Frequency Domain Energy Research Articles

Application and Research of Distributed Acoustic Sensing in Vibration Monitoring of Subway Tunnels

With the booming development of the rail transit industry and the increase in the construction and operation of mileage, the health status of infrastructure such as vehicles, tracks, and trains, as well as operational safety, have received widespread attention. Distributed optical fiber sensing technology has the characteristics of long monitoring distance, strong real-time performance, and highly economical, and has broad prospects in rail transit applications. This paper adopts Distributed Acoustic Sensing technology to obtain vibration information along the subway tunnel, analyzes the time-domain signal and frequency-domain energy characteristics of train vibration, as well as the passing time, direction, and location of the train, providing technical support for the safe operation of the subway.

TVP-VAR based time and frequency domain food & energy commodities connectedness an analysis for financial/geopolitical turmoil episodes

Amidst the current global inflationary challenges, the concurrent rise of energy and agricultural commodity prices, which constitute the primary components of consumer prices, has emerged as a matter of significant interest among both scholars and policymakers. To this end, this study examines the dynamic interlinkages between food and energy commodity indexes from 2005:1 to 2023:3, covering turmoil episodes such as the Global Financial Crisis (GFC), the COVID-19 pandemic, and the Russia-Ukraine Conflict (RUC). Additionally, following Broadstock et al. (2022), we perform dynamic portfolio analyses to determine portfolio performances under 3 different portfolio construction approaches. The empirical results presented in this paper allow for a number of important findings. First, both the time and frequency-domain connectedness indexes associate with major financial/geopolitical stress events. Second, the fuel energy and the crude oil price indexes are the largest propagators and recipients of spillovers Third, the cumulative portfolio returns exhibit significant growth during the early phase of the COVID-19, declining during the RUC, and a notable upswing during the GFC. Finally, our findings for frequency-dependent connectedness networks indicate that the market is particularly susceptible to short-term shocks. This paper has significant ramifications for investors, market players, and policymakers.

Parametric Doppler correction for wayside array acoustic signal via short-time reconstruction

The trackside acoustic detection system (TADS) plays a vital role in vehicle bearings condition monitoring. However, the inevitable Doppler distortion embedded in collected data will bring considerable difficulties to defect inspection and diagnosis in the system. The distortion elimination approaches mainly achieve spectrum recovery based on time-domain interpolation resampling (TIR) in a data-driven way. These will be further limited by the requirement to signal to noise ratio (SNR) or calculation speed. Considering the principle of wayside acoustic physical model and the benefits of array acoustic in practice, this study proposes an adaptive parametric Doppler correction (PDC) scheme based on short-time reconstruction (STR), including perception modeling, inverse perception optimization and Doppler correction. Firstly, mathematical modeling with multiple perception operators, including acoustic amplitude modulation operator, frequency modulation operator and array time delay operator, a wayside acoustic physical model based on array sensing is established. Secondly, through the corresponding inverse multiple perception operators, a transition signal with frequency-domain energy concentrated is obtained for the optimal moving parameters searching. Thirdly, within short-time sequence segments of the sound source, the real-time position recovery is realized via the proposed STR with formulaic propagation delay compensation. Theoretically, it can be seen that the proposed PDC scheme can simultaneously recover the amplitude, frequency distribution and phase of the Doppler signal, which can be applicable to all wayside acoustic diagnosis scenarios. With the correction analysis of simulation and experimental array defect signals, it can be confirmed that the proposed STR-based PDC scheme is effective for Doppler signal recovery in high fidelity, and has great potential to the real-time diagnosis of TADS.

Conformal Cylindrical Array Sound Source Localization at the Presence of Shadowed Elements

Sound source localization provides an absorbing capability for unmanned aerial vehicles (UAVs) in scenarios such as search and rescue operations. The shape fusion between the sound array and UAVs forms a special conformal property that is drawing more and more attention. However, the inevitable shadow effect caused by shape fusion seriously degrades the degrees of freedom (DOF) of the array. In this paper, a signal reconstruction-based direction of arrival (DOA) estimation method is proposed to address this limitation. Firstly, we establish a restricted signal model for the conformal cylindrical array (CCA), and then based on frequency domain energy detection, the elements are divided into receiving restricted elements and receiving normal elements. Secondly, according to the position vector of receiving restricted elements, the approximate range of the DOA is roughly estimated to reduce the complexity. Meanwhile, the signals of receiving restricted elements are reconstructed on the basis of receiving normal elements to eliminate the shadow effect and increase the DOF. Lastly, in the estimated approximate range of the DOA, the precise DOA is estimated by peak search. We also derive the 2-D Cramer-Rao lower bound (CRLB) for the CCA. Simulations show that the proposed SR-MUSIC-RS method can achieve satisfactory performance with lower complexity, and the RMSE is close to that of general signal model with normal elements.

