scholarly journals Recovery of Differential Equations from Impulse Response Time Series Data for Model Identification and Feature Extraction

Vibration ◽  
2019 ◽  
Vol 2 (1) ◽  
pp. 25-46 ◽  
Author(s):  
Merten Stender ◽  
Sebastian Oberst ◽  
Norbert Hoffmann
Keyword(s):  
Time Series ◽  
Differential Equations ◽  
Time Series Data ◽  
Model Identification ◽  
Transient Behavior ◽  
Series Data ◽  
Special Focus ◽  
Suitable Model ◽  
Reconstruction Method ◽  
Minimal Models

Time recordings of impulse-type oscillation responses are short and highly transient. These characteristics may complicate the usage of classical spectral signal processing techniques for (a) describing the dynamics and (b) deriving discriminative features from the data. However, common model identification and validation techniques mostly rely on steady-state recordings, characteristic spectral properties and non-transient behavior. In this work, a recent method, which allows reconstructing differential equations from time series data, is extended for higher degrees of automation. With special focus on short and strongly damped oscillations, an optimization procedure is proposed that fine-tunes the reconstructed dynamical models with respect to model simplicity and error reduction. This framework is analyzed with particular focus on the amount of information available to the reconstruction, noise contamination and nonlinearities contained in the time series input. Using the example of a mechanical oscillator, we illustrate how the optimized reconstruction method can be used to identify a suitable model and how to extract features from uni-variate and multivariate time series recordings in an engineering-compliant environment. Moreover, the determined minimal models allow for identifying the qualitative nature of the underlying dynamical systems as well as testing for the degree and strength of nonlinearity. The reconstructed differential equations would then be potentially available for classical numerical studies, such as bifurcation analysis. These results represent a physically interpretable enhancement of data-driven modeling approaches in structural dynamics.

scholarly journals Recovery of Differential Equations from Impulse Response Time Series Data for Model Identification and Feature Extraction

2018 ◽  
Author(s):  
Merten Stender ◽  
Sebastian Oberst ◽  
Norbert Hoffmann
Keyword(s):  
Time Series ◽  
Differential Equations ◽  
Time Series Data ◽  
Model Identification ◽  
Transient Behavior ◽  
Series Data ◽  
Special Focus ◽  
Suitable Model ◽  
Reconstruction Method ◽  
Minimal Models

Time recordings of impulse-type oscillation responses are short and highly transient. These characteristics may complicate the usage of classical spectral signal processing techniques for a) describing the dynamics and b) deriving discriminative features from the data. However, common model identification and validation techniques mostly rely on steady-state recordings, characteristic spectral properties and non-transient behavior. In this work, a recent method, which allows reconstructing differential equations from time series data, is extended for higher degrees of automation. With special focus on short and strongly damped oscillations, an optimization procedure is proposed that fine-tunes the reconstructed dynamical models with respect to model simplicity and error reduction. This framework is analyzed with particular focus on the amount of information available to the reconstruction, noise contamination and non-linearities contained in the time series input. Using the example of a mechanical oscillator, we illustrate how the optimized reconstruction method can be used to identify a suitable model and to extract features from uni-variate and multivariate time series recordings in an engineering-compliant environment. Moreover, the determined minimal models allow for identifying the qualitative nature of the underlying dynamical systems as well as testing for the degree and strength of non-linearity. The reconstructed differential equations would then be potentially available for classical numerical studies, such as bifurcation analysis. These results represent a physically interpretable enhancement of data-driven modeling approaches in structural dynamics.

