P and t vary in the same direction as En due to the sign of the partial derivative. Consequently, if En needs to be minimized, we must also minimize P and t (see Figure 2). This process is called in this article backward propagation. Fundamental Types of Variables in a Modeling Problem The bond graph modeling approach8,9 is a domainindependent graphical description of physical systems’ dynamic behavior. It introduces several categories of fundamental variables, including ■■ ■■ ■■

energy, power variables (efforts and flows), and state variables (displacements and momentums).

We use a fourth category, called connecting variables,10 in our DACM framework to describe material, component-specific properties, geometric dimensions, tolerances, and so on. Table 1 summarizes the categories used in our work. Design Structure Matrix and Domain Mapping Matrix A design structures matrix (DSM)10 is a way of representing a graph that can be used to list all of a system’s constituent parts or a process’s activities and the corresponding information exchange, interactions, and dependency patterns. DSMs compare interactions between elements of a similar nature, whereas the domain mapping matrix (DMM) is used to map elements belonging to different domains, for example, functions and physical subsystems. The DSM and DMM are used systematically in the software tool supporting our DACM framework to represent interconnections in the functional structures, causal graphs, and the laws July/August 2016

governing the system. DMMs map the functions with the variables. DMMs also map variables with elementary units of the International System of Units (SI) and variables with system laws. The DACM Framework We can summarize the DACM process into a few fundamental steps. Step 1: Indicate the Model’s Objectives The modeler starts by explicitly providing rationales for the model’s aim and its borders. The functional modeling process is controlled in this phase by using an ontology (http://protege.stanford.edu) and a normalized set of functional terms.11 Step 2: List the Problem’s Fundamental Variables Table 1 defines seven categories of possible variables when modeling a system. More specific terms for the variables can be defined by using a taxonomy described by Julie Hirtz and her colleagues.11 Step 3: Position System Variables on the Functional Structure The variables listed in Step 2 are placed on the functional decomposition built in Step 1, and a color is associated with each variable: ■■

■■

■■

■■

Exogenous variables colored in black are variables imposed by the system’s external environment. There’s no degree of freedom for changing exogenous variables. Independent design variables colored in green aren’t influenced by any other variable in the system and can be selected during the design process. Dependent design variables colored in blue are influenced by other variables and thus more difficult to control. These variables can be selected during the design process. Performance variables colored in red are a special class of dependent design variables that are important for evaluating overall system performance. Designers try to optimize them by minimizing or maximizing them or by obtaining a target value for them.

Step 4: Develop a Causal Ordering of the Variables The fourth step of the DACM process is fundamental. During this phase, the cause-effect relationships between variables are defined in the

Table 1. Fundamental categories of variables.* Primary type of variables

Secondary categories

Overall system variables

Energy (En) Efficiency rate (η)

Power variables (p)

Generalized effort (effort) Generalized flow (flow)

State variables

Generalized displacement (displacement) Generalized momentum (momentum) Connecting variables (connecting)

form of a causal graph. The algorithm shown in Figure 3 generates the causal graph by considering multiple rules derived from a bond graph and DA metrics.12 The algorithm is associated with a mapping of functional vocabulary with bond graph organs. Figure 4 provides a visualization of the causal algorithm generated by our DACM tool. Step 5: Construct the Model’s Behavioral Laws In Step 5, the DACM software tool automatically generates the system’s governing laws, which are derived from DA theory. Step 6: Determine the Objectives Associated with Performance Variables The sixth step assigns objectives to the performance variables colored in red in Step 3. Using the simulation machinery defined in Step 5, those objectives are propagated backward in the causal graph generated in Step 4. The objectives can be qualitative (that is, maximizing or minimizing). Step 7: Find the Contradictions The propagation of objectives in the causal graph can generate contradictions.13 For example, the resulting objective of propagation can lead to variables that should simultaneously answer contradictory objectives.14 Step 8: Determine Design Directions and Potential Added Values The eighth step involves generating a virtual design of an experiment and computing the impact of dif-


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Identify modelling problem Create a functional structure Map the functional structure with bond Graph organs Integrate more knowledge related to: Is it a bijective mapping?

No

-Type of conservative law considered (Force or Flow), -Type of Energy transmitted, -Type of variables associated with the functions

Yes

Travel into the structure from left to write by following the connections Use the causal rules associated with the individual Bond Graph components [8] for defining the causality for individual : -Flows, -Efforts Always add a bidirectional causality for associated Flows and Efforts

By time integration a flow entering in a box is causally linked with a displacement and Efforts is causally linked with a momentum

Use the causal rules of Shen & Peng [13] for defining the causality between: Displacement, Momentum and connecting variables

No

By time derivation a displacement is causally linked with a flow leaving a box and momentum is causally linked with an effort leaving a box

Are the variables of the structure completely ordered? Yes Display in form of a causal graph

End

Figure 3. The algorithm that generates the causal graph by considering multiple rules derived from a bond graph and dimensional analysis metrics.

