Ya-Fan Dong

Peng Zhang

Run-Hua Tan

Wei Liu

Rui-Qin Wang

Jian-Guang Sun

Study on establishing Functional Periodicity of new products based on TRIZ

Keywords: Functional Periodicity, Automatic Innovation, New Products, Function Model, TRIZ

Functional periodicity plays an important role in the process of product automatic innovation for ensuring stable systems. But there is no method of establishing Functional Periodicity. In order to establish the functional periodicity of a new product, an existed product called the goal product is firstly chosen, if it is similar to the new product on aspects of function, effect or structure. Subsequently, difference between the new product and the goal product is identified by establishing the mapping relationship between the functional requirements and design parameters. Using the tools from TRIZ, the function model of the new product is formulated based on the above-mentioned mapping relationship. Afterwards, the system functional periodicity of the new product is proposed in form of TRIZ function model by combining the results of proposed function model and the relationship among functions. Finally, the feasibility of the proposed method is verified with a specific design case.

Introduction

The function is the core of the concept design in the process of product automatic innovation, and it is also the foundation of establishing functional periodicity. Suh [START_REF] Suh | On functional periodicity as the basis for long-term stability of engineered and natural systems and its relationship to physical laws[END_REF] (2004) put forward the concept of functional periodicity, which is an important way to reduce system complexity. Functional periodicity plays an important role in the process of product automatic innovation for ensuring stable systems. The product function analysis mainly includes the function structure and the function model based on TRIZ [START_REF] Tan | Innovation design-TRIZ:Theory of innovation problem solving[END_REF]. The problems existing in the system can be found out by these two methods. However, they can't help the designers to build the system functional periodicity.

The literature [START_REF] Altshuller | Creativity as an exact science: The Theory of the Solution of Inventive Problems[END_REF]- [START_REF] Lu | Product innovation design based on the theory of TRIZ and functional analysis[END_REF] verified that the function model is an important way to solve problems for the innovation. However, most of the studies improved the present products, not a new product. The literature [START_REF] Lee | Complexity theory in axiomatic design[END_REF] emphasizes that functional periodicity is the foundation for a system operating stability. The literature [START_REF] Zhang | Design model for the combinatorial complexity elimination process[END_REF] verified that func-tional periodicity is the most important way to reduce the system complexity and introduced several functional periodicity determination methods based on TRIZ. However, they did not put forward a method of a new product functional periodicity established.

The traditional function model based on TRIZ is applied to improve the existing system, not to develop a new product, not to establish functional periodicity. In this paper, according to function, effect or structure, a product is found out similar to the new product function, the structure or the effect. Namely, it is regarded as the goal product. Subsequently, difference between the new product and the goal product is identified by establishing the mapping relationship between the functional requirements and design parameters. Using the tools from TRIZ, the function model of the new product is formulated based on the above-mentioned mapping relationship. According to the improved function model and the relationship between each function, the system functional periodicity is determined. The process model of functional periodicity assisted by function model is set up for the new product development.

2

Time independent complexity and functional analysis

Time independent complexities

The complexity concept in axiomatic design theory is defined as a measure of uncertainty in achieving the desired set of functional requirements [START_REF] Suh | Complexity: theory and applications[END_REF] (see Fig. 1). The size of the complexity is directly determined by the relationship between the design scope and system range. It may be a constant, and also may be changing over time.

There are four different types of complexity, namely, time-dependent combinatorial complexity, time-dependent periodic complexity, time-independent real complexity and time-independent imaginary complexity [START_REF] Suh | Complexity: theory and applications[END_REF]. Time-independent real complexity is that the system range is not fully in the design scope. Namely, the area of the shaded part is uncertain in Fig. 1. It is real and does not change with time. Because the designer is not fully familiar with the product design, the system produces the uncertainty. Time-independent imaginary complexity isn't really system complexity.

Function analysis

The carrier of the function is the product. The manifestation of the product is the function. In the 1940s American engineer Myers [START_REF] Tan | Innovation design-TRIZ:Theory of innovation problem solving[END_REF] put forward the concept of the function at first and put it on the core problems of value engineering research.

The main advantages of the function analysis are as follows: (a) Through the function analysis, unnecessary parts can be found out and be eliminated completely; (b) Through the function analysis, a cheaper alternative material can be found to instead of some parts, and even the total product; (c) Through the function analysis, the original design can be improved; (d) Through the function analysis, some parts which manufacturing tolerance is too high often can be found.

Function analysis is mainly from the total function and then divided into two directions: the function structure and the function model based on TRIZ. (a) The function structure

The basis of the function structure is regarding product design as the conversion of substance, energy and signal. Starting from the total function to decomposition for each sub-function, the function structure is comprised of system sub-function, as shown in Fig. 2 [START_REF] Tan | Innovation design-TRIZ:Theory of innovation problem solving[END_REF]. The function structure is widely used in new product innovation and design. According to a total function, the function model is from the total system to subsystems, until the typical components. Then a verb is used in each element, with the different linear representative of the interaction between components, such as harmful effects or shortage effect. The function model is set up. Function model which includes super systems, systems and products mainly improves the existing product or system. But there isn't a method of function model for a new product or system.

Functional periodicity

Based on the complexity of the axiomatic design theory, functional periodicity is defined as a set of functional requirements [START_REF] Suh | Complexity: theory and applications[END_REF]. Function mentioned is a functional periodicity, but it is repeating a set of the same function, not only a time period.

Namely, that has a fixed time period. In Axiomatic Design Complexity Theory, functional periodicity types include time periodicity, geometric periodicity, biological periodicity, chemical periodicity [START_REF] Prokoph | Periodicities in the emplacement of large igneous provinces through the Phanerozoic: Relations to ocean chemistry and marine biodiversity evolution[END_REF][START_REF] Zhang | Rapid acquirement method for ideal result of system complexity[END_REF], thermal cycle, power cycle and material cycle 8 etc. Functional periodicity is a kind of characteristic of the natural system and the technical system. This is an essential characteristic of the stable system. It is the premise and foundation of the stable operation of the system 8.

