Gregory M. Mocko

System modeling frameworks can be categorized into imperative and declarative paradigms. A model's paradigm effects its efficacy: imperative models allow simple execution, while declarative models capture the behavior of the underlying system. This paper compares these paradigms, as well as functional and object-oriented frameworks, in light of physics-based systems. This is done by exploring the principles of systems modeling and simulation. Simulation is shown to be the composition of functions representing system behavior. Simulatable frameworks can be differentiated by their ability to identify and compose these functions for a specific input and output pairing. The various frameworks are explored, applying concepts more typically studied in computer science to general systems engineering. The frameworks are investigated by comparing simulations of a driven double pendulum in various modeling languages. Observations include that functional, declarative models allow for greater reusability and holistic system simulation.

Systems design processes are increasingly reliant on simulation models to inform design decisions. A pervasive issue within the systems engineering community is trusting in the models used to make decisions about complex systems. This work presents a method of evaluating the trustworthiness of a model to provide utility to a designer making a decision within a design process. Trusting the results of a model is especially important in design processes where the system is complex, novel, or displays emergent phenomena. Additionally, systems that are in the pre-prototype stages of development often do not have sources of ground truth for validating the models. Developing methods of model validation and trust that do not require real-world data is a key challenge facing systems engineers. Model fidelity in this work refers to the adherence of a model to real-world physics and is closely tied to model trust and model validity. Trust and validity directly support a designer's ability to make decisions using physics-based models. The physics that are captured in a model and the complexity of the mathematical representation of the physics contribute to a model's fidelity, and this work leverages the included physical phenomena to develop a means of selecting the most appropriate for a given design decision.

Digital engineering has transformed the design and development process. However, the utility of digital engineering is fundamentally dependent on the assumption that a simulation provides information consistent with reality. This relationship is described as model fidelity. Despite the widespread use of the term, existing definitions of model fidelity often lack formal rigor in practical application, which leaves ambiguity in how this similarity should be evaluated. This paper presents seven fundamental axioms to aid the development of future fidelity evaluation frameworks. An example of a ground vehicle model is used under an existing fidelity evaluation framework to observe the applicability of these axioms. In addition, these axioms are used as a reference point for considering future opportunities in future work related to model fidelity.

This article describes the theory behind constraint hypergraphs: a novel modeling framework that can be used to universally represent and simulate complex systems. Multi-domain system models are traditionally compiled from many diverse frameworks, each based on a single domain. Incompatibilities between these frameworks prevent information from being shared resulting in data silos, duplicate work, and knowledge gaps. A constraint hypergraph addresses these problems by providing a universal modeling framework within which all model prescriptions can be expressed. This methodology expands mathematical structures previously explored in the abstract mathematics and systems theory into a new executable framework. Each hypergraph expresses the holistic behavior of a system in a declarative paradigm that describes the relationships between system properties. In addition to modeling, it is shown how constraint hypergraphs can be used for universal, cross-cutting simulation through principles of function composition. The theoretical framework of a constraint hypergraph is demonstrated with a practical representation of a hybrid system, combining a discrete-event simulation and continuous proportional-integral-derivative controller into a single model of an elevator lift system.

This paper formulates optimal pacing of a cyclist on hilly terrain time-trials as a minimum-time optimal control problem. Maximal power of a cyclist serves as a time-varying constraint and depends on fatigue and recovery which are captured via dynamic models proposed early in the paper. Experimental protocols for identifying the individualized parameters of the proposed fatigue and recovery models are detailed and results for six human subjects are shown. In an analytical treatment via necessary conditions of Pontryagin Minimum Principle, we show that the cyclist's optimal power in a time-trial is limited to only four modes of all-out, coasting, pedaling at a critical power, or constant speed (bang-singular-bang). To determine when to switch between these modes, we resort to numerical solution via dynamic programming. One of the subjects is then simulated on four courses including the 2019 Duathlon National Championship in Greenville, SC. The dynamic programming simulation results show 24% reduction in travel time over experimental results of the self-paced subject who is a competitive amateur cyclist. The paper concludes with description of a pilot lab experiment in which the subject trial time was reduced by 3% when the near-optimal pace was communicated to her in real-time.

Project 5.A79 Simulation Model Repository and Integration Architecture

Purpose: This study (i) investigates the effect of recovery power (P_rec) and duration (t _rec) on the recovery of the curvature constant (W′) of the power–duration relationship, (ii) compares the experimentally measured W′ balance to that predicted (W′ _bal) by two models (SK2 and BAR), and (iii) presents a case of real-time performance optimization using the critical power (CP) concept. Methods: Seven competitive amateur cyclists performed a ramp test to determine their V˙O_2peak and gas exchange threshold, two to four 3-min all-out tests to determine CP and W′, and nine intermittent cycling tests to investigate W′ recovery. The intermittent cycling tests involved a 2-min constant work-rate interval above CP, followed by a constant work-rate recovery interval below CP (P_rec and t _rec were varied), followed by a 3-min all-out interval. Results: There was a significant two-way interaction between P_rec and t _rec on W′ recovery, P = 0.004 (η ² = 0.52). Simple main effects were present only with respect to P_rec at each t _rec. The actual W′ balance at the end of the recovery interval was less than the W′ _bal predicted by both SK2 (P = 0.035) and BAR (P = 0.015) models. The optimal strategy derived from the subject-specific recovery model reduced the race time by 55 s as compared with the self-strategy. Conclusions: This study has shown that in a recovery interval, P_rec has a greater influence than t _rec on W′ recovery. The overprediction of W′ _bal from SK2 and BAR suggests the need for individualized recovery parameters or models for sub-CP exercise. Finally, the optimal strategy results provide encouraging signs for real-time, model-based performance optimization.