Electrostatic sensor particle coupling signal deconvolution integral peak method

Abstract

The embodiment of the invention relates to an electrostatic sensor particle coupling signal deconvolution integral peak method. The method comprises the following steps: S1, obtaining an electrostatic detection signal fragment containing a multi-abrasive-particle overlapping feature; s2, constructing a Gaussian mixture model of the electrostatic detection signal segment, wherein the Gaussian mixture model is formed by superposing a plurality of single Gaussian components; s3, estimating an initial parameter set of the Gaussian mixture model based on waveform geometric features of the electrostatic detection signal segments; s4, performing global search on the initial parameter set by using a global optimization algorithm to obtain a parameter approximate solution, taking the parameter approximate solution as an initial value, performing optimization by using a local optimization algorithm until a preset convergence condition is met, and obtaining an optimal parameter set; and S5, reconstructing each independent single Gaussian component according to the optimal parameter set, and determining the feature information of the single abrasive particle according to each independent single Gaussian component.

Description

Technical Field

[0001] This application relates to the field of mechanical equipment condition monitoring and fault diagnosis technology, and in particular to a method for decoupling and integrating peaks of particle-coupled signals from electrostatic sensors. Background Technology

[0002] In the operation of large mechanical equipment (such as wind turbine gearboxes, aircraft engines, and heavy mining equipment reducers), the wear condition of key friction pairs (such as bearings and gears) directly affects the overall operational safety and lifespan of the machine. Lubricating oil, as the "blood" of the mechanical system, carries a large amount of particle information reflecting the degree of equipment wear. Therefore, real-time online monitoring of abrasive particles in the lubricating oil is a crucial means to achieve early warning of equipment failures and condition-based maintenance.

[0003] Among numerous oil monitoring technologies, electrostatic monitoring technology is widely used in full-flow online monitoring systems due to its advantages such as simple sensor structure, high sensitivity to small abrasive particles, and ability to simultaneously reflect the charge characteristics of abrasive particles. Its basic principle is to utilize the electrostatic induction phenomenon generated when charged abrasive particles pass through an electrostatic probe, converting the abrasive particle's passage event into an induced voltage or current pulse signal. Then, by analyzing the amplitude, width, and frequency of the pulse, the size, charge, and wear rate of the abrasive particles can be deduced.

[0004] However, in actual industrial settings, especially when equipment is under heavy load or in the early stages of fault evolution, abrasive particles in the lubrication circuit often exhibit an "explosive" generation characteristic, causing multiple abrasive particles to continuously and rapidly flow through the electrostatic sensor within a very short time. According to the principle of electrostatic induction, the induced signal generated by a single abrasive particle has a certain pulse width in the time domain (usually approximating a Gaussian waveform). When the time interval between the passage of multiple abrasive particles is less than the pulse width, the induced signals they generate will undergo severe aliasing in the time domain, forming a complex, multi-peaked composite waveform.

[0005] Traditional abrasive particle signal processing methods are typically based on the single-pulse assumption, employing simple threshold detection or peak counting for identification. When faced with overlapping signals, existing technologies often have significant limitations: first, they easily misjudge multiple overlapping small abrasive particle signals as a single anomalous particle signal with a large amplitude, leading to misjudgments of wear severity; second, they are easily submerged or confused with background noise (such as electromagnetic interference and oil flow noise), making accurate extraction difficult. Although some technologies attempt to use signal decomposition or cross-correlation detection, they often fail to achieve accurate waveform separation when dealing with complex overlapping waveforms of high density and varying amplitude due to difficulties in parameter initialization or algorithms getting trapped in local optima, thus failing to meet the needs for refined quantitative diagnosis of wear conditions. Therefore, how to effectively decouple and recover the characteristic information of individual abrasive particles from noisy overlapping monitoring signals is a pressing technical challenge in the field of electrostatic monitoring. Summary of the Invention

[0006] One objective of this application is to provide a method for decoupling and integrating peaks of particle-coupled signals from electrostatic sensors, which at least addresses the aforementioned problems.