To ensure systems operating stability, it is very important to establish the functional periodicity. Suh [START_REF] Suh | On functional periodicity as the basis for long-term stability of engineered and natural systems and its relationship to physical laws[END_REF] shows that functional periodicity is defined as the period set by repeating a set of function requirements. It is very important to establish the functional periodicity of the new product in the process of new product development. But there isn't a method of function model for a new product or system.

Determining process model of functional periodicity of a new product

According to the product functional requirements (FRs), the similar products are determined in the market at present; the mapping relationship [START_REF] Matt | Achieving operational excellence through systematic complexity reduction in manufacturing system design[END_REF] between the functional requirements (FRs) and design parameters (DPs) is established; then considering the difference between the design and present products, the mapping relationship between the functional requirements and design parameters is established. Based on the mapping relationship, the function model of the goal product is set up using TRIZ tools, such as the trimming [START_REF] Yu | Study on trimming priority based on system functional model study[END_REF], substance-field analysis, 76 standard solutions, etc., and a new product function model is gotten; According to the relationship between each function, the functional periodicity of a new product is determined. The concrete steps are as follows: I. According to user requirements, the target patent is determined. Through the analysis functional domain and the domain of the similar products, the mapping relationship between the functional requirements (FRs) and design parameters (DPs) is established.

According to the product design requirements and market studies, the product to be designed is still blank in currently. The function model of the new product can't be established directly. Therefore, the existing products similar to the designed product are found out. Namely, starting from the function, the effect and the structure, a product similar to the new product function, the structure or the effect is found, namely, it is regarded as the goal product. The function model of the target product is set up. According to similarity principle [START_REF] Gitlow | Innovation on demand[END_REF] [START_REF] Qi | Principles and Key Technologies of Mass Customization[END_REF], the similarity between the products has different forms, mainly including the following several aspects:

(a) Similar to the new product function: it refers to the similarity between the product or system function.

(b) Similar to the new product working principle: it refers to the similarity between the product or system working principle.

(c) Similar to the new product structure: it refers to the similarity between the product or system structure.

(d) Similar to the new product function and structure: it refers to the similarity between the product or system function and structure.

(e) Similar to the new product function and working principle: it refers to the similarity between the product or system function and working principle.

(f) Similar to the new product function, working principle and structure: it refers to the similarity between the product or system function, working principle and structure.

As long as a product meets the above anyone, it can be regarded as a similar product to the new product. Through the analysis functional domain and the domain of the similar products, the mapping relationship between the functional requirements (FRs) and design parameters (DPs) is established (see Fig. 3 9). II. Compared to the new product functional requirements and design parameters, the problem parameters are determined in the mapping principle. The mapping principle applied to the new product design requirements between the FR's and DP's is established.

Relative to the original design, the mapping relationship of the similar product is right. However, in order to apply to the design requirements of new products, some of the original design parameters may be changed. Therefore, the system will have some problems, such as a big bulk, complexity, missing some functions and so on. And then, the DPs would change into DP's (see Fig. 4). Compared to the new product functional requirements and design parameters and based on the mapping relationship of the similar product, the mapping principle applied to the new product design requirements between the FR's and DP's is established (see Fig. 4).

III.

According to the mapping relationship between the FR's and DP's, the function model which has some problems is established (see Fig. 5). It is based on the similar product. Analysis of problem function model established, designers introduce TRIZ tools, such as the trimming, substance-field analysis, 76 standard solutions, etc., and get a new product function model.

V. According to each function of the new product and the order of each function under working, the functional periodicity is determined.

According to the improved function model and the work order, the functional periodicity can be determined (see Fig. 6). Therefore, the design requirements and the stability of the system can be ensured.

Case study

Nowadays since the German government put forward the strategy of "Industry 4.0", countries gradually raised a global upsurge of "Internet+", including China. Our country also puts forward "made in China 2025". Under the background of a more and more rapid pace of life today, People prefer to nutrition improvement of a healthy diet. But now most of the people are doing all kinds of porridge according to their own subjective consciousness. Therefore, the auto-mixed system of porridge needs to develop urgently to substitute manual work. The product should be simple and convenient, meet the gradually rapid pace of the life and work, and satisfy people the different preferences of porridge. What's more, according to the special groups of customers (such as diabetes, etc.) requirements, it can provide the correctly kind of porridge. At the same time, application of "Internet +" concept, it can realize the remote control, and realize the customer to make an appointment. The auto-mixed system of porridge is rare at present. There are more vast development space and a broad market.

I. According to the calculation method of similar products, the ore automatic batching system in the patent CN202656318U [START_REF]ore automatic batching system[END_REF] is similar to the auto-mixed system of porridge in function. Through the analysis of the similar products, the mapping relationship between the functional requirements (FRs) and design parameters (DPs) of the ore automatic batching system in the patent CN202656318U [START_REF]ore automatic batching system[END_REF] is established. Currently existing batching system is composed of storage hopper, weighing hopper, weighing sensor, unloading conveyor belt, devices, etc. such as ore automatic batching system (see Fig. 7 [START_REF]ore automatic batching system[END_REF]), having a large volume and high precision requirements. At the same time, technology is not very mature and less finished products in the food industry. Through the analysis of the similar products, the mapping relationship between the functional requirements (FRs) and design parameters (DPs) of the ore automatic batching system in the patent CN202656318U [START_REF]ore automatic batching system[END_REF] is established (see Fig. 8).

The proportion of materials obtained

All the materials

MAterials mached

Blanking Transportation

The ratio value of materials DP0 FR0 Automatic Control II. Compared to the new product function requirements and the mapping principle of the ore automatic batching system, the control systems are complex and the size of device is too large. Therefore, the DPs of controls are changed into DP's. The mapping principle applied to the auto-mixed system of porridge design requirements is established (see Fig. 9).

The proportion of materials obtained

All the materials

MAterials mached

Blanking Transportation

The ratio value of materials A clutch is referenced. Therefore, a set of control systems is applied to complete control of multiple storage bins. The function model of the new product system is shown in Fig. 12. V. According to the relationship between each function, the new product functional periodicity is determined. In working condition, the stepping motor and the clutch are electrified at the same time. Block material A and B rotate simultaneously. When they arrive at the asymmetric feed opening of the material storehouse, electromagnetic clutch with power off, block material A stops rotating and block material B continues. When the aperture of block material A is obscured completely, the stepping motor stops running. Now blanking, materials are directly into the material box. When the expected regulation is achieved, stepping motor controls block material B inversion until keeping out the blanking round hole of block material A. At this point, the first time the material is completed. As repeating operation, the automatic batching of porridge is completed (see Fig. 14). Therefore, according to the order of each function under working, functional periodicity is determined (see Fig. 14). The cylindrical structure of the new product can be designed according to the function model shown as Fig. 14. A new product is innovated. The prototype model is shown as Fig. 15.

