Study of Equivalence in Systems Engineering within the Frame of Verification

This dissertation contributes to the theoretical foundations of systems engineering (SE) and exposes an unstudied SE area of definition of verification models. In practice, verification models are largely qualitatively defined based on heuristic assumptions rather than science-based approach. For example, we may state the desire for representativeness of a verification model in qualitative terms of low, medium, or high fidelity in early phases of a system lifecycle when verification requirements are typically defined. Given that fidelity is defined as a measure of approximation from reality and that the (real) final product does (or may) not exist in early phases, we are stating desire for and making assumptions of representative equivalence that may not be true. Therefore, this dissertation contends that verification models can and should be defined on the scientific basis of systems theoretic principles.

Furthermore, the practice of SE is undergoing a digital transformation and corresponding desire to enhance SE educationally and as a discipline, which this research proposes to address through a science-based approach that is grounded in the mathematical formalism of systems theory. The maturity of engineering disciplines is reflected in their science-based approach, such as computational fluid dynamics and finite element analysis. Much of the discipline of SE remains qualitatively descriptive, which may suffer from interpretation discrepancies; rather than being grounded in, inherently analytical, theoretical foundations such as is a stated goal of the SE professional organization the International Council on Systems Engineering (INCOSE). Additionally, along with the increased complexity of modern engineered systems comes the impracticality of verification through traditional means, which has resulted in verification being described as broken and in need of theoretical foundations.

The relationships used to define verification models are explored through building on the systems theoretic lineage of A. Wayne Wymore; such as computational systems theory, theory of system design, and theory of problem formulation. Core systems theoretic concepts used to frame the relationship-based definition of verification models are the notions of system morphisms that characterize equivalence between pairs, problem spaces of functions that bound the acceptability of solution systems, and hierarchy of system specification that characterizes stratification. The research inquisition was in regard to how verification models should be defined and hypothesized that verification models should be defined through a combination of systems theoretic relationships between verification artifacts; system requirements, system designs, verification requirements, and verification models.

The conclusions of this research provide a science-based metamodel for defining verification models through systems theoretic principles. The verification models were shown to be indirectly defined from system requirements, through system designs and verification requirements. Verification models are expected to be morphically equivalent to corresponding system designs; however, there may exist infinite equivalence which may be reduced through defining bounding conditions. These bounding conditions were found to be defined through verification requirements that are formed as (1) verification requirement problem spaces that characterize the verification activity on the basis of morphic equivalence to the system requirements and (2) morphic conditions that specify desired equivalence between a system design and verification model. An output of this research is a system theoretic metamodel of verification artifacts, which may be used for a science-based approach to define verification models and advancement of the maturity of the SE discipline.