Bayesian Segmentation of Piecewise Linear Regression Models Using Reversible Jump MCMC Algorithm

Piecewise linear regression models are very flexible models for modeling the data. If the piecewise linear regression models are matched against the data, then the parameters are generally not known. This paper studies the problem of parameter estimation ofpiecewise linear regression models. The method used to estimate the parameters ofpicewise linear regression models is Bayesian method. But the Bayes estimator can not be found analytically. To overcome these problems, the reversible jump MCMC （Marcov Chain Monte Carlo） algorithm is proposed. Reversible jump MCMC algorithm generates the Markov chain converges to the limit distribution of the posterior distribution of the parameters ofpicewise linear regression models. The resulting Markov chain is used to calculate the Bayes estimator for the parameters of picewise linear regression models.

Piecewise Linear Analysis for Pseudo-elasticity of Shape Memory Alloy (SMA)

Based on the Brinson constitutive model of SMA, a piecewise linear model for the hysteresis loop of pseudo-elasticity is proposed and applied in the analysis of responses of an SMA-spring-mass system under initial velocity activation. The histories of displacement and velocity of the mass, and the response of stress of SMA are calculated with Brinson’s model and the piecewise linear model. The difference of results of the two models is not significant. The calculation with piecewise-linear model needs no iteration and is highly efficient.

A PIECEWISE LINEAR MODEL FOR ANALYZING THIN FILM/SUBSTRATE STRUCTURE IN FLEXIBLE ELECTRONICS

The conventional analytical method of predicting strain in a thin film under bending is restricted to the uniform material assumption, while in flexible electronics, the film/substrate structure is widely used with mismatched material properties taken into account. In this paper,a piecewise model is proposed to analyze the axial strain in a thin film of flexible electronics with the shear modification factor and principle of virtual work. The excellent agreement between analytical prediction and finite element results indicates that the model is capable of predicting the strain of the film/substrate structure in flexible electronics, whose mechanical stability and electrical performance is dependent on the strain state in the thin film.

Partition method for improvement of piecewise linear model with full envelope covered

Since ambient conditions vary in a wide range within the full flight envelope,the existing piecewise linear model(PLM),which is based on sea-level static condition with use of corrected parameters for other points in the flight envelope,cannot meet the accuracy for replacing the nonlinear model.To obtain more accurate linear models,a method of partitioning the flight envelope over a grid of Mach number and altitude boxes was suggested.Then,a set of linear models for a given operating condition was selected by picking the nearest(Mach number,altitude)box in the flight envelope.Through the selected set of linear models,interpolating for power level based on a weighted sum of corrected rotor speeds can obtain a linear model with acceptable accuracy.Simulation results of different points within the full flight envelope showed that the maximum error between nonlinear model and the existing PLM was more than 50%,while the maximum error between nonlinear model and the improved PLM was within 8%.It is concluded that the improved PLM performs accurately,especially under the non-standard conditions.In addition,the improved PLM can satisfy the real-time requirement better than the existing PLM.

Subspace Trajectory Piecewise-Linear Model Order Reduction for Nonlinear Circuits

Despite the efficiency of trajectory piecewise-linear(TPWL)model order re-duction(MOR)for nonlinear circuits,it needs large amount of expansion points forlarge-scale nonlinear circuits.This will inevitably increase the model size as well as the simulation time of the resulting reduced macromodels.In this paper,subspaceTPWL-MOR approach is developed for the model order reduction of nonlinear cir-cuits.By breaking the high-dimensional state space into several subspaces with much lower dimensions,the subspace TPWL-MOR has very promising advantages of re-ducing the number of expansion points as well as increasing the effective region of thereduced-order model in the state space.As a result,the model size and the accuracy of the TWPL model can be greatly improved.The numerical results have shown dra-matic reduction in the model size as well as the improvement in accuracy by using the subspace TPWL-MOR compared with the conventional TPWL-MOR approach.