Time-domain Statistics Research Articles

Statistical Inference for Networks of High-Dimensional Point Processes

Fueled in part by recent applications in neuroscience, the multivariate Hawkes process has become a popular tool for modeling the network of interactions among high-dimensional point process data. While evaluating the uncertainty of the network estimates is critical in scientific applications, existing methodological and theoretical work has primarily addressed estimation. To bridge this gap, we develop a new statistical inference procedure for high-dimensional Hawkes processes. The key ingredient for the inference procedure is a new concentration inequality on the first- and second-order statistics for integrated stochastic processes, which summarize the entire history of the process. Combining recent martingale central limit theorem with the new concentration inequality, we then characterize the convergence rate of the test statistics in a continuous time domain. Finally, to account for potential non-stationarity of the process in practice, we extend our statistical inference procedure to a flexible class of Hawkes processes with time-varying background intensities and unknown transition functions. The finite sample validity of the inferential tools is illustrated via extensive simulations and further applied to a neuron spike train dataset. Supplementary materials for this article are available online, including a standardized description of the materials available for reproducing the work.

Predicting Alzheimer's disease CSF core biomarkers: a multimodal Machine Learning approach.

Alzheimer's disease (AD) is a progressive neurodegenerative disorder. Current core cerebrospinal fluid (CSF) AD biomarkers, widely employed for diagnosis, require a lumbar puncture to be performed, making them impractical as screening tools. Considering the role of sleep disturbances in AD, recent research suggests quantitative sleep electroencephalography features as potential non-invasive biomarkers of AD pathology. However, quantitative analysis of comprehensive polysomnography (PSG) signals remains relatively understudied. PSG is a non-invasive test enabling qualitative and quantitative analysis of a wide range of parameters, offering additional insights alongside other biomarkers. Machine Learning (ML) gained interest for its ability to discern intricate patterns within complex datasets, offering promise in AD neuropathology detection. Therefore, this study aims to evaluate the effectiveness of a multimodal ML approach in predicting core AD CSF biomarkers. Mild-moderate AD patients were prospectively recruited for PSG, followed by testing of CSF and blood samples for biomarkers. PSG signals underwent preprocessing to extract non-linear, time domain and frequency domain statistics quantitative features. Multiple ML algorithms were trained using four subsets of input features: clinical variables (CLINVAR), conventional PSG parameters (SLEEPVAR), quantitative PSG signal features (PSGVAR) and a combination of all subsets (ALL). Cross-validation techniques were employed to evaluate model performance and ensure generalizability. Regression models were developed to determine the most effective variable combinations for explaining variance in the biomarkers. On 49 subjects, Gradient Boosting Regressors achieved the best results in estimating biomarkers levels, using different loss functions for each biomarker: least absolute deviation (LAD) for the Aβ42, least squares (LS) for p-tau and Huber for t-tau. The ALL subset demonstrated the lowest training errors for all three biomarkers, albeit with varying test performance. Specifically, the SLEEPVAR subset yielded the best test performance in predicting Aβ42, while the ALL subset most accurately predicted p-tau and t-tau due to the lowest test errors. Multimodal ML can help predict the outcome of CSF biomarkers in early AD by utilizing non-invasive and economically feasible variables. The integration of computational models into medical practice offers a promising tool for the screening of patients at risk of AD, potentially guiding clinical decisions.

Bubble detection and identification based on the vibration response for the sodium water reaction

Real-time bubble behavior characterization and localization are critical in the chemical industry, especially for leakage of sodium-water reactions. This research investigates the properties of bubble signals under different gas injection rates and sodium-water reactions by employing a vibration-based approach. Specifically, the time-frequency and energy characteristics of bubble signals were studied by vibration response. The bubble signals excited by the two kinds of experiments have the same characteristic frequency band of 200–400 Hz, and the maximum energy is obtained at 250 Hz. The bubble signal from the sodium-water reaction can be effectively recognized by identifying the differences in the characteristics of multiple parameters when the gas injection rate is 0.07 m3/h with a signal-to-noise ratio of 11.8–17.1 dB. On the basis of energy analysis of the bubble signal, a bubble signal source location method based on time domain statistics was proposed, and the trajectory curve of the bubble signal excited by the sodium water reaction in the initial 600 ms was successfully obtained with a position error rate less than 5%. Comparative analysis indicates that kurtosis was more sensitive for bubble signal recognition, while the Root Mean Square (RMS) and Standard Deviation (SD) values were more suitable for bubble positioning. Thus, this study complemented the present techniques and knowledge for bubble identification and localization in multiphase flow engineering.

