An integrated principle solution synthesis method in multi-disciplinary mechatronic product conceptual design

Abstract

Synthesizing suitable principle solutions together to form the design solution is a universal method in conceptual design. For the modern mechatronic product, the conceptual design is often multi-disciplinary, which would be extremely time consuming and labour-intensive for designers to synthesize multi-disciplinary principle solutions together. Taking advantage of functional knowledge and structural knowledge of principle solution, this article proposes an integrated principle solution synthesis method which not only achieves the automated synthesis of multi-disciplinary principle solutions but also solves the undesired physical conflicts among principle solutions to be synthesized. In integrated principle solution synthesis, a synthesis agent is developed to chain the functional flows of principle solutions to form the combinatorial principle solution set, and synthesis agent selects the combinatorial principle solution with highest availability value as the recommended combinatorial principle solution. Then extensic theory is employed to deal with the partial design conflicts hidden in recommended combinatorial principle solution by extending and transforming the conflict functional structures. A case study on the emergency cutting off device design is given to prove the industrial applicability of integrated principle solution synthesis, which indicates that compared with traditional synthesis method, integrated principle solution synthesis can not only get multi-disciplinary design result of emergency cutting off device but also further resolve the design conflict (i.e. vibration impact) to optimize the functional structure of emergency cutting off device.

Keywords

conceptual design design conflict design synthesis mechatronic product principle solution

Introduction

Generally, the main process of mechatronic product conceptual design is to identify the functional structure of product through (a) decomposing the desired function following the divide-and-conquer principle (Eppinger and Ulrich, 1995; Yuan et al., 2016), (b) searching for suitable principle solutions (PSs) corresponding to decomposed functions (Beitz and Pahl, 1988) and (c) synthesizing these PSs together to form the whole design solution (Chen et al., 2012). This decomposition-aggregation strategy is a common practice for lean product development in product lifecycle management (Prasad, 2014). Conceptual design methods using these basic PSs assume the availabilities of basic PS and the decomposability of its functional description. Several studies have proposed different forms of basic PS, such as function basis (Cheong et al., 2011), function element (Lu et al., 2017; Prasad, 2001), basic physical principle (Žavbi and Duhovnik, 2001), solution patterns (Kruse and Shea, 2016), functional micro-knowledge cell (Li et al., 2010a) and function-to-form mapping (Kurtoglu and Campbell, 2009). These basic PSs, also called as building blocks, comprise the knowledge base for the new conceptual design. Different from classical functionally oriented conceptual design, in modern product design activities, designers have to consider other physical disciplines, for example, kinematic, electrical, chemical, thermodynamic and electromagnetic, to meet the requirements and constraints (Komoto and Tomiyama, 2012). This prompted designers to explore in wide multi-disciplinary solution spaces for finding novel and optimal PSs. Currently, most of multi-disciplinary conceptual design (MCD) researches are predominantly characterized by the sophisticated MCD modelling technique based on unified ontology. Commercial system tools, for example, Modelica (De La Cruz et al., 2017) and 20-Sim have been also developed to support MCD. Komoto and Tomiyama (2011) constructed an integrated MCD model which support the concurrent development of functional and parameter-level product descriptions and comprehensive evaluation of these descriptions from functional, parameter-level, structural, and behavioural aspects. Prasad (2014) proposed smartpart in lean product development, and the smartpart contains multi-disciplinary knowledge. Designers can configure the parameters of smartparts to satisfy new design constraints and aggregate these smartparts to build product solution.

Although the MCD modelling technique solves the problem of consistent representation of multi-disciplinary PS, the principle solution synthesis (PSS) process largely still depends on designers’ own knowledge and experiences. The manual design synthesis method could result in the difficultly of reasoning out creative solutions in multi-disciplinary design systems because designers, who are merely taught with knowledge about certain disciplines, often rely on the solution knowledge in familiar disciplines (Chen et al., 2014). From this point, the PSS method, which acrosses the boundary of engineering domains, is urgent in MCD application. In recent years, different PSS methods based on functional knowledge or structural knowledge have been proposed in mechatronic product conceptual design. Both of them have advantages and disadvantages, and the related works will be discussed in the following section. Different from previous studies, this article tries to make comprehensive use of functional knowledge and structural knowledge of PS and presents an integrated principle solution synthesis (IPSS) method for MCD to solve two problems in PSS stage: one is how to find the most useful PS for desired function requirements and another is how to handle the internal conflicts among selected PSs. The detailed information of IPSS and its application example are described in our article, and the breakdown of this research is divided into six sections. Section ‘Automatic PSS in conceptual design’ gives a brief review of PSS and puts forward the motivation of this research. Section ‘The representation of PS’ discusses the representation of PS in IPSS. Section ‘PSS and conflict resolution’ makes specification on IPSS method. And a case study is provided to make a feasibility analysis in section ‘Case studies’. Section ‘Conclusion and remarks’ makes conclusions.

Automatic PSS in conceptual design

In the computer-aided MCD modelling and reasoning of modern mechatronic product, the PSs in various disciplines can be captured as building blocks in knowledge base. However, it would be impossible for human designers to exhaustively synthesize different multi-disciplinary PSs together, since the design synthesis work would be extremely time consuming and labour-intensive in a large multi-disciplinary solution space. So automatically synthesizing multi-disciplinary PSs for desired functions still remains a challenging problem. Among PSS researches, the structure-oriented principle solution synthesis (SPSS) methods have been first proposed since 1990s, where PSs are represented as the basic physical elements for decomposed functions, for example, electro-mechanical elements and mechanical elements (Chiou and Sridhar, 1999). Then the synthesized result for devices can be generated in terms of the structural relationships among PSs. To handle the structural complexity and computational complexity in SPSS, Prasad (2001) proposed a systematization methodology in product realization through a four-stage process: planning, systematization, solution and unification. Although SPSS establishes the mapping relationships between functional design and structural design, they rely on domain-specific structural knowledge representation and reasoning rules. Moreover, SPSS is unable to synthesize some PSs from other disciplines (e.g. magnetic deflector, heat exchanger, and electromagnetic radiator).

