This paper focuses on the application of complexity theory and entropy concepts in the design process. Broadly speaking, the design process involves three phases: problem definition, conceptual design and embodiment. In the conceptual design phase, concepts that satisfy the functional requirements of the desired product are identified and compared. It is said that approximately 75% of the total product life-cycle cost is committed in this phase. The conceptual design phase has two essential sub-phases, namely, obtaining a solution set and selecting the most suitable solutions. Our work focuses on the selection sub-phase. The aim within this sub-phase is to minimize the number of selected concept variants and to reduce their chances of rejection in later stages. However, the solution to this problem is quite elusive, mostly because information about concept variants is scarce and rather qualitative at this stage. A common method is to perform a cost-benefit analysis. However, the analysis relies heavily on expert intuition and is thus subjected to high uncertainties. Recently, axiomatic design is gaining popularity. This is a framework that incorporates two axioms, namely, the Independence Axiom and the Minimum Information Axiom, accompanied by several corollaries. However, criticism on the integrity of the Independence Axiom has appeared recently in the literature. Further, the formulation of axiomatic design appears to have logical flaws. Finally, the conceptual design phase, a distinct phase in the design process, cannot be distinguished clearly in axiomatic design. In this paper we try to improve the selection phase of the conceptual design by improving the existing cost-benefit approach. In this vein, performance features against which concepts would be evaluated are established. We propose the use of Kolmogorov complexity theory and entropy concepts from information theory and physics to evaluate the complexity of the performance features. The design concepts are then improved based on the rule to reduce complexity of each performance feature. Weights are finally assigned to each performance feature and an overall complexity index is obtained which is suitable to compare designs. The ideas are further elaborated on by examples.

https://ojs.library.queensu.ca/index.php/PCEEA/article/download/3924/3946

A formulation of the preliminary desing phase using complexity-based rules

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Task uncertainty and noise – generically referred to as uncertainties in the thesis – in the design and operation of robotic mechanical systems pose a major challenge to the designer. The aim of this thesis is to contribute to the laying down of the foundations on which the design of robotic mechanical systems, in the presence of uncertainties, is to be based. Uncertainties are accounted for by means of robustness. To this end, a theoretical framework as well as a general methodology for model-based robust design are proposed. Within this framework, all quantities involved in a design task are classified into three sets: the design variables (DV), which are to be assigned values as an outcome of the design task; the design-environment parameters (DEP), over which the designer has no control; and the performance functions (PF), representing the functional relations among performance, DV and DEP. A distinction is made between globally robust design and locally robust design, this thesis focusing on the latter. Locally robust design is amenable to mathematical modelling of the performance by means of smooth functions of the DV and DEP. Resorting to the mathematical model available for the object under design, a design performance matrix, mapping the space of relative variations in DEP – referred to as noise in the literature on robust design – into that of relative variations in PF, is derived. Then, the locally robust design problem is formulated as the minimization of a norm of the covariance matrix of the variations in the PF upon variations in the DEP. Moreover, one pertinent concept are introduced: design isotropy. Next, it is shown that an optimally robust design can be secured by means of isotropy, whenever this is achievable under the constraints of the problem at hand. As proven in the thesis, designs obtained via isotropy lead to robustness even in the absence of a priori knowledge of the statistical properties of the variations of%%%%In connection with robotic mechanical systems, the design task is decomposed into three subtasks, namely, kinetostatic, elastostatic, and elastodynamic, in this order. We show that parallel manipulators allow for isotropic designs, but their serial counterparts do not.%%%%The motivation behind the research work reported here being the design of robotic mechanical systems, the simulation of their dynamic response becomes an essential component in their design. In order to validate the proposed design, a robust algorithm for the simulation of conservative linear systems, which model accurately the systems of interest in the presence of "small" environment perturbations, is introduced. The robustness of the algorithm lies in its immunity to roundoff and truncation errors, which could lead to either instability or a dissipative response in the simulation results otherwise.

The robust design of robotic mechanical systems

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The robust design of robotic mechanical systems