Efficient Underground Target Detection of Urban Roads in Ground-Penetrating Radar Images Based on Neural Networks

Ground-penetrating radar (GPR) is an important nondestructive testing (NDT) tool for the underground exploration of urban roads. However, due to the large amount of GPR data, traditional manual interpretation is time-consuming and laborious. To address this problem, an efficient underground target detection method for urban roads based on neural networks is proposed in this paper. First, robust principal component analysis (RPCA) is used to suppress the clutter in the B-scan image. Then, three time-domain statistics of each A-scan signal are calculated as its features, and one backpropagation (BP) neural network is adopted to recognize A-scan signals to obtain the horizontal regions of targets. Next, the fusion and deletion (FAD) algorithm is used to further optimize the horizontal regions of targets. Finally, three time-domain statistics of each segmented A-scan signal in the horizontal regions of targets are extracted as the features, and another BP neural network is employed to recognize the segmented A-scan signals to obtain the vertical regions of targets. The proposed method is verified with both simulation and real GPR data. The experimental results show that the proposed method can effectively locate the horizontal ranges and vertical depths of underground targets for urban roads and has higher recognition accuracy and less processing time than the traditional segmentation recognition methods.

The broadband transport theory approach to model internal wave induced scattering across deep water acoustic time-fronts.

There are currently no models to fully predict the effects of internal wave induced scattering on acoustic pulses. Existing models, which predict time domain statistics, either use the ray-based path integral method or Monte Carlo type simulations. The path integral method fails to accurately predict all of the effects of scattering. The Monte Carlo methods base the statistics on ensemble averages and are not physics-based models. This paper overcomes these limitations by using the modes of the waveguide in a transport theory application. The transport theory equations have, thus far, been used only to explain diffusion of mode intensities and decorrelation due to internal waves at individual frequencies. This paper extends the current narrowband application predict mode correlations across different frequencies and, from that, the broadband time-front, time wander, travel time bias, and the amount of spread in intensity across time and depth. To validate these predictions, this paper uses separate parabolic equation simulations. The comparisons between the two are good, suggesting a success for the mode-based transport theory approach.

Research on Vibration Data-Driven Fault Diagnosis for Iron Core Looseness of Saturable Reactor in UHVDC Thyristor Valve Based on CVAE-GAN and Multimodal Feature Integrated CNN

The imbalance of data samples and fluctuating operating conditions are the two main challenges faced by vibration data-driven fault diagnosis for the iron core looseness of saturable reactors in UHVDC thyristor valves. This paper proposes a vibration data-driven saturable reactor iron core looseness fault diagnosis strategy named CVG-MFICNN based on CVAE-GAN and MFICNN to overcome the two challenges. This strategy uses a novel 1-D CVAE-GAN model to produce generated samples and expand the training set based on imbalanced training samples. An MFICNN model structure is designed to allow the simultaneous processing of multimodal features such as the SST time-frequency spectrum, time-domain vibration sequence, frequency-domain power spectrum sequence, and time-domain statistics. Using these multimodal features and the MFICNN model, the hidden fault information in vibration data can be effectively mined. An experiment is conducted to collect vibration data of saturable reactors with different faults. Models based on the proposed strategy and other methods are trained and tested using the collected data. The comparison results show that the performance of the proposed CVG-MFICNN approach is significantly superior to that of single-feature CNNs, traditional machine learning methods, and classical image classification CNNs in the application of UHVDC thyristor valve saturable reactor iron core looseness fault diagnosis.