Conclusions

Based on TRIZ, the process model of functional periodicity for the new product is established. There are two major innovations as follows:

(1) The traditional function model based on TRIZ is applied to improve the present product, not a new product. This paper puts forward a new direction for a new product design.

(2) Functional periodicity is determined based on conflict and others except the function model. This paper puts forward the calculation method of similar products and verifies the process of a functional periodicity based on function model.

The paper describes the meaning of the function structure and function model based on TRIZ. Starting from function, effect or structure, the similar product is found. At the same time, according to the mapping principle between the FRs and DPs and the function model, it puts forward the method of a functional periodicity of the new product. The validity of the method is proved by "the auto-mixed system of porridge ". It provides a new direction and lays a foundation for the new product design and innovation.

Fig. 1 .

 1 Fig.1. The schematic diagram of the design scope and system range[START_REF] Suh | Complexity: theory and applications[END_REF]

Fig. 2 .

 2 Fig. 2. Product function structure (b)The function modelAccording to a total function, the function model is from the total system to subsystems, until the typical components. Then a verb is used in each element, with the different linear representative of the interaction between components, such as harmful effects or shortage effect. The function model is set up. Function model which includes super systems, systems and products mainly improves the existing product or system. But there isn't a method of function model for a new product or system.

Fig. 3 .

 3 Fig.3. The mapping relationship between the FRs and DPs[START_REF] Suh | Complexity: theory and applications[END_REF]

Fig. 4 .

 4 Fig. 4. The mapping relationship between the FR's and DP's

Fig. 5 .

 5 Fig. 5. The function model based on the similar product IV. Introducing TRIZ tools, the improved function model of the new product is set up.Analysis of problem function model established, designers introduce TRIZ tools, such as the trimming, substance-field analysis, 76 standard solutions, etc., and get a new product function model.V. According to each function of the new product and the order of each function under working, the functional periodicity is determined.According to the improved function model and the work order, the functional periodicity can be determined (see Fig.6). Therefore, the design requirements and the stability of the system can be ensured.

Fn+1Fig. 6 .

 6 Fig. 6. Functional periodicity determined by function model

Fig. 7 .

 7 Fig. 7. The ore automatic batching system schematic diagram

Fig. 8 .

 8 Fig. 8. The mapping relationship of the ore automatic batching system

Fig. 9 .

 9 Fig. 9. The mapping relationship of the auto-mixed system of porridge

Fig. 12 .Fig. 13 .

 1213 Fig. 12. The function model of new product systemUsing substance-field analysis and 76 standard solutions, a convex flange is introduced, with the shaft directly, and then meets the block material A to eliminate the harmful effect. At the same time, it can strengthen the block material A rotational stability. The overall effect is as shown in Fig.13.

Fig. 14 .

 14 Fig. 14. The diagram of functional periodicity of the auto-mixed system of porridge

Fig. 15 .

 15 Fig. 15. Prototype model

Acknowledgement Supported by National Natural Science Foundation of China (Grant No. 51675159), National Natural Science Foundation of China (Grant No. 51305123), and the National Science and Technology Basic Project (Grant No.2017IM040100).

III.

According to the mapping relationship of the auto-mixed system of porridge, the function model is established. It is based on the ore automatic batching system.

Through the analysis of system function model (see Fig. 10), a Material Storehouse needs a set of control systems, namely two Material Storehouses need two sets of control systems, so the equipment is complex, big volume and complicated operation. IV. Introducing TRIZ tools, such as the trimming, substance-field analysis, 76 standard solutions, etc., the improved function model of the new product is set up.

The valve 1 is similar to the valve 2 and so on (see Fig. 10). Therefore, considering the principle of trimming, the control valves are regarded as trimming objects [START_REF] Bariani | A combined DFMA and TRIZ approach to the simplification of product structure[END_REF] [START_REF] Wang | Design of multi-function blade clean-polishing machine based on TRIZ theory[END_REF] (see Fig. 11).


L

  'archive ouverte pluridisciplinaire HAL, est destinée au dépôt   Distributed under a Creative Commons Attribution| 4.0 International License A Creative Design Approach Based on TRIZ and Knowledge Fusion Wei Liu, Run-Hua Tan, Ya-Fan Dong, Guozhong Cao, Limeng Liu To cite this version: Wei Liu, Run-Hua Tan, Ya-Fan Dong, Guozhong Cao, Limeng Liu. A Creative Design Approach Based on TRIZ and Knowledge Fusion. 18th TRIZ Future Conference (TFC), Oct 2018, Strasbourg, France. pp.167-179, 10.1007/978-3-030-02456-7_14. hal-02279771


Davide Russo

Pierre-Emmanuel Fayemi

Matteo Spreafico

Giacomo Bersano

Design Entity Recognition for Bio-inspired Design Supervised State of the Art

scientifiques de niveau recherche, publiés ou non, émanant des établissements d'enseignement et de recherche français ou étrangers, des laboratoires publics ou privés.


Justus Schollmeyer
email: justus@secondnegation.com

Viesturs Tamuzs
email: viesturs.tamuzs@gmail.com

Discovery on purpose? Toward the unification of Paradigm Theory and the Theory of Inventive Problem Solving (TRIZ)

Keywords: ARIZ, Paradigm Shift, Science

This essay relates Thomas Kuhn's Paradigm Theory with Genrich Altshuller's Theory of Inventive Problem Solving (TRIZ for short). Despite their clearly divergent cultural roots, both understand paradigm shifts as the result of problem-solving processes -Kuhn in science and Altshuller in technology. In contrast to Kuhn, Altshuller used paradigm shifts to study creative problem solving in technology in order to make invention on purpose possible. He summarized his finding in the Algorithm of Inventive Problems Solving (ARIZ), which, as we will show, can be made explicit in a more general system theoretical framework. This allows for its application outside of the technological domain without relying on crutches such as metaphorical analogies. In order to demonstrate the application of this generalized version of ARIZ, we reconstruct one of the most famous paradigm shifts in the history of science -the shift from the Ptolemaic geo-centric system to Copernicus' helio-centric one.

