scholarly journals An efficient method for vibration equations with time varying coefficients and nonlinearities

2021 ◽  
pp. 146134842110251
Author(s):  
Jinsong Yang ◽  
Jingsong Xie ◽  
Gaige Chen ◽  
Jinglong Chen
Keyword(s):  
Nonlinear Vibration ◽  
Efficient Method ◽  
Stiffness Matrix ◽  
Time Varying ◽  
Rotor Systems ◽  
Varying Coefficients ◽  
Multistage System ◽  
Shaft System ◽  
Time Varying Coefficients ◽  
Time Required

An efficient method for solving vibration equations is the basis of the vibration analysis of a cracked multistage blade–disk–shaft system. However, dynamic equations are usually time varying and nonlinear, and the time required for solving is greatly increased accompanied by an increase in the model order caused by the multistage system and the nonlinearity caused by cracks. In this article, an efficient method for solving the time varying and nonlinear vibration equation is investigated. In the proposed method, the time varying terms are transformed into constant terms, while the local nonlinear matrix of the cracked blade is separated from the assembly stiffness matrix under the constraint of proper orthogonal decomposition (POD) transformation rules. Furthermore, the POD transformations of the constant terms and the linear assembled stiffness matrix can be implemented in the pretreatment steps to achieve a more efficient POD reduction operation. This research provides a method for efficiently performing the comprehensive and rapid analysis of nonlinear vibration characteristics of rotor systems.

COINTEGRATING REGRESSIONS WITH TIME VARYING COEFFICIENTS

1999 ◽  
Vol 15 (5) ◽  
pp. 664-703 ◽  
Author(s):  
Joon Y. Park ◽  
Sang B. Hahn
Keyword(s):  
Efficient Method ◽  
Demand Function ◽  
Model Specification ◽  
Time Varying ◽  
Smooth Functions ◽  
Varying Coefficients ◽  
Automobile Demand ◽  
Time Varying Coefficients ◽  
The U.S ◽  
Over Time

This paper considers cointegrating regressions with time varying coefficients. The coefficients are modeled as smooth functions evolving over time. It is shown that they can be estimated nonparametrically, using suitably modified series estimators. Presented is the efficient method of estimation, which relies on simple prefiltering of the data and preestimation of the model. The test for the adequacy of model specification is also developed. Our model and statistical methods are applied to analyze the U.S. automobile demand function.

scholarly journals The VIT Transform Approach to Discrete-Time Signals and Linear Time-Varying Systems

Eng ◽  
2021 ◽  
Vol 2 (1) ◽  
pp. 99-125
Author(s):  
Edward W. Kamen
Keyword(s):  
Discrete Time ◽  
Initial Conditions ◽  
Linear Time ◽  
Order Term ◽  
Initial Time ◽  
Time Varying ◽  
Varying Coefficients ◽  
Time Signals ◽  
Time Varying Systems ◽  
Time Varying Coefficients

A transform approach based on a variable initial time (VIT) formulation is developed for discrete-time signals and linear time-varying discrete-time systems or digital filters. The VIT transform is a formal power series in z−1, which converts functions given by linear time-varying difference equations into left polynomial fractions with variable coefficients, and with initial conditions incorporated into the framework. It is shown that the transform satisfies a number of properties that are analogous to those of the ordinary z-transform, and that it is possible to do scaling of z−i by time functions, which results in left-fraction forms for the transform of a large class of functions including sinusoids with general time-varying amplitudes and frequencies. Using the extended right Euclidean algorithm in a skew polynomial ring with time-varying coefficients, it is shown that a sum of left polynomial fractions can be written as a single fraction, which results in linear time-varying recursions for the inverse transform of the combined fraction. The extraction of a first-order term from a given polynomial fraction is carried out in terms of the evaluation of zi at time functions. In the application to linear time-varying systems, it is proved that the VIT transform of the system output is equal to the product of the VIT transform of the input and the VIT transform of the unit-pulse response function. For systems given by a time-varying moving average or an autoregressive model, the transform framework is used to determine the steady-state output response resulting from various signal inputs such as the step and cosine functions.

scholarly journals Estimating latent group structure in time-varying coefficient panel data models

2019 ◽  
Author(s):  
Jia Chen
Keyword(s):  
Panel Data ◽  
Data Models ◽  
Panel Data Models ◽  
Time Varying ◽  
Clustering Method ◽  
Varying Coefficient ◽  
Varying Coefficients ◽  
Time Varying Coefficients ◽  
Latent Group ◽  
Group Structures