A System-Level Performance Evaluation for a 5G System under a Leaky Coaxial Cable MIMO Channel for High-Speed Trains in the Railway Tunnel

As one of the typical application scenarios in the fifth generation (5G) mobile communication system, the situation of high-speed mobile communication is receiving increasing attention. The railway tunnel is a typical environment for high-speed mobile communications. Railway tunnels for high-speed trains are generally installed with leaky coaxial cables (LCXs), which can radiate and receive electromagnetic waves through slots; thus, providing communication. To evaluate the system-level performance of the LCX channel in a tunnel, we propose a modified geometrically based single-bounce multiple-input-multiple-output (GBSB-MIMO) channel model considering the effect of Doppler spread. The time-domain statistics of the channel model are studied from numerical simulations. Based on the proposed channel model, we also simulate and analyze the effects of different factors on the 5G system-level performance, including the interval of cable slots and the quantity and location of LCX.

A Bayesian deep learning approach for random vibration analysis of bridges subjected to vehicle dynamic interaction

Vehicle actions represent the main operational loading for various types of bridges. It is essential to conduct random vibration analysis due to the unavoidable uncertainties arising from both the vehicle and bridge structure. This paper proposes a novel approach for the vehicle-induced random vibration analysis of bridges integrating Bayesian deep learning. The dynamic equation of the stochastic vehicle-bridge interaction system in state space form is deduced, based on which an ensemble of deep neural network is proposed to construct the surrogate model consisting of two designed functional modules, i.e., convolutional layers for excitation input feature extraction and long short-term memory (LSTM) layers for bridge response time series prediction. According to the deduced state space equation, the conventional LSTM cell is modified by introducing randomness to a portion of cell parameters. Probability distributions of the selected network parameters are then estimated by Bayesian inference, enabling the surrogate model to convey the uncertainties of the vehicle-bridge interaction system and rapidly estimate random vibration responses of the bridge. The proposed approach is applied on a railway bridge under high-speed train loading to demonstrate its efficacy. A deep Bayesian neural network is tailored and developed using the present methodology for the studied train-bridge coupling dynamic system. Time-domain statistics and frequency-domain responses of the bridge are acquired through the Bayesian deep learning model and compared with the results from a validated vehicle-bridge interaction model. Robustness of the Bayesian deep learning approach is further examined by investigating the influence of training dataset size, vehicle speed, and model input noise.

Engine Vibration Data Increases Prognosis Accuracy on Emission Loads: A Novel Statistical Regressions Algorithm Approach for Vibration Analysis in Time Domain

Statistical regression models have rarely been used for engine exhaust emission parameters. This paper presents a three-step statistical analysis algorithm, which shows increased prediction accuracy when using vibration and sound pressure data as a covariate variable in the exhaust emission prediction model. The first step evaluates the best time domain statistic and the point of collection of engine data. The univariate linear regression model revealed that non-negative time domain statistics are the best predictors. Also, only one statistic evaluated in this study was a statistically significant predictor for all 11 exhaust parameters. The ecological and energy parameters of the engine were analyzed by statistical analysis. The symmetry of the methods was applied in the analysis both in terms of fuel type and in terms of adjustable engine parameters. A three-step statistical analysis algorithm with symmetric statistical regression analysis was used. Fixed engine parameters were evaluated in the second algorithm step. ANOVA revealed that engine power was a strong predictor for fuel mass flow, CO, CO2, NOx, THC, COSick, O2, air mass flow, texhaust, whereas type of fuel was only a predictor of tair and tfuel. Injection timing did not allow predicting any exhaust parameters. In the third step, the best fixed engine parameter and the best time domain statistic was used as a model covariate in ANCOVA model. ANCOVA model showed increased prediction accuracy in all 11 exhausted emission parameters. Moreover, vibration covariate was found to increase model accuracy under higher engine power (12 kW and 20 kW) and using several types of fuels (HVO30, HVO50, SME30, and SME50). Vibration characteristics of diesel engines running on alternative fuels show reliable relationships with engine performance characteristics, including amounts and characteristics of exhaust emissions. Thus, the results received can be used to develop a reliable and inexpensive method to evaluate the impact of various alternative fuel blends on important parameters of diesel engines.

