Forecasting Bifurcation of Parametrically Excited Systems: Theory & Experiments

A system is parametrically excited when one or some of its coefficients vary with time. Parametric excitation can be observed in various engineered and physical systems. Many systems subject to parametric excitation exhibit critical transitions from one state to another as one or several of the system parameters change. Such critical transitions can either be caused by a change in the topological structure of the unforced system, or by synchronization between a natural mode of the system and the parameter variation. Forecasting bifurcations of parametrically excited systems before they occur is an active area of research both for engineered and natural systems. In particular, anticipating the distance to critical transitions, and predicting the state of the system after such transitions, remains a challenge, especially when there is an explicit time input to the system. In this work, a new model-less method is presented to address these problems based on monitoring transient recoveries from large perturbations in the pre-bifurcation regime. Recoveries are studied in a Poincare section to address the challenge caused by explicit time input. Numerical simulations and experimental results are provided to demonstrate the proposed method. In numerical simulation, a parametrically excited logistic equation and a parametrically excited Duffing oscillator are used to generate simulation data. These two types of systems show that the method can predict transitions induced by either bifurcation of the unforced system, or by parametric resonance. We further examine the robustness of the method to measurement and process noise by collecting recovery data from an electrical circuit system which exhibits parametric resonance as one of its parameters varies

The effects of viscoelastic fluid on kinesin transport

Kinesins are molecular motors which transport various cargoes in the cytoplasm of cells and are involved in cell division. Previous models for kinesins have only targeted their in vitro motion. Thus, their applicability is limited to kinesin moving in a fluid with low viscosity. However, highly viscoelastic fluids have considerable effects on the movement of kinesin. For example, the high viscosity modifies the relation between the load and the speed of kinesin. While the velocity of kinesin has a nonlinear dependence with respect to the load in environments with low viscosity, highly viscous forces change that behavior. Also, the elastic nature of the fluid changes the velocity of kinesin. The new mechanistic model described in this paper considers the viscoelasticity of the fluid using subdiffusion. The approach is based on a generalized Langevin equation and fractional Brownian motion. Results show that a single kinesin has a maximum velocity when the ratio between the viscosity and elasticity is about 0.5. Additionally, the new model is able to capture the transient dynamics, which allows the prediction of the motion of kinesin under time varying loads.Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/98600/1/0953-8984_24_37_375103.pd

Data-Driven Causal Modeling of the Manufacturing System

In manufacturing system management, the decisions are currently made on the base of ‘what if’ analysis. Here, the suitability of the model structure based on which a model of the activity will be built is crucial and it refers to multiple conditionality imposed in practice. Starting from this, finding the most suitable model structure is critical and represents a notable challenge. The paper deals with the building of suitable structures for a manufacturing system model by data-driven causal modelling. For this purpose, the manufacturing system is described by nominal jobs that it could involve and is identified by an original algorithm for processing the dataset of previous instances. The proposed causal modelling is applied in two case studies, whereby the first case study uses a dataset of artificial instances and the second case study uses a dataset of industrial instances. The causal modelling results prove its good potential for implementation in the industrial environment, with a very wide range of possible applications, while the obtained performance has been found to be good

Sensitivity Enhancement of Modal Frequencies for Sensing using System Augmentation and Optimal Feedback Auxiliary Signals

Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/76542/1/AIAA-2008-2085-567.pd

Exploiting Chaotic Dynamics for Detecting Parametric Variations in Aeroelastic Systems

Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/76656/1/AIAA-9556-135.pd