At present, most of the PSS methods in MCD researches are function-oriented principle solution synthesis (FPSS), where the knowledge of PS primarily refers to a general relationship between the input and output functional flows, and FPSS methods follow the flow transformation-based philosophy. According to Beitz and Pahl (1988), the energy, matter and signal are the basic concepts in any design problem, and many FPSS studies (Kruse and Shea, 2016; Li et al., 2010b; Stone and Wood, 2000) consider the design synthesis process as the transformation of energy, material and signal flows among different PSs. However, Komoto and Tomiyama (2011) pointed out that some physical implementations have nothing to do with transformation of energy, material and signal (e.g. a function to fix connection between two mechanical components, a function that holds a position, and a function that keeps a constant speed). Other FPSS studies tried to parameterize the multi-disciplinary functional flows by using specific attributes. Chakrabarti (2004) used fixed attribute set and flow-naming taxonomy to represent the flow respectively, and Chen et al. (2012) proposed the dynamic attribute set to define the functional flow. Moreover, the agent technique has been introduced into FPSS researches (Chen et al., 2014; Ostrosi et al., 2012), where the design agent senses the input flow of desired function as the environmental flow and selects the suitable PS that can act on the environmental flow, and finally, the design agent employs the output flow of this PS as the new environmental flow for further PSS. Despite the easy operation of design synthesis, a main problem of FPSS is that its output design results are the combinations of physical principles which are often difficult for human designers to embody with physical components. An undesired physical phenomenon could be overlooked in the process of conceptual design synthesis, which often leads to design failures and decreases the efficiency of the entire product development process (Liu et al., 2012). For example, the cooling water could dilute nitric acid in primary conceptual design result of nitric-acid cooler, if PS, water cooling, is selected to reduce the temperature of nitric acid.

This article attempts to develop an IPSS method with a combination of PS functional and structural knowledge. Note that, this article is not only to achieve the automated synthesis of PSs but also more importantly to solve the undesired physical conflicts among PSs initiatively, which has not been appeared in other literatures. The conflict-resolving strategies of extensic theory, a conflict-resolving theory in the cross-disciplinary (Li et al., 2010b), are incorporated into the IPSS approach to deal with possible unexpected physical phenomena.

The representation of PS

The framework of PS

To perform IPSS method, there must be a formal approach for representing the design knowledge of known PS (He and Hua, 2017; Yuan et al., 2016). As mentioned before, the functional knowledge and structural knowledge of PS are utilized simultaneously in IPSS to satisfy the functional requirement and remove the design conflict in primary design result. Accordingly, the framework of PS is composed of two parts, that is, PS’s functional knowledge represented as multivariable functional flow (including input and output flows) and PS’s structural knowledge represented as hierarchical structural tree (including component and sub-components), as depicted in Figure 1.

Figure 1.

Framework of principle solution.

Representation of functional knowledge

Based on the dynamic attribute representation method (Chen et al., 2014), the functional flow in this study is represented with a combination of a standard name and a set of attribute values, expressed as: flow name {attribute 1: value; attribute 2: value; … }. A standard and taxonomy variable is used to standardize the flow’s name since a flow is probably given different names in different disciplines or by different domain experts. To avoid ambiguity, a flow name should correspond to a physical variable in physical science, so each flow name can correspond to a physical concept. For example, the physical variable names, linear_ motion, angular_ motion, electrical_current and linear_force, denote the names of flows, translation, rotation, electricity and thrust. The attribute-value pair is employed to describe the detailed features of a flow, and different kinds of flows may have different feature sets. For example, the translational motion flow can be explicitly defined as: ‘Linear_ Motion {stability: Constant; orientation: X; direction: To-and-Fro; intermittence: Continuous; type: Linear; field: Motion}’. The more detailed descriptions about dynamic attribute representation can be obtained from studies of Beitz and Pahl (1988) and Chen et al. (2014, 2016).

Representation of structural knowledge

A notion of top-down structural tree is introduced to describe the hierarchical structural knowledge of PS. Let S be the hierarchical structure, as shown in Figure 2, and its mathematical expression can be written as

\begin{array}{l} S = {S_{i}^{k} | k = 1, 2, \dots, N; i = 1, 2, \dots, N^{k}} \\ S_{i}^{k} = {S_{i, j}^{k} | j = 1, 2, \dots, N_{i}^{k}} \end{array}

(1)

where $S_{i, j}^{k}$ is the jth sub-structure of $S_{i}^{k}$ , and $S_{i}^{k}$ is the ith structure node in decomposition layer k. Thus, the identity of $S_{i, j}^{k}$ can be expressed as: $S_{i, j}^{k} = (k, i, j)$ . N is the number of decomposition layer, $N^{k}$ is the number of structure nodes in layer k, and $N_{i}^{k}$ is the number of sub-structures of $S_{i}^{k}$ .

Accordingly, the design knowledge of PS, which is integrated by function knowledge (denoted as F) and structural knowledge (denoted as S), can be expressed as follows

\begin{array}{l} P S = F \oplus S = (I^{F}, O^{F}) \oplus \\ {S_{i, j}^{k} | k = 1, 2, \dots, N; i = 1, 2, \dots, N^{k}; j = 1, 2, \dots, N_{i}^{k}} \end{array}

(2)

where $I^{F}$ and $O^{F}$ are the input and output functional flows of F, composed by standard flow names and attribute-value sets. $I^{F}$ can be used by IPSS to judge whether or not the PS can act on an input flow during the design synthesis process, and $O^{F}$ determines the possible values of the output flow’s attributes.

Figure 2.

The representation of hierarchical structural tree.

PSS and conflict resolution

PSS based on agent technique

The process of PSS

Referring to Blanco et al. (2016), Chen et al. (2014), Liu et al. (2012) and Ostrosi et al. (2012), this article employs agent technique to develop a synthesis agent (SA) to perform the multi-discipline PSS. The basic working mechanism of an agent can be regarded as an iterative sense-action process. At first, an agent senses its surrounding environment, and then, it selects a suitable action to change its state. The sense-action process will continue until its new state reaches the desired goal. In agent-based PSS process, the known PSs in the knowledge base is regarded as the agent’s action tools for transforming flows. The input flow of a desired function can be regarded as the SA’s initial environment, and the output flow can be regarded as the goal environment that it wants to reach. The SA’s aim is to find a set of PSs to transform it from the current environment to the goal environment. The exhaustive process of synthesis is briefly described as below:

Step 1: A designer inputs a desired function represented with input and output flows (including flow names and attribute values) and prescribes the maximal search depth to prevent SA from falling into an endless cycle;