Two new kurtosis-based similarity evaluation indicators for grinding chatter diagnosis under non-stationary working conditions

Chatter is one of the most critical errors in the grinding process, the occurrence of which will directly degrade the ultimate geometrical surface quality of the workpiece. Most of the present grinding chatter detection methods are based on the energy level monitoring of indicators that constructed from time domain statistics or fault characteristic frequencies. However, the grinding parameters, e.g., grinding force, feed rate, speed, etc. are time varying during the grinding process, and traditional indicators relying on energy level suffer degradation in the grinding chatter detection. In order to overcome this problem, a new grinding chatter detection method under non-stationary working conditions is proposed in this paper. With the proposed method, the kurtosis possibility density function (KPDF) is first utilized to assess the impact characteristics of the vibration signal, and a larger central moment and long tail of KPDF is probably observed in case of grinding chatter. Then two similarity evaluation indicators, i.e., intersection area and correlation distance are newly constructed to measure the variation of KPDF by taking the average of healthy KPDFs as benchmark. After that, the k-means clustering method is applied to detect the grinding chatter fault. The effectiveness of the proposed method is successfully verified by both simulation and experiment under non-stationary working conditions. The results show that the proposed method achieves higher grinding chatter detection accuracy and more compact clustering than traditional methods.

Pipeline anti-vandalism monitoring system based on time division multiplexing interferometric fiber optic sensor array

A pipeline anti-vandalism monitoring system based on time division multiplexing (TDM) interferometric fiber optic sensor array is proposed and demonstrated in this paper to realize the anti-vandalism monitoring of buried pipelines. The sensor unit of the TDM quasi-distributed system can be responsible for a continuous monitoring area due to its high sensitivity through sensitization. Therefore, the TDM-supported quasi-distributed sensor technique only needs to dig at several sites to avoid digging deeply into ground along the pipeline. This can greatly reduce the system cost and accelerate the construction process. In addition, a phase detection method based on the rectangular pulse binary (RPB) phase modulation is used to realize the phase detection, and a field programmable gate array (FPGA)-based signal acquisition interrogation controller is adopted to realize the rapid and real-time acquisition of returned interference signals in the system. For the demodulated phase signals, by judging the three eigenvalues of level crossing time-domain statistics, peak-to-average ratio, and short-term energy, effective anti-vandalism alarm can be achieved. The system is tested and verified. The experiment results show that the system can achieve effective and real-time anti-vandalism alarm with accuracy rate over 90% within 1 ms.

모터의 전류치를 활용한 전동차 출입문의 특징추출 및 고장진단 예지 알고리즘 선정 방안 연구

Recently, the manufacturing requirements of Rolling Stock are required to diagnose and manage the condition of major safety devices (doors, brake, signals, etc.) to suggest a plan for efficient maintenance. Based on these backgrounds and technology trends, research on Condition-Based Maintenance (CBM) and Prognostic Health Management (PHM) has been actively conducted in recent years. In this study, the current value of the engine drive motor of the door of a Rolling Stock is measured by dividing it into four classes (normal open/abnormal open, normally closed/abnormally closed), and statistically analyzed 13 factors of time domain statistics based on time domain statistics. After verifying the significance, suitable Features were extracted. Based on the machine learning theory, a predictive algorithm that can classify the extracted Features was selected, and the accuracy was verified against the actual measured data class with the selected prognosis algorithm.

Fault severity detection of a worm gearbox based on several feature extraction methods through a developed condition monitoring system

This study presents the severity detection of pitting faults on worm gearbox through the assessment of fault features extracted from the gearbox vibration data. Fault severity assessment on worm gearbox is conducted by the developed condition monitoring instrument with observing not only traditional but also multidisciplinary features. It is well known that the sliding motion between the worm gear and wheel gear causes difficulties about fault detection on worm gearboxes. Therefore, continuous monitoring and observation of different types of fault features are very important, especially for worm gearboxes. Therefore, in this study, time-domain statistics, the features of evaluated vibration analysis method and Poincaré plot are examined for fault severity detection on worm gearbox. The most reliable features for fault detection on worm gearbox are determined via the parallel coordinate plot. The abnormality detection during worm gearbox operation with the developed system is performed successfully by means of a decision tree.

