The realization of large-scale complex engineered systems is contingent upon satisfaction of the preferences of the stakeholder. With numerous decisions being involved in all the aspects of the system lifecycle, from conception to disposal, it is critical to have an explicit and rigorous representation of stakeholder preferences to be communicated to key personnel in the organizational hierarchy. Past work on stakeholder preference representation and communication in systems engineering has been primarily requirement-driven. More recent value-based approaches still do not offer a rigorous framework on how to represent stakeholder preferences but assume that an overarching value function that can precisely capture stakeholder preferences exists. This article provides a formalism based on modal preference logic to aid in rigorous representation and communication of stakeholder preferences. Formal definitions for the different types of stakeholder preferences encountered in a systems engineering context are provided in addition to multiple theorems that improve the understanding of the relationship between stakeholder preferences and the solution space.

Detecting causality between variables in a time series is a challenge, particularly when the relationship is nonlinear and the dataset is noisy. Here, we present a novel tool for detecting causality that leverages the properties of symmetry transformations. The aim is to develop an algorithm with the potential to detect both unidirectional and bidirectional coupling for nonlinear systems in the presence of significant sampling noise. Most of the existing tools for detecting causality can make determinations of directionality, but those determinations are relatively fragile in the presence of noise. The novel algorithm developed in the present study is robust and very conservative in that it reliably detects causal structure with a very low rate of error even in the presence of high sampling noise. We demonstrate the performance of our algorithm and compare it with two popular model-free methods, namely transfer entropy and convergent cross map. This first implementation of the method of symmetry transformations is limited in that it applies only to first-order autonomous systems.

Many problems in the study of dynamical systems—including identification of effective order, detection of nonlinearity or chaos, and change detection—can be reframed in terms of assessing the similarity between dynamical systems or between a given dynamical system and a reference. We introduce a general metric of dynamical similarity that is well posed for both stochastic and deterministic systems and is informative of the aforementioned dynamical features even when only partial information about the system is available. We describe methods for estimating this metric in a range of scenarios that differ in respect to contol over the systems under study, the deterministic or stochastic nature of the underlying dynamics, and whether or not a fully informative set of variables is available. Through numerical simulation, we demonstrate the sensitivity of the proposed metric to a range of dynamical properties, its utility in mapping the dynamical properties of parameter space for a given model, and its power for detecting structural changes through time series data.