Step 9: Generate Innovative Solutions to Design Contradictions The ninth step applies inventive design principles to remove design contradictions. In the next section, we describe a case study with a torpedo in which we attempted to transform exogenous variables into a design variable by increasing the studied system’s boundaries.

Figure 4. Causal graph visualization. The example presents the causal graph of a pressure regulator regulating an output pressure (Pout). The variables describe the fluid properties and the internal structure of the piston and spring used in the pressure regulator’s architecture.

ferent variables on performance variables. These variables are then ranked according to their impact level. 6

Two Case Studies To evaluate the DACM framework’s capacity for M&S conceptual design solutions, we set up two case studies. Several other inventive principles have been developed in this research but aren’t presented in this article. Those principles are independent of the TRIZ approach,15,16 providing an alternative approach for generalizing inventive principles. Case Study 1: A Torpedo To present our framework’s innovative usage, we focused on a torpedo moving into water. SpecifiJuly/August 2016

Water resist to the torpedo movement

Torpedo move into water

μ

A

ρ

V

ρ µ

Fd

V Torpedo move by acting on the water

A

Torpedo and water interact together

Energy is dissipated into water

Fd

Figure 5. Functional representation of the interaction of a torpedo and water. The variables in green, blue, and black are listed in Table 2.

cally, the designers want to increase the torpedo’s speed under water. The case study’s two initial objectives in the context of this article were to extract the most important set of variables and the units required to model the torpedo in water, and to define the causal relationships between those variables, The torpedo model takes into account both the torpedo and its interaction with the water; its internal structure isn’t described in this model. Rather, we’re studying the function of moving into water. The water resists this movement and generate a drag force Fd. To generate the model of the torpedo moving into water, we need to apply Steps 1, 2, and 3 of our framework. Figure 5 summarizes those three steps of the DACM framework. From the steps summarized in Figure 5 and and by using the causal ordering algorithm and tool presented in Step 4, we can create the causal ordering graph for the torpedo (see Figure 6). To derive the mathematical laws, we need to know each variable’s SI (International System of Units) units. Table 2 shows the list of variables governing the problem with their SI elementary units. Qualitative objectives are defined for the performance variables presented in red in Figure 6. We want to maximize the torpedo speed and to minimize the drag force. The propagation of those objectives in the causal graph is done by using a simulation machinery.7 The computation of the associated ∏number is provided as follows17 π Fd = Fd ⋅ V

−3

2

⋅µ

−1

2

⋅ρ

−1

2

⋅A

−3

4

, (10)

A Fd

µ

V

ρ Figure 6. Causal ordering graph for the torpedo case study. (Independent design variables are green, exogenous variables are black, and performance variables are red.) The variables listed in the causal graph are the same presented in Table 2.

where πFd is both a dimensionless primitive and drag coefficient Cd. A second dimensionless primitive can be formed for V: πV = V ⋅ Fd

1

2

1

3

⋅ A 2 ⋅ ρ 2 ⋅ µ −2 . (11)

With these two equations, we’ve proven that the DACM framework can rediscover formulas related to fluid dynamics. The computation leading to both equations uses DMMs (Domain Mapping Matrices) presented in Tables 3 and 4.


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Table 2. List of problem variables and International System of Units (SI) elementary units. Categories (objectives, other variables)

Variables

SI elementary units (L = length, M = mass, T = time)

Performance variables

Speed (V )

LT–1

Drag force (Fd)

MLT–2

Other variables

Fluid density (ρ)

ML–3

Torpedo reference surface (related to shape and length, A)

L2

Fluid dynamic viscosity (μ)

ML–1T–1

Table 3. Domain mapping matric (DMM) representing node Fd in Figure 6.* [B]

[A]

Unit/variables

Drag force (Fd)

Torpedo reference surface (A)

Fluid density (ρ); fluid dynamic velocity (μ)

Speed (V )

Mass (M)

1

0

2

0

Length (L)

1

2

–4

1

Time (T )

–2

0

–1

–1

*[A] represents the different variables influencing this node; [B] is the matrix representing the variables influenced by [A].