Step 2: SA puts the desired input flow into its environment and defines the attribute values of desired input and output flows as the start condition and end condition, respectively;

Step 3: Through sensing its environment, the SA selects an environmental flow that has never been explored before and that does not exceed the maximal search depth, if successful, sets it as the current flow; else, goes to step 6;

Step 4: SA then selects all suitable PSs whose input flows matches the current flow and uses their functional knowledge about the relationships between input-output flows to release some new output flows;

Step 5: SA defines the output flows as new desired input flows and puts the new flows into its environment and then returns to step 3;

Step 6: SA selects a flow that satisfies the end condition of PSS from its environment; if successful, sets it as the current output flow for backtrack, and continue; else, goes to step 9;

Step 7: SA traces the flow-transforming path back from the desired output flow, with a result of a sequence of flows and a chain of PSs that enables such transformations. These selected PSs compose of the combinatorial principle solution (CPS) for desired function;

Step 8: SA removes this current output flow from its environment and returns to step 6;

Step 9: If there have been some CPSs generated, SA selects the most promising CPS from all candidates according to the pre-defined evaluation criteria and exits with success; else, exits with failure.

The evaluation of CPS

As stated above, a shortcoming of traditional agent–based PSS method is the generation of large number of candidate CPSs. It is impossible to pick out the best one from massive candidate CPSs through the human-computer interaction in complex product design. Moreover, as Prasad (2002) pointed out that in industrial applications, practical problems are much more complex and involve trade-off among multiple objectives, like time, cost, integrity, weight, performance and aesthetic considerations. In this article, we consider these objectives as evaluation criteria, so the selection of best CPS is carried out through the multi-criteria decision-making (MCDM) process, and the selected CPS is a compromise solution which takes into account different such objectives. We employ fuzzy technique ordered preference by similarity to the ideal solution (TOPSIS) algorithm, a sophisticated fuzzy MCDM method (Chang and Chen, 2014), to evaluate the alternatives and select the best one under conditions of uncertainty and imprecision, rather than depending on the designer’s subjective judgement.

Assume that, there are P CPSs generated by SA and Q evaluation criteria for CPS pre-defined by designer, then a fuzzy decision matrix $\tilde{D}$ can be constructed as follows

\begin{matrix} E_{1} E_{2} \dots E_{q} \dots E_{Q} \\ \tilde{D} = [\begin{matrix} {\tilde{e}}_{11} & {\tilde{e}}_{12} & \dots & {\tilde{e}}_{1 q} & \dots & {\tilde{e}}_{1 Q} \\ {\tilde{e}}_{22} & {\tilde{e}}_{22} & \dots & {\tilde{e}}_{2 q} & \dots & {\tilde{e}}_{2 Q} \\ \dots & \dots & \dots & \dots & \dots & \dots \\ {\tilde{e}}_{p 1} & {\tilde{e}}_{p 2} & \dots & {\tilde{e}}_{pq} & \dots & {\tilde{e}}_{pQ} \\ \dots & \dots & \dots & \dots & \dots & \dots \\ {\tilde{e}}_{P 1} & {\tilde{e}}_{P 2} & \dots & {\tilde{e}}_{Pq} & \dots & {\tilde{e}}_{PQ} \end{matrix}] \begin{matrix} CP S_{1} \\ CP S_{2} \\ \dots \\ CP S_{p} \\ \dots \\ CP S_{P} \end{matrix}, \\ \tilde{W} = [{\tilde{w}}_{1}, {\tilde{w}}_{2}, \dots, {\tilde{w}}_{q}, \dots, {\tilde{w}}_{Q}]^{T} \\ p = 1, 2, \dots, P; q = 1, 2, \dots, Q \end{matrix}

(3)

where ${\tilde{e}}_{pq}$ refers to a linguistic evaluation value of alternative $CP S_{p}$ with respect to criterion $E_{q}$ , which can be expressed in a triangular fuzzy number, that is, ${\tilde{e}}_{pq} = (e_{pq}^{L}, e_{pq}^{M}, e_{pq}^{H})$ , and ${\tilde{w}}_{q}$ is a linguistic important weight of $E_{q}$ , expressed as ${\tilde{w}}_{q} = (w_{q}^{L}, w_{q}^{M}, w_{q}^{H})$ . The values of ${\tilde{e}}_{pq}$ and ${\tilde{w}}_{q}$ are defined in Table 1, and the basic definitions of triangular fuzzy number can be obtained from studies of Wei et al. (2016).

Table 1.

The definition of ${\tilde{e}}_{pq}$ and ${\tilde{w}}_{q}$ for CPS.

Evaluation value ${\tilde{e}}_{pq}$				Important weight ${\tilde{w}}_{q}$
Linguistic variables	$e_{pq}^{L}$	$e_{pq}^{M}$	$e_{pq}^{H}$	Linguistic variables	$w_{q}^{L}$	$w_{q}^{M}$	$w_{q}^{H}$
Very poor	0	0	1	Very low	0	0	0.1
Poor	0	1	3	Low	0	0.1	0.3
Medium poor	1	3	5	Medium low	0.1	0.3	0.5
Fair	3	5	7	Medium	0.3	0.5	0.7
Medium good	5	7	9	Medium high	0.5	0.7	0.9
Good	7	9	10	High	0.7	0.9	1.0
Very good	9	10	10	Very High	0.9	1.0	1.0

To avoid the complicated normalization formula used in classical TOPSIS, the linear scale transformation is employed here to transform the various criteria scales into a comparable scale. Therefore, a weighted normalized fuzzy decision matrix $\tilde{X}$ can be figured out as follows

\begin{matrix} \tilde{X} = {[{\tilde{x}}_{pq}']}_{P \times Q} \\ {\tilde{x}}_{pq}' = {\tilde{x}}_{pq} (\times) {\tilde{w}}_{q} = (x_{pq}^{L} \times w_{q}^{L}, x_{pq}^{M} \times w_{q}^{M}, x_{pq}^{H} \times w_{q}^{H}) \\ {\tilde{x}}_{pq} = (x_{pq}^{L}, x_{pq}^{M}, x_{pq}^{H}) = {\begin{matrix} ((\frac{e_{pq}^{L}}{e_{p}^{H +}}), (\frac{e_{pq}^{M}}{e_{p}^{H +}}), (\frac{e_{pq}^{H}}{e_{p}^{H +}})), e_{p}^{H +} = max_{p} e_{pq}^{H} if E_{q} \in Benefit criteria \\ ((\frac{e_{pq}^{L -}}{e_{pq}^{H}}), (\frac{e_{pq}^{L -}}{e_{pq}^{M}}), (\frac{e_{pq}^{L -}}{e_{pq}^{L}})), e_{pq}^{L -} = min_{p} e_{pq}^{L} if E_{q} \in Cost criteria \end{matrix} \end{matrix}