Introduction

From an epistemological point of view, Genrich Altshuller's Theory of Inventive Problem Solving -TRIZ - [START_REF] Altshuller | Creativity as an exact science: the theory of the solution of inventive problems[END_REF] is built upon four crucial decisions:

• (i) Technological objects are viewed from a system perspective.

• (ii) The focus of attention is on the development of these objects as systems.

• (iii) The development is studied in terms of concrete changes within the inner-systemic hierarchy.

• (iv) These changes are reconstructed as if they were the results of intentional problem solving.

Altshuller assumed that studying the development of technological systems in this way could serve as a suitable window into the black box of creative problem solving. What is more, he showed that a clear understanding of the logic that underlies these processes can make creative problem solving teachable. The further TRIZ developed, the more the character of Altshuller's epistemological decisions crystalized. This can be best appreciated by following the roughly 30-year development of the Algorithm for Inventive Problem Solving -starting in 1956 and ending in 1985 -with Altshuller's final version: ARIZ-85C [START_REF] Fey | Innovation on demand[END_REF]. In contrast to the earlier versions [START_REF] Altshuller | About Technical Creativity (In Russian)[END_REF], the latest has almost entirely stripped off any reminiscence of its original domain: technology. Only a few terms, such as "tool," are reminiscent of the engineering discourse. Upon closer examination, however, they turn out to be placeholders for more abstract vocabulary concerning systems in general. We will call it vocabulary for systemic thinking.

The goal of our paper is to bridge the gap between the application of ARIZ in technology and other domainsparticularly science. To do so, we will develop the vocabulary of systemic thinking as far as it is needed to express the ! 1 structure of ARIZ in more general terms. Then, we will address development in science much as Altshuller addressed 1 development in technology. For this purpose, we introduce Thomas Kuhn's famous three phase distinction of prenormal, normal and revolutionary science [START_REF] Kuhn | The Structure of Scientific Revolutions[END_REF] and draw the attention to Altshuller's distinction of two different types of scientific discoveries -new explanations and new detections [START_REF] Altshuller | How to discover? Thoughts on the methodology of scientific work[END_REF]. After matching Kuhn's distinction with Altshuller's, we will limit our attention to the application of ARIZ to explanatory discoveries alone. Having outlined to which extent explanations can be understood as explanatory systems, we will finally apply ARIZ, in its system theoretical form, to one of the most famous paradigm shifts in the history of science: the transition from the Ptolemaic to the Copernican planetary system. We conclude with suggesting the unification of both paradigm theory and TRIZ within a system theoretical framework. Since the goal of our paper is to show why and how ARIZ can be used in science, we will say very little about its application to technology. For a deeper understanding, we recommend the study of Altshuller's own example [START_REF] Fey | Innovation on demand[END_REF][START_REF] Bukhman | TRIZ: Technology for Innovation[END_REF].

Elements of a Vocabulary for Systemic Thinking

Systems can be described as finite sets of elements that are organized according to certain rules. These elements stand in relation to one another such that the system is more than the mere sum of its parts. The set that comprises the set of all elements of a system and the set of all the relations between them is called the system structure. While this structure determines the system's (context-dependent) behavior -i.e., the set of all of its states over time -, the same behavior might be realizable by alternative system structures [START_REF] Hubka | Theory of Technical Systems[END_REF].

That the concept of systems is primarily a pragmatic methodological category that helps to describe, explain and control subjects of our interest can be seen from the way the term element is used. Whether or not it is convenient to consider an element of a system to be (i) elementary and not in the need for further decomposition or (ii) itself a system with its own system structure depends upon the pragmatic context of the analysis. An element of a system S that has its own system structure is called a sub-system of S. In return, a system S that has another system S' as one of its elements, is called a super-system of S'.

From a subjective standpoint, a system's behaviour -or parts of it -can appear to be desirable or undesirable in certain contexts. Although most artificial -i.e. human-made -systems are designed for a purpose that is desired by someone, parts of their behaviour can be undesirable. A purpose can be described as a hierarchically ordered system of aims [START_REF] Hubka | Theory of Technical Systems[END_REF], where primary aims can be distinguished from secondary ones. Primary aims are expressed in the form of answers to the question of what the system was designed (or put into place) for, while secondary aims play an auxiliary role. The latter are either means to the end of achieving other aims, or they express a certain desirable behaviour of the system -for example, the elimination of some undesirable side-effect. Thanks to their system structure, systems have the capacity to achieve primary and secondary aims. A system's capacity to achieve a primary aim will be called a primary function of the system and its capacity to achieve a secondary aim a secondary function. Note that, according to this definition, the term function is only used for capacities that are considered desirable (which does not exclude the possibility that the enabling structure might be the cause for effects that are considered undesirable). As a consequence, a change in the structure of a system that results in the loss of a function without further compensation yields undesirable effects (since a desirable effect can be understood as the negation of an undesirable effect).

At first sight, it might seem that a similar effect could be achieved by comparing the TRIZ-specific ontology with the specific 1 ontology of the target domain. This, however, would only forge the foundation for an application of TRIZ in this specific target domain. In contrast to this strategy, we claim that TRIZ is itself an application of a more general framework of system thinking in the field of technology. Its ontology can be seen as an effect of this application. By spelling out this general way of thought, we hope to provide a framework for its application beyond the technical sphere.

! 2

The phenomenon of pragmatic relativity that shows in the use of the term element also applies to the distinction between the terms primary function and secondary function. On the one hand, the primary function of a system might only be a secondary function when viewed from the perspective of its super-system. On the other hand, a sub-system might only be in charge of a secondary function within a wider system. However, when only looking at the very same sub-system, the former secondary function might turn out to be the primary function. 2 Sub-systems (or elements) that provide a primary function will be called primary sub-systems and those providing secondary functions will be called secondary sub-systems.

