Research Gaps and Conclusion of Axiomatic Design Principles (Part 4)

Axiomatic design is a robust system that has seen substantial refinement over the years. As a result, the majority of gaps present are in the interrelationships between axiomatic design and similar design methodologies. One such set of gaps exists in the Theory of Inventive Problem Solving (TRIZ). TRIZ has had substantial study in combining TRIZ methodologies with axiomatic design principles.
Kim and Cochran conducted a similar review of TRIZ and axiomatic design. They concluded that the differences found in TRIZ and axiomatic design are primarily due to the development focus of the two systems. Axiomatic design was founded with a central theme of inflexible design axioms. TRIZ was founded by the inductive study of patent databases. TRIZ lacks the ability to calculate the total sum of undesirable functions; rather, discerning undesirable characteristics must be resolved using a system like axiomatic design. Similarly, axiomatic design lacks the ability to innovate new functional requirements that are identified mid-design. This is solved in TRIZ by using the law of increasing ideality. This allows for design evolution towards an ideal solution [20].

TRIZ allows for a wide set of tools to be used in design. TRIZ regarded as a mature design methodology which may be combined with axiomatic design to produce a unified design theory [21]. It has been observed by Mann, however, that the two systems are not fully compatible. Unfortunately, the analytics-based axioms from axiomatic design sometimes come into conflict with TRIZ. While both design methodologies attempt to codify design metrics, TRIZ attempts a much broader view of engineering design. This causes conflict immediately due to TRIZ focusing on an idealized concept rather than a material resolution. The ideal axiomatic design would include a decoupled solution meets each functional requirement. The ideal TRIZ concept is a solution which requires no physical manifestation [22].
Although this may seem counter-intuitive, it can best be explained as an external system taking on the role of solving the problem such that no physical product is required. Using the example of a sink faucet temperature/flow lever, axiomatic design would indicate that the ideal solution is a sink faucet control valve that allows for flow rate and temperature control by one lever. The TRIZ ideal concept would be one where flow-rate and temperature control are not required as the problem of improper flow-rate and temperature have been eliminated by an outside source. The sink could always receive water with a regulated temperature with an on-demand flow-rate when an individual approaches the sink. This has solved the problem without requiring a sink flow/temperature control lever [22].
Although TRIZ and axiomatic design are sometimes at odds, some researchers have found that some conflicts may be resolved through abstracting design parameter. This abstraction occurs specifically when dealing with coupled axiomatic design parameters. Duflou and Dewulf found that by replacing specific design parameters with generic engineering parameters during the domain mapping phase of axiomatic design, conflicts were eliminated between axiomatic design and TRIZ [23].
Within both the axiomatic design and TRIZ methodologies, there exist irreconcilable conflicts that arise during design. In TRIZ, the primary source of conflicts come from physical conflicts where an object must exist in mutually exclusive states [20]. This can be defined as a situation where an element must have a property to perform one action while it must also have an opposite property to perform a separate, simultaneous action. This can be resolved through separating properties such that conflicts do not arise. These direct contradictions can be eliminated through ensuring that axiomatic design concepts are not permitted. If design parameters are held to constraints, functional coupling is minimized, and design matrices are non-triangular, TRIZ contradictions should not arise [20].
Ogot found that the strength of axiomatic design was chiefly in the problem identification and formulation steps. Ogot compared this to the strength of TRIZ which was in problem identification and concept generation. The conclusion reached by Ogot is that conflicts between TRIZ and axiomatic design can be resolved by utilizing axiomatic design within the context of a TRIZ framework. Specifically, axiomatic design was used for early stage elaboration up to and including the generation of an engineering systems matrix and resolving the linear algebra steps inherent to axiomatic design. At this point, Ogot shifted to TRIZ for concept generation and elaboration. By siloing axiomatic design and TRIZ in this way, conflicts were found to be minimized [24].
Axiomatic design sees frequent use in modern design engineering. It has become so widespread that there is a conference held every year since 2006 devoted to axiomatic design. The International Conference on Axiomatic Design sees presentations on modern usage of Suh’s axiomatic design principles as applied to today’s engineering problems.