Long-Time Coherent Integration for Marine Targets Based on Segmented Compensation

Long-time coherent integration is an effective method for dim target detection from heavy sea clutter. To detect dim targets, a novel long-time coherent integration method based on segmented compensation is proposed in this paper. The method models the complex motion of a marine target as the combination of multi-stage uniformly accelerated motions. According to the difference of energy distribution in Doppler frequency domain, this method can suppress sea clutter and detect the regions of interest (ROIs). Using time–frequency domain energy analysis, the potential target can be extracted. After estimating the parameters and segmentation, for the potential targets, the phase compensation factor can be used to eliminate the Doppler frequency modulation caused by the complex motion. Finally, for the compensated signal, long-time coherent integration is performed to realize the target detection and discrimination under low signal-to-clutter ratio. To verify the effectiveness of the proposed method, we apply simulation data and measured CSIR data in the experiments. The results show that the proposed method can integrate the energy of target more effectively than MTD and RFrFT, and the novel method has better detection performance for complex moving targets under low signal-to-clutter ratio situation.

A depth discrimination method based on the scintillation of frequency domain

An innovative algorithm of target depth discrimination suitable for passive horizontal array in shallow sea is discussed in this paper. Based on the idea of modal scintillation theory, a new target depth discrimination method of high calculation speed for horizontal array is proposed by analysing the commonness between frequency domain energy of low-frequency broadband signals and modal excitation. This method avoids the mode decomposition of the horizontal array signals, greatly reduces the complexity, improves the stability, has a fast calculation speed and can perform the real-time depth judgment. In this paper, the principle of the algorithm is derived in detail in the theoretical aspect, and then the algorithm is simulated in the shallow sea environment to verify its effectiveness, and the influence of different influencing factors on the performance of the algorithm is explored. At the same time, the algorithm is verified by the actual experimental data and achieves good results, indicating that the algorithm has certain practical application value in the target depth discrimination domain.

Asymmetrical Fault Detection in Induction Motors Through Elimination of Load Torque Oscillations Effects in the Slight Speed Variations and Steady-State Conditions

Recently, motor current signature analysis (MCSA) has been widely considered for fault detections due to its simplicity, availability, and cost-effectiveness. The rotor asymmetry fault (RAF) is the most common fault that occurs in induction machines. It is extremely challenging to detect RAF indices occurred at the vicinity of the supply frequency. Moreover, load torque oscillations (LTOs) <bold xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">which</b> appear as a sinusoidal phase modulation of the supply frequency, exhibit similar indications as the RAF, especially in gearbox-based electromechanical systems. Since LTOs lead to false alarm of RAF, separation of LTOs indices from RAF characteristic components is inevitable. In this paper, normalized frequency domain energy operator (NFDEO) is evaluated for demodulation and separation of RAF and LTOs in steady-state and transient conditions. Moreover, the proposed method is tested in both with-and-without speed control strategies. In this regard, the effects of RAF in the presence of LTOs investigated through both synthetic signals and experimental data in steady-state and transient conditions with slight variation in rotor speed. The obtained results show that NFDEO along with Winger-Ville can effectively detect RAF in the presence of LTOs even with speed control strategy.

Research on Transformer Voiceprint Feature Extraction Oriented to Complex Noise Environment

Transformer fault diagnosis based on acoustic characteristics is a new non-contact and non-destructive monitoring method. It has the advantages that the acoustic signal detection is not disturbed by electric and magnetic fields, and the monitoring process does not affect the normal operation of the transformer. Aiming at the difficulty of extracting transformer voiceprint features in complex noise environment, a transformer voiceprint feature extraction method based on Variable Mode Extraction (VME) is proposed. In this method, the center frequency of the Intrinsic Mode Function(IMF) is set according to the generation mechanism of transformer radiated noise, thus the uncertainty of decomposition results caused by random distribution and other frequency search methods is eliminated; Then, taking the frequency-domain energy aggregation of IMF and the minimum center frequency energy of residual signal as the optimization objectives, the cyclic iterative decomposition is used to identify and extract the transformer voiceprint features, so as to reduce the impact of environmental noise and other equipment noise. The analysis results of simulation signals and field signals show that this method can effectively reduce the impact of environmental noise and extract more clear and accurate transformer voiceprint features.