(4)

Then, we can determine the fuzzy positive ideal solution of CPS (denoted as $CP S^{+}$ ) and fuzzy negative ideal solution of CPS (denoted as $CP S^{-}$ ) and get the distances of alternatives $CP S_{p}$ from $CP S^{+}$ and $CP S^{-}$ as

\begin{array}{l} C P S^{+} = ({\tilde{x}}_{1}^{+}, {\tilde{x}}_{2}^{+}, \dots, {\tilde{x}}_{q}^{+}, \dots, {\tilde{x}}_{Q}^{+}) {\tilde{x}}_{q}^{+} = (1.0, 1.0, 1.0) \\ C P S^{-} = ({\tilde{x}}_{1}^{-}, {\tilde{x}}_{2}^{-}, \dots, {\tilde{x}}_{q}^{-}, \dots, {\tilde{x}}_{Q}^{-}) {\tilde{x}}_{q}^{-} = (0.0, 0.0, 0.0) \\ d_{p}^{+} = d_{p} (C P S_{p}, C P S^{+}) = \sum_{q = 1}^{Q} d ({\tilde{x}}^{'}_{p q}, {\tilde{x}}_{q}^{+}) = \sum_{q = 1}^{Q} \sqrt{{(x_{p q}^{L} \times w_{q}^{L} - 1)}^{2} + {(x_{p q}^{M} \times w_{q}^{M} - 1)}^{2} + {(x_{p q}^{H} \times w_{q}^{H} - 1)}^{2}} \\ d_{p}^{-} = d_{p} (C P S_{p}, C P S^{-}) = \sum_{p = 1}^{Q} d ({\tilde{x}}^{'}_{p q}, {\tilde{x}}_{q}^{-}) = \sum_{q = 1}^{Q} \sqrt{{(x_{p q}^{L} \times w_{q}^{L} - 0)}^{2} + {(x_{p q}^{M} \times w_{q}^{M} - 0)}^{2} + {(x_{p q}^{H} \times w_{q}^{H} - 0)}^{2}} \\ \forall p = 1, 2, \dots, P \end{array}

(5)

where $d (\cdot, \cdot)$ is the distance measurement between two fuzzy numbers. Based on the $d_{p}^{+}$ and $d_{p}^{-}$ , an availability coefficient of $CP S_{p}$ is calculated to determine its ranking order among all CPS alternatives, that is

ac (CP S_{p}) = \frac{d_{p}^{+}}{d_{p}^{-} + d_{p}^{+}}, \forall p = 1, 2, \dots, P

(6)

where $ac (CP S_{p})$ is the availability coefficient of $CP S_{p}$ . Obviously, $CP S_{p}$ would be closer to $CP S^{+}$ and farther from $CP S^{-}$ if $ac (CP S_{p})$ approaches 1. So, the availability value can determine the ranking order of all CPSs, and indicates the best one as the recommended CPS among a set of given feasible CPS alternatives.

Conflict resolution based on extensic theory

The extending of conflict functional structures

Each PS has its own embodiment way from function to functional structure. Although the best CPS can be found out to satisfy the desired function, some partial design conflicts still exist in CPS from the perspective of functional structure, if each PS involved in CPS is used to establish the concrete structure system. For example, there is a conflict between PS1, nitric-acid transporting, and PS2, nitric-acid cooling, in nitric-acid cooler conceptual design because the cooling water from PS2 could dilute the nitric acid. Resolving those conflicts will guarantee the smooth performance of the design process. After the iteration of top-down comparing between sub-structures and design constraints by designers, the partial conflicts, which need further extension, will be identified. Then the extensic’s theory of resolving conflicts (Li et al., 2010b) is used to deal with these kinds of partial conflicts. According to the theory of extensic, the functional structure S can be described by matter-element R which is expressed as

\begin{matrix} R = {R_{i}^{k} | k = 1, 2, \dots, N; i = 1, 2, \dots, N^{k}} \\ R_{i}^{k} = (A_{i}^{k}, C_{i}^{k}, V_{i}^{k}) \end{matrix}

(7)

where $R_{i}^{k}$ is the child matter-element of R and is also the matter-element of $S_{i}^{k}$ . $A_{i}^{k}$ , $C_{i}^{k}$ and $V_{i}^{k}$ refer to the name, characteristic set and characteristic value set of $R_{i}^{k}$ , respectively. Moreover, according to the extensic theory, a matter-element may have many characteristics called one matter many characteristics, that is

R_{i}^{k} = (A_{i}^{k}, C_{i}^{k}, V_{i}^{k}) = [\begin{matrix} A_{i}^{k} & [\begin{matrix} c_{i, 1}^{k} & v_{i, 1}^{k} \\ c_{i, 2}^{k} & v_{i, 2}^{k} \\ ⋮ & ⋮ \\ c_{i, M}^{k} & v_{i, M}^{k} \end{matrix}] \end{matrix}]

(8)

where $c_{i, j}^{k}$ and $v_{i, j}^{k}$ $(j = 1, 2, \dots, M)$ are the jth characteristic and corresponding value of $R_{i}^{k}$ , and M is the number of characteristics of $R_{i}^{k}$ . This divergent nature of matter-element can help designer to change the original structure $S_{i}^{k}$ by changing the and $v_{i, j}^{k}$ .

