Modelling Consensus Emergence With Nonlinear Dynamics

The study of emergent, bottom-up, processes has long been of interest within organizational and group research. Emergent processes refer to how dynamic interactions among lower-level units (e.g. individuals) over time form a new, shared, construct or phenomena at a higher level (e.g. work group). To properly study emergence of shared constructs one needs models, and data, that both take into account variability across individuals and groups (multilevel), and variability over time (longitudinal). This article makes three contribution to the modelling and theory of of consensus emergence. First, we formulate two separate patterns of consensus emergence; homogeneous and heterogeneous. Homogeneous consensus emergence is characterized by gradual and almost deterministic adjustments of the individual trajectories, whereas heterogeneous consensus emergence show more randomly oscillating trajectories towards consensus. Second, we introduce a model-invariant statistic that measures the strength of the consensus; and allows for comparisons between different models and patterns of consensus emergence. Third, we show how Gaussian Processes can be used to further extend the consensus emergence models, allowing them to capture nonlinear dynamics, on both individual and group level, in emergent processes. Using an established data set, we show that conclusions on the pattern of consensus emergence can change depending on whether the nonlinear group mean change over time is adequately modelled or not. Thus it is crucial to correctly capture the group dynamics to properly understand the consensus emergence.

Marketing Resource Allocation Strategy Optimization Based on Dynamic Game Model

Game theory has become an important tool to study the competition between oligopolistic enterprises. After combing the existing literature, it is found that there is no research combining two-stage game and nonlinear dynamics to analyze the competition between enterprises for advertising. Therefore, this paper establishes a two-stage game model to discuss the effect of the degree of firms’ advertising input on their profits. And the complexity of the system is analyzed using nonlinear dynamics. This paper analyzes and studies the dynamic game for two types of application network models: data transmission model and transportation network model. Under the time-gap ALOHA protocol, the noncooperative behavior of the insiders in the dynamic data transmission stochastic game is examined as well as the cooperative behavior. In this paper, the existence of Nash equilibrium and its solution algorithm are proved in the noncooperative case, and the “subgame consistency” of the cooperative solution (Shapley value) is discussed in the cooperative case, and the cooperative solution satisfying the subgame consistency is obtained by constructing the “allocation compensation procedure.” The cooperative solution is obtained by constructing the “allocation compensation procedure” to satisfy the subgame consistency. In this paper, we propose to classify the packets transmitted by the source nodes, and by changing the strategy of the source nodes at the states with different kinds of packets, we find that the equilibrium payment of the insider increases in the noncooperative game with the addition of the “wait” strategy. In the transportation dynamic network model, the problem of passenger flow distribution and the selection of service parameters of transportation companies are also studied, and a two-stage game theoretical model is proposed to solve the equilibrium price and optimal parameters under Wardrop’s criterion.

Diagnosis of internal cracks in concrete using vibro-acoustic modulation and machine learning

This paper investigates the utility of physics-informed machine learning models for vibro-acoustic modulation (VAM)–based damage localization in concrete structures. Vibro-acoustic modulation is a nonlinear dynamics-based non-destructive testing method, which was initially developed to perform damage detection and later extended to accomplish damage localization. The VAM-based damage (hidden crack) diagnosis is performed by analyzing the damage index pattern on the surface of the component to arrive at the size and location of the hidden damage. Past investigations have employed heuristically selected damage index thresholds as well as computationally expensive Bayesian estimation methods for VAM-based damage localization in two (surface) dimensions. Compared to these studies, the proposed methodology automates the threshold selection (algorithmic instead of heuristic), increases the speed of the probabilistic damage diagnosis process, and enables the estimation of damage depth. We generate training data (damage index) for the machine learning models using the pertinent nonlinear dynamics (finite element) models using different combinations of test parameters. The (supervised) machine learning models are thus informed by computational physics models. These include two types of artificial neural network (ANN) models: classification models that identify whether a sensor location is damaged or not and regression models that enable Bayesian estimation to obtain the posterior probability distribution of damage location and size. The accuracy of machine learning-based diagnosis is evaluated using both numerical and laboratory experiments. The proposed physics-informed machine learning models for VAM-based damage diagnosis are able to achieve an accuracy of about 60–64% in the validation experiments, indicating the potential of these methods for internal crack detection. The results show that for complex (nonlinear dynamics-driven) diagnostic methods, damage index patterns learned from physics models could be successfully used for damage detection as well as localization.