An improved probabilistic diagnosis imaging algorithm for quantifying Hole-edge crack growth

Probabilistic damage imaging (PDI) algorithm based on Lamb wave is one of the most promising structural health monitoring technologies for quantifying the hole-edge crack. However, it is still a challenge how to use a limited number of sensors to quantify the hole-edge crack. This paper proposed an improved probabilistic damage imaging algorithm (IPDI) to track the hole-edge crack growth. A simulation has been conducted to deeply study the interaction of cracks and Lamb waves. A damage index calculated by the frequency-domain energy has been found to have a good capacity for monotonically characterizing crack propagation. The further study derives a unifying relationship between damage index and the ellipse size control factor from the crack to transmitter–receiver paths with different lengths and angles. The unifying relation is used to define a new dynamic elliptical control parameter in PDI algorithm to improve the capacity of crack quantification. The improved PDI algorithm is verified by both of simulation and experiments with different exciting frequencies, whose results show that the crack imaging error of the IPDI algorithm is below 1 mm, and the accuracy is much higher than that of the traditional PDI algorithm. The proposed IPDI algorithm can effectively quantify the hole-edge crack growth.

Prediction on the Remaining Useful Life of Rolling Bearings Using Ensemble DLSTM

As a significant component of rotation machinery, bearing plays a role in supporting and transmitting power. However, bearings are subject to complex operating conditions and are prone to failure. To avoid ineffectiveness and improve the reliability of bearings, a data-driven method is used to predict the remaining useful life (RUL). However, this method is less stable and can only forecast the RUL of bearings under training sample conditions. An ensemble deep, long-term, and short-term memory (EDLSTM) method is proposed to solve this problem. First, the feature of the forecast-bearing RUL was extracted including time-domain features, frequency-domain energy features, and Shannon entropy. Then, a deep long- and short-term memory network prediction model of the bearing RUL was constructed. To resolve the instability of DLSTM predictions, multiple DLSTMs were ensembled using the maximum information component (MIC) criterion. The model i trained using bearing data with different failure modes under difficult operating conditions to improve the predictive stability of the model. Finally, an EDLSTM was constructed to achieve the bearing RUL prediction. In the prediction result of the training set, the cumulative relative accuracy (CRA) was above 0.9 for most of the bearings. According to the experimental results in the test set, the mean CRA was over 0.80. For some of the bearing’s RUL, the CRA was more than 0.90. The above results show that the proposed approach can effectively predict the RUL of a bearing and has a more stable prediction ability than the bagging integration method.

Parameters optimization of electro-hydraulic power steering system based on multi-objective collaborative method

Electro-hydraulic power steering (EHPS) systems are widely used in commercial vehicles due to their adjustable power assist and energy-saving advantages. In this paper, a dynamic model of the EHPS system is developed, and quantitative expressions for three evaluation indexes, steering road feel, steering sensibility and steering energy loss, are derived for the first time. A multi-objective collaborative optimization model of the EHPS system is then established, which consists of one total system and three parallel subsystems, based on collaborative optimization theory. Considering the coupled variables of each subsystem, the total system is optimized by a multi-objective algorithm, while the subsystems are optimized by a single-objective algorithm. The optimization results demonstrate that the average frequency domain energy of the steering road feel is increased by 69.1%, the average frequency domain energy of steering sensitivity is reduced by 19.2%, and steering energy consumption is reduced by 10.8% compared to the initial value. The non-dominated sorting genetic algorithm-II (NSGA-II) shows superior comprehensive performance compared to the other two multi-objective algorithms, and the optimization performance can be further improved by setting appropriate algorithm parameters.

