A Fast and Efficient Recursive Parameter Estimation Algorithm in Time Series Analysis

2015 ◽  
Vol 738-739 ◽  
pp. 423-429
Author(s):  
Jian Jun Zhang
Keyword(s):  
Time Series ◽  
Parameter Estimation ◽  
Time Series Analysis ◽  
Time Complexity ◽  
Computation Time ◽  
Estimation Algorithm ◽  
Theoretical Research ◽  
Estimation Methods ◽  
Estimation Accuracy ◽  
Series Analysis

High calculation precision and speed of the model parameter estimation has become the theoretical research emphasis and the key link of the applications of the time series analysis based methods. Aiming at the problem that some of the previous parameter estimation methods exist the weakness of stronger constraints, higher time complexity, lower precision of the whole recurrence process and insufficient online diagnosis power, this paper proposes an approach which repeatedly uses the auto-covariance function and the autocorrelation function throughout the recurrent process while guaranteeing not to increase the time complexity of the proposed algorithm and, hence improve the calculation speed and accuracy of parameter estimation simultaneously. As compared to related work, it has lower time complexity, shorter computation time and higher parameter estimation accuracy. The fault diagnosis steps based on the proposed parameter estimation approach are also suggested.

A Residual Variance Based Discriminant Function and its Algorithm

2015 ◽  
Vol 738-739 ◽  
pp. 354-360
Author(s):  
Jian Jun Zhang ◽  
Ye Xin Song ◽  
Yong Qu
Keyword(s):  
Time Series ◽  
Fault Diagnosis ◽  
Time Series Analysis ◽  
Discriminant Function ◽  
Time Complexity ◽  
Reference Model ◽  
Computation Time ◽  
Observation Data ◽  
Residual Variance ◽  
Series Analysis

Time series analysis is advantageous since it offers insight into the underlying dynamics and forecasts system behavior. The construction of the discriminant function is of vital importance in the time series analysis based fault diagnosis. Aiming at the problem that some of the time series analysis based fault diagnosis methods exist the weakness of higher time complexity, weaker discriminant ability and insufficient online diagnosis power, this paper proposes an approach which makes full use of the characteristics of the model and observation data to construct the discriminant function, and presents an efficient algorithm which can effectively recognize the system state by the proposed discriminant function. As compared to the related work, it has the characteristics of lower time complexity, shorter computation time and stronger distinguished ability, without the requirement of same orders of the reference model and the detected model. The fault diagnosis steps based on the proposed discriminant function and its algorithm are also suggested.

Research on Weighted Iterative Stage Parameter Estimation Algorithm of Time Series Model

2014 ◽  
Vol 687-691 ◽  
pp. 3968-3971
Author(s):  
Wei Shan ◽  
Lei Li ◽  
Qun He
Keyword(s):  
Time Series ◽  
Parameter Estimation ◽  
Time Series Analysis ◽  
Arima Model ◽  
Estimation Algorithm ◽  
Least Square ◽  
Good Convergence ◽  
Series Analysis ◽  
Parameter Estimation Algorithm ◽  
Convergence Performance

Time series analysis has been extensively used in many fields, such as system identification, modeling and data predication, and played an important role in system design, planning and performance analysis. The focus of time series application study is how to improve the accuracy and computation speed of the parameter estimation. Many researchers have carried out system modeling study by applying time series analysis and have gained their research results. The traditional methods such as maximum likelihood estimation, moment estimate and least square estimate which exit the defect of low precision, poor convergence and parameter estimation white noises coupling, are mostly utilized in parameter estimation for model. Taking this as basis the data forecasting and anomaly detection are conducted, which is hard to ensure the system’s stability. Different from the traditional algorithm, this paper proposes a new weighted iterative stage parameter estimation algorithm which avoids the coupling with white noise estimation of ARMA model parameter and improves the accuracy of parameter estimation. In theory, this algorithm tends to provide a good convergence performance. The experimental results based on ARIMA model show that the algorithm can improve the accuracy of parameter estimation and provide a good convergence performance.