[0007] To achieve the above objectives, some embodiments of this application provide a method for decoupling and integrating peaks of particle-coupled signals from electrostatic sensors, comprising the following steps: S1: Acquire an electrostatic detection signal segment containing multiple abrasive grain overlap features; S2: Construct a Gaussian mixture model for the electrostatic detection signal segment, wherein the Gaussian mixture model is composed of multiple single Gaussian components superimposed. S3: Based on the waveform geometric features of the electrostatic detection signal segment, estimate the initial parameter set of the Gaussian mixture model; S4: Use a global optimization algorithm to perform a global search on the initial parameter set to obtain an approximate solution for the parameters, and use the approximate solution for the parameters as the initial value. Use a local optimization algorithm to find the optimal parameter set until the preset convergence condition is met. S5: Reconstruct each independent single Gaussian component based on the optimal parameter set, and determine the characteristic information of each individual abrasive grain based on each independent single Gaussian component.

[0008] Compared with related technologies, the solution provided in this application, by constructing a Gaussian mixture model, transforms the complex continuous overlapping electrostatic signal of abrasive particles into a linear superposition of multiple single Gaussian components. This achieves effective decoupling of overlapping waveforms from a physical mechanism perspective, overcoming the limitation of traditional cross-correlation detection methods in separating densely overlapping pulses. In particular, it employs a hierarchical optimization strategy combining global search and local approximation. This not only utilizes a global algorithm to quickly lock the parameter convergence domain within a broad solution space, effectively avoiding the risk of getting trapped in local optima in complex multi-peak fitting, but also combines local algorithms for refined optimization, significantly improving fitting accuracy and convergence efficiency while ensuring algorithm robustness. This embodiment can reconstruct independent single-abrasive-particle waveforms from severely aliased monitoring signals, achieving accurate quantitative extraction of characteristic information such as the time and amplitude of individual abrasive particles in dense abrasive flow, providing reliable technical support for refined monitoring of the wear state of mechanical equipment. Attached Figure Description

[0009] One or more embodiments are illustrated by way of example with reference numerals in the accompanying drawings. These illustrations do not constitute a limitation on the embodiments. Elements with the same reference numerals in the drawings are denoted as similar elements. Unless otherwise stated, the figures in the drawings are not to be limited by scale.

[0010] Figure 1 This is a flowchart illustrating a method for decoupling and integrating peaks of particle-coupled signals from an electrostatic sensor.

[0011] Figure 2 This is a detailed flowchart of the signal enhancement and deconvolution identification algorithm in a specific embodiment.

[0012] Figure 3 It is a waveform diagram of the original electrostatic detection signal with random Gaussian white noise.

[0013] Figure 4 It is a graph of the intrinsic mode functions (IMF) components obtained by decomposing the original signal using the variational mode decomposition (VMD) algorithm.

[0014] Figure 5 This is a waveform diagram of the abrasive enhancement signal after reconstruction of the effective IMF components.

[0015] Figure 6 This is a schematic diagram of the original waveform and Gaussian mixture model of the electrostatic signal of continuous abrasive grains overlapping.

[0016] Figure 7 This is a schematic diagram of the original waveform and two reconstructed independent Gaussian components.

[0017] Figure 8This is a schematic diagram of the initial parameter estimation of a Gaussian mixture model based on waveform geometric features under the condition that the charge of the two abrasive particles is the same.

[0018] Figure 9 This is a schematic diagram of the waveform separation and identification results after optimization by the method in this embodiment, under the condition that the charge of the two abrasive particles is the same.

[0019] Figure 10 This is a schematic diagram of the initial parameter estimation of the Gaussian mixture model based on waveform geometric features under different working conditions of dual abrasive grain charge.

[0020] Figure 11 This is a schematic diagram of the waveform separation and identification results after optimization by the method in this embodiment under different working conditions of dual abrasive grain charge.

[0021] Figure 12 This is a schematic diagram of the initial parameter estimation of a Gaussian mixture model based on waveform geometric features under the condition that the three abrasive particles have the same charge.