Thomas Kuhn's Distinction of Pre-normal, Normal and Revolutionary Science

Having developed the vocabulary needed to view Altshuller's approach from a systemic perspective we can now turn our attention towards the concept of development by building upon Thomas Kuhn's Structure of Scientific Revolutions [START_REF] Kuhn | The Structure of Scientific Revolutions[END_REF]. Summarising the findings from his studies in the history of science, Kuhn describes a pattern of evolution in science by distinguishing three phases: (i) Pre-Normal Science, (ii) Normal Science, and (iii) Revolutionary Science. Drawing on the tradition of American pragmatism, Kuhn explains these three different phases in terms of different types of problem solving. During the first phase, it is not yet clear how to best frame the problem. Consequently, different schools develop their own explanatory strategies, which compete with one another until an explanatory paradigm is developed that outcompetes alternative approaches such that researchers now rely on this paradigm when coping with the problems in their field. Kuhn calls this phase normal science. For example, when the Ptolemaic model was established, the European history of astronomy entered such a phase of normal science. By sticking to this paradigm, astronomers were able to solve well-defined problems, such as predicting the position of certain vagabonds at a given time (vagabonds was the term for moving celestial bodies at this time). Accordingly, one major parameter for the model's improvement was the accuracy of predictions. Among other things, the vagabonds moving on spheres around the Earth were themselves placed on further spheres in order to account for the appearance of planets moving backward.

The more the model's accuracy was improved, the more obvious an internal contradiction in the model became: minor improvements in accuracy caused major deterioration in simplicity, even though full accuracy could not be achieved.

When the Ptolemaic geo-centric paradigm was replaced by Copernicus' heliocentric one, the model's simplicity improved dramatically. Kuhn calls such replacements paradigm shifts. They are the result of problem-solving processes This relativity of the terms primary and secondary function points to a deeper problem in approaches of systemic functional analysis 2 in non-artificial systems such as [START_REF] Cummins | Functional Analysis[END_REF] and [START_REF] Machamer | Thinking about Mechanisms[END_REF]. Analyzing an object as a system is, in the first place, a methodological choice made by an inquiring subject for the sake of explaining some phenomenon. What the roles of a system's parts are (and the way in which these parts are individualized, too) partly depends on the explanatory choice of the inquiring subject. Take for example a human's heart: If we choose to consider its role in the context of blood circulation, we will conclude its role is to pump blood. If, however, we want to explain the entire sound spectrum in human bodies, the role of the heart will consist in creating a more or less rhythmical beat. This criticism of arbitrariness in systemic approaches has been prominently articulated by proponents of etiological theories [START_REF] Wright | Functions[END_REF][START_REF] Neander | The Teleological Notion of 'Function[END_REF]. Moreover, etiologists argue that because of its dependency on subjective explanatory choices, systemic functional analysis cannot account for the normative dimension of proper functioning. In other words, whether or not a system's part works well cannot be judged on the basis of systemic approaches alone. All they explain is how the system actually behaves. Whether or not a heart, for example, beats too quickly or too slowly, too much or too little, exceeds the limits of the explanatory framework. As a consequence, the value judgement becomes again a matter of subjective consideration. Etiologists try to solve both of these problems by including the dimension of history into their understanding of functionality. Looking for the proper function of some part P in a system S, they argue, means to ask the question: How come that P is a part of S? Take for example a breathing apparatus that contains a filter. One could ask: How come this filter is part of the breathing apparatus? Moreover, they argue it can be said that the proper function of P in S is the effect E if and only if P was selected to be a part of X, because of having the effect E in X. In the breathing apparatus, the proper function of the filter is to filter the air just because the designer of the breathing apparatus put it in for the sake of achieving exactly this effect. In engineering this selection implies conscious decision-making, while it is a matter of natural selection when it comes to biological systems [START_REF] Neander | The Teleological Notion of 'Function[END_REF]. In other words, the proper function of the heart -to pump blood -, etiologists would argue, is the effect for the sake of which it has been picked by natural selection. Note that this framework also allows to assign multiple proper functions to a system's part in case that this part was selected for multiple effects (for a more detailed discussion of this debate see [START_REF] Gayon | Do biologist need the concept of function? Philosophical perspectives[END_REF]).

! 3 during the phase of revolutionary science and foster a redefinition of a discipline's paradigm, yielding a new phase of normal science.

Discoveries as Detections or Explanations

During all three phases, scientists aim at producing knowledge -some of it being called discovery. As Altshuller points out in a paper on creative problem solving in science [START_REF] Altshuller | How to discover? Thoughts on the methodology of scientific work[END_REF], the term "discovery" refers to two different phenomena: new detections and new explanations. Explanation as purposeful practice is crucial for science and faces different kinds of challenges during each of Kuhn's three phases. During the phase of pre-normal science, there is no established paradigm that the explanation could draw upon. For this reason, scientists need to come up with their own groundbreaking approaches. This leads to competition between various attempts. In the phase of normal science, when paradigms have been established for the vast majority of scientists, explanation consists in the application of such established paradigms. During the phase of revolutionary science, however, a standard paradigm is challenged by a new and presumably superior way of explanation that can, for example, account for anomalies that were not explicable by means of the former.

Unlike the development of most explanations, detection of something new can be the result of both purposeful action and lucky coincidence. Here again, the nature of each of these two types of detection differs during the three phases of pre-normal, normal, and revolutionary science. Matching Altshuller's three types of discovery with Kuhn's three phases allows us to set up a 3 by 3 matrix (see Table 1). It illustrates nine different types of discoveries with examples from the history of science. While all of these matter for development in science, we will limit our focus in this paper to the last row, which covers explanation.

In the next chapter, we will give an example of how explanations can be viewed as explanatory systems and thereafter apply ARIZ to reconstruct in hindsight the respective paradigm shift from a problem-solving perspective.

Discoveries that are new detections can be viewed similarly by studying them as experimental systems. This, however, goes beyond the scope of our paper.

Detections by accident

A phenomenon is accidentally detected during research in a field for which no dominant paradigm has yet been established.

While doing research in the tradition of an established paradigm, anomalies are detected that cannot be explained.

The established paradigm is already challenged, while an unexpected phenomenon is unintentionally detected.