An Efficient Weak-Constraint Gradient-Based Parameter-Estimation Algorithm Using Representer Expansions

SPE Journal ◽  
2009 ◽  
Vol 15 (01) ◽  
pp. 18-30 ◽  
Author(s):  
J.R.. R. Rommelse ◽  
J.D.. D. Jansen ◽  
A.W.. W. Heemink
Keyword(s):  
Parameter Estimation ◽  
Computation Time ◽  
Estimation Algorithm ◽  
Basis Functions ◽  
Estimation Methods ◽  
Model Output ◽  
Model Errors ◽  
Unknown Parameters ◽  
Gradient Based ◽  
Minimization Scheme

Summary The discrepancy between observed measurements and model predictions can be used to improve either the model output alone or both the model output and the parameters that underlie the model. In the case of parameter estimation, methods exist that can efficiently calculate the gradient of the discrepancy to changes in the parameters, assuming that there are no uncertainties in addition to the unknown parameters. In the case of general nonlinear parameter estimation, many different parameter sets exist that locally minimize the discrepancy. In this case, the gradient must be regularized before it can be used by gradient-based minimization algorithms. This article proposes a method for calculating a gradient in the presence of additional model errors through the use of representer expansions. The representers are data-driven basis functions that perform the regularization. All available data can be used during every iteration of the minimization scheme, as is the case in the classical representer method (RM). However, the method proposed here also allows adaptive selection of different portions of the data during different iterations to reduce computation time; the user now has the freedom to choose the number of basis functions and revise this choice at every iteration. The method also differs from the classic RM by the introduction of measurement representers in addition to state, adjoint, and parameter representers and by the fact that no correction terms are calculated. Unlike the classic RM, where the minimization scheme is prescribed, the RM proposed here provides a gradient that can be used in any minimization algorithm. The applicability of the modified method is illustrated with a synthetic example to estimate permeability values in an inverted- five-spot waterflooding problem.

scholarly journals catch22: CAnonical Time-series CHaracteristics selected through highly comparative time-series analysis

2019 ◽  
Author(s):  
Carl H Lubba ◽  
Sarab S Sethi ◽  
Philip Knaute ◽  
Simon R Schultz ◽  
Ben D Fulcher ◽  
...  
Keyword(s):  
Time Series ◽  
Time Series Analysis ◽  
Computation Time ◽  
Classification Performance ◽  
Series Length ◽  
Programming Environments ◽  
Scaling Properties ◽  
Series Analysis ◽  
Clustering And Classification ◽  
Feature Based

AbstractCapturing the dynamical properties of time series concisely as interpretable feature vectors can enable efficient clustering and classification for time-series applications across science and industry. Selecting an appropriate feature-based representation of time series for a given application can be achieved through systematic comparison across a comprehensive time-series feature library, such as those in the hctsa toolbox. However, this approach is computationally expensive and involves evaluating many similar features, limiting the widespread adoption of feature-based representations of time series for real-world applications. In this work, we introduce a method to infer small sets of time-series features that (i) exhibit strong classification performance across a given collection of time-series problems, and (ii) are minimally redundant. Applying our method to a set of 93 time-series classification datasets (containing over 147 000 time series, including biomedical datasets) and using a filtered version of the hctsa feature library (4791 features), we introduce a generically useful set of 22 CAnonical Time-series CHaracteristics, catch22. This dimensionality reduction, from 4791 to 22, is associated with an approximately 1000-fold reduction in computation time and near linear scaling with time-series length, despite an average reduction in classification accuracy of just 7%. catch22 captures a diverse and interpretable signature of time series in terms of their properties, including linear and non-linear autocorrelation, successive differences, value distributions and outliers, and fluctuation scaling properties. We provide an efficient implementation of catch22, accessible from many programming environments, that facilitates feature-based time-series analysis for scientific, industrial, financial and medical applications using a common language of interpretable time-series properties.

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