Non-linear threshold autoregressive models for non-linear random vibrations

Time series models for non-linear random vibrations are discussed from the viewpoint of the specification of the dynamics of the damping and restoring force of vibrations, and a non-linear threshold autoregressive model is introduced. Typical non-linear phenomena of vibrations are demonstrated using the models. Stationarity conditions and some structural aspects of the model are briefly discussed. Applications of the model in the statistical analysis of real data are also shown with numerical results.

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Local Gaussian modelling of stochastic dynamical systems in the analysis of non-linear random vibrations

Journal of Applied Probability ◽

10.1017/s0021900200117115 ◽

1986 ◽

Vol 23 (A) ◽

pp. 241-255 ◽

Cited By ~ 1

Author(s):

Tohru Ozaki

Keyword(s):

Time Series ◽

Present Method ◽

Linear Time ◽

Time Series Models ◽

Random Vibrations ◽

Stochastic Dynamical Systems ◽

Stochastic Dynamical System ◽

Modelling Method ◽

Non Linear ◽

Dynamical System Models

Stochastic dynamical system models for non-linear random vibrations are considered and their discrete-time version, non-linear time series models are introduced using the local Gaussian modelling method. Some computational problems and implications of the present method in non-linear time series analysis are discussed.

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Non-linear time series models for non-linear random vibrations

Journal of Applied Probability ◽

10.2307/3212926 ◽

1980 ◽

Vol 17 (1) ◽

pp. 84-93 ◽

Cited By ~ 50

Author(s):

T. Ozaki

Keyword(s):

Time Series ◽

Linear Time ◽

Time Series Models ◽

Random Vibrations ◽

Duffing's Equation ◽

Duffing’S Equation ◽

Non Linear ◽

Linear Vibrations ◽

Typical Behaviour

Non-linear time series models for non-linear vibrations are presented. Some typical behaviour of non-linear vibrations generated from Duffing's equation or van der Pol's equation are explained through the models.

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Non-linear time series models for non-linear random vibrations

Journal of Applied Probability ◽

10.1017/s0021900200046829 ◽

1980 ◽

Vol 17 (01) ◽

pp. 84-93 ◽

Cited By ~ 8

Author(s):

T. Ozaki

Keyword(s):

Time Series ◽

Linear Time ◽

Time Series Models ◽

Random Vibrations ◽

Duffing's Equation ◽

Duffing’S Equation ◽

Non Linear ◽

Linear Vibrations ◽

Typical Behaviour

Non-linear time series models for non-linear vibrations are presented. Some typical behaviour of non-linear vibrations generated from Duffing's equation or van der Pol's equation are explained through the models.

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Comparison of predictions of rainfall-runoff models for changes in rainfall in the Murray-Darling Basin

Hydrology and Earth System Sciences Discussions ◽

10.5194/hessd-8-917-2011 ◽

2011 ◽

Vol 8 (1) ◽

pp. 917-955 ◽

Cited By ~ 3

Author(s):

J. M. Whyte ◽

A. Plumridge ◽

A. V. Metcalfe

Keyword(s):

Time Series ◽

Finite Impulse Response ◽

Daily Rainfall ◽

Time Series Models ◽

Rainfall Runoff ◽

Threshold Autoregressive ◽

Threshold Autoregressive Model ◽

Murray Darling Basin ◽

Nonlinear Autoregressive ◽

Selection Of

Abstract. Management of water resources requires an appreciation for how climate change, in particular changes in rainfall, affects the volume of water available in runoff. While there are many studies that use hydrological models for this purpose, comparisons of predictions appear much less commonly in the literature. This paper aims to contribute to this discussion by proposing methods for evaluating the effect on daily runoff projections of rainfall-runoff models when historical daily rainfall inputs are scaled by factors that increase and decrease the rainfall. Considered are the widely used lumped conceptual model SIMHYD and a selection of time series models which feature lagged runoff and rainfall terms. In particular these are AutoRegressive with eXogenous input (ARX), a variant containing nonlinear autoregressive runoff terms (NARX), a model for the log transform of runoff, a finite impulse response model (FIR) and a two regime threshold autoregressive model with exogenous input (TARX). Results show that SIMHYD and the single regime time series models considered have very different behaviour under scaled input rainfall. Reasons for the discrepancy are discussed. The amplification of the rainfall change observed for SIMHYD is consistent with claims that a 1% change in rainfall leads to a 2–3% change in runoff in the Murray-Darling Basin.

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Local Gaussian modelling of stochastic dynamical systems in the analysis of non-linear random vibrations

Journal of Applied Probability ◽

10.2307/3214356 ◽

1986 ◽

Vol 23 (A) ◽

pp. 241-255 ◽

Cited By ~ 3

Author(s):

Tohru Ozaki

Keyword(s):

Time Series ◽

Present Method ◽

Linear Time ◽

Time Series Models ◽

Random Vibrations ◽

Stochastic Dynamical Systems ◽

Stochastic Dynamical System ◽

Modelling Method ◽

Non Linear ◽

Dynamical System Models

Stochastic dynamical system models for non-linear random vibrations are considered and their discrete-time version, non-linear time series models are introduced using the local Gaussian modelling method. Some computational problems and implications of the present method in non-linear time series analysis are discussed.