[0022] Figure 13 This is a schematic diagram of the waveform separation and identification results after optimization by the method in this embodiment, under the condition that the three abrasive particles have the same charge.

[0023] Figure 14 This is a schematic diagram of the initial parameter estimation of the Gaussian mixture model based on waveform geometric features under different working conditions of three abrasive grains with different charge amounts.

[0024] Figure 15 This is a schematic diagram of the waveform separation and identification results after optimization by the method of this embodiment under different working conditions of three abrasive grain charge amounts.

[0025] Figure 16 These are the coefficients of determination for the initial parameter estimates and the model fitting after hybrid optimization in this embodiment under different simulation conditions. Compare the bar charts. Detailed Implementation

[0026] To make the objectives, technical solutions, and advantages of the embodiments of this application clearer, the technical solutions of the embodiments of this application will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some embodiments of this application, not all embodiments. Based on the embodiments of this application, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of this application.

[0027] The terms "first," "second," etc., used in the specification, claims, and accompanying drawings of this disclosure are used to distinguish similar objects and are not necessarily used to describe a specific order or sequence. It should be understood that such data can be interchanged where appropriate for the embodiments of this disclosure described herein. Furthermore, the terms "comprising" and "having," and any variations thereof, are intended to cover non-exclusive inclusion.

[0028] In this disclosure, the terms "upper," "lower," "inner," "middle," "outer," "front," and "rear," etc., indicate the orientation or positional relationship based on the orientation or positional relationship shown in the accompanying drawings. These terms are primarily for better description of the embodiments of this disclosure and their implementations, and are not intended to limit the indicated devices, elements, or components to having a specific orientation, or to require them to be constructed and operated in a specific orientation. Furthermore, some of the aforementioned terms may be used to indicate other meanings besides orientation or positional relationship; for example, the term "upper" may in some cases indicate a dependency or connection relationship. Those skilled in the art can understand the specific meaning of these terms in the embodiments of this disclosure according to the specific circumstances.

[0029] Furthermore, the terms "set up," "connect," and "fix" should be interpreted broadly. For example, "connection" can be a fixed connection, a detachable connection, or an integral structure; it can be a mechanical connection or an electrical connection; it can be a direct connection or an indirect connection through an intermediate medium, or it can be an internal connection between two devices, components, or parts. Those skilled in the art can understand the specific meaning of the above terms in the embodiments of this disclosure according to the specific circumstances.

[0030] Unless otherwise stated, the term "multiple" means two or more.

[0031] In this embodiment of the disclosure, the character " / " indicates that the objects before and after it are in an "or" relationship. For example, A / B means: A or B.

[0032] The term "and / or" describes an association between objects, indicating that three relationships can exist. For example, A and / or B means: A or B, or A and B.

[0033] It should be noted that, unless otherwise specified, the embodiments and features described in the present disclosure can be combined with each other.

[0034] Combination Figures 1 to 16 As shown in the figure, an embodiment of this disclosure provides a method for decoupling and integrating the peak of an electrostatic sensor particle coupling signal, which includes the following steps: S1: Acquire an electrostatic detection signal segment containing multiple abrasive grain overlap features; S2: Construct a Gaussian mixture model for the electrostatic detection signal segment. The Gaussian mixture model is composed of multiple single Gaussian components. S3: Estimate the initial parameter set of the Gaussian mixture model based on the waveform geometric features of the electrostatic detection signal segment; S4: Use a global optimization algorithm to perform a global search on the initial parameter set to obtain an approximate solution for the parameters. Use the approximate solution as the initial value and use a local optimization algorithm to find the optimal parameter set until the preset convergence condition is met. S5: Reconstruct each independent single Gaussian component based on the optimal parameter set, and determine the characteristic information of each individual abrasive grain based on each independent single Gaussian component.

