Piecewise Aggregate Approximation Research Articles

A Synchrosqueezed Transform Method Based on Fast Kurtogram and Demodulation and Piecewise Aggregate Approximation for Bearing Fault Diagnosis.

Synchrosqueezed transform (SST) is a time-frequency analysis method that can improve energy aggregation and reconstruct signals, which has been applied in the fields of medical treatment, fault diagnosis, and seismic wave processing. However, when dealing with time-varying signals, SST suffers from poor time-frequency resolution and is unable to deal with long signals. In order to accurately extract the characteristic frequency of variable speed rolling bearing faults, this paper proposes a synchrosqueezed transform method based on fast kurtogram and demodulation and piecewise aggregate approximation (PAA). The method firstly filters and demodulates the original signal using fast kurtogram and Hilbert transform to reduce the influence of background noise and improve the time-frequency resolution. Then, it compresses the signal by using piecewise aggregate approximation, so that the SST can deal with long signals and, thus, extract the fault characteristic frequency. The experimental data verification results indicate that the method can effectively identify the fault characteristic frequency of variable-speed rolling bearings.

Complex CFRP damage detection with dual multiscale 1DCNNs and self-selective fusion technique of guided waves

This article presents an innovative damage detection method, named DMS1DCNNs, based on new dual multiscale one-dimensional convolutional neural networks (MS1DCNNs) and a novel self-selective fusion technique for damage localization and quantification in complex carbon fiber reinforced plastic (CFRP) structures. Firstly, a new multiscale piecewise aggregate approximation algorithm (MIPA) is proposed to compress the guided wave (GW) signals and extract damage features at various time scales. Considering that signals from low-information sensing paths may interfere with the diagnostic performance of the model, a new method for self-selective fusion of GW sensing paths is proposed. This method can automatically fuse paths with more damage information and remove paths with less damage information. Then, a new DMS1DCNNs model is presented, capable of obtaining multiscale damage features in GW signals from both data and network levels. The model takes GW data as input and employs regression methods for direct prediction of the damage location and size. Finally, the method is validated using the GW testbed, and the mean relative error of location on complex CFRP is 8.32 % and the mean absolute error of quantification is 1.20 mm, superior to other state-of-the-art methods.

Multiscale 1-DCNN for Damage Localization and Quantification Using Guided Waves With Novel Data Fusion Technique and New Self-Attention Module

This article proposes an innovative damage localization and size quantification method named as MSCNNSAM based on new multiscale convolutional neural network (MSCNN) and novel small-weighted zero-setting self-attentive module (SAM) in carbon fiber reinforced plastic structures. Firstly, an improved piecewise aggregate approximation algorithm (IPAA) is developed to compress the guided wave signal and extract a series of damage indexes (DI). Considering the different effects of the damage location on the different sensing paths, a new method of damage information targeting enhancement and multipath data fusion is proposed. Then, a novel MSCNN architecture is also proposed for the inherent multiscale characteristics of the guided wave signal, which takes the multipath fused data as input and uses regression and classification methods to directly predict the location and size of the damage. Finally, to further improve the performance of the MSCNN, a SAM is proposed to effectively avoid the influence of low-information channel features and improve the damage feature extraction capability of the network. The proposed method is evaluated through experiments on a guided wave testing platform. Experimental results and comprehensive comparison analysis with respect to the state-of-the-art damage localization and quantification methods have demonstrated the superiority of the proposed MSCNNSAM.

