Stochastic Modeling of Time Series with Application to Local Damage Detection in Rotating Machinery

2013 ◽  
Vol 569-570 ◽  
pp. 441-448 ◽  
Author(s):  
Jakub Obuchowski ◽  
Agnieszka Wylomanska ◽  
Radoslaw Zimroz
Keyword(s):  
Time Series ◽  
Good Condition ◽  
Real Data ◽  
Statistical Properties ◽  
Normal Operation ◽  
Local Damage ◽  
Data Set ◽  
Time Frequency ◽  
Frequency Map ◽  
Vibration Time

Raw vibration signals measured on the machine housing in industrial conditions are complex and can be modeled as an additive mixture of several processes (with different statistical properties) related to normal operation of machine, damage related to one (or more) of its part, some noise, etc. In the case of local damage in rotating machines, contribution of informative process related to damage is hidden in the raw signal so its detection is difficult. In this paper we propose to use the statistical modeling of vibration time series to identify these components. Building the model of raw signal may be ineffective. It is proposed to decompose signal into set of narrowband sub-signals using time-frequency representation. Next, it is proposed to model each sub-signal in the given frequency range and classify all signals using their statistical properties. We have used several parameters (called selectors because they will be used for selection of sub-signals from time-frequency map for further processing) for analysis of sub-signals. They have base in statistics theory and can be useful for example in testing of normality of data set (vibration time series from machine in good condition is close to Gaussian, damaged not). Results of such modeling will be used in the sub-signals classification procedure but also in defects detection. We illustrate effectiveness of novel technique using real data from heavy machinery system.

scholarly journals Fractional Calculus as a Simple Tool for Modeling and Analysis of Long Memory Process in Industry

Mathematics ◽  
2019 ◽  
Vol 7 (6) ◽  
pp. 511 ◽  
Author(s):  
Ivo Petráš ◽  
Ján Terpák
Keyword(s):  
Time Series ◽  
Fractional Calculus ◽  
Fractional Order ◽  
Long Memory ◽  
Real Data ◽  
Data Set ◽  
Modeling And Analysis ◽  
Long Memory Process ◽  
Real Process ◽  
Definition Of

This paper deals with the application of the fractional calculus as a tool for mathematical modeling and analysis of real processes, so called fractional-order processes. It is well-known that most real industrial processes are fractional-order ones. The main purpose of the article is to demonstrate a simple and effective method for the treatment of the output of fractional processes in the form of time series. The proposed method is based on fractional-order differentiation/integration using the Grünwald–Letnikov definition of the fractional-order operators. With this simple approach, we observe important properties in the time series and make decisions in real process control. Finally, an illustrative example for a real data set from a steelmaking process is presented.

Anomalies and False Rejections

2020 ◽  
Vol 33 (5) ◽  
pp. 2134-2179 ◽  
Author(s):  
Tarun Chordia ◽  
Amit Goyal ◽  
Alessio Saretto
Keyword(s):  
Time Series ◽  
Hypothesis Testing ◽  
Real Data ◽  
Multiple Hypothesis Testing ◽  
Statistical Properties ◽  
Trading Strategies ◽  
Cross Sectional ◽  
Publication Process ◽  
Multiple Hypothesis ◽  
Expected Proportion

Abstract We use information from over 2 million trading strategies randomly generated using real data and from strategies that survive the publication process to infer the statistical properties of the set of strategies that could have been studied by researchers. Using this set, we compute $t$-statistic thresholds that control for multiple hypothesis testing, when searching for anomalies, at 3.8 and 3.4 for time-series and cross-sectional regressions, respectively. We estimate the expected proportion of false rejections that researchers would produce if they failed to account for multiple hypothesis testing to be about 45%.

Bayesian Structural Time Series

2020 ◽  
Vol 12 (1) ◽  
pp. 54-61
Author(s):  
Abdullah M. Almarashi ◽  
Khushnoor Khan
Keyword(s):  
Time Series ◽  
Stock Prices ◽  
Predictive Accuracy ◽  
Local Level ◽  
Real Life ◽  
Secondary Data ◽  
Real Data ◽  
Data Set ◽  
Structural Time Series ◽  
Structural Time

The current study focused on modeling times series using Bayesian Structural Time Series technique (BSTS) on a univariate data-set. Real-life secondary data from stock prices for flying cement covering a period of one year was used for analysis. Statistical results were based on simulation procedures using Kalman filter and Monte Carlo Markov Chain (MCMC). Though the current study involved stock prices data, the same approach can be applied to complex engineering process involving lead times. Results from the current study were compared with classical Autoregressive Integrated Moving Average (ARIMA) technique. For working out the Bayesian posterior sampling distributions BSTS package run with R software was used. Four BSTS models were used on a real data set to demonstrate the working of BSTS technique. The predictive accuracy for competing models was assessed using Forecasts plots and Mean Absolute Percent Error (MAPE). An easyto-follow approach was adopted so that both academicians and practitioners can easily replicate the mechanism. Findings from the study revealed that, for short-term forecasting, both ARIMA and BSTS are equally good but for long term forecasting, BSTS with local level is the most plausible option.