EFFECTS OF TREND AND PERIODICITY ON THE CORRELATION DIMENSION AND THE LYAPUNOV EXPONENTS

2008 ◽  
Vol 18 (12) ◽  
pp. 3679-3687 ◽  
Author(s):  
AYDIN A. CECEN ◽  
CAHIT ERKAL
Keyword(s):  
Time Series ◽  
Lyapunov Exponent ◽  
Lyapunov Exponents ◽  
Correlation Dimension ◽  
Time Series Data ◽  
Logistic Map ◽  
Model Identification ◽  
Series Data ◽  
Largest Lyapunov Exponent ◽  
The Impact

We present a critical remark on the pitfalls of calculating the correlation dimension and the largest Lyapunov exponent from time series data when trend and periodicity exist. We consider a special case where a time series Zi can be expressed as the sum of two subsystems so that Zi = Xi + Yi and at least one of the subsystems is deterministic. We show that if the trend and periodicity are not properly removed, correlation dimension and Lyapunov exponent estimations yield misleading results, which can severely compromise the results of diagnostic tests and model identification. We also establish an analytic relationship between the largest Lyapunov exponents of the subsystems and that of the whole system. In addition, the impact of a periodic parameter perturbation on the Lyapunov exponent for the logistic map and the Lorenz system is discussed.

Inference of gene regulatory networks based on nonlinear ordinary differential equations

2020 ◽  
Vol 36 (19) ◽  
pp. 4885-4893 ◽  
Author(s):  
Baoshan Ma ◽  
Mingkun Fang ◽  
Xiangtian Jiao
Keyword(s):  
Gene Expression ◽  
Time Series ◽  
Steady State ◽  
Differential Equations ◽  
Gene Regulatory Networks ◽  
Regulatory Networks ◽  
Time Series Data ◽  
Series Data ◽  
State Data ◽  
Gene Regulatory

Abstract Motivation Gene regulatory networks (GRNs) capture the regulatory interactions between genes, resulting from the fundamental biological process of transcription and translation. In some cases, the topology of GRNs is not known, and has to be inferred from gene expression data. Most of the existing GRNs reconstruction algorithms are either applied to time-series data or steady-state data. Although time-series data include more information about the system dynamics, steady-state data imply stability of the underlying regulatory networks. Results In this article, we propose a method for inferring GRNs from time-series and steady-state data jointly. We make use of a non-linear ordinary differential equations framework to model dynamic gene regulation and an importance measurement strategy to infer all putative regulatory links efficiently. The proposed method is evaluated extensively on the artificial DREAM4 dataset and two real gene expression datasets of yeast and Escherichia coli. Based on public benchmark datasets, the proposed method outperforms other popular inference algorithms in terms of overall score. By comparing the performance on the datasets with different scales, the results show that our method still keeps good robustness and accuracy at a low computational complexity. Availability and implementation The proposed method is written in the Python language, and is available at: https://github.com/lab319/GRNs_nonlinear_ODEs Supplementary information Supplementary data are available at Bioinformatics online.

scholarly journals Inferring mechanism from time-series data: Delay-differential equations

1997 ◽  
Vol 110 (3-4) ◽  
pp. 182-194 ◽  
Author(s):  
Stephen P. Ellner ◽  
Bruce E. Kendall ◽  
Simon N. Wood ◽  
Edward McCauley ◽  
Cheryl J. Briggs
Keyword(s):  
Time Series ◽  
Differential Equations ◽  
Delay Differential Equations ◽  
Time Series Data ◽  
Series Data ◽  
Delay Differential

scholarly journals KAJIAN MODEL PERAMALAN KUNJUNGAN WISATAWAN MANCANEGARA DI BANDARA KUALANAMU MEDAN TANPA DAN DENGAN KOVARIAT

2019 ◽  
Vol 3 (1) ◽  
pp. 18-32
Author(s):  
Isti Rochayati ◽  
Utami Dyah Syafitri ◽  
I Made Sumertajaya ◽  
Indonesian Journal of Statistics and Its Applications IJSA
Keyword(s):  
Time Series ◽  
Time Series Data ◽  
Multivariate Time Series ◽  
Model Identification ◽  
Series Data ◽  
Explanatory Variables ◽  
Foreign Tourist ◽  
Currency Exchange ◽  
Inflation Rates ◽  
Internal And External Factors