[0035] The method provided in this disclosure transforms complex continuous overlapping electrostatic signals of abrasive particles into a linear superposition of multiple single Gaussian components by constructing a Gaussian mixture model. This achieves effective decoupling of overlapping waveforms at the physical mechanism level, overcoming the limitation of traditional cross-correlation detection methods in separating densely overlapping pulses. In particular, a hierarchical optimization strategy combining global search and local approximation is employed. This not only utilizes a global algorithm to quickly lock the parameter convergence domain within a broad solution space, effectively avoiding the risk of getting trapped in local optima in complex multi-peak fitting, but also combines local algorithms for refined optimization, significantly improving fitting accuracy and convergence efficiency while ensuring algorithm robustness. This embodiment can reconstruct independent single-particle waveforms from severely aliased monitoring signals, achieving accurate quantitative extraction of characteristic information such as the passage time and amplitude of individual abrasive particles in dense abrasive flow, providing reliable technical support for refined monitoring of the wear state of mechanical equipment.

[0036] Optionally, the process of obtaining the electrostatic detection signal segment containing the overlapping features of multiple abrasive particles in step S1 includes: decomposing the acquired original signal using a variational mode decomposition algorithm to obtain several bandwidth-limited intrinsic mode function components, and selecting effective components containing abrasive impact features from the intrinsic mode function components for signal reconstruction.

[0037] This embodiment employs Variational Mode Decomposition (VMD) as a preprocessing method to adaptively decompose the typical nonlinear and non-stationary characteristics of abrasive electrostatic monitoring signals into several bandwidth-limited intrinsic mode function components. Compared to traditional decomposition methods, this step effectively overcomes mode aliasing and can separate weak abrasive impact signals hidden in broadband background noise. By selecting effective components for signal reconstruction, the key characteristics of abrasive electrostatic induction pulses are preserved while significantly suppressing environmental noise and operating condition interference, thereby improving the signal-to-noise ratio of the input signal.

[0038] Optionally, effective components containing abrasive impact characteristics are selected, including: calculating the kurtosis value of each intrinsic mode function component and the cross-correlation coefficient between each intrinsic mode function component and the original signal envelope, and selecting components with kurtosis values ​​greater than a preset first threshold and cross-correlation coefficients greater than a preset second threshold as effective components.

[0039] Furthermore, this embodiment constructs a dual screening criterion based on kurtosis value and envelope cross-correlation coefficient, achieving precise locking of effective modal components. Utilizing the high sensitivity of the kurtosis index, modal components containing rich impact information can be quickly identified, effectively distinguishing stable random white noise. Simultaneously, morphological verification is performed using the envelope cross-correlation coefficient, ensuring that the energy fluctuation trend of the selected components remains highly consistent with the original signal. Through a joint discrimination mechanism of impact characteristics and waveform similarity, the omission of effective information or misselection of false pulses that might result from screening with a single index is avoided, thereby maximizing the restoration of the true physical characteristics of the abrasive particles during the signal reconstruction stage.

[0040] For example, considering that the kurtosis index is highly sensitive to impact signals (the kurtosis coefficient of random white noise is usually about 3, while the kurtosis value increases significantly when the signal contains abrasive pulses), the kurtosis values ​​of each intrinsic mode function (IMF) component are first calculated and sorted in descending order, with a focus on examining the top 6 IMF components to prevent omission of abrasive impact components with small amplitudes.

[0041] Subsequently, to further enhance the target signal using the waveform morphology similarity principle, the cross-correlation coefficient between the original signal envelope and the IMF components was used as a secondary screening criterion. An effective threshold of 0.7 was set for the correlation coefficient; that is, when the absolute value of the calculated cross-correlation coefficient was greater than 0.7, the IMF component was deemed to maintain strong morphological consistency with the original signal and was retained as an effective component. For example, in the processing of a certain measured data, the correlation coefficients between IMF5 and IMF6 and the original signal envelope were both greater than 0.7, indicating that these two components were mainly dominated by abrasive pulses. Therefore, they were selected as reconstructed components for signal synthesis. Through the above screening and reconstruction, the potential abrasive signal characteristics were significantly enhanced, and background noise was effectively suppressed.

