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## Design science

Design is a fundamental activity directed toward the fulfilment of human needs. The activity of design, which is called Designing by Matsuoka [Matsuoka 2010], can be considered as the activity of building a set of specifications, and their evaluations, for the conception of a product or system. It involves creativity and decision-making. Creativity means the generation of alternative solutions and decision-making is the selection among these alternatives.

Hubka and Eder introduced Design Science as a system of logically related knowledge, which should contain and organize the complete knowledge about and for designing [Hubka and Eder 1996]. Matsuoka summarized the framework of Design Science by representing the design knowledge and designing (see Figure 2) [Matsuoka 2010]. Design knowledge consists of general objective knowledge and special subjective knowledge. Objective knowledge holds generalities that are independent of human’s preferences, while subjective knowledge depends on human’s preferences, opinions and interpretations. Designing is defined as an action to be pursued based on design knowledge. It is represented as a scale containing four layers: design practice, design method, design methodology, and design theory. Design theory expresses the generality of phenomena found in every design. Design methodology identifies the principles of how to apply a design method while a design method signifies specific procedures to integrate, analyze, or evaluate the phenomenon of a design object. Applying a design method produces new design ideas based on the designer’s previous knowledge. Design practice consists of actual practices conducted in various design domains like product design, architectural design, graphic design, etc. Compared to the other layers, design practice can be defined as the most specific and detailed layer [Sakae et al. 2016]. In the four layers scheme, specialty and dependence on the design object increase as the layer proceeds from a lower layer to a higher layer. In contrast, generality and abstractness increase as the design proceeds from the upper layer to the lower layer [Matsuoka 2010].

It may be noted that design theory considers the relationship between design elements which can be classified into two types: psychological design elements and physical design elements. The psychological design elements express the concept of a value that each user carries or a functionality and an image of a design object. The physical design elements consist of a measurable physical quantity and a physical property [Sakae et al. 2016]. For example, in the case of designing a vehicle, comfort and sense of fitting are defined as psychological design elements, whereas performance and material resistance are classified as physical design elements. Typically, in an industrial context, in the preliminary design phases, designers often interactively deal with psychological elements and physical elements, while in the late design phases, designers unidirectionally deal with physical elements [Sakae et al. 2018].

**Design Theory and Methodology (DTM)**

As an example of early Design Science, in 1946 Altshuller has introduced the Theory of Inventive Problem Solving, known as TRIZ (Teoriya Resheniya Izobretatelskikh Zadatch in Russian) [Altshuller and Altov 1996]. This theory comprises a set of sequential steps, invention support methods and tools that led to innovations in the fields of engineering [Altshuller 1999]; therefore, the TRIZ decision-making process is based on filtering non-acceptable solutions with a non-iterative process. In 1960, Herbert Simon also started a new scientific approach of design study by considering decision-making in design through an iterative process and not an event, aiming for rational process [Simon 1960].

In fact, the essence of rationality lies in the loops of the process, in the iterations and feedbacks, which must be numerous, between the three phases: Intelligence (problem finding) and Design and Choice (problem solving). Figure 3 shows Simon’s proposal for this iterative process as presented in [Tomiyama et al. 2009]. Since then, many design theories and methodologies have been proposed and developed, and the field of Design Theory and Methodology (DTM), which is a part of Design Science from Matsuoka point of view, has been intensively studied.

DTM is a rich collection of advances and knowledge resulting from studies and experiments on design processes and activities. Several classifications of DTM have been proposed by researchers [Finger and Dixon 1989a, 1989b; Tomiyama 1997]. Table 2 presents an adapted classification of DTM based on the Tomiyama classification. This classification is based on the scope of applicability (concrete/abstract) and level of abstraction (general/individual) of DTM. With the exception of abstract design theories, most of these DTMs are either a generalisation of design methods, and therefore may be applicable to a wide range of products, or computational methods that are only applicable to a specific class of products.

Within the abstract and general category, the most famous theory is the General Design Theory (GDT) which is a theory of design knowledge developed by Yoshikawa [Yoshikawa 1981; Yoshikawa and Uehara 1985; Tomiyama and Yoshikawa 1986; Reich 1995]. The GDT theory is in line with Suh’s axiomatic set theory [Suh 1990] in which design is defined as : “… the creation of a synthesized solution in the form of product, processes or systems that satisfy perceived needs though mapping between the functional requirements (FRs) in the functional domain and the design parameters (DPs) of the physical domain, through proper selection of the DPs that satisfy the FRs”.