Interference fading suppression for distributed acoustic sensor using frequency-shifted delay loop

In order to suppress the interference fading of phase-sensitive optical time domain reflectometer (Φ-OTDR), a multi-frequency detection method based on frequency-shifted delay loop (FSDL) is proposed. A probe pulse train with up to five consistent frequency components are generated by periodic frequency-shifted, amplification, delay and filtering processing in FSDL. The piecewise aggregate approximation (PAA) is introduced to compress the amount of operational data. Wavelet energy spectrum analysis and support vector machine (SVM) are used to extract features and realize the fading classification. With the help of fading label making and restoration, the multi-frequency signals are intelligently aggregated using rotated-vector-sum (RVS). Experimental results show that PAA has applicability in data compression of beat signals. After 5-layer wavelet energy spectrum analysis, the fading binary classification accuracy can reach 96.77 %, and the fading signals identified after segmentation can be restored to the original data. The fading probability based on SVM output labels can be reduced to 1.89 %. The SVM-based classification output labels aggregation shows that the vibration positioning signal-to-noise ratio (SNR) can be increased to 13.52 dB, the phase demodulation curve is smoother, and the demodulation SNR can be up to 17.63 dB. Finally, the R-Square of 0.997 for the amplitude of demodulated vibration signal in repeatability experiment verifies the validity of this effective scheme for fading recognition and suppression.

Correlation Joins over Time Series Data Streams Utilizing Complementary Dimension Reduction and Transformation

A common analysis task over a stream of time series is to find all pairs of windows whose correlation is above a given threshold. For a large number of streams, doing so naively, i.e., checking the Cartesian product, is too expensive. In essence, finding correlated pairs in a non-naive way boils down to a high-dimensional similarity join in a Euclidean space. While there are similarity join algorithms, such as Quickjoin and ε-kdB tree, they are inefficient for high-dimensional data. We propose CorrJoin, short for Correlation Join, that combines a complementary dimension reduction and transformation step with a subsequent double-filtering step. In the first step, we reduce the dimensionality of data stream windows by combining a fast but inaccurate method, Piecewise Aggregate Approximation (PAA), with an accurate and slow one, Singular Value Decomposition (SVD). Not only does SVD compensate for the weaknesses of PAA, it also transforms the data to make the first filter based on bucketing more effective. The second filter, which uses Euclidean distances, reduces the number of false positives before computing exact correlations. Our experiments reveal that in common settings, CorrJoin is an order of magnitude faster than state-of-the-art approaches (up to 20 times faster than Quickjoin).

Shape-based clustering for demand response potential evaluation: A perspective of comprehensive evaluation metrics

With the wide deployment of smart meter and advanced communication technology, customers in demand side have large potential to participate in demand response (DR). Therefore, suitable DR potential evaluation methods are needed to select customers for proper DR programs. In this work, an evaluation procedure based on multiple metrics is proposed. First, a bi-level clustering method is proposed to group load profiles into clusters based on the similarity in shape. Adaptive k-Shape clustering is proposed to automatically generate clusters based on the defined threshold. To evaluate the variability of the load profiles in each cluster, adaptive piecewise aggregate approximation (APAA) method is proposed to divide time series into segments based on load features. Then, one-step Markov chain is utilized to model the dynamics of load profiles. And the multiple evaluation metrics is calculated which can reflect variability, sensitivity, and quantity of electricity consumption to generate potential evaluation criterion. A numerical case study based on Low Carbon London dataset is conducted. The results show that the proposed method is feasible in terms of cluster division, metric calculation, and customer selection.

Quantum Algorithm for Anomaly Detection of Sequences

AbstractAnomaly detection of sequences is a hot topic in data mining. Anomaly detection using piecewise aggregate approximation in the amplitude domain (called ADPAAD) is one of the widely used methods in anomaly detection of sequences. The core step in the classical algorithm for performing ADPAAD is to construct an approximate representation of the subsequence, where the elements of each subsequence are divided into several subsections according to the amplitude domain, and then the average of the subsections is computed. It is computationally expensive when processing large‐scale sequences. In this paper, a quantum algorithm for ADPAAD is proposed, which can divide the subsequence elements and compute the average in parallel. The quantum algorithm can achieve polynomial speedups on the number of subsequences and the length of subsequences over its classical counterpart.