Assuming that $\overset{\lor}{S_{i}^{k}}$ is the conflict functional structure which includes $N_{i}^{k}$ sub-structures and needs transformation, and T is an extendable transformation, the transformation process of $\overset{\lor}{R_{i}^{k}}$ is present as follows

\begin{array}{l} T (\overset{\lor}{R_{i}^{k}}) = T (\overset{\lor}{R_{i, 1}^{k}}, \overset{\lor}{R_{i, 2}^{k}}, \dots, \overset{\lor}{R_{i, N_{i}^{k}}^{k}}) \\ = (T_{1} (\overset{\lor}{R_{i, 1}^{k}}), T_{2} (\overset{\lor}{R_{i, 2}^{k}}), \dots, T_{N_{i}^{k}} (\overset{\lor}{R_{i, N_{i}^{k}}^{k}})) \end{array}

(9)

where $T_{1}, T_{2}, \dots, T_{N_{i}^{k}}$ is the extendable transformation which meets the design requirements. Moreover, according to the dependent principle of extensic, any active conversions $T_{α}$ of $\overset{\lor}{R_{i, g}^{k}}$ , will cause the compelled conversions $T_{β}$ of dependent $\overset{\lor}{R_{i, h}^{k}}$ , so the transformation T can be denoted as $T = [\begin{matrix} T_{α} \\ T_{β} \end{matrix}]$ . Let $\overset{\land}{R_{i}^{k}}$ be the resulting matter-element after conversions, the conversion process can be expressed as

\begin{array}{l} \overset{\land}{R_{i}^{k}} = T (\overset{\lor}{R_{i}^{k}}) = [\begin{matrix} T_{α} \\ T_{β} \end{matrix}] • [\begin{matrix} \overset{\lor}{R_{i, g}^{k}} \\ \overset{\lor}{R_{i, h}^{k}} \end{matrix}] \\ = {[\begin{matrix} T_{α} (\overset{\lor}{R_{i, g}^{k}}) & T_{β} (\overset{\lor}{R_{i, h}^{k}}) \end{matrix}]}^{T} = [\begin{matrix} \overset{\land}{R_{i, g}^{k}} \\ \overset{\land}{R_{i, h}^{k}} \end{matrix}] \\ = {(\overset{\land}{R_{i, g}^{k}} \cup \overset{\land}{R_{i, h}^{k}}) | j = 1, 2, \dots, N_{i}^{k}} \end{array}

(10)

During the transformation process, the reasoning knowledge of extensic is adopted, which includes not only the practical reasoning methods of the extension theory such as radiation, relationship, addition, deletion, substitution and so on but also includes the several regularities and rules in a special design field. After that, many viable solutions of $\overset{\lor}{R_{i}^{k}}$ can be found, and the expression is presented as

\begin{array}{l} \overset{\lor}{R_{i}^{k}} - | {[\begin{matrix} A_{i}^{k} & \begin{matrix} {C^{'}}_{i}^{k} & {V^{'}}_{i}^{k} \end{matrix} \end{matrix}], [\begin{matrix} A_{i}^{k} & \begin{matrix} {C^{″}}_{i}^{k} & {V^{″}}_{i}^{k} \end{matrix} \end{matrix}], \dots} \\ = | {[\begin{matrix} A_{i}^{k} & [\begin{matrix} {c^{'}}_{i, 1}^{k} & {v^{'}}_{i, 1}^{k} \\ {c^{'}}_{i, 2}^{k} & {c^{'}}_{i, 2}^{k} \\ ⋮ & ⋮ \end{matrix}] \end{matrix}], [\begin{matrix} A_{i}^{k} & [\begin{matrix} {c^{″}}_{i, 1}^{k} & {v^{″}}_{i, 1}^{k} \\ {c^{″}}_{i, 2}^{k} & {c^{″}}_{i, 2}^{k} \\ ⋮ & ⋮ \end{matrix}] \end{matrix}], \dots} = \overset{\land}{R_{i}^{k}} \end{array}

(11)

where $({C^{'}}_{i}^{k}, {V^{'}}_{i}^{k}), ({C^{″}}_{i}^{k}, {V^{″}}_{i}^{k}), \dots$ are the possible characteristic-value options to eliminate the design conflict of $\overset{\lor}{R_{i}^{k}}$ . Thus, by using various extendable strategies and extendable conversions based on reasoning knowledge, various contradictions and conflicts of the functional structures can be resolved by transforming from infeasibility to feasibility and from opposition to coexist (Li et al., 2010b).

The evaluation of extension functional structure

Following the extendable transformation of conflict functional structures, many new alternatives of $\overset{\land}{R_{i}^{k}}$ with different child matter-elements will be yielded. Similar to CPS evaluation, the selection of optimal functional structure has to be considered as different practical objectives (Prasad, 2002) to get a trade-off among multiple objectives, hence a hierarchical evaluation method for extension functional structures is presented, which is based on the availability coefficient computation of child matter-element as discussed in section ‘The evaluation of CPS’. The corresponding evaluation process is illustrated as follows:

Step 1: The evaluation standards of functional structure that comply with the design requirements are set up. Then the fuzzy decision matrix ${\tilde{D}}^{S}$ and weighted normalized fuzzy decision matrix ${\tilde{X}}^{S}$ for alternative child matter-element can be constructed. The definition of evaluation value in ${\tilde{D}}^{S}$ is displayed in Table 1.

Step 2: By using equations (4) to (6), the availability coefficient of each child matter-element can be figured out.

Step 3: The arithmetic average is used to integrate the availability coefficient of each child matter-element to get the availability value of resulting matter-element $\overset{\land}{R_{i}^{k}}$ .

The $\overset{\land}{R_{i}^{k}}$ with the highest availability value is chosen to enable the design solution meet the design requirements. The process of our proposed IPSS is similar to four-stage systematization process similar to that of a study by Prasad (2001), which pointed out that one or two iterations of design process would not lead to a good solution, as several of the constraints would be conflict. Thus, it may require some iterations of IPSS for complex product conceptual design.

Case studies

Searching suitable PS

To validate the IPSS method, we intend to design an emergency cutting off (ECO) device in top gas pressure recovery turbine (TRT) system. The main function of ECO device is to cut the blast-furnace coal gas in pipe rapidly to protect the whole TRT system when the pressure of coal gas is too high. Therefore, the desired input flow of ECO device can be represented as: ‘Force_Signal {stability: Variable; intermittence: Continuous; type: Force; field: Signal}’, while the desired output flow of ECO device is the shutting behaviour of this device, which can be represented as: ‘Boole_ Motion {stability: Variable; orientation: X or Y; direction: Clockwise or To-and-Fro; intermittence: Pulse; type: Boole; filed: Motion}’.