One recent submission to ICAD was an Internet of Things enabled CNC machine tele-operator. This system allowed a remote operator to have virtual control of some CNC system functionality. As this requires a smooth interaction between hardware, software, data flow, people, and manufacturing processes, axiomatic design principles were used to ensure all functional requirements could be met with the proposed design from Oliveira et. al. This system made use of 11 defined customer needs, 5 design constraints, 5 functional requirements, and 5 design parameters spread across two tiers of operation [25]. Without axiomatic design as a design tool, this system may not have been possible.
Axiomatic design has also seen adoption in other design methodologies. Additive manufacturing is a novel method of creating products and components that removes many limitations associated with casting, forging, and injection molding. As a result, design methodologies must adapt to this new technology.
One common problem with modern design methodologies is that they frequently ignore the unique opportunities afforded by additive manufacturing technologies. Thus, costly redesign may occur later in the product development cycle than otherwise would be necessary. To combat this shortfall, Salonitis has proposed incorporation of axiomatic design into the emerging field of Design for Additive Manufacturing [26]. By ensuring that axiomatic design practitioners have an existing framework for incorporating AM technologies, Salonitis hopes to improve adoption of rapid prototyping and additive manufacturing technology in the design space.
Quality Function Deployment and axiomatic design principles have shown synergistic effects when used together. Quality Function Deployment makes used of design tools such as House of Quality and relationship matrices. The House of Quality system allows for weighted relationships to be established between customer needs and design requirements as well as mapping attributes from one phase of design to the next in a way similar to axiomatic design [2,27,28].
It is no surprise that the two would see simultaneous deployment in design. To demonstrate this, a case study was presented by Gilbert, Omar, and Farid involving lifecycle-based construction of temporary housing. According to Marchesi, Kim, and Matt, modern architecture design requires a more rational approach with regards to appearance, costs, and performance [29]. This is in part due to the growing complexity faced by developers to ensure that all stakeholders are satisfied with the result. Typical design procedures in temporary housing often ignore using formal design methodologies such as QFD and axiomatic design.
As a result, complex designs tend to see cost overruns. This is frequently blamed on failing to ensure that customer requirements are treated in a systematic method to ensure resolution [30]. As a result, the construction industry is increasing its reliance on design tools such as QFD and axiomatic design [31]. Although combining the two processes have been proposed previously, prior proposals have not streamlined the incorporation of both processes [32]. Future civil engineering projects are likely to see a seamless incorporation of these design methodologies. One such example can be seen by modifying the house of quality to incorporate axiomatic design principles as shown in Figure 7.
The cells from Figure 7 are arranged as follows:
1. Customer Needs (CN)
2. Relative Importance of CN
3. Planning Matrix
4. Technical Requirements
5. Non-Functional Requirements
6. Constraints
7. Functional Requirements
8. Non-functional Requirement Interrelations
9. Constraint Interrelations
10. Functional Requirement Interrelations
11. Non-FR/Constraint Relations
12. Constraint/Functional Requirement Relations
13. Non-functional Requirement/Functional Requirement Relations
14. Direction of Improvement
15. Relationship Between Customer Needs and Technical Requirements
16. Technical Ratings of Technical Requirements
17. Rankings of Technical Requirements

Figure 7 – Modified House of Quality with Built-in Axiomatic Design [31]
Although complex in nature, this system provides a ground-up redesign of the House of Quality system. By doing this, it allows for seamless switching between axiomatic design and Quality Function Deployment methods. By utilizing this system, designers may find that complex system requirements can be refined to meet customer requirements with a higher degree of accuracy [31].
New linguistic design systems are allowing for unique application of axiomatic design principles. Knowledge supplier and demander pairing can be accomplished using fuzzy algorithms. These algorithms are used in a knowledge brokering service. Historic versions of these services attempted to make use of numerical matching schemes; however, this was proven to be less effective than linguistic assessments. By imposing Suh’s systematic axioms into the algorithm, an improved matching scheme was devised. As a result, proper matching rates were improved in a test case using the improved axiomatic design algorithm [33].