SLAFusion: Attention fusion based on SAX and LSTM for dangerous driving behavior detection

Dangerous driving behaviors are the main cause of most traffic accidents, and the detection of these behaviors is one of the extremely important researches in Intelligent Transportation System (ITS). Although some recent approaches consider dangerous driving behavior as a process containing multiple instantaneous points, which is ignored by traditional methods, they fail to take into account the loss of temporal information due to the reasonable division of instantaneous points. Therefore, this paper proposes a Symbolic Aggregate approXimation (SAX) and Long Short-Term Memory (LSTM)-based Attention Fusion method (SLAFusion) to detect dangerous driving behavior more accurately. This method evaluates various granularity of driving processes and explores the association between adjacent processes. First, a D-value Piecewise Aggregate Approximation (DPAA) is designed to model the change of vehicle state in mining driving processes with diverse granularity. Then, the features of multiple driving processes are fused to enhance each other to solve the problem of information loss due to segmentation of driving processes. Further, the auxiliary information is fused to incorporate the environmental features of the vehicle during driving. Finally, the experimental results on real datasets indicate that the proposed SLAFusion method improves the recall and F-score by 3.2% and 2.6% respectively in comparison with the existing benchmark methods.

Damage localization for composite structure using guided wave signals with Gramian angular field image coding and convolutional neural networks

Accurate detection of damage in composite structures is of great significance to ensure safe service and avoid catastrophic accidents. In this paper, a novel damage diagnosis method, integrating guided wave (GW)-based structural health monitoring (SHM) with Gramian angular field (GAF) image coding and convolutional neural networks (CNNs), is proposed to improve the accuracy of damage localization in composite structures. Firstly, an improved piecewise aggregate approximation (PAA) algorithm is proposed to achieve guided wave data compression and obtain a series of damage indexes (DIs) characterizing the damage for effectively improving the localization accuracy. Then, the multi-path fused DI sequences are converted into two-dimensional (2-D) images using GAF to take full advantage of the significant benefits of CNN in machine vision. Secondly, a CNN model is constructed to learn high-level feature representations and conduct damage location regression. Finally, the proposed method is tested and assessed on measured GW signal datasets with the addition of zero-mean Gaussian noise. The experimental results show that the mean relative error of the proposed method for damage localization on the invisible datasets is 3.59%. The proposed method demonstrates better generalization and localization performance than other selected state-of-the-art damage localization techniques.

Investigation of rolling bearing weak fault diagnosis based on cnn with two-dimensional image

In this paper, we choose convolution neural network (CNN) as the method to diagnosis weak fault of rolling bearings. In order to improve the training effect of CNN, different two-dimensional image conversion algorithms which include Gramian angular sum difference fields, wavelet time-frequency diagram, Markov transition field are introduced in to convert one-dimensional time series of bearing vibration signals into images. To relieve the pressure of hardware calculation and shorten the time of training and validation, we use the piecewise aggregate approximation (PAA) to compress the data as much as possible while preserving the whole signal information. We add the batch normalization layer to avoid the gradient saturation problem of ReLU function and minibatch method is used to overcome the instability of stochastic gradient descent with momentum (SGDM) while designing CNN. Each kind of images are made as the training sample, and the results show that both the wavelet time-frequency diagram and the Gramian sum or difference angle field diagram can better identify the fault state, and the wavelet time-frequency diagram was relatively better. By comparing with different recurrent neural network (RNN) diagnosis models, the validity of the model was proved. At the same time, the model is applied to the performance degradation identification of fault parts, and the results shows that the model can effectively identify the degradation of inner ring, outer ring and rolling body, while the accuracy of inner ring and the outer ring is better. This paper provides a new idea for weak fault diagnosis of rolling bearings.

Quantum-behaved particle swarm optimization of convolutional neural network for fault diagnosis

ABSTRACT As a deep learning method, Convolutional Neural Network (CNN) can be used in image recognition, fault diagnosis and so on. Due to the internal parameter optimisation problem, the Particle Swarm Optimisation (PSO) has been introduced, but PSO is easy to fall into local optimal solution. In this paper, an adaptive CNN based on Quantum Particle Swarm Optimisation (QPSO-CNN) is proposed and applied to rolling bearings fault diagnosis, which increases the richness of particles and makes it easy to find the global optimal solution. Firstly, the one-dimensional time-series data is compressed by piecewise aggregate approximation algorithm and converted into the heat map by the Gramian angular field algorithm; Secondly, QPSO algorithm is used to search the best CNN model to fit the data set; Finally, the training and validation set are used to search the best network architecture, and the test set is used to test the diagnostic accuracy of the best CNN model, which show that the proposed method has high accuracy.