First, SA puts the desired input flow into its environment as an initial environment flow, and this flow is set as the current flow as well. Second, SA explores the knowledge base and searches the PSs whose input flows match the current flow. As a result, the PS pressure-sensor is selected as the suitable PS. Third, SA employs the functional knowledge of PS pressure-sensor to act on the current flow and gets an output flow ‘Digital_Signal {stability: Constant; intermittence: Pulse; type: Digital; field: Signal}’, according to the input–output flow pair of PS pressure-sensor. The output flow is considered as the new desired input flow and is put into SA environment again. Then SA finds the PS PLC-controller from knowledge base as the second PS, whose input flow and output flow are ‘Digital_Signal’ flow and ‘Electrical_Current’ flow, respectively. The output flow ‘Electrical_Current {stability: Constant; direction: positive; intermittence: Continuous or Step; type: DC; field: Electricity}’ is also put into SA environment. Later, SA continues to sense its environment until all environmental flows have been searched. When a flow is sensed as unsearched, SA will find eligible PSs to act on it, and the newly generated output flows will be added to its environment. Finally, when the above search process ends, SA will get all related flows through a backtracking process to form some CPSs. For example, SA can get the related flows and chain the corresponding PSs as a CPS, that is, ‘Pressure-sensor → PLC-Controller → DC-Motor → Stem-Plate’. If the maximal search depth is set as 5, then total eight CPSs (CPS1–CPS8) consist of eleven PSs (pressure-sensor, PLC-controller, DC-motor, electromagnetic-armature, fluid-pump, air-pump, piston-rod, magnet-plug, spring-plunger, gear-plate and stem-plate) are generated as shown in Figure 3, and the details of these PSs are listed in Table 2.

Figure 3.

The generation of CPS of ECO device design.

Table 2.

The PSs related to ECO device design.

	Principle solution	Input flow		Output flow
	Principle solution	Name	Attribue-value	Name	Attribue-value
1	Pressure-sensor	Force_signal	Stability: variableIntermittence: continuousType: forceField: signal	Digital_signal	Stability: constantIntermittence: pulseType: digitalField: signal
2	PLC-controller	Digital_signal	Stability: constantIntermittence: pulseType: digitalField: signal	Electrical_current	Stability: constantIntermittence: continuousType: DC or ACField: electricity
3	DC-motor	Electrical_current	Stability: constantDirection: positiveIntermittence: continuousType: DC>Field: electricity	Angular_motion	Stability: constantOrientation: X or YDirection: clockwiseIntermittence: continuousType: angularField: motion
4	Electromagnetic-armature	Electrical_current	Stability: constantDirection: positiveIntermittence: pulseType: ACField: electricity	Linear_force	Stability: constantOrientation: XDirection: to-and-froIntermittence: pulseType: linearField: force
5	Fluid-pump	Electrical_current	Stability: constantDirection: positiveIntermittence: pulseType: AC Field: electricity	Linear_force	Stability: constantOrientation: XDirection: to-and-froIntermittence: continuousType: linearField: force
6	Air-pump	Electrical_current	Stability: constantDirection: positiveIntermittence: pulseType: ACField: electricity	Linear_force	Stability: constantOrientation: XDirection: to-and-froIntermittence: continuousType: linearField: force
7	Piston-rod	Linear_force	Stability: constantOrientation: XDirection: to-and-froIntermittence: continuousType: linearField: force	Linear_motion	Stability: constantOrientation: XDirection: to-and-froIntermittence: continuousType: linearField: motion
8	Magnet-plug	Linear_force	Stability: constantOrientation: XDirection: to-and-froIntermittence: pulseType: linearField: force	Boole_motion	Stability: variableOrientation: XDirection: to-and-froIntermittence: pulseType: booleField: motion
9	Spring-plunger	Linear_motion	Stability: constantOrientation: XDirection: to-and-froIntermittence: continuousType: linearField: motion	Boole_motion	Stability: variableOrientation: XDirection: to-and-froIntermittence: pulseType: booleField: motion
10	Gear-plate	Linear_motion	Stability: constantOrientation: XDirection: to-and-froIntermittence: continuousType: linearField: motion	Boole_motion	Stability: variableOrientation: X or YDirection: clockwiseIntermittence: pulseType: booleField: motion
11	Stem-plate	Angular_motion	Stability: constantOrientation: X or YDirection: clockwiseIntermittence: continuousType: angularField: motion	Boole_motion	Stability: variableOrientation: X or YDirection: clockwiseIntermittence: pulseType: booleField: motion

PLC: programmable logic controller.

Selecting the best CPS

The latter step is to evaluate these CPSs to select the most suitable CPS under several uncertainty and imprecision criteria. In this example, considering the high temperature and high pressure working condition of ECO device, we first remove CPS1 whose PS DC-motor is not suitable for such condition, and CPS2–CPS8 are left to build up the candidate CPS set. Table 3 shows the linguistic evaluation values and crisp evaluation values of alternative CPSs with respect to four criteria, that is, shutting time, load leakage, pollution resistance and cost control, given by experienced designers. Each criteria has equal weights.

Table 3.

CPS2–CPS8 with respect to evaluation criteria.

	Principle solution chain	Shutting time (s)	Load leadage(ml/min)	Pollutionresistance	Cost control
CPS2	Pressure-sensor → PLC-controller → electromagnetic-armature → magnet-plunger	0.55	3.65	Good	Poor
CPS3	Pressure-sensor → PLC-controller → electromagnetic-armature → piston-rod → spring-plunger	0.3	2.6	Medium good	Medium good
CPS4	Pressure-sensor → PLC-controller → electromagnetic-armature → piston-rod → gear-plate	0.4	3.05	Good	Medium good
CPS5	Pressure-sensor → PLC-controller → fluid-pump → piston-rod → spring-plunger	0.8	4.3	Poor	Medium good
CPS6	Pressure-sensor → PLC-controller → fluid-pump → piston-rod → gear-plate	1	5.1	Medium good	Very good
CPS7	Pressure-sensor → PLC-controller → air-pump → piston-rod → spring-plunger	0.7	5.15	Very good	Medium poor
CPS8	Pressure-sensor → PLC-controller → air-pump → piston-rod → gear-plate	0.6	4.3	Very good	Medium poor

CPS: combinatorial principle solution; PLC: programmable logic controller.