Integrating old and new complexity measures toward automated seizure detection from long-term video EEG recordings

SummaryAutomated seizure detection in long-term video-EEG recordings is far from being integrated into common clinical practice. Here, we leverage classical and state-of-the-art complexity measures to robustly and automatically detect seizures from scalp recordings. Brain activity is scored through eight features, encompassing traditional time domain and novel measures of recurrence. A binary classification algorithm tailored to treat unbalanced dataset is used to determine whether a time window is ictal or non-ictal from its features. The application of the algorithm on a cohort of ten adult patients with focal refractory epilepsy indicates sensitivity, specificity, and accuracy of 90%, along with a true alarm rate of 95% and less than four false alarms per day. The proposed approach emphasizes ictal patterns against noisy background without the need of data preprocessing. Finally, we benchmark our approach against previous studies on two publicly available datasets, demonstrating the good performance of our algorithm.

Multi-frequency characterization of particle-wall interactions in a solid-liquid dispersion conveying pipe flow using a non-intrusive vibration detection method

Particle-wall interaction behaviour is related to the optimization of chemical and petroleum production, and the real-time characterization of particles in liquid flow by accurate and convenient methods is still a challenge worldwide. In this work, the particle-wall behaviours collision and friction were distinguished from water flow behaviours based on a time-frequency method at four pipe positions. The specific refined frequency responses were calculated by zoom fast Fourier transform (Zoom-FFT) and multiscale frequency analysis methods, and eigenvectors were established based on the corresponding time-domain statistics. The test positions, flow velocities and particle sizes were auto-classified. A verification experiment was performed, and good agreement was found between the content (0.05–0.2 wt%) of particles with a size range of 96–212 μm and the vibration response of ten discovered particle multiscale frequencies ranging from 43.2 to 50 kHz. In particular, high recognition rates were obtained for the different test positions (94.45%), flow velocities (95.33%), and particle sizes (91.00%) by the support vector machine (SVM) method. The best three characteristic particle frequency bands were 45.6–46.4 kHz, 46.4–47.2 kHz and 47.2–48.0 kHz in the elbow. The relevant sand content detection error rates were 9.57%, 4.81%, and 6.78%, which were improved greatly compared with those of our previous method. Therefore, this study complements the existing techniques and knowledge for particle characterization in multiphase flow.

Propulsion performance and unsteady forces of a pump-jet propulsor with different pre-swirl stator parameters

Rotor-stator interaction of a pump-jet propulsor can induce strong pressure fluctuations and vibrations, which may deteriorate the vibration and acoustic performance and cause damage to the propulsion system at some severe working conditions. In this paper, the role of stator parameters, such as the prewhirl angle, the rotor-stator spacing and the chord length of the stator blades, in the propulsion performance and unsteady forces of a pump-jet propulsor is investigated through a numerical simulation. The shear-stress transport (SST) k–omega turbulence model together with the sliding mesh technique are employed to simulate the three-dimensional unsteady flow. The propulsion performance is obtained from the steady simulation at nine advance ratios. Take the steady result as the initial flow field, the convergence usually occurs in one revolution of the rotor in the unsteady computations. For the unsteady computation analysis, the line-spectrum amplitudes of the unsteady rotor forces are analyzed, and a method based on time domain statistics is employed to reflect the fluctuating amplitude characteristic of the unsteady pressures on the whole blade surface of the rotor. Since the pitch angle of the rotor blade decreases sharply along the radial direction, the velocity circumferential angle is corrected based on the blade pitch angle to reflect the fluctuation of rotor incidence angle in the circumferential direction.

The Classification of EEG Signals with Multi-Domain Fusion Based on D-S Evidence Theory

The classification of electroencephalogram (EEG) signals is a key technique of brain–computer interface (BCI) system. In view of the complexity of EEG signals and the low accuracy in EEG signals recognition, a motor imagery EEG signals classification method with multi-domain fusion based on Dempster–Shafer (D-S) evidence theory is presented in this paper. Firstly, time domain statistics (TDS), autoregressive (AR) model and discrete wavelet transform (DWT) are used to extract features from EEG signals, respectively, and three probabilistic output support vector machine (SVM) classification models are trained based on these three feature sets. Secondly, using the output of each SVM, we construct basic probability assignment (BPA) function and get fusion BPA through D-S evidence theory. Finally, determining the class of test samples based on decision rules. Four databases from BCI competition are employed to evaluate the proposed approach, and the highest classification accuracy reaches 92.83%. Results show that this method acquires higher accuracy and has strong individual adaptability.

