A Sparse Random Feature Model for Signal Decomposition

Signal decomposition and multiscale signal analysis provide useful tools for time-frequency analysis. In this thesis, an overview of the signal decomposition problem is given and popular methods are discussed. A novel signal decomposition algorithm is presented: Sparse Random Mode Decomposition (SRMD). This method sparsely represents a signal as a sum of random windowed-sinusoidal features before clustering the time-frequency localized features into the constituent modes. SRMD outperforms state-of-the-art methods on a variety of mathematical signals, and is applied to real-world astronomical and musical examples. Finally, we discuss a neural network approach to tackle challenging musical signals

Seeing sound: a new way to illustrate auditory objects and their neural correlates

This thesis develops a new method for time-frequency signal processing and examines the relevance of the new representation in studies of neural coding in songbirds. The method groups together associated regions of the time-frequency plane into objects defined by time-frequency contours. By combining information about structurally stable contour shapes over multiple time-scales and angles, a signal decomposition is produced that distributes resolution adaptively. As a result, distinct signal components are represented in their own most parsimonious forms.  Next, through neural recordings in singing birds, it was found that activity in song premotor cortex is significantly correlated with the objects defined by this new representation of sound. In this process, an automated way of finding sub-syllable acoustic transitions in birdsongs was first developed, and then increased spiking probability was found at the boundaries of these acoustic transitions. Finally, a new approach to study auditory cortical sequence processing more generally is proposed. In this approach, songbirds were trained to discriminate Morse-code-like sequences of clicks, and the neural correlates of this behavior were examined in primary and secondary auditory cortex. It was found that a distinct transformation of auditory responses to the sequences of clicks exists as information transferred from primary to secondary auditory areas. Neurons in secondary auditory areas respond asynchronously and selectively -- in a manner that depends on the temporal context of the click. This transformation from a temporal to a spatial representation of sound provides a possible basis for the songbird's natural ability to discriminate complex temporal sequences

A Synchrosqueezed Wavelet Transform assisted machine learning framework for time series forecasting Contributions to KDWEB poster session, a.d. 2016

Abstract. The attention of researchers in the field of signal analysis has recently been captured by several kinds of reassignment techniques. Among the reallocation methods the Synchrosqueezing approach maps a continuous wavelet transform from the time-scale to the time-frequency plane, allowing a much more definite and consistent representation of the frequency content of a signal. Its mathematical foundations prove that the Synchrosqueezing Wavelet Transform is directly related to the Empirical Mode Decomposition -EMD, since both methods allow the decomposition of a signal having finite energy in its intrinsic mode functions, each having time-varying frequency and amplitude. We develop a fast 1 C++ implementation of the Synchrosqueezed Wavelet Transform -SST suitable for the synchronic extrusion of instantaneous frequency information from univariate time series. Such module, totally configurable and adaptable to input datasets having different statistical properties, can be coupled with a predictor system to the purpose of real value forecasting. We project such a composite application and plan to research the forecasting accuracy achievable, using different types of non parametric statistical estimators or neural regressors

A fault diagnosis approach of reciprocating compressor gas valve based on local mean decomposition and autoregressive-generalized autoregressive conditional heteroscedasticity model

Vibration signal of reciprocating compressor gas valve represents nonlinear, non-stationary and multiple impulse characteristics. To extract the features of the signal, an integration approach based on local mean decomposition (LMD) method and autoregressive-generalized autoregressive conditional heteroscedasticity (AR-GARCH) model is proposed. First, the property of LMD is investigated in the paper, which indicates that LMD method not only can effectively alleviate non-stationary feature and restrain the end effect of non-stationary signal, but also can accurately improve the resolution of time-frequency analysis. Then, the first five PF components of gas valve signal are modeled by AR(1)-GARCH(1, 1) model as the feature vectors without any prior knowledge about the fault mechanism. Finally, the BP neural networks are applied to diagnose the faults of reciprocating compressor gas valve based on the feature vectors above. The results indicate that high diagnosis accuracy can be obtained by integrating LMD method and AR-GARCH model. So the approach proposed in the paper provides an effective measure to extract the fault feature of reciprocating compressor gas valve

Bearing fault diagnosis based on EMD-KPCA and ELM

In recent years, many studies have been conducted in bearing fault diagnosis, which has attracted increasing attention due to its nonlinear and non-stationary characteristics. To solve this problem, this paper proposes, a fault diagnosis method based on Empirical Mode Decomposition (EMD), Kernel Principal Component Analysis (KPCA), and Extreme Learning Machines (ELM) neural network, which combines the existing self-adaptive time-frequency signal processing with the advantages of non-linear multivariate dimensionality reduction KPCA approach and ELM neural network. First, EMD is applied to decompose the vibration signals into a finite number of intrinsic mode functions, in which the corresponding energy values are selected as the initial feature vector. Second, KPCA is used to further reduce the dimensionality for a simplified low-dimension feature vector. Finally, ELM is introduced to classify the extracted fault feature vectors for lessening the human intervention and reducing the fault diagnosis time. Experimental results demonstrate that the proposed diagnostic can effectively identify and classify typical bearing faults

Dynamic Decomposition of Spatiotemporal Neural Signals

Neural signals are characterized by rich temporal and spatiotemporal dynamics that reflect the organization of cortical networks. Theoretical research has shown how neural networks can operate at different dynamic ranges that correspond to specific types of information processing. Here we present a data analysis framework that uses a linearized model of these dynamic states in order to decompose the measured neural signal into a series of components that capture both rhythmic and non-rhythmic neural activity. The method is based on stochastic differential equations and Gaussian process regression. Through computer simulations and analysis of magnetoencephalographic data, we demonstrate the efficacy of the method in identifying meaningful modulations of oscillatory signals corrupted by structured temporal and spatiotemporal noise. These results suggest that the method is particularly suitable for the analysis and interpretation of complex temporal and spatiotemporal neural signals

Wind Power Forecasting Methods Based on Deep Learning: A Survey

Accurate wind power forecasting in wind farm can effectively reduce the enormous impact on grid operation safety when high permeability intermittent power supply is connected to the power grid. Aiming to provide reference strategies for relevant researchers as well as practical applications, this paper attempts to provide the literature investigation and methods analysis of deep learning, enforcement learning and transfer learning in wind speed and wind power forecasting modeling. Usually, wind speed and wind power forecasting around a wind farm requires the calculation of the next moment of the definite state, which is usually achieved based on the state of the atmosphere that encompasses nearby atmospheric pressure, temperature, roughness, and obstacles. As an effective method of high-dimensional feature extraction, deep neural network can theoretically deal with arbitrary nonlinear transformation through proper structural design, such as adding noise to outputs, evolutionary learning used to optimize hidden layer weights, optimize the objective function so as to save information that can improve the output accuracy while filter out the irrelevant or less affected information for forecasting. The establishment of high-precision wind speed and wind power forecasting models is always a challenge due to the randomness, instantaneity and seasonal characteristics