However, design research cannot be limited to DTM [Finger and Dixon 1989a, 1989b; Horvath 2004]. Many other practices and techniques, such as the so-called Toyota Product Development System, are used in the industry [Sobek II et al. 1999; Morgan and Liker 2006]. Nowadays, in the industrial areas, V-model of Systems Engineering (SE) (see 3.2.2) became the standard approach, especially when dealing with multidisciplinary product development.

**Function-Behavior-Structure (FBS) ontology**

From the GDT framework, descriptive models of design processes have been derived. In 1990, Gero proposed his design ontology [Gero 1990; Gero and Rosenman 1990]. This design ontology extends GDT by taking into account the interactions between the designer and its environment. Gero’s aimed at unifying the whole design approaches by defining the being of design, the invariant of design or the ontology of design leading to a robust process. Gero’s design ontology is named FBS and describes three different concepts related to system design which are the Function (F), which corresponds to the purposes of the design being designed, Behavior (B), which are the attributes derivable from structure or expected structure, and Structure (S), which represents the elements of design and their relationships [Vermaas and Dorst 2007]. Figure 4 shows the eight elementary design steps of the FBS framework as described in [Gero and Kannengiesser 2004]. The term ontology comes from the Greek ontos meaning being, and logos meaning word [Breitman et al. 2007]. It is therefore a speech about becoming, existence and reality, in general. It has appeared in recent decades in the field of cognitive sciences and computer science. An ontology can take different forms, but it will necessarily include a vocabulary of terms and a specification of their meaning. Gruber defined ontology as an explicit specification of a conceptualization [Gruber 1993] which means that an ontology is a way of showing the properties and their relations, in a subject area, by defining a set of concepts and categories that represent the subject. According to Merril “ontological modeling in science is more fundamental than mathematical modeling since its result is the basic structure to which mathematical modeling is applied and on which theories are built” [Merrill 2011].

The FBS is considered as the ontos or the fundamentals of design since each system has structure and functions to achieve. According to Gero, there is no direct connection between function and structure. In fact, through experience, designers link function (F) to expected behavior (Be) by the formulation step (1). Then, the expected behavior is transformed into a solution structure (S) by a synthesis step (2). From this solution structure, an actual behavior (Bs) is derived by the analysis step (3). This actual behavior is evaluated (4) and compared to the desired behavior. If the evaluation is satisfactory, a design description D is documented (5) for manufacturing the product. Otherwise, designers have to iterate with previous steps in the sequence in order to reformulate (6, 7, and 8) structure variables, behavior variables and function variables.

The FBS ontology has been declined in processes (like OIA, discussed in 2.2.2.1) used in several design disciplines including engineering design [Collignan 2011; Quirante 2012], architectural design [Fontenelle and Bastos 2014] and computer aided design [Shih et al. 2017]. Yannou maps his Radical Innovation Design (RID) [Yannou 2015], which is a methodology supporting innovative design purposes, in the FBS framework [Yannou et al. 2018]. The FBS ontology has also been used to integrate and to analyze work situations during design phases [Sadeghi et al. 2017].

### Decision making in engineering design process

Engineering design is a process that engineers use to identify and solve problems. This process is a difficult and mandatory activity of the conception of complex products. Engineering design uses widely scientific principles and multi-physics domain interactions for simulation. The goal of the process is mainly to find at least one acceptable solution that responds to the multiple objectives demanded by the stakeholders of the design project, whereas candidate solutions belong to the set of all conceivable solutions. Candidate solutions are extremely numerous because of the combinatorial character of the design problem in nature.

Decision-making in selection between alternatives is then a crucial aspect of the design process. According to several researchers in design decision-making methods, the principal difficulty in design lies in the selection among design alternatives and not in the generation of alternatives [Okudan and Tauhid 2008; Tomiyama et al. 2009]. This difficulty is principally related to the opposite relationship between the numerous design objectives and the inherent uncertainties in the design process [Pahl and Beitz 1996].

Design problems are always Multi-Objective Optimization (MOO) problems. Theoretically, MOO problems have many solutions that respect constraints. Generally, the main issues to choose one solution in MOO are related to the accurate modelling of decision-makers’ judgments (preferences and priorities). As presented in Table 3, most MOO methodologies and techniques can be classified according to a priori, interactive or a posteriori preferences modelling [Korhonen et al. 1992; Marler and Arora 2004].

