Feature Extraction And Cluster Analysis Of Delayed Time Series Based On Tensor Space

PVDF piezoelectric-film sensor is a new type of flexible energy-transducing material of high molecular polymer,which can be processed into efficient,reliable and low-cost vibration sensor,accelerometer and dynamic switch,etc.However,because of the characteristic of hysteresis and nonlinearity appeared in PVDF piezoelectric-film sensor,the PVDF piezoelectric-film sensor has a slow transient position response and poor controllability and is difficult to control in application.However,there is great difference between the performance of the sensor with different fabrication process,different size and different thickness,which takes a long time for a control system to choose a demanded sensor.So in this thesis,for the lack of intelligent sorting method for PVDF of smart materials,the characteristic of hysteresis is measured in the experiment and dimensionality reduction of hysteretic time series data is studied according to characteristic data.Also,the characteristic data are clustered to realize the precise sort for smart materials.Thus,it saves time for the design of control system and its complexity is reduced,and the control accuracy is enhanced.1)According to different characteristic of hysteresis of different piezoelectric films,an experiment is designed for the acquisition of the hysteresis of piezoelectric films.Three different piezoelectric films with different thickness are chosen and different input signals and corresponding output data of the strained voltage of piezoelectric films are acquired in the experiment.First,Butterworth filter is applied to the hysteretic signal of the piezoelectric films and the signal is divided into single period.2)The thesis raises a dimension reduction method based on tensor decomposition to deal with multivariable and high-dimensional data of the piezoelectric film.First,the hysteretic data of the piezoelectric film are changed into tensor data.Then,Multilinear Principle Component Analysis(MPCA)dimensionality reduction is applied to the data in tensor space.Finally,K-means clustering is applied to the data to which PCA,KPCA and MPCA dimensionality reduction is applied;Different results of dimensionality reduction are evaluated by clustering evaluation index and another two multivariable and high-dimensional datasets(Multiperiodic time series dataset and piezoelectric ceramics dataset)are used to verify the validityof the method.The experiments show that the clustering result of data with MPCA dimensionality reduction based on tensor space is 10% higher than that of data with PCA or KPCA dimensionality reduction.3)For the fact that K-means clustering is for the traditional Euclidean distance based on vector samples,the thesis proposes a K-means clustering method based on matrix samples.In this method,the hysteretic data whose dimension has been reduced are turned into matrix.Then,calculate the average distance between the hysteresis loop of each matrix sample and the cluster center as the distance of K-means clustering.The method is applied to the characteristic dataset which has been dimensionally reduced to classify different piezoelectric films.The method is also applied to two other multivariable and high-dimensional datasets(Multiperiodic time series dataset and piezoelectric ceramics dataset)to verify its validity.The experiment shows that the result of K-means clustering based on matrixes is better than that of K-means clustering based on vectors.4)For the problem that K-means clustering is sensitive to initial value,the thesis proposes a method based on half-cosine difference degree to determine initial value.First,two maximum values of cosine difference degree are set as two cluster centers.Then,set the point which is closest to the half of the distance of the maximum values of cosine difference degree as the third cluster center,and deduce like this until all the cluster centers are found.The method is applied to the characteristic dataset which has been dimensionally reduced to classify different piezoelectric films.The method is also applied to two other multivariable and high-dimensional datasets(Multiperiodic time series dataset and piezoelectric ceramics dataset)to verify its validity.The experiment shows that the result of K-means clustering based on half-cosine difference degree is better and more stable than that of calculating the average by running the random cluster center for 100 times.