Example: While conducting experiments with a dissected frog nearby an electrical machine, Luigi Galvani's assistant accidentally touched an inner nerve with a scalpel so that the frog's limbs twitched. A debate with at least three competing schools arose [START_REF] Whittaker | A History of the Theories of Aether & Electricity: Two Volumes Bound as One[END_REF].

Example: Experimenting with air, Lord Rayleigh and Sir William Ramsay found out that the nitrogen extracted from the air was by 0.5 % heavier than the chemically produced element.

Looking for the cause, they discovered Argon [START_REF] Rayleigh | Argon, a New Constituent of the Atmosphere[END_REF].

Example: Heike Kamerlingh Onnes synthesized liquid Helium, then studied current flows at low temperatures, discovered superconductivity and detected what has later been studied under the name super-fluidity [START_REF]This Month in Physics History -January 1938: Discovery of Superfluidity[END_REF].

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When it comes to studying creative problem solving in science, the focus of attention is to be put on the creation of new kinds of explanations that either yield a shift from the pre-normal phase to the normal phase or successfully end a revolutionary phase.

Scientific Explanation as System

Equipped with the above definition of system and the brief excursion into the history of science, the difference between technological objects and scientific explanations can be outlined on a common ground. Technical objects can be viewed as artificial systems (a) insofar as they are designed for certain purposes, and (b) insofar as they can be decomposed into functional parts. (c) If one of these parts was missing, actual or potential undesirable effects would arise within the system or its context (at least if the part's function was not somehow compensated or made irrelevant). Scientific explanations or theories, in return, can also be viewed as artificial systems [START_REF] Gayon | Do biologist need the concept of function? Philosophical perspectives[END_REF][START_REF] Whittaker | A History of the Theories of Aether & Electricity: Two Volumes Bound as One[END_REF] -at least (a) insofar as they are designed for explaining something in certain contexts (explanatory purpose), and (b) insofar as they can be decomposed into functional parts. (c) As mentioned before, parts are functional if taking one of them out results in effects that are undesirable in some context. In the case of scientific explanation, these effects most often turn out to be epistemic in nature. Potential sub-system-system-super-system relations can be found in both the technological and the epistemic context.

Detections on purpose

There is no paradigm that can explain a phenomenon that was detected as the result of purposeful experimentation.

Investigation of a phenomenon, for which the established paradigm suggests a certain outcome.

The established paradigm is already challenged and based on a new paradigm a heretofore undetected phenomenon is detected on purpose Example: Michael Faraday experimented with electric currents and magnets in order to determine the laws of induction of currents, which resulted in the detection of phenomena of electro-magnetism [START_REF] Whittaker | A History of the Theories of Aether & Electricity: Two Volumes Bound as One[END_REF].

Example: Based on his general theory of relativity, Albert Einstein predicted gravitational waves in 1916 (Einstein, 1916).

When his theory became accepted, scientists started to look for these waves. In 2015, they were finally detected [START_REF] Collins | Gravity's Kiss: The Detection of Gravitational Waves[END_REF].

Example: In 1915, Albert Einstein predicted the bending of light by the gravity of the sun. Sir Arthur Eddington and his team took advantage of a total solar eclipse in 1919, detected the deviation and contributed to the acceptance of Einstein's General Theory of Relativity [START_REF] Dyson | A Determination of the Deflection of Light by the Sun's Gravitational Field, from Observations Made at the Total Eclipse of May 29, 1919[END_REF].

Explanations on purpose

In the absence of an existing paradigmatic way of explaining certain phenomena, attempts of explanation are undertaken.

Phenomena are explained with the help of an established paradigm.

The established paradigm is challenged by a new paradigm that claims to be superior.

Example: In the early days of studying phenomena of electricity, a group of theories existed that considered attraction and factional generation as fundamental electrical phenomena [START_REF] Kuhn | The Structure of Scientific Revolutions[END_REF] Example: The paradigm of covalent bonds allows for explanation of a compound's chemical properties even if this substance has not yet been synthesized.

Example: Nikolas Copernicus challenged the well established geo-centric model of planetary motion by suggesting his heliocentric model [START_REF] Kuhn | The Structure of Scientific Revolutions[END_REF].

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Explanatory Sub-systems

We can analyze the system structure of technical objects by singling out their components and functional relations.

These components might themselves be systems and appear from the perspective of the analyzing subject as subsystems. Something similar happens in explanations, which are based on the use of concepts in judgements and inferences. Most of the time, we need additional concepts, judgements and inferences in order to explain the ones that we are using in our explanations. Moreover, digging deeper into the system structure of explanations (the concepts, judgements, and inferences) leads us to the epistemic practices and the experimental technologies that provide referential data.

Take for example the Ptolemaic geo-centric model that was used for predicting the position of vagabonds at a given time. An astronomer from the Ptolemaic tradition would approach this task with the help of her explanatory model. When asked for the exact reasons why this and not another position was predicted, she would have to refer to the system structure of her explanatory model. Her simplified answer might look like this: The vagabond revolves with speed S1 around a point P1, while P1 revolves with speed S2 around a point P2 that is close to the Earth (see Figure 3). This formulation alone already refers to at least eight explanatory concepts: 1) speed S1, 2) point P1, 3) speed S2, 4) point P2, 5) revolution around P1, 6) revolution around P2, 7) the vagabond in question and 8) the Earth. Given each of these concepts, we could ask for further explanation, for example: What is speed? -and at the time of Ptolemy we might have received an answer like: The speed of a moving object tells us how far the object gets in a certain amount of time (see for example [START_REF] Rayleigh | Argon, a New Constituent of the Atmosphere[END_REF]). In other words, the explanatory concept speed appears to be an explanatory sub-system in Ptolemy's explanatory system of the vagabonds' motion. The same holds for the other explanatory concepts listed above.

Explanatory Super-systems

From the above definition of system, we also derived the concept of a super-system. Technological systems, for example, can merge and build such super-systems: Multiple computers connected as a network build, for instance, the internet. Likewise, we can join explanatory concepts in order to explain a phenomenon that is more complex: Among others, the concept of movement, for example, could be applied to (i) a body and a straight line or (ii) a body and a ! 6 circular line. The first might result in the concept of a body moving straight forward and the latter in the concept of a body revolving around something.