Bearing Fault Diagnosis Using Piecewise Aggregate Approximation and Complete Ensemble Empirical Mode Decomposition with Adaptive Noise.

Complete ensemble empirical mode decomposition with adaptive noise (CEEMDAN) effectively separates the fault vibration signals of rolling bearings and improves the diagnosis of rolling bearing faults. However, CEEMDAN has high memory requirements and low computational efficiency. In each iteration of CEEMDAN, fault vibration signals are added with noises, both the vibration signals added with noises and the added noises are decomposed with classical empirical mode decomposition (EMD). This paper proposes a rolling bearing fault diagnosis method that combines piecewise aggregate approximation (PAA) with CEEMDAN. PAA enables CEEMDAN to decompose long signals and to achieve enhanced diagnosis. In particular, the method first yields the vibration envelope using bandpass filtering and demodulation, then compresses the envelope using PAA, and finally decomposes the compressed signal with CEEMDAN. Test data verification results show that the proposed method is more effective and more efficient than CEEMDAN.

An Inconsistency Fault Diagnosis Method for Lithium-Ion Cells in the Battery Pack Based on Piecewise Dimensionality Reduction and Outlier Identification

Abstract The inconsistency of cells in the battery pack is one of the main causes of battery failure. In practical applications, the terminal voltage is an important parameter that is easy to obtain and can characterize the inconsistency of cells. In this paper, a fault diagnosis method based on piecewise dimensionality reduction and outlier identification is proposed according to the voltage inconsistency of cells in the battery pack. This method uses a piecewise aggregate approximation (PAA) algorithm with a shift factor to reduce the dimension of the cell voltage time series, after which a deletion mechanism is designed based on the clustering algorithm and outlier identification to calculate the clustering quality after deleting each cell, reflecting the deviate degree of each cell. In addition, a safety management strategy is designed based on the Z-score method, and an abnormality coefficient is set to evaluate the inconsistency of cells. The effectiveness of the proposed diagnosis method is verified by monitoring the voltage data of two real-world electric vehicles. The verification results show that the method can not only detect the inconsistency before the failure of the faulty cell in the battery pack in advance, but also reduce the risk of computational explosion caused by the voltage time series and accurately locate the faulty cell.

Multi-scale local cues and hierarchical attention-based LSTM for stock price trend prediction

Stock price trend prediction is to seek profit maximum of stock investment by estimating future stock price tendency. Nevertheless, it is still a tough task due to noisy and non-stationary properties of stock market. Thus, it is important how to relieve such negative effects and to improve prediction accuracy. In this paper, we leverage four diverse local descriptors in short durations to alleviate noisy fluctuations of stock price. In detail, piecewise aggregate approximation (PAA) collects relatively stable average values; the derivatives of short-time series reflect the change ratio of stock price; the slope implies the short-time price trend; hog-1D aggregates different oriented gradients into histograms in a statistical fashion. They provide diverse and comprehensive cues about the stock price series across different aspects. Building upon such local descriptors, we propose a multi-scale local cues and hierarchical attention-based LSTM model (MLCA-LSTM) to capture the underlying price trend patterns. It has two advantages: 1) multi-scale information is further enriched by performing different scale sliding windows over stock price series to induce diverse local descriptors, 2) temporal dependency and multi-scale interactions are jointly attended and aggregated through the hierarchical attention mechanism and multi-branch LSTM structure. Experiments on the real stock price data confirm the efficacy of the proposed model as compared to the state-of-the-art counterparts.

Distance- and Momentum-Based Symbolic Aggregate Approximation for Highly Imbalanced Classification.