The a priori articulation of preferences makes it possible to solve the problem by integrating the modeling of the decision-makers’ judgments into the optimization process. The interactive approach articulates the decision-makers’ judgments during the optimization process, whereas the a posteriori approach integrates the decision-makers’ judgments only after the generation of a set of effective solutions like Pareto frontier which is an illustration of the Pareto optimality concept. Pareto’s optimality is discussed in 2.2.1.

In a priori formulation, preferences are introduced at different levels of the problem formulation, from the definition of objective functions to the definition of a global objective value. These new constraints reduce the number of degrees of freedom of the multi-objective problem to a single-objective problem. In addition, we aim at developing a decision-support tool which is an interactive design tool (see 4.7), where decision-makers are able to modify their preferences in order to see the consequences of their decisions directly and in an online mode. Therefore, the research work presented in this thesis falls within the scope of the a priori and interactive formulations.

**Pareto optimality**

Some problems can be formulated to correspond to a maximization (or minimization) problem of the observation variables, vector Y. In a single-objective maximization problem, the optimal solution would be the one that maximizes the single observation variable. In a multi-objective problem, the concept of optimality is therefore replaced by that of Pareto’s optimality.

In the case of maximization problems, a candidate solution X* is a non-dominated solution if there is no other solution X such as Y ≥ Y* i.e. there is not at least one observation variable such as yi > yi*. All non-dominated solutions define the Pareto frontier in the objective space. Pareto-optimal is the set of non-dominated solutions included within the feasible design space.

Figure 5 : Mapping between design space and objective space for a bi-objective maximization problem with two design variables (x) and two design constraints (g)

Figure 5 represents the mapping between design space – defined by the domain of values of x1 and x2 – and objective space for a bi-objective maximization problem with two design variables (x) and two design constraints (g). The Pareto frontier is represented in the objective space. The determination of the Pareto frontier is technically relevant in engineering since it represents the set of the most effective solutions among all possible candidate solutions. Visualization of this set of optimal solutions allows a better understanding of the behavior of the problem. In multi-objective problems, several mathematical and numerical methods focus on the search for the Pareto frontier. The Non-dominated Sorting Genetic Algorithm (NSGA-II) [Deb et al. 2002] is a leading algorithm in the field of multi-objective evolutionary optimization.

However, in practice, it appears that Pareto’s frontier is confusing to decision-makers because it contains too many solutions. More to the point, visualizing Pareto frontier is not really possible when facing problems where the number of objectives exceeds three.

**Morphogenesis, Observation, Interpretation, Aggregation (MOIA) ontology**

Figure 6: Mapping between MOIA models spaces

In order to illustrate the a priori and interactive formulations targeted in this manuscript, the proposed framework consists of design inputs, iterative design optimization and design output. The iterative design optimization is the core of the proposed framework, and it consists of four models Morphogenesis, Observation, Interpretation, and Aggregation. Figure 6 shows a mapping between the design, observation, interpretation and aggregation spaces. Between these spaces, models must be defined. The observation model, interpretation model, aggregation model and morphogenesis model correspond to simulation, normalization, weighting and generation respectively. All these models are discussed in detail in the following.

**Observation, Interpretation and Aggregation (OIA)**

OIA is a framework for design optimization activities that can be derived from the FBS ontology. OIA has been initiated and developed by the I2M team at the University of Bordeaux [Collignan 2011; Quirante 2012]. OIA combines three kinds of models, which are the observation (µ), the interpretation (δ) and aggregation (ζ) models. Figure 7 shows those models within the FBS framework:

– The structure (S) – to be designed – is defined by a set of design variables (X). The observation model (µ) allows computing the desired observation variables (Y), which define the actual behavior (Bs), from the set of design variables (X).

– The actual behavior (Bs) must be compared to the expected behavior (Be). The interpretation model (δ) is a satisfaction evaluation model that quantifies the degree of desirability (acceptability) of each observation variable and generates a set of interpretation variables (Z); it is based on design constraints and clients or designers’ expectations.