Magnetic Anomaly Detection Based on Energy-Concentrated Discrete Cosine Wavelet Transform

The magnetic anomaly signal tends to be contaminated by ambient environmental noise due to the complexity and diversity in the field of magnetic anomaly detection (MAD). The current denoising methods are effective in improving the signal-to-noise ratio (SNR). However, most of them are only applicable to the Gaussian noise and perform poorly for the practical geomagnetic noise, that is the nonstationary noise with a power spectral density (PSD) of 1/ <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">f^a</i> . To solve this issue, a MAD method based on energy concentrated discrete cosine wavelet transform is proposed in this paper. A novel framework through fusing wavelet transform and discrete cosine transform, dubbed WT-DCT, is constructed, which consists of abnormal signal acquisition, frequency domain energy concentration, and discrete wavelet transformation. The SNR of the magnetic anomaly is improved by extracting the principal components of the scale signal in wavelet transformation through the discrete cosine transform. Through comparing the WT-DCT to four commonly used and accepted methods with extensive simulations and field tests, the results demonstrate that with variations of the geomagnetic noise strengths in the range from 250 nT to 1000 nT, the proposed WT-DCT achieves the highest SNR improvement by about 44.81% and the best structural similarity (SSIM) improvement by about 84.75%.

Health diagnosis of marine engine room equipment based on BP and D-S evidence theory

Aiming at the problems of poor resolution and low precision in traditional health diagnosis of Marine engine room equipment, this paper proposes a health diagnosis method of intelligent Marine engine room equipment based on BP neural network and D-S evidence theory. Firstly, the time-domain parameters of the obtained acceleration signal are extracted and the energy in frequency domain after wavelet decomposition is calculated. Then the eigenvectors of time domain and wavelet packet energy were constructed respectively, and the normalized processing was input into two BP neural networks to obtain the classification results. Finally, the fault classification results in time domain and frequency domain are combined with the D-S evidence theory and output diagnosis. Through experimental analysis and verification of rolling bearing data from electrical Engineering Laboratory of Case Western Reserve University, the accuracy of the proposed method is better than that of time domain and frequency domain analysis alone, which improves the accuracy and reliability of fault classification.

Viscoelastic or viscoplastic glucose theory (VGT #54): Estimating relative energy carried by glucose under the influence of body weight while using the collected data from the daily estimated average glucose and body weight in the early morning over three triple-year periods, Y2013-Y2015, and Y2016-Y2018, Y2019-Y2021, along with the application of a VGT tool and frequency domain energy method based on

The author was a professional engineer working in the fields of the space shuttle, naval battleships, nuclear power plants, computer hardware and software, artificial intelligence, and semiconductor chips. After retiring from his work, he started to self-study and research internal medicine with an emphasis on the exploration of various biomarker relationships and the prevention of metabolic disorder-induced chronic diseases. Since 2010, he utilized the disciplines learned from 7 different universities along with various work experiences to formulate his current medical research work during the past 13 years. One thing he discovered in engineering and medicine, we frequently seek answers, illustrations, or explanations for the relationships between the input variable (force applied on a structure or cause of a disease) and output variable (deformation of a structure or symptom of a disease). However, the multiple relationships between input and output could be expressed with many different matrix formats of 1 x 1, 1 x n, m x 1, or m x n (m or n means different multiple variables). In addition to these described mathematical complications, the output resulting from one or more inputs can also become an input of another output, i.e. a symptom of certain causes can become a cause of another different symptom. This phenomenon is a complex scenario with “chain effects”. Engineering and biomedical complications are fundamentally mathematical problems that correlate or conform with many inherent physical laws or principles. Over the past 13 years, in his medical research work, he has encountered more than 100 different sets of biomarkers with almost equal amounts of cause/input variables versus symptom/output variables. For example, food and exercise influence both body weight and glucose level, where persistent high glucose can result in diabetes. When diabetes combines with hypertension (high blood pressure) and hyperlipidemia (high blood lipids), it can cause cardiovascular diseases. Furthermore, obesity and diabetes are also linked with various kinds of cancers. These multiple sets of biomedical input versus output have been researched by the author using different tools he has learned from academic fields of mathematics, physics, computer science, and engineering. For example, he has applied a signal processing technique to separate 19 components from the combined postprandial plasma glucose (PPG) wave. He identified the carbs/sugar intake amount and post-meal exercise as the two most important contributing factors to PPG formation. Based on these findings, he then applied the theory of elasticity to develop a linear elastic glucose theory (LEGT) to predict PPG value with high prediction accuracy, using fasting plasma glucose (FPG), carbs/sugar grams, and post-meal walking k-steps as three major input components of predicted PPG formation.