Time-series representation is the most important task in time-series analysis. One of the most widely employed time-series representation method is symbolic aggregate approximation (SAX), which converts the results from piecewise aggregate approximation to a symbol sequence. SAX is a simple and effective method; however, it only focuses on the mean value of each segment in the time-series. Here, we propose a novel time-series representation method—distance- and momentum-based symbolic aggregate approximation (DM-SAX)—that can secure time-series distributions by calculating the perpendicular distance from the time-axis to each data point and consider the time-series trend by adding a momentum factor reflecting the direction of previous data points. Experimental results for 29 highly imbalanced classification problems on the UCR datasets revealed that DM-SAX affords the optimal area under the curve (AUC) among competing time-series representation methods (SAX, extreme-SAX, overlap-SAX, and distance-based SAX). We statistically verified that performance improvements resulted in significant differences in the rankings. In addition, DM-SAX yielded the optimal AUC for real-world wire cutting and crimping process dataset. Meaningful data points such as outliers could be identified in a time-series outlier detection framework via the proposed method.

An intelligent fault diagnosis framework based on piecewise aggregate approximation, statistical moments, and sparse autoencoder

Rotating machines (RMs) have vast applicability in almost all the industries in mechanical domain. Rolling element bearings (RBs) are the key elements to ensure that the RMs perform efficiently. RBs are highly prone to wear and tear which could have devastating consequences such as massive economic losses and accidents. In the past, many time-domain based condition-indicators such as root mean square (RMS), skewness and kurtosis, etc. have been proposed by researchers to diagnose the bearing faults and prevent RM failures. However, they are often insensitive to early stage faults, affected by outliers and possess poor degradation tracking characteristics. To overcome these shortcomings, this paper proposes a novel statistical feature extraction technique called as multiscale statistical moment (MSM) analysis, in combination with sparse autoencoder to detect the incipient faults as well as track the progression of wear. Firstly, the vibration signal are acquired from the bearings to be monitored. Secondly, the MSM features are extracted from the vibration signals. Thirdly, the MSM features corresponding to normal conditions are utilized to train the sparse autoencoder network. Fourthly, the MSM features corresponding to test conditions are supplied to the pre-trained sparse autoencoder model. The MSM technique offers the advantage that it extracts the fault properties contained in multiple time-scales of the vibration signals instead of a single time-scale only. Finally, the dissimilarity between the actual and predicted output is measured to obtain the bearing health indicator (BHI). The experimental results demonstrate that the suggested BHI detects the faults at early stages, possess better sensitivity and trends the bearing degradation more accurately as compared to the traditional techniques such as RMS, kurtosis, and BHI obtained with statistical moment features at single-scale only.

Multiclass recognition of AD neurological diseases using a bag of deep reduced features coupled with gradient descent optimized twin support vector machine classifier for early diagnosis

SummaryAlzheimer's disease (AD) is an advanced neurodegenerative disease of the brain that affects the nerve system of brain. Previously, several feature extraction and classification methods were discussed, but that methods provide high over fitting problem, which leads to minimization of detection accuracy. To overcome these issues, the multi class classification of AD diseases using bag of deep feature reduction technique and twin support vector machine classifier (TSVM) optimized with gradient decent optimizer is proposed in this manuscript for classifying the AD disease as severe AD, mild cognitive impairment, healthy control. At first, the input EEG signals are pre‐processed. To decrease the execution time and processing time with feature size, a bag of deep features reduction technique is used. The reduced feature signals are classified by optimized TSVM. The simulation process is implemented in MATLAB environment. The proposed model achieves higher accuracy 33.84%, 28.93%, 33.03%, 27.93%, higher precision 22.87%, 16.97%, 16.97%, and 36.97%, compared with the existing methods, such as piecewise aggregate approximation support vector machine (MCC‐EEG‐PAA‐SVM), convolutional neural network (MCC‐EEG‐CNN), conformal kernel‐based fuzzy support vector machine (MCC‐EEG‐CKF‐SVM), Pearson correlation coefficient‐based feature selection strategy with linear discriminant analysis classifier (MCC‐EEG‐ PCC‐LDA).