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Downside risk asset pricing revisited: a new non-linear threshold model

The Journal of Risk ◽

10.21314/jor.2010.218 ◽

2010 ◽

Vol 13 (1) ◽

pp. 129-159

Author(s):

Jose Olmo

Keyword(s):

Asset Pricing ◽

Threshold Model ◽

Downside Risk ◽

Linear Threshold ◽

Non Linear ◽

Linear Threshold Model

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Multivariate linear time series models

Advances in Applied Probability ◽

10.2307/1427286 ◽

1984 ◽

Vol 16 (3) ◽

pp. 492-561 ◽

Cited By ~ 107

Author(s):

E. J. Hannan ◽

L. Kavalieris

Keyword(s):

Limit Theorems ◽

Analysis Of Algorithms ◽

Linear Time ◽

Asymptotic Properties ◽

Real Data ◽

Rates Of Convergence ◽

Structure Theory ◽

Time Series Models ◽

Transfer Model ◽

Rational Transfer

This paper is in three parts. The first deals with the algebraic and topological structure of spaces of rational transfer function linear systems—ARMAX systems, as they have been called. This structure theory is dominated by the concept of a space of systems of order, or McMillan degree, n, because of the fact that this space, M(n), can be realised as a kind of high-dimensional algebraic surface of dimension n(2s + m) where s and m are the numbers of outputs and inputs. In principle, therefore, the fitting of a rational transfer model to data can be considered as the problem of determining n and then the appropriate element of M(n). However, the fact that M(n) appears to need a large number of coordinate neighbourhoods to cover it complicates the task. The problems associated with this program, as well as theory necessary for the analysis of algorithms to carry out aspects of the program, are also discussed in this first part of the paper, Sections 1 and 2.The second part, Sections 3 and 4, deals with algorithms to carry out the fitting of a model and exhibits these algorithms through simulations and the analysis of real data.The third part of the paper discusses the asymptotic properties of the algorithm. These properties depend on uniform rates of convergence being established for covariances up to some lag increasing indefinitely with the length of record, T. The necessary limit theorems and the analysis of the algorithms are given in Section 5. Many of these results are of interest independent of the algorithms being studied.

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Seismic Strengthening Effects of Full-Size Reinforced Concrete Frame Retrofitted with Novel Concrete-Filled Tube Modular Frame by Pseudo-Dynamic Testing

Applied Sciences ◽

10.3390/app11114898 ◽

2021 ◽

Vol 11 (11) ◽

pp. 4898

Author(s):

Jin-Seon Kim ◽

Ju-Seong Jung ◽

Dong-Keun Jung ◽

Eui-Yong Kim ◽

Kang-Seok Lee

Keyword(s):

Dynamic Analysis ◽

Shear Failure ◽

Dynamic Testing ◽

Seismic Intensity ◽

Seismic Retrofitting ◽

Restoring Force ◽

Rc Structures ◽

Linear Dynamic ◽

Non Linear ◽

Force Characteristics

The present study proposes a new seismic retrofitting method using a concrete-filled tube modular frame (CFT-MF) system, a novel technique to overcome and improve the limitations of existing seismic strengthening methods. This CFT-MF seismic retrofitting method makes the most of the advantages of both concrete and steel pipes, thereby significantly improving constructability and increasing integration between the existing structure and the reinforcement joints. This method falls into the category of typical seismic retrofitting methods that focus on increasing strength, in which the required amount of seismic reinforcement can be easily estimated. Therefore, the method provides an easy solution to improving the strength of existing reinforced concrete (RC) structures with non-seismic details that are prone to shear failure. In the present study, a full-size two-story test frame modeled from existing domestic RC structures with non-seismic details was subjected to pseudo-dynamic testing. As a result, the effect of the CFT-MF system, when applied to existing RC structures, was examined and verified, especially as to its seismic retrofitting performance, i.e., restoring force characteristics, stiffness reinforcement, and seismic response control. In addition, based on the pseudo-dynamic testing results, a restoring force characteristics model was proposed to implement non-linear dynamic analysis of a structure retrofitted with the CFT-MF system (i.e., the test frame). Finally, based on the proposed restoring force characteristics, non-linear dynamic analysis was conducted, and the results were compared with those obtained by the pseudo-dynamic tests. The results showed that the RC frame (building) with no retrofitting measures applied underwent shear failure at a seismic intensity of 200 cm/s2, the threshold applied in seismic design in Korea. In contrast, in the frame (building) retrofitted with the CFT-MF system, only minor earthquake damage was observed, and even when the maximum seismic intensity (300 cm/s2) that may occur in Korean was applied, small-scale damage was observed. These results confirmed the validity of the seismic retrofitting method based on the CFT-MF system developed in the present study. The non-linear dynamic analysis and the pseudo-dynamic test showed similar results, with an average deviation of 10% or less in seismic response load and displacement.

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Subgeometric ergodicity and β-mixing

Journal of Applied Probability ◽

10.1017/jpr.2020.108 ◽

2021 ◽

Vol 58 (3) ◽

pp. 594-608

Author(s):

Mika Meitz ◽

Pentti Saikkonen

Keyword(s):

Markov Chains ◽

Autoregressive Model ◽

The Self ◽

Geometric Ergodicity ◽

Threshold Autoregressive ◽

Threshold Autoregressive Model ◽

Mixing Coefficients ◽

Initial Distributions

AbstractIt is well known that stationary geometrically ergodic Markov chains are $\beta$ -mixing (absolutely regular) with geometrically decaying mixing coefficients. Furthermore, for initial distributions other than the stationary one, geometric ergodicity implies $\beta$ -mixing under suitable moment assumptions. In this note we show that similar results hold also for subgeometrically ergodic Markov chains. In particular, for both stationary and other initial distributions, subgeometric ergodicity implies $\beta$ -mixing with subgeometrically decaying mixing coefficients. Although this result is simple, it should prove very useful in obtaining rates of mixing in situations where geometric ergodicity cannot be established. To illustrate our results we derive new subgeometric ergodicity and $\beta$ -mixing results for the self-exciting threshold autoregressive model.

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