scholarly journals The KM-Algorithm Identifies Regulated Genes in Time Series Expression Data

2009 ◽  
Vol 2009 ◽  
pp. 1-10
Author(s):  
Martina Bremer ◽  
R. W. Doerge
Keyword(s):  
Gene Expression ◽  
Time Series ◽  
Statistical Power ◽  
Regulatory Networks ◽  
Real Data ◽  
Model Parameters ◽  
Expression Data ◽  
Data Set ◽  
Gene Expression Time Series ◽  
Expression Time

We present a statistical method to rank observed genes in gene expression time series experiments according to their degree of regulation in a biological process. The ranking may be used to focus on specific genes or to select meaningful subsets of genes from which gene regulatory networks can be built. Our approach is based on a state space model that incorporates hidden regulators of gene expression. Kalman (K) smoothing and maximum (M) likelihood estimation techniques are used to derive optimal estimates of the model parameters upon which a proposed regulation criterion is based. The statistical power of the proposed algorithm is investigated, and a real data set is analyzed for the purpose of identifying regulated genes in time dependent gene expression data. This statistical approach supports the concept that meaningful biological conclusions can be drawn from gene expression time series experiments by focusing on strong regulation rather than large expression values.

scholarly journals An Empirical Study of Error Evaluation in Trend and Seasonal Time Series Forecasting Based on SSA

2018 ◽  
pp. 945-960
Author(s):  
Winita Sulandari ◽  
Subanar Subanar ◽  
Suhartono Suhartono ◽  
Herni Utami ◽  
Muhammad Hisyam Lee
Keyword(s):  
Time Series ◽  
Numerical Study ◽  
Singular Spectrum Analysis ◽  
Real Data ◽  
Time Series Forecasting ◽  
Percentage Error ◽  
Error Evaluation ◽  
Data Set ◽  
Seasonal Time Series ◽  
Deterministic Function

SSA (Singular Spectrum Analysis) starts to become a popular method in decomposing time series into some separable and interpretable series. This study provides an error evaluation in the SSA-based model for trend and multiple seasonal time series forecasting. This error evaluation is obtained by means of a numerical study on the mean square error of the estimators and mean absolute percentage error of the forecast values. Four distinct types of data generating processes (DGP) with varying sample sizes are considered in this experimental study. The parameters are estimated from the component series of SSA. Each DGP is decomposed into trend, periodic and irregular components. All these components except the irregular one are fitted by appropriate deterministic function separately. Based on the numerical simulation results, the estimated parameters are closer to the true values as the sample size increases. As the illustrative example of the real data set implementation, we used the monthly atmospheric concentrations of CO2 from Moana Loa observatory for period January 1959 to June 1972. The proposed method produces better forecast values than the results of SSA-LRF (Linear Recurrent Formula) and TLSAR (Two Level Seasonal Autoregressive). The results encourage the improvement in the time series modeling on the more complex pattern.

A new one-parameter discrete distribution with associated regression and integer-valued autoregressive models

2020 ◽  
Vol 70 (4) ◽  
pp. 979-994
Author(s):  
Emrah Altun
Keyword(s):  
Time Series ◽  
Regression Model ◽  
Count Data ◽  
Discrete Distribution ◽  
Real Data ◽  
Autoregressive Process ◽  
Important Application ◽  
Statistical Properties ◽  
Data Sets ◽  
Application Fields

AbstractThis study introduces the Poisson-Bilal distribution and its associated two models for modeling the over-dispersed count data sets. The Poisson-Bilal distribution has tractable properties and explicit forms for its statistical properties. A new over-dispersed count regression model and integer-valued autoregressive process with flexible innovation distribution are defined and studied comprehensively. Two real data sets are analyzed to prove empirically the importance of proposed models. Empirical findings show that the Poisson-Bilal distribution has important application fields in time series and regression modeling.

scholarly journals An Intelligent Bearing Fault Diagnosis Method Based on SF-SVM

2021 ◽  
Vol 1210 (1) ◽  
pp. 012004
Author(s):  
Bao’an Qiu ◽  
Pan Sun ◽  
Lili Li
Keyword(s):  
Fault Diagnosis ◽  
Rolling Bearing ◽  
Support Vector ◽  
Time Frequency ◽  
Diagnosis Method ◽  
Bearing Vibration ◽  
Frequency Map ◽  
The Stability ◽  
Vibration Time ◽  
Short Time

Abstract Rolling bearing, as a key component of rotating machinery, its health status directly determines the stability and reliability of the whole machine. The research on its intelligent diagnosis method has important engineering value and academic significance. However, due to actual engineering conditions, the types of bearing failures and the amount of data are limited. Aiming at the difficulty of extracting and selecting bearing vibration features under limited sample constraints, this pa-per proposes an intelligent fault diagnosis method of SF-SVM. On the basis of the short-time Fourier change, the L2 regularized sparse filter is used to extract the unsupervised feature of the bearing vibration time-frequency map. After obtaining the typical features of the bearing, the support vector machine is used for diagnosis.

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