Hierarchy and Complexity

It follows from the definition of system that each system might be built from multiple sub-systems and that likewise, each super-system consists of more than one system. This means that complexity increases no matter where we start to explain a phenomenon. Let us distinguish two perspectives on hierarchies of explanatory concepts -(i) top down and (ii) bottom up. (i) When explaining from a top-down perspective, we start with the help of an explanatory concept from the top of the hierarchical order and (ii) when explaining from a bottom-up perspective, we start with one from the bottom.

Potential Problems of Top-Down Approaches

Starting with explanatory concepts from the top of the hierarchy allows us to see the whole picture and to unite explanatory concepts from different domains. However, misconceptions on higher levels can block or misguide conceptual developments on the lower levels. The transition from a physically and not-only-mathematically-understood geo-centric model of planetary motion to a helio-centric, for example, was complicated by the Christian doctrine of the Earth as the center of the universe. This belief was imbedded in an overall vision of life and our (humans') role in a world created by God. Conceiving of the Earth as one planet among others was not only radical in the domain of astronomy, but also implied conceptual modifications higher up the hierarchy.

Potential Problems of Bottom-Up Approaches

Starting with a concept from the bottom in order to explain a phenomenon is a feature of reductionist strategies: A concept seems to have so much explanatory power that its scope is to be extended either to other phenomena or to other aspects. Ptolemy, for example, used a circle to model the revolution of vagabonds around the Earth. Seen from a geocentric perspective, year by year the sun takes about 365 days for one whole cycle, Venus about 225 days, and Mars about 687 days. These regularities can be perfectly explained in terms of revolution and geometrically modeled with the help of a circle.

However, from the perspective of our Earth, it seems that both Venus and Mars move backward from time to time. The Ptolemaic model accounted for these phenomena by using the same explanatory concept again. Instead of the vagabonds themselves, the center of much smaller circles -so-called epi-cycles -revolved around the Earth. The vagabonds, in return, were revolving around the center of their epi-cycles.

Thanks to this analogous usage of the explanatory concept of revolution around something, the model could explain, not only the occasional backward movement, but also its periodicity and the changes in speed that the vagabonds seem to undergo during these periods. In order to improve the model's accuracy even further, additional epicycles where added and the Earth was slightly moved out of the center of the epi-cycles' revolutions. Although the system's predictive power increased, it became increasingly complicated (see Figure 5).

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Primary and Secondary Explanatory Concepts

Note that there is not only a historical but also a functional priority behind the use of circles in the Ptolemaic model.

From a functional perspective, the role of the larger circle was to explain the periodic revolution of vagabonds around the Earth, while epi-cycles were introduced in order to explain details of this overall motion. Let us call the larger circle a primary explanatory concept of the model and the epi-cycle a secondary explanatory concept. The first has historical and, more importantly, functional priority, since the whole model would break down if the concept of the revolution of planets around the Earth was eliminated. It is of primary importance, since it directly affects the realization of the model's primary function. The concept of epi-cycles, in contrast, could be eliminated without causing the model's collapse. It is true that without epi-cycles, the model could no longer account for the vagabonds' backward movement, but it would still get the periodicity of their overall revolutions right. In this sense, the explanatory role of the epi-cycles is only of secondary importance.

Applying ARIZ-85C to the Shift from Ptolemy's to Copernicus' Explanatory System

We now possess all the distinctions needed for applying ARIZ-85C to explanatory systems in science (following the ARIZ version in [START_REF] Fey | Innovation on demand[END_REF]). For the sake of brevity, we slightly simplified the algorithm without compromising on the overall logical structure (see Figure 6). The way we are counting the steps does not fully match the original version of ARIZ-85C. We abbreviate the series of steps, since we neither go through the full analysis of the Ptolemaic system nor discuss all intra-systemic problems. Moreover, if not explicitly highlighted, we refer to ARIZ-85C simply by ARIZ.

Step 1 -Towards an Understanding of the System Conflict

Step 1.1: According to ARIZ, the guiding thread for the development of a system is its primary function (or its primary functions). In case of Ptolemy's system, the primary function consists in explaining the vagabonds' movement.

Step 1.2: Since ARIZ views its subject as a system with a primary function, it can be further decomposed into interacting parts or (if they are further decomposable) sub-systems. Altogether, these sub-systems have to achieve the system's primary aim -which is the original reason why it exists at all. Moreover, sub-systems often have to achieve secondary aims. A functional analysis of the Ptolemaic explanatory system reveals that the backward motion of some of the vagabonds could not be explained without the help of epi-cycles. The explanation of this backward movement, for example, is such a secondary aim.

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Step 1.3: Both primary and secondary problems turn into systemic conflicts when the solution to them yields a tradeoff.

As we have seen, dealing with epi-cycles yields the tradeoff between the system's accuracy and its simplicity.

Step 2 -Stating the Task to be Solved

Step 2.1: After having identified the system-conflict, ARIZ asks whether or not the conflict is due to a secondary subsystem. If so, its elimination is suggested. Since the epi-cycles are responsible for the tradeoff between simplicity and accuracy, and since they are secondary sub-systems, their elimination is suggested. Seen from a historical perspective, this decision implies that the ongoing search for solutions starts from a problem situation prior to the introduction of the malfunctioning sub-system. If, in contrast, the analysis in step 1 had concluded that the problem to be solved was due to a primary sub-system, ARIZ would not suggest its elimination because, given such an elimination, the primary aim could no longer be achieved, which would amount to an elimination of the entire system. Rather, ARIZ suggests here an extreme intensification of the requirements and conditions for the system's performance.

Step 2.2: The elimination of the malfunctioning secondary sub-system leads to a new system conflict: The malfunctioning of the eliminated sub-system disappears, but the secondary problem that had been solved before reemerges. When eliminating the epi-cycles from the Ptolemaic system the conflict arises: The system is simple but it cannot explain the backward movement of the vagabonds.

Step 2.3: As soon as the system conflict is clearly understood, the task to be solved can be stated in an abstract but precise way (see Figure 6): Find a resource (within the system itself or in its environment) that -when slightly modified -helps to explain the backward movement of the vagabonds without complicating the system.

Step 3 -Looking for Potential Resources that Might Help to Solve the Task

Step 3: In order to facilitate the creation of a solution concept, ARIZ recommends to list potential problem-solving resources within the system and its environment. In the case of Ptolemy's system, the system's center, the Earth, the Sun and the Moon (these two vagabonds never move backward) appear to be particularly interesting.