Foreign tourist arrivals could be considered as time series data. Modelling these data could make use of internal and external factors. The techniques employed here to model these time series data are SARIMA, SARIMAX, VARIMA, and VARIMAX. SARIMA is a model for seasonal data and VARIMA is a model for multivariate time series data. If some explanatory variables are incorporated and have significant influence on the response, the former two models become SARIMAX and VARIMAX respectively. Three stages of creating the model are model identification, parameter estimation, and model diagnostics. The variables used in this study were foreign tourist visits, international passenger arrivals, inflation rates, currency exchange rates, and Gross Regional Domestic Product (GRDP) over the period of 2010-2017. All four models fulfill their model assumptions and therefore could be applied. The best model of foreign tourist arrivals was VARIMA with the value of MAPE testing data = 6.123.

scholarly journals Dynamic Modelling of Sharia-Based Corporate, Islamic Index and Exchange Rate: VAR Model Application

2020 ◽  
Vol 6 (2) ◽  
pp. 195
Author(s):  
Hasrun Afandi Umpusinga ◽  
Atika Riasari ◽  
Fajrin Satria Dwi Kesumah
Keyword(s):  
Time Series ◽  
Exchange Rate ◽  
Time Series Data ◽  
Multivariate Time Series ◽  
Dynamic Modelling ◽  
Series Data ◽  
Var Model ◽  
Suitable Model ◽  
Data Set ◽  
Dynamic Relationship

Indonesia is one of largest users of sharia-based compliant recently which bring into many concerns how the sharia stocks listing in the most valuable sharia stocks index in Indonesia perform and correlate with other variables, particularly exchange rates. The study aims to analysis the causal relationship and to forecast the performances of sharia-based stocks and its Islamic index in Indonesia along with the volatility of exchange rate. Vector Autoregressive (VAR) model is applied as the method to analyse the multivariate time series as it is believed as the suitable model in predicting such time-series data in the scope of multivariate variables. The finding suggests VAR(1) model is the fitted model as such to both analyse its dynamic relationship and forecast the data set for the next 24 weeks. While the prediction shows the JII has an increasing data, both ANTM and EXR are predicted to have a stable volatility. In addition, granger causality defines variables to have effect in its respective variables, and IRF describes the shocks in one variable cause another variable is relatively difficult in reaching its zero condition in short-term period.

scholarly journals Self-Identification ResNet-ARIMA Forecasting Model

2020 ◽  
Vol 15 ◽  
Keyword(s):  
Time Series ◽  
Autocorrelation Function ◽  
Time Series Data ◽  
Moving Average ◽  
Arima Model ◽  
Model Identification ◽  
Series Data ◽  
Percentage Error ◽  
Forecasting Model ◽  
Partial Autocorrelation Function

The challenging endeavor of a time series forecast model is to predict the future time series data accurately. Traditionally, the fundamental forecasting model in time series analysis is the autoregressive integrated moving average model or the ARIMA model requiring a model identification of a three-component vector which are the autoregressive order, the differencing order, and the moving average order before fitting coefficients of the model via the Box-Jenkins method. A model identification is analyzed via the sample autocorrelation function and the sample partial autocorrelation function which are effective tools for identifying the ARMA order but it is quite difficult for analysts. Even though a likelihood based-method is presented to automate this process by varying the ARIMA order and choosing the best one with the smallest criteria, such as Akaike information criterion. Nevertheless the obtained ARIMA model may not pass the residual diagnostic test. This paper presents the residual neural network model, called the self-identification ResNet-ARIMA order model to automatically learn the ARIMA order from known ARIMA time series data via sample autocorrelation function, the sample partial autocorrelation function and differencing time series images. In this work, the training time series data are randomly simulated and checked for stationary and invertibility properties before they are used. The result order from the model is used to generate and fit the ARIMA model by the Box-Jenkins method for predicting future values. The whole process of the forecasting time series algorithm is called the self-identification ResNet-ARIMA algorithm. The performance of the residual neural network model is evaluated by Precision, Recall and F1-score and is compared with the likelihood basedmethod and ResNET50. In addition, the performance of the forecasting time series algorithm is applied to the real world datasets to ensure the reliability by mean absolute percentage error, symmetric mean absolute percentage error, mean absolute error and root mean square error and this algorithm is confirmed with the residual diagnostic checks by the Ljung-Box test. From the experimental results, the new methodologies of this research outperforms other models in terms of identifying the order and predicting the future values.

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