Measurement Theory and Dimensional Analysis: Methodological Impact on the Comparison and Evaluation Process

Abstract

Comparison and ranking of solutions are central tasks of the design process. Designers have to deal with decisions simultaneously involving multiple criteria. Those criteria are often inconsistent in the sense that they are expressed according to different types of metrics. This means that usual engineering performance indicators are expressed according to physical quantities (i.e. SI system) and indicators such as preference functions can be “measured” by using other type of qualitative metrics. This aspect limits the scientific consistency of design because a coherent scientific framework will at first require the creation of a unified list of fundamental properties. A combined analysis of the measurement theory, the General Design Theory (GDT) and the dimensional analysis theory give an interesting insight in order to create guidelines for establishing a coherent measurement system. This article establishes a list of fundamental requirements. We expect that these guidelines can help engineers and designers to be more aware of the drawbacks linked with the use of wrong comparison procedures and limitations associated with the use of weak measurement scales. This article makes an analysis of the fundamental aspects available in major scientific publications related to comparison, provides a synthesis of these basic concepts and unifies those concepts together from a designing perspective. A practical design methodology using the fundamental results of this article as prerequisites has been implemented by the authors.

Relational and Euclidean Temporal Space

“…The system also allows for addition, a type of ordered subtraction as well as Euclidean 1D temporal space, and it is open to n-dimensional metric space, each of which is consistent with a strong measurement system. Journal of Applied Mathematics and Physics [13] It would be prudent to embark on a comprehensive assessment of the suggested temporal space measurement system to determine if it is a weak or strong form of measurement on a set of objects, taking into account the criteria outlined by Brazilai [45] or other relevant sources.…”

Dimensional Methods Used in the Additive Manufacturing Process

“… We only tested the efficiency of MDA for specimen optimization. However, this approach, using the dimensional analysis conceptual modeling (DACM) framework developed by Coatanéa [ 157 , 158 , 159 , 160 , 161 , 162 , 163 , 164 , 165 , 166 , 167 ], can also be extended and successfully implemented in different areas of additive manufacturing. The MLs we deduced are also fully applicable to metals.…”

“…The most appropriate dimensional approach for efficiently establishing a set of dimensionless variables, bearing in mind Szirtes’ theory [ 149 , 150 ], is the dimensional analysis conceptual modeling (DACM) framework developed by Coatanéa [ 156 , 157 , 158 , 159 , 160 , 161 , 162 , 163 , 164 , 165 , 166 , 167 ]. The DACM provides the following main results.…”

“…In his Ph.D. thesis [ 157 , 159 ], Coatanéa proposed a new approach, which he called conceptual modeling of life-cycle design, subsequently perfecting and renaming it the conceptual modeling and simulation framework for system design [ 158 , 159 , 160 , 161 , 162 ]. Currently, modeling and simulation are widely applied to achieve a more efficient final product using AM.…”

Formal approach to security metrics.

“…Note, that Definition 3 already includes a measurement function: before defining the distance the mapping from empirical quantities to real numbers is established [1,3].…”