Step 4 -Creation of Solution Concepts

Step 4.1: Each resource that can be selected form the list might contribute to the potential solution. Selecting the Earth, for example, yields the question: How can the Earth help to explain the vagabonds' temporary backward motion without complicating things? The answer to this question is far from obvious.

Step 4.2: However, when asking which contradicting properties P and not-P the Earth might need to have in order to help explain the backward movement of the vagabonds, we put ourselves on the right track. We know, for example, that the Earth must be in the center of the vagabonds' movement, because that is how we observe the phenomena we want to explain. Being in the center is thus a property of the Earth within our explanatory system. But could it be the case that the Earth must not be in the center such that the backward movement of the vagabonds can be explained? Following this line of reasoning, we force ourselves to imagine the Earth as being in the center of the vagabonds movement (in order to explain the observations) and not being in the center of their movement (in order to explain their backward movement).

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Step 4.3: When facing this type of contradiction -something needs to have both property P and not-P -ARIZ recommends the application of three separation principles. The goal of their application is to resolve the contradiction by finding a way in which the selected resource can have both properties in two different regards:

• 1) Separation in time: At time T1, the Earth is in the center of the vagabonds' movement and at time T2, the Earth is not in their center.

• 2) Separation in space: Within the spacial part P1, the Earth is in the center of the vagabonds' movement, but within the spacial part P2, the Earth is not in their center.

• 3) Separation between the system and its sub-systems: From the sub-system perspective, the Earth is in the center of the vagabonds' movement; from the system perspective, the Earth is not in their center.

While the first two separation principles do not articulate concepts that could explain the backward movement, the third gives a surprisingly clear description of what the Copernican shift is about: The Earth is only in the center of the appearances of the vagabonds' movement. We observe the overall system from the perspective of Earth (as sub-system) -in this sense the Earth is in the system's center. However, as a sub-system among others (the system perspective), the Earth itself is not in the center of the system. As soon as a sub-system (a vagabond) overtakes another, it looks from the respective vagabond's perspective as if the other would turn into the opposite direction. Only when viewed from the real center of the system, no vagabond appears to change direction.

This raises the question as to which sub-system is to be placed in the center. Here the Sun and the Moon come into play. Neither shows any backward motion, which makes them promising candidates. Putting the Moon into the center would imply that the Sun moved back and forth from time to time. Moreover, it would be impossible to make sense of the observations of any of the vagabonds' movements. In contrast, placing the Sun in the center of the vagabonds' revolutions matches the observations quite well. However, it raises the question why the Moon never changes its direction. Copernicus' answer was straight forward: While all vagabonds -the Earth included -were revolving around the Sun, the Moon was revolving around the Earth.

Step 5 -What if no Solution was Found?

In case that no solution could be found, ARIZ recommends to check whether the solution criterion in step 2 was correctly stated. If so, the restoration of the previously eliminated sub-system in step 2 is recommended; ARIZ then continues at step 2 -without the elimination of any sub-system (see Figure 6, step 2 and step 5). On this track, ARIZ recommends intensifying the conditions and requirements for the system's performance. This was Johannes Kepler's path. He had been working for Tycho Brahe, Europe's leading astronomer at the time. Brahe had been working on the improvement of tools for observing the sky and had perfected the geo-centric Ptolemaic system to an extent that outclassed the Copernican predictions. In contrast to Brahe, Kepler preferred the Copernican model for its simplicity.

It's predictions, however, were not sufficiently accurate. Seen from the perspective of ARIZ, the inaccuracies were due to one of Copernicus' primary explanatory sub-systems: circular revolutions. Kepler was thus dealing with the intensified task (see step 2.1) of having to develop a fully accurate model by sticking to the Copernican paradigm. In order to do so, he had to rethink Copernicus' primary sub-system of circular revolutions. As a result, he turned them into ellipses.

Conclusion

We have shown that ARIZ-85C -originally designed for solving problems in technology -can be expressed in a more general vocabulary of systemic thinking. This allows for its application outside of the technological domain ! 10

without relying on crutches such as metaphorical analogies. The application of this generalized version of ARIZ was tested on one of the most famous paradigm shifts in the history of science -the shift from the Ptolemaic geo-centric system to Copernicus' helio-centric one. Many more such tests are needed to evaluate whether or not the study of Kuhnian paradigm shifts can shed light upon the nature of creative problem solving in science. It seems, however, to be a promising path. Before Genrich Altshuller and Raphael Shapiro started to systematically examine the nature of paradigm shifting solutions in technology, not much knowledge about this type of problem solving was available.

Kuhn's position [START_REF]This Month in Physics History -January 1938: Discovery of Superfluidity[END_REF] is a quintessential example of a widely shared pessimism on this topic:

What the nature of that final stage is -how an individual invents (or finds he has invented) a new way of giving order to data now all assembled -must here remain inscrutable and may be permanently so.

Considering the abundance of examples of such shifts in the history of science and technology, this pessimism is surprising. It seems that Altshuller and Shapiro were the first who systematically studied these transformations in technology in order to gain insight into the logical operations necessary for bringing about paradigm shifts. In this way, they became the founders of the Theory of Inventive Problem Solving (TRIZ), which aims at making invention on purpose possible. With this paper, we want to suggest that something similar is possible in science. The goal of the resulting theory could be called discovery on purpose.

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Fig. 3 .

 3 Fig. 3. Simplified version of an elementary explanatory unit in the Ptolemaic model: A planet revolves in epi-cycles (smaller circle) around the Earth, which is close to the centre of the planet's revolution.

Fig. 5 .

 5 Fig. 5. The model for explaining the periodic movement of vagabonds was further extended to explain the backward movement as well.

Fig. 6 :

 6 Fig. 6: General structure of ARIZ-85C

Table 1 :

 1 Altshuller's three types of discoveries -accidental detections, purposeful detections, and purposeful explanations -are viewed in Kuhn's pre-normal, normal, and revolutionary phase.

	Types of Disco-very	Pre-normal Phase (no established paradigm)	Normal Phase (established paradigm)	Revolutionary Phase (established paradigm is challenged)