Table 4. DMM representing node V in Figure 6. [B]

[A]

Unit/variables

V

Fd × A

ρ

Fluid dynamic velocity (μ)

Mass

0

1

1

1

Length

1

3

–3

–1

Time

–1

-2

0

–1

The linear algebra transformation used to generate Equations 10 and 11 is presented in the following Equation 12 in which C is the vector representing the exponents of Equations 10 and 11. B is the matrix representing the dimensions of the performance variable and A represents the dimensions of the repeating variables.17 C = −( A−1 ⋅ B )T . (12)

Two contradictions appear in Figure 7 on the drag force Fd and on the speed V both must be maximized and minimized to fulfill the initial objectives, which contradicts the initial design objectives. Let’s select the contradiction on the 8

drag force Fd as the constraint to be solved. An approach based on virtual design of experiment (DOE) is proposed in this article to evaluate the impact of the different parameters influencing the drag force Fd. To conduct this DOE, orders of magnitude have to be proposed for variables V [84 m/s, 250 m/s], A [1.5 m 2 , 4 m 2], µ [0,000653 Pa·s, 0,00179 Pa·s], and ρ [0.179 kg/m 3, 1.03 kg/ m 3]. These ranges are extracted from a technical database, and we use the Taguchi approach18 to conduct the DOE. Four variables influence Fd: V, A, µ and ρ. The degrees of freedom (DOF) allowing us to select the proper Taguchi table is computed by using the following method: a DOF is allocated for each variable and for the model’s mean value (DOF = 1 + 1 + 1 + 1 + 1 = 5). At a minimum, an L5 orthogonal array is used to analyze variable sensitivity. We select low and high quantitative levels for V, A, µ, and ρ compute the effect of the variables on Fd: Xi = ∑ 1

n

G X −High i n

− ∑1

n

G X −Low i . (13) n

The parameters V, A, µ, and ρ in Equation 10 that have a significant influence on Fd are ranked by order of magnitude in Figure 8. July/August 2016

Case Study 2: Laser Light Interacting with Metal Powder Our second case study focuses on the development of a simulation model to analyze the interaction between a laser source and a metal. This case study’s objective is to present in detail the method used to compute the model’s mathematical laws. Figure 9 shows the functional model and a list of variables influencing the process. Table 5 shows the variable names and units, and Figure 10 shows the causal graph associated with the process and the variables. The example in our case study develops the mathematic machinery associated with the part of the causal graph surrounded in red in Figure 10. The melted metal rate mm is influenced by multiple variables, including the metal and the equipment properties. We used a DMM for representing the machine and material variables influencing mm (see Table 6). A short calculation shows that we have eight variables because ε is dimensionless and can be removed from this list (ε is reintegrated at the end of the process when the different dimen-

min MAX min

A

Fd

min

V

min

MAX

µ MAX min

ρ

Figure 7. Causal graph of a torpedo with the propagation of the two given objectives in blue. The propagated objectives7 are represented in red in the figure.

Ranked effect on the drag force (%)

The fluid properties have a significant impact on Fd since the A, the reference surface of the torpedo, is already a parameter that has been optimized in the design. V can’t be considered because it’s also a final objective of the study. The central question is how to modify µ and ρ. Finding an answer to this question limits or removes the contradictions detected in the causal graph in Figure 7. Transforming µ and ρ into a design parameter that can be controlled implies modifying the torpedo system’s borders. The fluid in which the torpedo is moving must be integrated in the system’s boundaries. How do we do this in practice? The DOE helps us notice that gases such as CO2 have very low density and viscosity, µ. Thus, integrating a pressurized bottle of CO2 into the torpedo and injecting the gas in front of it is a possible solution. This is what the Russian torpedo Skval does. Another option is to generate bubbles of gas at the torpedo’s surface by creating very high local temperatures or local difference of pressure. These changes in torpedo design modify the causal graph in Figure 7, which create other contradictions in turn. The torpedo might, for example, become more difficult to control. This analysis process will have to be iterated to another parts of the torpedo architecture in order to solve the other contradicitons emerging from this new design.

Ranking of influences

250 200 150 100 50 0 –50 –100

Effect of ρ

Effect of V

Effect of A

Effect of µ

–150 –200 –250

Variables affecting the drag force

Figure 8. Order of magnitude of the different parameters influencing drag force Fd.

sionless primitives are combined). We have eight variables and four initial dimensions (mass, length, time, and temperature), so we can form 8 – 4 = 4 dimensionless primitives. Consequently, matrix [B] has four columns, selected by priority of dependent or independent design variables. Matrix [A] also has four columns; the last variable ε is kept outside the two matrixes because of being dimensionless already (see Table 5 and 6). The next element to consider is the value of the determinant of [A]. A computation of det[A] shows that its value is null, meaning the rank of [A] is lower than 4. By removing mass because all values are null in [A] and by combining two columns, we get a new matrix [A] of rank 3, non-null (see Table 7). We can now use Equation 12 (presented in case study 1) to determine the following d imensionless groups. Equation 14 is generated by using Table 8, Equation 15 is generated by