In 2016, a human-driven exoskeleton was discussed at the International Conference on Axiomatic Design. This robotic system was intended to assist in the rehabilitation of disabled users [34]. This project built on an earlier work by Tan Zhang. Zhang’s work used axiomatic design theory to define multiple use-states for his robot to allow for recovery from damage [35]. This resulted in the robot having a self-healing resiliency characteristic that would later be adopted by Zhu et al. Zhu’s work capitalized on the resiliency characteristic shown by Zhang while adapting the lessons learned into a novel system. This system translated customer requirements based on the needs of the patient into design requirements for lower limb dysfunction correction and assistance. Further use of axiomatic design principles can be found in the incorporation of customized walking gait features in the exoskeleton. Customer requirements necessitated this ergonomic solution. Additionally, axiomatic principles can be found in features as fundamental as the drive system. Zhu et al. write that determining the sizing of the drive system was based primarily on the bio-compatibility of the device for each user. Due to the sheer volume of requirements of this design, an 11×11 matrix was necessary to map functional requirements to design parameters [34].
Some researchers have proclaimed that axiomatic design exists as one of the most promising methodologies being developed in the area of conceptual design systems. Ashtiany and Alipour state that the ability of axiomatic design in innovation is superior to other methods. They cite the design of an airplane tail section as an example. The Beech Baron 58 tail section was designed using modern engineering design methodologies such as Quality Function Deployment, Axiomatic Design, Design for Manufacturing, and several other novel methods. For this project, functional requirements were given such as trim moments and wing vortex generation. Design parameters were composed of component sizing. By utilizing these engineering design methodologies, a redesign was made possible for this aircraft [8].
Incorporation of axiomatic design with other modern engineering tools has shown success as well. In the redesign of a grading bin system in the foodstuffs industry, it was determined that weld joins were seeing excessive failure. By combining axiomatic design principles with finite element modeling, a new design was created which met the customer needs of a robust, durable transfer bin system [36].
Similarly, system decomposition principles have been combined with axiomatic design principles to create novel designs. In 2016, an electromechanical steering system was developed by Schuh, Rudolf, and Breunig by way of decomposing the system into mechatronic function modules. Due to the difficulty of integrating disparate fields of technology together into one coherent package, axiomatic design was married together with the mechatronic function module system to achieve a product. This allowed for the creation of a function-oriented product that made use of modular systems [37].
In engineering design, reliability engineering supports the longevity of products while ensuring that they are properly tested and maintained. Because axiomatic design leads into improving design concepts, treating reliability as a customer need allows for improvement in the product’s lifespan. Shao, Lu, Zeng, and Xu analyzed both traditional reliability engineering as well as axiomatic design principles [38].
Traditional reliability design considers a systematic analysis of life-cycle limiting items. One drawback of this system that was discovered was that reliability engineering does not lend itself well to original design of a system. In order to combat this shortcoming, Shao, Lu, Zeng, and Xu recently developed the axiomatic quality and reliability methodology as shown in Figure 8.
This system utilizes Quality Function Deployment, axiomatic design, conceptual design methods, and parametric-based design to accomplish the goal of providing the customer with a long-lived solution [38]. By considering the implementation of axiomatic design into other engineering sub-disciplines, the field of engineering as a whole can be developed.
Figure 8 – Axiomatic Quality and Reliability Methodology [38]
Axiomatic design has proven itself to be an invaluable tool for design engineers seeking to efficiently design complex systems. Through new developments in the field such as SysML and TRIZ incorporation, the ability to describe functional requirements of large, complex systems has blossomed into an entire field of study. New technologies are constantly being developed that readily incorporate axiomatic design such as software APIs and robot firmware. With the expansion into other engineering disciplines such as civil and biomedical engineering, axiomatic design sees a bright future ahead of it. As design engineers continue to expand upon the field through new developments, axiomatic design will continue to be adopted as a standard engineering practice to ensure customer requirements are met by the design.
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