[0042] In this embodiment, considering the actual working conditions of abrasive particle monitoring in lubricating oil, the original electrostatic signal collected by the sensor is first subjected to noise reduction and enhancement processing. Because charged abrasive particles generated by friction wear induce a weak charge signal when passing through the probe of the electrostatic sensor, and this signal is converted into a voltage output by the conditioning circuit, the generated pulse signals overlap in the time domain under continuous and rapid abrasive particle passage, and are accompanied by complex background noise (such as...). Figure 3 As shown in the figure, this makes direct identification difficult.

[0043] Therefore, this embodiment employs the Variational Mode Decomposition (VMD) algorithm to construct the signal enhancement model. The VMD algorithm adaptively decomposes a non-stationary input signal into several bandwidth-limited intrinsic mode function (IMF) components, effectively solving the mode aliasing problem. The specific processing procedure is as follows: Figure 2 As shown: VMD decomposition of the original noisy signal yields several IMF components (such as...) Figure 4 Subsequently, a dual screening criterion involving kurtosis value and envelope cross-correlation coefficient is introduced. The kurtosis value of each IMF component is calculated to measure its impact characteristics, while the cross-correlation coefficient between each component and the original signal envelope is calculated to measure its waveform similarity. Components with high kurtosis values ​​and cross-correlation coefficients greater than a preset threshold (e.g., 0.7) are selected as effective abrasive impact components for reconstruction, ultimately yielding an enhanced signal with a significantly improved signal-to-noise ratio (e.g., ...). Figure 5 As shown in the figure, this provides a high-quality data foundation for subsequent deconvolution identification.

[0044] Optionally, in step S2, the Gaussian mixture model is represented as The linear combination of a single Gaussian component is expressed mathematically as follows: ; in, The fitting function representing the electrostatic detection signal segment. For time variables, 、 and Representing the first The amplitude, time center, and standard deviation of a single Gaussian component.

[0045] By clearly defining the specific mathematical analytical expression of the Gaussian mixture model, a precise mapping relationship between the electrostatic induction phenomenon generated by abrasive particle motion and its mathematical expression is constructed. Since the induced electromotive force generated when a single charged abrasive particle passes through a ring-shaped probe exhibits a typical Gaussian-like shape in the time domain, this mathematical model can most realistically reproduce the essential characteristics of the physical waveform. By deconstructing the complex overlapping pulse signal into a set of single Gaussian components controlled by three key parameters—amplitude, time center, and standard deviation—this formula not only provides a standardized fitting objective function for subsequent mixture optimization algorithms, ensuring that the convergence direction of the numerical solution conforms to physical laws, but more importantly, it allows each component decoupled from the aliased signal to directly correspond to specific physical properties of the abrasive particle (such as charge magnitude, passing time, and motion state), thereby guaranteeing that the finally identified abrasive particle features have high physical interpretability and accuracy.

[0046] Optionally, the initial parameter set in step S3 includes the initial amplitude and the initial time center. The method for estimating the initial amplitude and the initial time center is as follows: perform a waveform peak finding operation on the electrostatic detection signal segment, determine the identified peak extreme value as the initial amplitude of the corresponding single Gaussian component, and determine the time point corresponding to the peak extreme value as the initial time center of the corresponding single Gaussian component.

[0047] By using waveform peak finding, the initial amplitude and time center of the Gaussian component are anchored directly using the geometric extrema points in the electrostatic detection signal segment. This maps the physical and spatiotemporal distribution characteristics of the abrasive signal to the initial state of the mathematical model. Compared to blind random initialization, this provides a good initial value in the neighborhood of the global optimum for subsequent hybrid optimization algorithms. This not only reduces the computational complexity of multidimensional parameter space search, but also effectively avoids the risk of the algorithm getting stuck in local extrema or producing false pulse fitting when fitting complex overlapping waveforms, thereby greatly improving the speed of iterative convergence and the stability of model identification.