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Electrical energy

Guide and convey powder Pr

Light energy

Convert ener gy

P

m Metallic powder

ρ

Convert powder state ρ

T

ε

α

Cp

hf

mm Melted metal

Pc

Nd

D Figure 9. Functional model of a process using a laser to melt a metallic powder. The variables listed in the figure are listed in Table 5.

using Table 9, Equation 16 is generated by using Table 10, and Equation 17 is generated by using Table 11:

Table 5. Variables involved in the laser melting process. Variable Name

Unit

Quantity

mm

Melted metal rate

Kg/s

MT−1

Nd

Nozzle diameter

m

L

P

Laser power

Watt

ML2T−3

m

Powder flow rate

Kg/s

MT−1

πmm = mm ⋅ h f −2 ⋅ C p1 ⋅ (T ⋅ α )1 , (14) π P −Pc = ( P − Pc ) ⋅ h f −3 ⋅ C p1 ⋅ (T ⋅ α )1 , (15)

−1 −2

Pr

Powder feed pressure

Pa

ML T

D

Laser spot diameter

m

L

ρ

Powder density

Kg/m3

ML−3

t

Melting point

°C

t

Cp

Specific heat capacity

Joule/g°C

L2T−2t−1

hf

Heat of fusion

Joule/g

L2T−2

Pc

Critical power

ML2T−3

α

Thermal diffusivity

Watt m2 /s

ε

Absorptivity

--

Dimensionless

πm = m ⋅ h f −2 ⋅ C p1 ⋅ (T ⋅ α )1 , (16)

πD = D ⋅ h f

Cp

L2T −1

P –Pc

πmm = K ⋅ π P −Pc α ⋅ πm β ⋅ π D γ .

ρ ε Nd

m

ρ

Pr

Figure 10. Causal graph generated via the causal ordering software.

10

πmm = f ( π P −Pc , πm , π D ). (18)

According to the product theorem, 3,4 it’s also possible to write Equation 18 in the following form:

mm

T

⋅ C p−1 ⋅ (T ⋅ α )−1 . (17)

Equation 1 in this article shows that the individual dimensionless groups can be combined together. We can then combine them in the following form:

Input extrapolation hf

−3 2

The constant K and exponents α, β, and γ should be defined using experiments on additive manufacturing equipments. The experiments can also be used to adjust the model and verify the real influence of the parameters considered in the model. It can be possible that some parameters have little impact on the performance parameters, and those experiments should help to detect them and remove them from the model without losing its dimensional homogeneity. July/August 2016

Table 6. Initial DMM for the causal relations related to the melted metal rate mm. Unit/variables

[B]

[A]

∏mm

mm

P – Pc

m

D

hf

Cp

T

α

ε

Mass

1

1

1

0

0

0

0

0

0

Length

0

2

0

1

2

2

0

2

0

Time

–1

–3

–1

0

–2

–2

0

–1

0

Temperature

0

0

0

0

0

–1

1

0

0

Table 7. DMM for mm with determinant of [A], non-null.

Table 10. DMM for the third dimensionless primitive.

Unit/ variables

Unit/variables

[B]

[A]

[B] mm

P – Pc

M

D

hf

Cp

∏mm

m

∏mm

hf

Cp

Tα

Tα

Length

0

2

2

2

Length

0

2

0

1

2

2

2

Time

–1

–2

–2

–1

Time

–1

–3

–1

0

–2

–2

–1

Temperature

0

0

–1

1

Temperature

0

0

0

0

0

–1

1

[A]

Table 11. DMM for the fourth dimensionless primitive.

Table 8. DMM for the first dimensionless primitive. Unit/variables

[B]

[A]

∏mm

mm

hf

Cp

Tα

Length

0

2

2

2

Time

–1

–2

–2

–1

Temperature

0

0

–1

1

Unit/variables

[B]

[A]

∏mm

D

hf

Cp

Tα

Length

1

2

2

2

Time

0

–2

–2

–1

Temperature

0

0

–1

1

if needed. We’ve demonstrated here that it’s possible to use this approach to determine complex relations between parameters. However, the relations between dimensionless primitives should be validated using an experimental process.