Viscoelastic or Viscoplastic Glucose Theory (VGT #89): Using Frequency-Domain Energy Method to Verify the Results from Space-Domain VGT Energy Method for Cardiovascular Disease, Chronic Kidney Disease, and Type 2 Diabetes Resulting from Body Weight Changes over Two Periods, Y12-Y16 Versus Y17-Y22, Based on GH-Method: Math-Physical Medicine (No. 679)

The author is a mathematician and engineer who has conducted medical research work over the past 13 years in the fields of endocrinology, metabolic disorder-induced chronic diseases (especially diabetes), and their resulting various medical complications. Thus far, he has written and published 600+ research papers in various journals using different math-physical medicine methodologies (MPM). Beginning with paper No. 578 dated 1/8/2022, he has written 80+ medical papers and 4 economics papers using viscoelasticity and viscoplasticity theories (VGT) tools from physics and engineering disciplines. These papers aim to explore some hidden physical behaviors and provide a deeper quantitative understanding of the inter-relationships of a selected output (symptom) versus singular input or multiple inputs (root causes, risk factors, or influential factors). In the field of medical research, the hidden biophysical behaviors and possible inter-relationships exist among lifestyle details, medical conditions, chronic diseases, and certain medical complications, such as heart at- tacks, stroke, cancers, dementia, and even longevity concerns. He has noticed that most of the medical subjects with their associated data, multiple symptoms, and influential factors are “time-dependent” which means that all biomedical variables change from time to time because body living cells are dynamically changing. This is what Professor Norman Jones, the author’s adviser at MIT, suggested to him in December 2021 and why he utilizes the VGT tools from physics and engineering to conduct his medical research work since then. Papers No. 671 through No. 674 focused on the COVID infectious disease as input and three key US economic measurements as outputs. From this economics exercise, he realized that the established theory of viscoelasticity and viscoplasticity (from the physics branch of science) should not only be limited to the scope of engineering applications. Its ability to link certain time-dependent variables and their physical characteristics and associated energy estimation via the hysteresis loop area are equally powerful for applications in many other research fields, such as economics and medicine.

Viscoelastic or Viscoplastic Glucose Theory (VGT #92): Using Two Cases of Frequency-Domain Variables and Frequency-Domain Energy Analysis Results to Compare Against the Findings Using Space Domain-VGT Energy Tool for Cardiovascular Disease Risk % Versus Daily Estimated Average Glucose, Body Weight, and Food Quantity from a Type 2 Diabetes Patient Over 11 Years from Y2012 to Y2022 Based on GH-Method: Math-Physical

The author is an engineer who has conducted medical research work over the past 13 years in the fields of endocrinology, metabolic disorder-induced chronic diseases (especially diabetes), and their resulting various medical complications. Thus far, he has written and published more than 600 research papers in various jour- nals using math-physical medicine methodology (MPM). Beginning with Paper No. 578 dated 1/8/2022, he has written nearly 90 medical papers and 4 economics pa- pers using viscoelasticity and viscoplasticity theories (VGT) tools from physics and engineering disciplines. These papers aim to explore some hidden physical behaviors and provide a deeper quantitative understanding of the inter-relationships of a selected output (symptom) versus singular input or multiple inputs (root causes, risk factors, or influential factors). In the field of medical research, the hidden biophysical behaviors and possible inter-relationships exist among lifestyle details, medical conditions, chronic diseases, and certain medical complications, such as heart attacks, stroke, cancers, dementia, and even longevity concerns. He has noticed that most medical subjects with their associated data, multiple symptoms, and influential factors are “time-dependent” which means that all biomedical variables change from time to time because body living cells are dynamically changing. This is what Professor Norman Jones, the author’s adviser at MIT, suggested to him in December 2021 and why he utilizes the VGT tools from physics and engineering to conduct his medical research work since then. Papers No. 671 through No. 674 focused on the COVID infectious disease as the input and three key US economic measurements as the outputs. From this economics exercise, he realized that the established theory of viscoelasticity and viscoplasticity (from the physics branch of science) should not only be limited to the scope of engineering applications. Its ability to link certain time-dependent variables and their physical characteristics and associated energy estimation via the hysteresis loop area is equally powerful for applications in many other research fields, such as economics and medicine.