[0048] Optionally, the initial parameter set in step S3 also includes an initial standard deviation. The method for estimating the initial standard deviation is as follows: calculate the second derivative of the electrostatic detection signal segment, determine the waveform inflection point based on the position of the zero-crossing point of the second derivative, and use the absolute value of the time difference between the waveform inflection point and the corresponding peak as the initial standard deviation of the corresponding single Gaussian component.

[0049] This embodiment further utilizes the method of locating waveform inflection points by the zero-crossing point of the second derivative to accurately extract the initial standard deviation parameter characterizing the pulse width from the curvature change of the signal. This allows for the preliminary determination of the time span and influence range of each abrasive pulse before the optimization iteration begins. This is particularly crucial for solving the problem of overlapping signal identification. This embodiment prevents excessive fusion of adjacent waveforms or erroneous splitting of single waveforms due to improper initial waveform width settings. It ensures that under dense abrasive flow conditions, the model can accurately distinguish and lock onto each weak signal that is crowded together, enhancing the algorithm's ability to analyze the edges of overlapping signals.

[0050] Optionally, in step S4, the global optimization algorithm adopts the differential evolution algorithm, and the local optimization algorithm adopts the nonlinear least squares method.

[0051] This embodiment employs a hierarchical optimization strategy using a differential evolution algorithm and a nonlinear least squares method. It fully leverages the superior global search capability and insensitivity to initial conditions of the differential evolution algorithm, enabling it to effectively traverse complex multi-peak terrains formed by noise and overlapping interference in the multi-dimensional parameter space, reliably locating the attraction domain where the global optimum lies. Subsequently, the powerful local convergence performance of the nonlinear least squares method is utilized, leveraging its rapid gradient descent characteristic to fine-tune the parameters. This organic combination of coarse search and fine-tuning overcomes the shortcomings of single local algorithms that easily get trapped in local optima, and solves the problems of low search efficiency and insufficient accuracy in the later stages of convergence for single evolution algorithms. This achieves efficient and high-precision solution for the parameters of the deconvolution model of overlapping electrostatic signals.

[0052] After acquiring the enhanced signal, a mathematical model of the overlapping waveform is performed based on the principle of abrasive grain electrostatic induction. Since the induced signal waveform generated by a single abrasive grain through the annular probe approximately follows a Gaussian distribution in the time domain, this embodiment will... Figure 6 The overlapping waveform shown is modeled as a Gaussian mixture model (GMM). This model is composed of the linear superposition of multiple single Gaussian components, where the functional form of a single Gaussian component is constructed as follows: ; In the formula, For this component in Amplitude at time, , , These are the amplitude parameter, time center parameter, and standard deviation parameter of the Gaussian component, respectively. An overlapping signal is the sum of multiple such functions.

[0053] Subsequently, the model parameters are initialized and estimated. To address the sensitivity of nonlinear optimization to initial conditions, this embodiment analyzes the geometric morphological characteristics of the waveform and determines the number of peaks and their corresponding extreme point locations by performing peak-finding operations on the signal segments. and amplitude This is used as the initial time center and amplitude; the zero-crossing point (inflection point) of the second derivative of the Gaussian function is located at... The geometric properties of the waveform are used to locate inflection points by calculating the second derivative of the waveform, and the initial standard deviation of each component is estimated by using the time difference between the inflection point and the peak. .

[0054] After obtaining the initial parameter set, an optimization function is established with the objective of minimizing the model fitting error, and its expression is as follows: ; in, The objective function value, This refers to actual observation data (i.e., the enhanced electrostatic signal). These are the theoretical values ​​calculated for the Gaussian mixture model.

[0055] To achieve accurate parameter determination, this embodiment employs a hierarchical hybrid optimization strategy combining differential evolution algorithm and nonlinear least squares method. First, the global search capability of the differential evolution algorithm is utilized to quickly locate the convergence region of the global optimum within the multidimensional parameter space. Then, using the result of differential evolution as initial values, the nonlinear least squares method is used for local fine-tuning, leveraging gradient information to accelerate convergence, ultimately yielding the optimal parameter set.