Intelligent Fault Diagnosis of Diesel Engines via Extreme Gradient Boosting and High-Accuracy Time-Frequency Information of Vibration Signals.

Accurate and timely misfire fault diagnosis is of vital significance for diesel engines. However, existing algorithms are prone to fall into model over-fitting and adopt low energy-concentrated features. This paper presents a novel extreme gradient boosting-based misfire fault diagnosis approach utilizing the high-accuracy time–frequency information of vibration signals. First, diesel engine misfire tests were conducted under different spindle speeds, and the corresponding vibration signals were acquired via a triaxial accelerometer. The time-domain features of signals were extracted by using a time-domain statistics method, while the high-accuracy time–frequency domain features were obtained via the high-resolution multisynchrosqueezing transform. Thereafter, considering the nonlinearity and high dimensionality of the original characteristic data sets, the locally linear embedding method was employed for feature dimensionality reduction. Eventually, to avoid model overfitting, the extreme gradient boosting algorithm was utilized for diesel engine misfire fault diagnosis. Experiments under different spindle speeds and comprehensive comparisons with other evaluation methods were conducted to demonstrate the effectiveness of the proposed extreme gradient boosting-based misfire diagnosis method. The results verify that the highest classification accuracy of the proposed extreme gradient boosting-based algorithm is up to 99.93%. Simultaneously, the classification accuracy of the presented approach is approximately 24.63% higher on average than those of algorithms that use wavelet packet-based features. Moreover, it is shown that it obtains the minimum root mean squared error and can effectively prevent the model from falling into overfitting.

Tool wear state recognition based on GWO–SVM with feature selection of genetic algorithm

Tool wear is an important consideration for Computerized Numerical Control (CNC) machine tools as it directly affects machining precision. To realize the online recognition of tool wear degree, this research develops a tool wear monitoring system using an indirect measurement method which selects signal characteristics that are strongly correlated with tool wear to recognize tool wear status. The system combines support vector machine (SVM) and genetic algorithm (GA) to establish a nonlinear mapping relationship between a sample of cutting force sensor signal and tool wear level. The cutting force signal is extracted using time domain statistics, frequency domain analysis, and wavelet packet decomposition. GA is employed to select the sensitive features which have a high correlation with tool wear states. SVM is also applied to obtain the state recognition results of tool wear. The gray wolf optimization (GWO) algorithm is used to optimize the SVM parameters and to improve prediction accuracy and reduce internal parameters’ adjustment time. A milling experiment on AISI 1045 steel showed that when comparing with SVM optimized by commonly used optimization algorithms (grid search, particle swarm optimization, and GA), the proposed tool wear monitoring system can accurately reflect the degree of tool wear and achieves strong generalizability. A set of vibration signals are adopted to verify the presented research. Results show that the proposed tool wear monitoring system is robust.

Gear pitting fault diagnosis using disentangled features from unsupervised deep learning

Effective feature extraction is critical for machinery fault diagnosis and prognosis. The use of time–frequency features for machinery fault diagnosis has prevailed in the last decade. However, more attentions have been drawn to machine learning–based features. While time–frequency domain features can be directly correlated to fault types and fault levels, data-driven features are typically abstract representations. Therefore, classical machine learning approaches require large amount of training data to classify these abstract features for fault diagnosis. This article proposed a fully unsupervised feature extraction method for “meaningful” feature mining, named disentangled tone mining. It is shown that disentangled tone mining can effectively extract the hidden “trend” associated with machinery health state, which can be used directly for online anomaly detection and prediction. Compared with wavelet transform and time domain statistics, disentangled tone mining can better extract fault-related features and reflect the fault degradation process. Shallow methods, such as principal component analysis, multidimensional scaling and single-layer sparse autoencoder, are shown to be inferior in terms of disentangled feature learning for machinery signals. Simulation analysis is also provided to demonstrate and explain the potential mechanism underlying the proposed method.