Table 9. DMM for the second dimensionless primitive. Unit/variables

[B]

[A]

∏mm

P – Pc

hf

Cp

Tα

Length

2

2

2

2

Time

–3

–2

–2

–1

Temperature

0

0

–1

1

This second case study is a very general presentation of the DACM approach and is only limited by the requirement of having parameters that can be measured. It’s also possible to add measuring units not belonging to the SI system of units

O

ne aspect not covered in this article is the possibility of using DACM as a specification tool. The specification framework is based on a set of DSMs and DMMs populated by numbers; these matrices form a “fingerprint” of the design problem and its conceptual solution. This “identity card”19 can be used to specify problem requirements in a compact manner and validate the produced solution. The DACM framework can also be used to specify the development of reusable modeling primitives and create new models to address alternative problems.


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DACM is supported by a computer-aided tool that’s currently in its test phase in an industrial context. The development team’s future work is to create a user interface for the tool. Alternative usages of the DACM framework are also currently under development. References 1. D. Kahneman, Thinking, Fast and Slow, Farrar, Straus and Giroux, 2011.

2. M. Kistler, Causation and Laws of Nature, Routledge, 2006.

3. P.W. Bridgman, “Dimensional Analysis,” Encyclopaedia Britannica, vol. 7, 1969, pp. 439–449.

4. G.I. Barenblatt, Scaling, Self-Similarity, and Intermediate Asymptotics, Cambridge Univ. Press, 1996.

5. J.C. Maxwell, A Treatise on Electricity and Magne-

17. T. Szyrtes and P. Rozsa, Applied Dimensional Analysis and Modeling, Elsevier Science & Technology, 2006

18. P. Goos and B. Jones, Optimal Design of Experiments: A Case Study Approach, Wiley, 2011

19. G. Sirin et al., “A Model Identity Card to Support Simulation Model Development Process in a Collaborative Multidisciplinary Design Environment,” IEEE Systems J., vol. 9, no. 4, pp. 1151–1162 Eric Coatanéa is a full professor in the Department of Mechanical Engineering and Industrial Systems at Tampere University of Technology. His research interests include system engineering, design methodologies, and manufacturing. Coatanéa received a double doctorate in engineering design and product development from Aalto University and the University of West Brittany. Contact him at [email protected].

tism, 3rd ed., Dover, 1954.

6. W. Matz, Le Principe de Similitude en Génie Chimique (in French), Dunod, 1959. 7. R. Bhashkar and A. Nigam, “Qualitative Physics Using Dimensional Analysis,” Artificial Intelligence, vol. 45, 1990, pp. 73–111. 8. H.M. Paynter, Analysis and Design of Engineering Systems, MIT Press, 1961. 9. T. Shim, Introduction to Physical System Modelling Using Bond Graphs, University of Michigan-Dearborn, 2002. 10. D.V. Steward, “The Design Structure System: A Method for Managing the Design of Complex Systems,” IEEE Trans. Eng. Management, vol. 28, no. 3, 1981, pp. 71–74. 11. J. Hirtz et al., “A Functional Basis for Engineering Design: Reconciling and Evolving Previous Efforts,” Research in Eng. Design, Springer-Verlag, 2002, pp. 65–82. 12. Q. Shen and T. Peng, “Combining Dimensional Analysis and Heuristics for Causal Ordering,” In Memory of Rob Milne: A Tribute to a Pioneering AI Scientist, Entrepreneur and Mountaineer, A. Bundy and S. Wilson, eds., IOS Press, 2006. 13. J. Ring “Discovering the Real Problematic Situation: The First Aspect of Conceptual Design,” INCOSE INSIGHT, vol. 17, no. 4, 2014, pp. 11–14. 14. J.N. Warfield, Understanding Complexity: Thought and Behavior, AJAR Publishing Co., 2002 15. G. Altshuller, Creativity as an Exact Science, Gordon & Breach, 1984. 16. S.D. Savransky, Engineering of Creativity, Introduction to TRIZ Methodology of Inventive Problem Solving, CRC Press, 2000.

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Ric Roca is a member of the professional staff at Johns Hopkins University Applied Physics Laboratory. His research interests include modeling and simulation projects and technologies. He sponsored the development of the DACM framework during his tenure as deputy director of the Joint Assessment and Enabling Capabilities Office within the Personnel & Readiness Directorate in the Office of the Undersecretary of Defense for Readiness, US Department of Defense. Contact him at [email protected]. Hossein Mokhtarian is a joint doctoral student in the Department of Mechanical Engineering and Industrial Systems at Tampere University of Technology and the University of Grenoble. Contact him at [email protected]. Faisal Mokammel is a doctoral student in the Department of Engineering Design and Production at Aalto University. Contact him at [email protected]. Kimmo Ikkala is a doctoral student in the Department of Mechanical Engineering and Industrial Systems at Tampere University of Technology. Contact him at [email protected].

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July/August 2016