Module Integral Method for the Calculation of Frequency-Dependent Leakage Inductance of High-Frequency Transformers

The accurate calculation of frequency-dependent leakage inductance of high-frequency transformers is critical for the optimized design of power electronic transformers. The leakage inductance can be obtained through the magnetic energy, usually calculated by the phasor integral of the magnetic energy density in the literature. This article analyzes the difference between the module and the phasor integral based on frequency-domain energy and proposes to take the module integral of magnetic energy density as the periodic averaged magnetic energy. Furthermore, the closed-form formula of the leakage inductance is given accordingly. The modules under different frequencies correspond to the intrinsic constant magnetic densities. Thus, the proposed method has a better physical interpretation compared with the previous phasor integral method. The finite element method simulation and experimental results of five transformers are taken as benchmarks to compare the proposed method with the phasor integral method. The comparison shows that the proposed module integral method has satisfying effectiveness and accuracy in the whole frequency band for all the cases involving both noninterleaved and interleaved windings.

Time-Frequency Characteristics of Fluctuating Pressure on the Bottom of the Stilling Basin with Step-Down Floor Based on Hilbert–Huang Transform

Fluctuating pressure is an important feature of the bottom of a stilling basin with step-down floor. To analyze the frequency domain characteristics and energy distribution of this fluctuating pressure, the Hilbert–Huang transform (HHT) method is used. First, empirical mode decomposition is performed on the pressure fluctuation signal to obtain a number of intrinsic mode functions (IMFs), and then the Hilbert transformation is performed on each IMF to obtain the Hilbert spectrum and marginal spectrum for characterizing the pressure fluctuation signal. The results show that the fluctuating pressure signal of the stilling basin with step-down floor has obvious characteristics of low frequency and large amplitude. The dominant frequencies of the head and tail of the stilling basin are very prominent, and most of the energy is concentrated below 5.0 Hz; with the increase in the relative position of the measuring point, the energy distribution in stilling basin with step-down floor changes from high-frequency component to low-frequency component. The fluctuating pressure signal of the stilling basin with step-down floor has random amplitude modulation and frequency modulation. The marginal spectrum obtained by the HHT method can obtain the local characteristics of the signal more accurately and is more suitable for processing nonlinear and nonstationary signals.

Identification of multi-defects in an arched composite structure by the corrected probabilistic diagnostic imaging with the fused damage index

Due to the complicacy of geometry and structure in the arched composite structure, it is difficult to monitor various kinds of defects accurately. The developed damage probabilistic diagnostic imaging approach based on ultrasonic guided wave energy signal characteristics is very feasible for the structural health monitoring in the arched composite structures. However, the conventional probabilistic diagnostic imaging (PDI) approaches united with the signal energy damage indices ( DIs) have some limitations in the identification of the number, location and specific size information of multi-defects. Thus, the damage shape factor from the single damage-impaired path imminently demands to be majorized to raise the precision and stability of PDI approach in the damage recognition. A corrected probabilistic diagnostic imaging (CPDI) approach integrated with the damage shape factor [Formula: see text] needs to be recommended to precisely inspect the expansion of defect zones and different multi-defects in the arched composite structure. The availability and feasibility of the proposed methods has been validated by the experiments in the tested specimen. The results show that the fused frequency-domain energy DIs can be applied to indicate the expansion of defect zones quantitatively. It is proved that the defect identification accuracy of multi-defects from the CPDI approach can be improved by the majorization of damage shape factor, effectively. It is also clearly observed that the number, location and specific size information of different conditions of multi-defects can be distinguished by using the CPDI algorithm, availably.

Dynamic welding process monitoring based on microphone array technology

Abstract In this paper, microphone array technology was used to monitor the dynamic pulsed GMAW process. At first, the splash sound signal is successfully separated out based on FastICA blind signal separation algorithm, and its frequency domain energy distribution is mainly concentrated in the high frequency band of 6000−8000 Hz. Through time and frequency domain analysis, it is found that the short-time energy of 500−1000 Hz band of observed signal and the short-time energy of splash signal can identify the burn-through defects well, furthermore the ratio of them can be used as a robust feature because of its high sensitivity and anti-interference performance. Since the splash sound signal is a characteristic signal separated by microphone array, it is shown that the abundant dynamic information provided by microphone array can better assist in the identification and monitoring of welding defects compared to a single microphone. In order to solve the serious imbalance problem between positive and negative samples, the logistic regression and BP neural network model are improved based on the machine learning method. The experimental results show that the recognition accuracy of the optimization models have been greatly improved, even could reach 99.6 %.