Detecting anomalies in time series data via a deep learning algorithm combining wavelets, neural networks and Hilbert transform. (1st November 2017)

• Record Type: Journal Article
• Authors: Kanarachos, Stratis; Christopoulos, Stavros-Richard G.; Chroneos, Alexander; Fitzpatrick, Michael E.
• Is Part Of: Expert systems with applications. Volume 85(2017)
• Page Start: 292
• Page End: 304
• Publication Date: 2017-11-01
• Subjects: Anomaly detection -- Deep learning -- Receiver operating characteristics; A Amplitude -- ADF Anomaly Detection Filter -- AP Anomalous Pulses -- AUC Area Under Curve -- DNN Deep neural network -- DR Dichotomous representation -- FN False Negative -- FP False Positive -- FPr False Positive rate -- IMS-SEPI Ioannina Measuring Station of the Solid Earth Physics Institute -- L's-I, L', L Length of dipoles -- M Dichotomous representation index -- M2 Anomalous pulses index -- MEMS Micro Electro-Mechanical Systems -- NDEEF Normalized Deflection of the Earth's Electric Field -- Nq Polynomial degree -- NN Neural networks -- ROC Receiver Operating Characteristics -- Sm, n Approximation coefficients -- SES Seismic Electric Signal -- Tm, n Detail coefficients -- TN True Negative -- TP True Positive -- TPr True Positive rate -- V2I Vehicle-to-infrastructure -- V2V Vehicle-to-vehicle -- Wm Neural network interconnection matrices for the output layer -- Vm Neural network interconnection matrices for the hidden layer -- WANEH WAvelets, NEural networks and Hilbert transform -- ΔV Voltage difference -- ao Dilation parameter -- bo Location parameter -- dm Signal detail at scale m -- ddm Filter signal detail at scale m -- e Error -- eH Hilbert transfrom of error e -- k Estimator value -- ki Threshold value -- m meter -- m Parameter controlling the wavelet dilation -- m0 Arbitrary scale -- n Parameter controlling the wavelet translation -- nh Number of hidden neurons -- p Probability -- q Scaling function shift -- s Second -- x Signal in time domain -- xd Filtered signal -- xm Approximation signal at scale m -- y Neural network output -- ym Neural network output at scale m -- βm Bias vector -- θ Instantaneous phase -- λ Noise threshold -- τm Scale dependent phase lag -- φ Scaling function -- φm, n Wavelet (father) basis -- ψ Wavelet -- ψm, n Wavelet (mother) basis; Expert systems (Computer science) -- Periodicals; Systèmes experts (Informatique) -- Périodiques; Electronic journals; 006.33
• DOI: 10.1016/j.eswa.2017.04.028
• Languages: English
• ISSNs: 0957-4174

Abstract

Highlights: Design of a transferable time series anomaly detection method. Novel deep neural network structure facilitates learning short and long-term pattern interdependencies. Detection of anomalies in the Seismic Electrical Signal for predicting earthquake activity. Detection of road anomalies using smartphone data, facilitating crowdsourcing applications. Abstract: The quest for more efficient real-time detection of anomalies in time series data is critically important in numerous applications and systems ranging from intelligent transportation, structural health monitoring, heart disease, and earthquake prediction. Although the range of application is wide, anomaly detection algorithms are usually domain specific and build on experts' knowledge. Here a new signal processing algorithm – inspired by the deep learning paradigm – is presented that combines wavelets, neural networks, and Hilbert transform. The algorithm performs robustly and is transferable. The proposed neural network structure facilitates learning short and long-term pattern interdependencies; a task usually hard to accomplish using standard neural network training algorithms. The paper provides guidelines for selecting the neural network's buffer size, training algorithm, and anomaly detection features. The algorithm learns the system's normal behavior and does not require the existence of anomalous data for assessing its statistical significance. This is an essential attribute in applications that require customization. Anomalies are detected by analysing hierarchically the instantaneous frequency and amplitude of the residual signal using probabilistic Receiver Operating Characteristics. The method is shown to be able to automatically detect anomalies in the Seismic Electrical Signal that could be used to predict earthquake activity. Furthermore, the method can be used in combination with crowdsourcing of smartphone data to locate road defects such as potholes and bumps for intervention and repair.