Summary This paper studies the estimation of latent group structures in heterogeneous time-varying coefficient panel data models. While allowing the coefficient functions to vary over cross-sections provides a good way to model cross-sectional heterogeneity, it reduces the degree of freedom and leads to poor estimation accuracy when the time-series length is short. On the other hand, in a lot of empirical studies, it is not uncommon to find that heterogeneous coefficients exhibit group structures where coefficients belonging to the same group are similar or identical. This paper aims to provide an easy and straightforward approach for estimating the underlying latent groups. This approach is based on the hierarchical agglomerative clustering (HAC) of kernel estimates of the heterogeneous time-varying coefficients when the number of groups is known. We establish the consistency of this clustering method and also propose a generalised information criterion for estimating the number of groups when it is unknown. Simulation studies are carried out to examine the finite-sample properties of the proposed clustering method as well as the post-clustering estimation of the group-specific time-varying coefficients. The simulation results show that our methods give comparable performance to the penalised-sieve-estimation-based classifier-LASSO approach by Su et al. (2018), but are computationally easier. An application to a panel study of economic growth is also provided.

scholarly journals Gray’s Time-Varying Coefficients Model for Posttransplant Survival of Pediatric Liver Transplant Recipients with a Diagnosis of Cancer

2013 ◽  
Vol 2013 ◽  
pp. 1-13 ◽  
Author(s):  
Yi Ren ◽  
Chung-Chou H. Chang ◽  
Gabriel L. Zenarosa ◽  
Heather E. Tomko ◽  
Drew Michael S. Donnell ◽  
...  
Keyword(s):  
Liver Transplant ◽  
Failure Time ◽  
Penalized Splines ◽  
Time Varying ◽  
Piecewise Constant ◽  
Varying Coefficients ◽  
Covariate Effects ◽  
Pediatric Liver ◽  
Time Varying Coefficients ◽  
Pediatric Liver Transplant

Transplantation is often the only viable treatment for pediatric patients with end-stage liver disease. Making well-informed decisions on when to proceed with transplantation requires accurate predictors of transplant survival. The standard Cox proportional hazards (PH) model assumes that covariate effects are time-invariant on right-censored failure time; however, this assumption may not always hold. Gray’s piecewise constant time-varying coefficients (PC-TVC) model offers greater flexibility to capture the temporal changes of covariate effects without losing the mathematical simplicity of Cox PH model. In the present work, we examined the Cox PH and Gray PC-TVC models on the posttransplant survival analysis of 288 pediatric liver transplant patients diagnosed with cancer. We obtained potential predictors through univariable(P<0.15)and multivariable models with forward selection(P<0.05)for the Cox PH and Gray PC-TVC models, which coincide. While the Cox PH model provided reasonable average results in estimating covariate effects on posttransplant survival, the Gray model using piecewise constant penalized splines showed more details of how those effects change over time.

scholarly journals Survey Expectations and Learning

2021 ◽  
pp. 3-27
Author(s):  
Sergey Slobodyan ◽  
◽  
Raf Wouters ◽  
◽  
Keyword(s):  
Real Time ◽  
Time Variation ◽  
Autoregressive Model ◽  
Dsge Models ◽  
Inflation Expectations ◽  
Time Varying ◽  
Time Data ◽  
Varying Coefficients ◽  
Real Time Data ◽  
Time Varying Coefficients

In this paper, we evaluate a model that describes real-time inflation data together with the inflation expectations measured by the Survey of Professional Forecasters (SPF). We work with a second-order autoregressive model in which the agents learn over time the intercept and persistence coefficients based on real-time data. To model the process of revisions in real time data, we allow for news and noise disturbances. In contrast to the usual time-varying parameter vector autoregression, we use non-linear Kalman filter techniques to estimate the time-varying coefficients of the underlying inflation process. We identify systematic changes in the persistence of the inflation process and in the long-run expected inflation rate that are implied by the model. The inflation forecasts implied by the model are then compared with the SPF forecasts. As we cannot reject the hypothesis that the SPF forecasts are produced based on our model, we re-estimate the model using Survey nowcasts and forecasts as additional observables. This augmented model does not change the nature and magnitude of the time variation in the coefficients of the autoregressive model, but it does help to reduce the uncertainty in the estimates. Overall, the estimated time-variation confirms our results on the perceived inflation process present in estimated DSGE models with learning (Slobodyan and Wouters, 2012a, 2012b).

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