Figure 7: OIA within the FBS framework

– The design problem is always a multi-objective optimization problem. For solving this kind of problem, the optimization process passes through an aggregation of the interpretation variables (Z) in order to obtain a global desirability index (GDI) that must be maximized. The majority of multi-objective optimization methods do not use an explicit aggregation step and are satisfied with the localization of the set of optimal solutions (Pareto frontier). Faced with these confusion optimal solutions, decision-makers often make non-rational choices. The aggregation model (ζ) makes a selection rule among the set of possible solutions based on the decision makers’ preferences. Briefly, after the formulation of the observation, interpretation and aggregation models, OIA operates as a simulation/optimization/decision-support process giving a global desirability index (GDI) of a given design represented by design variables (X). GDI=ζ∘δ∘μ(X) (1)

The GDI is therefore an objective function of X. GDI has to be maximized to perform the optimization process. To find the optimal solution, an optimization algorithm is implemented. Figure 8 shows the global optimization process. The presented aggregation model aims at aggregating all the interpretation variables to compute the design objectives indexes (DOI) and from them, the global desirability index (GDI).

It is noticeable that, using this OIA approach, designing is regarded as a mono-objective optimization problem from a mathematical point of view. Indeed, the design constraints and objectives are aggregated in a single desirability index. The formulation of the design problem takes into account the flexibility of designers’ reasoning through both interpretation and aggregation functions. OIA covers many processes used by human experts in order to judge solutions and make a decision since the interpretation and aggregation functions can take many different forms.

In order to conclude, OIA integrates the observation model which corresponds to the system behavior, the interpretation and aggregation models which formulate designers’ preferences and the optimization which allows the exploration of the design space and study different design solutions (see 2.2.2.7). Each design optimization process must consider these fundamental steps; then, OIA is considered as the ontos or the fundamentals of optimization. For this reason, it is referred to as the OIA ontology in the following.

#### Observation model

In OIA, system, or candidate solution, is characterized by different values of the design variables X. The observation model (μ) is a simulation model of the system behavior that uses operational scenarios to compute the observation variables Y. Generally, these performances derived from the client specifications. They are required to support the decision-making process. These performances can be of different orders: cost, mass, volume, etc. Operational scenarios include all the information related to the context of the design such as the environmental parameters that describe the surrounding environment of the product like operating temperature, humidity, etc. The observation model is generally composed of physical, technical and economic models that compute the observation variables using simulation. One of the challenges today is how to deduce the appropriate observation model from the system specifications and constraints. [Sohier et al. 2019] propose a tooled approach based on MBSE models for the description of the system architecture and the concept of MIC (Model Identity Card) [Sirin et al. 2015] which allows to capitalize simulation models and make them available for the construction of the adapted observation model. Sohier et al. applied MIC on an autonomous driving application [Sohier et al. 2019].

**Interpretation model**

Interpretation is the process of verifying how well the values obtained from observation variables match the expectations and preferences of the decision-makers. Observation variables are always of different nature and always measured on different scales. Because of this, in order to obtain a single value that represents a candidate solution, Lawson mentioned that “Because in design there are often so many variables which cannot be measured on the same scale, value judgements seem inescapable” [Lawson 2006].

Desirability is a preference measurement which reflects the level of satisfaction achieved by the properties of a design according to the designers’ points of view. Desirability functions are non-dimensional, monotonous, or piecewise monotone functions. They express the level of satisfaction of designers on observation variables’ values. Their values are ranged in the interval [0, 1]. A desirability value of 1 means that the observation variable value is fully satisfactory in relation to the decision-makers’ expectations. A desirability value of 0 corresponds to a totally unsatisfactory observation variable value. This approach has been widely used in engineering design [Derringer and Suich 1980; Derringer 1994; Kim and Lin 2000; Réthy et al. 2004; Trautmann and Mehnen 2005; Kruisselbrink et al. 2009; Trautmann and Mehnen 2009; Chen 2011]. Different forms of desirability functions exist.

**Simon’s function**

In 1956, Simon introduced the name “satisficing” for this function, made from a combination of two words: “satisfy” and “sufficient” [Simon 1956]. In a context of maximization of the benefit of an action, even if all the information required is available, Simon mentioned that the human mind is not able to process information properly because the human mind is bound by “cognitive limits”. As a result, decision-makers are often inclined to accept the action completely (Extremely satisfied) or not at all (Not at all satisfied). Simon’s satisficing functions can be expressed as presented in Table 4.

It may be noted that by using Simon’s functions, there are usually a large number of fully satisfactory solutions or no solutions at all. The fully satisfactory solutions are not classified, then, an optimal solution is unfindable.

