Time Series Piecewise Linear Representation And Qualitative Trend Analysis

A time series is a set of observations generated sequentially in time. It exists in almost all of scientific and commercial application fields, especially in real-time condition monitoring of large-scale mechanical equipment and chemical system, a large number of time series data of the key parameters will be obtained. If data processing and analyzing are carried out directly on the raw data, it will result in the excessive consumption of hardware, the lack of effective information, the low efficiency of algorithm and so on.The piecewise linear representation of time series refers to the original time series being represented approximately by ordinal connective straight lines. This technique can compress the original data and keep the main characteristics of the data. Meanwhile, it can reduce the consumption of the data stored on hardware greatly and improve the efficiency and accuracy of the other time series analysis. The qualitative trend analysis of time series is a process to extract qualitative trend information from quantitative data and represent trend information simply by using sign language. The trend information is an important feature of the time series, which reflects the evolution speed and level of data and provide an effective tool to the early fault detection and diagnostics of mechanical equipment or process control. The main contents of this paper are the piecewise linear representation of time series and the qualitative trend analysis.Piecewise linear representation of time series is reviewed in detail and an approach of time series piecewise linear representation based on local maximum, minimum and extremum (LMME) is putted forward. The algorithm is defined and described. Through the experiments on three sets of data, the experiment results show that LMME has a good performance in dealing with the main morphological characteristics of time series. In the adjacent data value less volatile datasets, the LMME is very effective, not only compression ratio is high but also the fitting error is very small. However, in the adjacent data value of datasets volatile very large, a nice result is achieved by using LMME when the compression ratio is low. Furthermore the result is not very good when the CR becomes higher.However, the piecewise linear representation of time series usually is just the pre-processing of the data processing and analyzing. This paper proposes a qualitative trend analysis method of time series based on global constrained multi-segment polynomial fitting (GCMPF). This approach integrates the ideas of traditional polynomial fitting and LMME for reasonable segment point extraction method. Trend description language contains nine primitives. The detailed mathematical description and process of trend analysis are given in this paper. At the constraint points smooth connection basis, GCMPF trend extraction achieves the smallest global fitting error. The experimental results on three groups of simulated data indicate that GCMPF has a nice effect of trend extraction in less noise and low complexity time series. Furthermore it is not very effective and locally distorted when the noise is serious and the complexity is high.For the application of the research content of this paper to the practice, LMME for time series piecewise linear representation is written into the software combining MATLAB and C#programming techniques. First of all, the Calculation and drawing functions of LMME are achieved by the MATLAB COM component which is compiled by the MATLAB code for calculating and drawing. Second, the COM component is referenced in the C#program. Finally, the software of LMME is released to the target computer.