From Table 3, we can construct the normalized fuzzy decision matrix $\tilde{X}$ . $\tilde{X}$ has both real numbers and triangular fuzzy numbers, expressed as

\tilde{X} = [\begin{matrix} 0.5455 & 0.7123 & (0.7, 0.9, 1.0) & (0.3, 0.5, 0.7) \\ 1.0000 & 1.0000 & (0.5, 0.7, 0.9) & (0.5, 0.7, 0.9) \\ 0.7500 & 0.8525 & (0.7, 0.9, 1.0) & (0.5, 0.7, 0.9) \\ 0.3750 & 0.6047 & (0.3, 0.5, 0.7) & (0.5, 0.7, 0.9) \\ 0.3000 & 0.5098 & (0.5, 0.7, 0.9) & (0.9, 1.0, 1.0) \\ 0.4286 & 0.5049 & (0.9, 1.0, 1.0) & (0.1, 0.3, 0.5) \\ 0.5000 & 0.6047 & (0.9, 1.0, 1.0) & (0.1, 0.3, 0.5) \end{matrix}]

(12)

Then we can calculate the distances of CPS2–CPS8 from $CP S^{+}$ and $CP S^{-}$ on four criteria, and get the availability value of each CPS finally. The corresponding results are shown in Table 4, from which CPS3 with highest availability value is considered as the most suitable solution for design requirement, that is, recommended CPS, and the functional structure of CPS3 is depicted in Figure 4.

Table 4.

CPS⁺ and CPS⁻ values of CPS2–CPS8 on evaluation criteria.

CPSs	Availabilitycoefficient	Total		Shutting time (s)		Load leadage (ml/min)		Pollution resistance		Cost control
CPSs	Availabilitycoefficient	CPS⁺	CPS⁻	CPS⁺	CPS⁻	CPS⁺	CPS⁻	CPS⁺	CPS⁻	CPS⁺	CPS⁻
CPS2	0.4320	0.8549	0.6503	0.1687	0.0603	0.0828	0.0430	0.0745	0.2134	0.2789	0.1155
CPS3	0.7445	0.4009	1.1684	00000	0.4306	0.0000	0.2451	0.1700	0.1155	0.1700	0.2309
CPS4	0.6843	0.4789	1.0379	0.0306	0.2316	0.0218	0.1208	0.0745	0.2134	0.1944	0.2309
CPS5	0.2333	1.1571	0.3521	0.3452	0.0047	0.1563	0.0100	0.2789	0.0000	0.1700	0.2309
CPS6	0.3388	0.9896	0.5071	0.4306	0.0000	0.2412	0.0000	0.1700	0.1155	0.0000	0.3916
CPS7	0.2754	1.1057	0.4203	0.2649	0.0200	0.2451	0.0000	0.0000	0.2789	0.3916	0.0000
CPS8	0.3554	0.9692	0.5344	0.1773	0.0553	0.1563	0.0100	0.0000	0.2789	0.3916	0.0000

CPS: combinatorial principle solution.

Figure 4.

The functional structure of CPS3.

Resolving design conflict

Although CPS3 is the best choice for ECO device design, it could also cause an unexpected vibration problem for the TRT system. This is because the electromagnetic-armature is used as the tool to drive the piston-rod, and it will produce large magnetic impact force instantaneously once it is electrified. The great impact from electromagnetic-armature could inevitably bring large vibration effect to ECO device and coal gas transmission pipe. Meanwhile, the inertia of spring-plunger movement could also cause the vibration, when the coal gas pipe is cut off instantly by the fast moving of the plunger. So, there are design conflicts existing in piston-rod and spring-plunger.

In order to make the CPS3 satisfy the vibration-resistant requirement, this article attempts to eliminate the conflict in piston-rod and spring-plunger by using conflicting resolution extensic theory. The initial design result of ECO device in terms of CPS3 can be described in the form of matter-element, expressed as

\begin{matrix} R_{1}^{1} & = [\begin{matrix} \begin{matrix} Emergency cutting off device \end{matrix} & \begin{matrix} Energy resource \\ Transfer medium \\ Energy control \\ Energy transfer \end{matrix} & \begin{matrix} Electromagnetic force \\ Air \\ Magnetic control switch \\ Piston — rod mechanism \end{matrix} \end{matrix}] \\ = {[\begin{matrix} R_{1, 1}^{1} & R_{1, 2}^{1} & R_{1, 3}^{1} & R_{1, 4}^{1} & R_{1, 5}^{1} & R_{1, 6}^{1} \end{matrix}]}^{T} \end{matrix}

(13)

R_{1, 1}^{1} = [\begin{matrix} Accessories & Air filter & Dry \\ Filter material & Non — woven \end{matrix}]

(14)

R_{1, 2}^{1} = [\begin{matrix} Piston — rod & Piston & Nonsupercharged type \\ Resource & Electromagnetic force \\ Rod & Common \\ Medium & Air \end{matrix}]

(15)

R_{1, 3}^{1} = [\begin{matrix} Spring — plunger & Spring & Compression \\ Actuator & Plunger \\ Bracket & Plunger barrel \\ Direction & To — and — Tro \end{matrix}]

(16)

R_{1, 4}^{1} = [\begin{matrix} Pressure — sensor & Range & 1 ~ 150 (MPa) \\ Output & RS 485 digital signal \\ Accuracy & \pm 0.1 % FS \end{matrix}]

(17)

R_{1, 5}^{1} = [\begin{matrix} PLC — controler & Working voltage & DC 24 (V) \\ Controler & PLC \end{matrix}]

(18)

R_{1, 6}^{1} = [\begin{matrix} Electromagnetic — armature & Solenoid & Mongline \\ Ferromagnet & Steel piston \\ Altemating current & 220 V \end{matrix}]

(19)

In the matter-element framework, the matter-element of piston-rod and spring-plunger are the conflict matter-elements. The extensible reasoning methods are used to enable the piston-rod and spring-plunger matter-elements to meet the vibration resistant. For piston-rod, through the radiation reasoning, two types of methods can be found to cushion the blow of plunger, one is to add the rapid responsive resistance and the other is to reduce the electromagnetic force. The concrete implementation strategies include regulating spring, introducing electrorheological effect, adjusting the intensity of electrical current and so on. Among them, the usage of electrorheological fluid under electric current to increase the responsive resistance of medium is a viable solution because it only changes the transformational medium in piston-rod from air to electrorheological fluid. So the matter-element of piston-rod is changed as

\begin{array}{l} \overset{\land}{R_{2}^{1}} = T (\overset{\lor}{R_{2}^{1}}) \\ = T [\begin{matrix} Piston — Rod & Piston & Nonsupercharged type \\ Resource & Electromagnetic force \\ Rod & Common \\ Medium & Air \end{matrix}] \\ = [\begin{matrix} Piston — Rod & Piston & Nonsupercharged type \\ Resource & Electromagnetic force \\ Rod & Common \\ Medium & Electrorheological fluid \end{matrix}] \end{array}