**Harrington’s function**

In 1965, Harrington introduced the concept of “desirability” and “desirability functions” to deal with multi-criteria optimization in quality engineering [Harrington 1965]. Table 5 presents the three functions proposed by Harrington. They are adapted to three different decision problems: maximization, minimization and targeting.

Harrington’s desirability functions have many advantages. Thanks to their exponential form, they have no discontinuities and they allow a progressive but strong variation of desirability when approaching − and +; Harrington called these values the Accurate Constraint value (AC) and the Soft Limit value (SL) for the maximization problem, for example. Since the two desirability values, = 0 and = 1, are never reached, it becomes possible to classify all design alternatives, including acceptable and unacceptable alternatives. The range between the two control points − and + is named satisfaction range in the following.

Harrington’s desirability functions appear to be relevant functions to interpret property’s values and models based on design requirements and designers’ expectations.

**Table of contents :**

**Chapter 1. General introduction **

1.1. Research motivations:

1.1.1. General context

1.1.2. Design process challenges

1.2. Research Objectives

1.3. Structure of the thesis

**Chapter 2. Design: State of the art **

2.1. Introduction

2.1.1. Design science

2.1.2. Design Theory and Methodology (DTM)

2.1.3. Function-Behavior-Structure (FBS) ontology

2.2. Decision making in engineering design process

2.2.1. Pareto optimality

2.2.2. Morphogenesis, Observation, Interpretation, Aggregation (MOIA) ontology

2.2.2.1. Observation, Interpretation and Aggregation (OIA)

2.2.2.2. Observation model

2.2.2.3. Interpretation model

2.2.2.3.1. Simon’s function

2.2.2.3.2. Harrington’s function

2.2.2.3.3. Derringer’s desirability function

2.2.2.4. Aggregation model

2.2.2.5. About the modelling of the interpretation and aggregation

2.2.2.5.1. Kolmogorov complexity

2.2.2.5.2. Ordinal and cardinal ranking

2.2.2.5.3. Parametrization of interpretation functions

2.2.2.5.4. Parametrization of aggregation functions

2.2.2.6. Determination of the weighting parameters

2.2.2.6.1. Analytic Hierarchy Process (AHP)

2.2.2.6.2. Adapted Failure Mode Effects and Criticality Analysis (FMECA)

2.2.2.6.3. Delphi method

2.2.2.7. Morphogenesis (Optimization algorithm)

2.2.2.7.1. Morphogenesis definition

2.2.2.7.2. The targeted solutions

2.2.2.7.3. Optimization algorithm

2.2.2.8. Stopping criteria

**Chapter 3. Integration of MOIA ontology into Systems Engineering **

3.1. Introduction

3.2. Systems Engineering (SE)

3.2.1. Model Based Systems Engineering (MBSE)

3.2.2. Global V-model

3.2.3. Local V-model

3.2.4. SCTO method

3.3. Integration of MOIA into MBSE

3.4. Substitution models

3.5. The optimization of ELM

3.5.1. Optimized-ELM algorithm

3.5.2. Test functions

3.5.3. Optimized-ELM vs random-ELM

3.5.4. Optimized-ELM vs test functions for the minimum search

3.6. Integration of ELM into MOIA

3.6.1. Dynamic optimization process

3.6.2. The practical perspective

**Chapter 4. Use cases **

4.1. Studied cases

4.2. Introduction

4.3. Electric vehicle powertrain case study

4.3.1. Main objective

4.3.2. Powertrain system specifications

4.3.3. Powertrain system architecture

4.3.3.1. Battery

4.3.3.2. Inverter and electric motor

4.3.3.3. Gearbox

4.3.4. Global EV simulation model

4.3.5. Design variables

4.3.6. Interpretation parameters

4.3.7. Aggregation parameters

4.4. A comparison with the sequential approach

4.5. ELM models

4.6. Numerical results using ELM

4.7. User interface

**Chapter 5. Acceptability of optimization **

5.1. Introduction

5.2. Participants

5.3. Materials and methods

5.3.1. Initial presentation

5.3.2. Questionnaire

5.3.3. Final presentation

5.4. Questionnaire results

5.5. Conclusion

**Chapter 6. Conclusion and perspectives **

6.1. Conclusion

6.2. Perspectives: Towards Intelligence Augmentation

**References **

Appendix I. Drone taxi

Appendix II. Questionnaire