Ranking surgical skills using an attention-enhanced Siamese network with piecewise aggregated kinematic data.

Surgical skill assessment using computerized methods is considered to be a promising direction in objective performance evaluation and expert training. In a typical architecture for computerized skill assessment, a classification system is asked to assign a query action to a predefined category that determines the surgical skill level. Since such systems are still trained by manual, potentially inconsistent annotations, an attempt to categorize the skill level can be biased by potentially scarce or skew training data. We approach the skill assessment problem as a pairwise ranking task where we compare two input actions to identify better surgical performance. We propose a model that takes two kinematic motion data acquired from robot-assisted surgery sensors and report the probability of a query sample having a better skill than a reference one. The model is an attention-enhanced Siamese Long Short-Term Memory Network fed by piecewise aggregate approximation of kinematic data. The proposed model can achieve higher accuracy than existing models for pairwise ranking in a common dataset. It can also outperform existing regression models when applied in their experimental setup. The model is further shown to be accurate in individual progress monitoring with a new dataset, which will serve as a strong baseline. This relative assessment approach may overcome the limitations of having consistent annotations to define skill levels and provide a more interpretable means for objective skill assessment. Moreover, the model allows monitoring the skill development of individuals by comparing two activities at different time points.

Distribution Agnostic Symbolic Representations for Time Series Dimensionality Reduction and Online Anomaly Detection

Due to the importance of the lower bounding distances and the attractiveness of symbolic representations, the family of symbolic aggregate approximations (SAX) has been used extensively for encoding time series data. However, typical SAX-based methods rely on two restrictive assumptions; the Gaussian distribution and equiprobable symbols. This paper proposes two novel data-driven SAX-based symbolic representations, distinguished by their discretization steps. The first representation, oriented for general data compaction and indexing scenarios, is based on the combination of kernel density estimation and Lloyd-Max quantization to minimize the information loss and mean squared error in the discretization step. The second method, oriented for high-level mining tasks, employs the Mean-Shift clustering method and is shown to enhance anomaly detection in the lower-dimensional space. Besides, we verify on a theoretical basis a previously observed phenomenon of the intrinsic process that results in a lower than the expected variance of the intermediate piecewise aggregate approximation. This phenomenon causes an additional information loss but can be avoided with a simple modification. The proposed representations possess all the attractive properties of the conventional SAX method. Furthermore, experimental evaluation on real-world datasets demonstrates their superiority compared to the traditional SAX and an alternative data-driven SAX variant.

Tri-Partition Alphabet-Based State Prediction for Multivariate Time-Series

Recently, predicting multivariate time-series (MTS) has attracted much attention to obtain richer semantics with similar or better performances. In this paper, we propose a tri-partition alphabet-based state (tri-state) prediction method for symbolic MTSs. First, for each variable, the set of all symbols, i.e., alphabets, is divided into strong, medium, and weak using two user-specified thresholds. With the tri-partitioned alphabet, the tri-state takes the form of a matrix. One order contains the whole variables. The other is a feature vector that includes the most likely occurring strong, medium, and weak symbols. Second, a tri-partition strategy based on the deviation degree is proposed. We introduce the piecewise and symbolic aggregate approximation techniques to polymerize and discretize the original MTS. This way, the symbol is stronger and has a bigger deviation. Moreover, most popular numerical or symbolic similarity or distance metrics can be combined. Third, we propose an along–across similarity model to obtain the k-nearest matrix neighbors. This model considers the associations among the time stamps and variables simultaneously. Fourth, we design two post-filling strategies to obtain a completed tri-state. The experimental results from the four-domain datasets show that (1) the tri-state has greater recall but lower precision; (2) the two post-filling strategies can slightly improve the recall; and (3) the along–across similarity model composed by the Triangle and Jaccard metrics are first recommended for new datasets.