(20)

For spring-plunger, according to extensible substitution reasoning, the movement pattern of plunger is changed from to-and-fro to clockwise. In detail, the spring-shifter is employed to replace the spring-plunger, where the shifting fork only swings back and forth within limited scope to eliminate the vibration caused by the inertia of plunger, and the new matter-element of spring-shifter is represented as

\begin{array}{l} \overset{\land}{R_{3}^{1}} = T (\overset{\lor}{R_{3}^{1}}) \\ = T [\begin{matrix} Spring — Plunger & Spring & Compression \\ Actuator & Plunger \\ Bracket & Plunger barrel \\ Direction & To — and — Tro \end{matrix}] \\ = [\begin{matrix} Spring — Shifter & Spring & Compression \\ Actuator & Shifter fork \\ Bracket & Shifting fork box \\ Direction & Clockwise \end{matrix}] \end{array}

(21)

Moreover, there are always some relationships among the design matter-elements, so the active reasoning conversions of a certain matter-element will lead to the compelling conversion of some other related matter-elements. Because the medium of piston-rod is changed as electrorheological fluid, the corresponding matter-element of accessories will be changed by compelled conversion including the changing from air filtre to oil filtre and adding electrodes. So the matter-element of whole ECO device should be conversed as

\begin{matrix} \overset{\land}{R} = T (\overset{\lor}{R}) = {[\begin{matrix} T_{α} (\overset{\lor}{R_{2}^{1}}) & T_{β} (\overset{\lor}{R_{1}^{1}}) \end{matrix}]}^{T} \\ = [\begin{matrix} T_{α} [\begin{matrix} Piston — Rod & Piston & Nonsupercharged type \\ Resource & Electromagnetic force \\ Rod & Common \\ Medium & Air \end{matrix}] \\ T_{β} [\begin{matrix} Accessories & Air filter & Dry \\ Filter material & Non — woven \end{matrix}] \end{matrix}] \\ = [\begin{matrix} [\begin{matrix} Piston — Rod & Piston & Nonsupercharged type \\ Resource & Electromagnetic force \\ Rod & Common \\ Medium & Electrorheological fluid \end{matrix}] \\ [\begin{matrix} Accessories & Oil filter & Network \\ Oil box & Entirety \\ Filter material & Stainless steel wire \\ Electrodes & EDM 3 \end{matrix}] \end{matrix}] \end{matrix}

(22)

Generating final design result

After the conflict resolution process, the final design result of ECO device can be generated, as shown in Figure 5. When the pressure of coal gas pipe sensed by pressure-sensor is too large (>22 Mpa), pressure-sensor will send digital signal to PLC-controller, and PLC-controller could make electromagnetic-armature to be electrified to generate the electromagnetic force. Then the piston will be moved to drive the shifting fork to cut off the gas pipe. Meanwhile, the electrorheological fluid will be electrified as well, and it could produce damping force to reduce the vibration effect caused by magnetic impact force. By controlling the intensity of electrical current, the strengths of electromagnetic force and electrorheological force can be adjusted to make piston move with different speeds. It enables the shifting fork to slowly turn on, slowly cut off and quickly cut off. In Figure 5, the new components have different striped backgrounds.

Figure 5.

The design result of new emergency cutting off device.

Compared with classical PSS methods, the proposed approaches can not only get suitable CPS of ECO device from candidate CPSs but also further resolve the design conflicts hidden in CPS (e.g. vibration impact) to optimize the functional structure of design result. It illustrates that our proposed method can produce more acceptable and feasible design result than traditional methods.

Conclusion and remarks

To support the MCD, this article proposes an IPSS method which utilizes both functional knowledge and structural knowledge of PS. IPSS can not only get the suitable PSs to satisfy the desired function but also solve possible physical conflicts that could take place unexpectedly among different selected PSs. A case test of IPSS for ECO device design is carried out, and it shows that IPSS can not only successfully generate multi-disciplinary design result of ECO device but also eliminate the vibration effect problem in design result.

Today, customers want products optimized to their unique requirements in shorter time and attractive price. Product designers need to consider many variations of parts or features to quickly come up with innovative product. Dynamics of change requests and need for design reuse requires that such designs are ‘Responsive to Change’ (Prasad et al., 2010). Therefore, there are still several works to be done in future to tackle this challenge to quickly build different product concepts, although significant progresses have been made on automatic PSS of conceptual design in this article, such as the development of PSS based on multi-input and multi-output functional flows to improve the design synthesis speed, the research of automatic design conflict detection mechanism to reduce the manual intervention, and deploying similar power-copies in studies of Prasad et al. (2010) in our structure model to quickly generate new functional structure.

Footnotes

Declaration of conflicting interests

The author(s) declared no potential conflicts of interest with respect to the research, authorship and/or publication of this article.

Funding

The author(s) disclosed receipt of the following financial support for the research, authorship and/or publication of this article: This research is supported by the National Natural Science Foundation of China (Grant Nos.: 51675329 and 51605302), the National Key Scientific Instruments and Equipment Development Programme of China (Grant Nos.: 2016YFF 0101602 and 2016YFC0104104), and the National Social Sciences Fund of China (Grant No: 17ZDA020).

ORCID iD

Jin Qi

Author biographies

Jin Qi is an associate researcher at Shanghai Jiao Tong University. His research interests include knowledge-based design, case-based reasoning, and artificial intelligence. He is in charge of several national funded research projects.

Jie Hu is a professor at Shanghai Jiao Tong University. His research interests include artificial intelligence and its applications in engineering design. He has published over 80 Journal papers and 3 books.

Yinghong Peng is a professor at Shanghai Jiao Tong University. His research interests include knowledge-based engineering and its applications in manufacturing process. He has published over 200 Journal papers and 3 books.

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