Деякі особливості використання ядер лінійних AR та ARMA-процесів як діагностичних ознак технічного стану обертових вузлів генераторів вітроустановок

Розглянуто деякі методи діагностування технічного стану вузлів генераторів вітроустановок. Як математичні моделі вібрацій вузлів генераторів вітроустановок пропонується використати лінійні процеси авторегресії (AR) та авторегресії – ковзного середнього (ARMA). Показано приклади оцінки ядер лінійних процесів авторегресії різних порядків. Наведено результати оцінки ядер вібраційних сигналів підшипникового вузла генератора вітроустановки, що встановлений на дослідницькому стенді.Methods of technical state of wind generator parts aare discussed. Linear AR and ARMA mathematical models are proposed as mathematical models of vibration signals of wind generator parts. Examples of linear AR and ARMA kernel estimation for the different processes with different orders are represented. Estimation of vibration signals kernels estimations of wind generator part which stand at special experimental stand

Least squares estimation of a shift in linear processes

This paper considers a mean shift with an unknown shift point in a linear process and estimates the unknown shift point (change point) by the method of least squares. Pre-shift and post-shift means are estimated concurrently with the change point. The consistency and the rate of convergence for the estimated change point are established. The asymptotic distribution for the change point estimator is obtained when the magnitude of shift is small. It is shown that serial correlation affects the variance of the change point estimator via the sum of the coefficients (impulses) of the linear process. When the underlying process is an ARMA, a mean shift causes overestimation of its order. A simple procedure is suggested to mitigate the bias in order estimation.Mean shift; linear processes; change point; rate of convergence; order estimation; generalized residuals

A construction of continuous-time ARMA models by iterations of Ornstein-Uhlenbeck processes

We present a construction of a family of continuous-time ARMA processes based on p iterations of the linear operator that maps a Lévy process onto an Ornstein-Uhlenbeck process. The construction resembles the procedure to build an AR(p) from an AR(1). We show that this family is in fact a subfamily of the well-known CARMA(p,q) processes, with several interesting advantages, including a smaller number of parameters. The resulting processes are linear combinations of Ornstein-Uhlenbeck processes all driven by the same L´evy process. This provides a straightforward computation of covariances, a state-space model representation and methods for estimating parameters. Furthermore, the discrete and equally spaced sampling of the process turns to be an ARMA(p, p-1) process. We propose methods for estimating the parameters of the iterated Ornstein-Uhlenbeck process when the noise is either driven by a Wiener or a more general Lévy process, and show simulations and applications to real data.Peer ReviewedPostprint (published version

A construction of continuous-time ARMA models by iterations of Ornstein-Uhlenbeck processes

We present a construction of a family of continuous-time ARMA processes based on p iterations of the linear operator that maps a Lévy process onto an Ornstein-Uhlenbeck process. The construction resembles the procedure to build an AR(p) from an AR(1). We show that this family is in fact a subfamily of the well-known CARMA(p,q) processes, with several interesting advantages, including a smaller number of parameters. The resulting processes are linear combinations of Ornstein-Uhlenbeck processes all driven by the same L´evy process. This provides a straightforward computation of covariances, a state-space model representation and methods for estimating parameters. Furthermore, the discrete and equally spaced sampling of the process turns to be an ARMA(p, p-1) process. We propose methods for estimating the parameters of the iterated Ornstein-Uhlenbeck process when the noise is either driven by a Wiener or a more general Lévy process, and show simulations and applications to real data.Peer ReviewedPostprint (published version

Exact Discrete Representations of Linear Continuous Time Models with Mixed Frequency Data

The time aggregation of vector linear processes containing (i) mixed stock- ow data and (ii) aggregated at mixed frequencies, is explored, focusing on a method to translate the parameters of the underlying continuous time model into those of an equivalent model of the observed data. Based on manipulations of a general state-space form, the results may be used to model multiple frequencies or aggregation schemes. Estimation of the continuous time parameters via the ARMA representation of the observable data vector is discussed and demonstrated in an application to model stock price and dividend data. Simulation evidence suggests that these estimators have superior properties to the traditional approach of concentrating the data to a single low frequency

Analytic performance evaluation of cumulant-based arma system identification methods

The authors perform an analytic study of some cumulant-based methods for estimating the AR parameters of ARMA processes. The analysis includes new AR identifiability results for pure AR process and the analytic performance evaluation of system identification methods based on cumulants. The authors present examples of pure AR processes that are not identifiable via the normal equations based on the diagonal third-order cumulant slice. The results of the performance evaluation are illustrated graphically with plots of the variance of the estimates as a function of the parameters of the process.Peer ReviewedPostprint (published version