[0056] Finally, waveform segmentation and feature extraction are performed. Substituting the optimized parameters into each Gaussian component function allows for the reconstruction of each independent abrasive grain waveform, achieving precise segmentation of overlapping peaks (as shown in the image). Figure 7 (As shown). Based on the segmented results, extract the time center parameters. To determine the passage time of the abrasive grains, the amplitude parameter is extracted. To reflect the relative size or charge characteristics of abrasive particles.

[0057] Optionally, in step S4, the convergence condition is constructed based on an objective function configured to minimize the mean square error between the calculated output value of the Gaussian mixture model and the actual observed value of the electrostatic detection signal segment.

[0058] This embodiment ensures that the iterative process consistently moves towards achieving a high degree of energy distribution alignment between the Gaussian mixture model output curve and the actual acquired electrostatic monitoring signal waveform. Parameter correction is driven by the fitting residual between the quantized calculated values ​​and the observed values. This not only guarantees that the reconstructed waveform can restore the temporal details of the original signal to the greatest extent possible, but also ensures that the finally extracted abrasive particle feature parameters have a solid mathematical fit, enabling the identification results to truly reflect the physical state of the abrasive particles as they pass through the sensor, thus improving the reliability of the monitoring data.

[0059] Optionally, determining the feature information of a single abrasive grain in step S5 specifically includes: extracting the time center parameters of each independent single Gaussian component after reconstruction. Characterize the time when the corresponding abrasive grain passes through the sensor and extract the amplitude parameter. It characterizes the relative size or charge of the corresponding abrasive grains.

[0060] By reconstructing the time center parameters of the independent single Gaussian components Defined as the moment of abrasive grain passage, this enables precise temporal positioning of the abrasive grain's trajectory; simultaneously, the amplitude parameter... Directly correlated with the relative size or charge of abrasive particles, this enables quantitative characterization of the physical properties of microscopic wear products. Thus, the abstract data after deconvolution decoupling can directly reflect the real-time wear status of the mechanical system, providing intuitive and quantifiable data support for subsequent wear trend analysis, fault severity assessment, and maintenance decisions.

[0061] Optionally, before using the variational mode decomposition algorithm to decompose the acquired raw signal, the method further includes: performing zero-mean processing on the acquired raw electrostatic monitoring signal to remove the DC component in the signal, so as to eliminate the influence of baseline drift on the accuracy of subsequent mode decomposition.

[0062] By introducing a zero-means processing step before mode decomposition, the DC bias component that may be introduced into the original monitoring signal due to temperature drift of the sensor circuit or slow changes in the ambient electromagnetic field is eliminated in advance. This effectively prevents uncorrelated DC or extremely low-frequency trend terms from interfering with the center frequency iteration during variational mode decomposition (VMD), avoids the generation of spurious low-frequency modes caused by baseline drift, and thus improves the accuracy of subsequent mode decomposition and the ability to focus on weak abrasive pulse signals.

[0063] Optionally, the variational mode decomposition algorithm is constructed based on a constrained variational problem, the constraint of which is that the sum of the superposition of the intrinsic mode function components in the time domain is equal to the input signal, and the optimization objective is to minimize the sum of the estimated bandwidths of the intrinsic mode function components.

[0064] By forcing each intrinsic mode function (IMF) to minimize the sum of its estimated bandwidths while still fully reconstructing the input signal, this algorithm adaptively decomposes complex electrostatic monitoring signals into several narrow-band sub-signals with discrete center frequencies and limited bandwidths. This mathematically ensures that the abrasive impact signal can be accurately extracted from broadband background noise and focused on specific modes, effectively overcoming the mode aliasing problem common in traditional decomposition methods and ensuring the physical authenticity and signal-to-noise ratio of the extracted abrasive feature signals.

[0065] Optionally, components with kurtosis values ​​greater than a preset first threshold and cross-correlation coefficients greater than a preset second threshold are selected as valid components, including: sorting the kurtosis values ​​of each intrinsic mode function component in descending order and selecting the top two components as candidate components; calculating the cross-correlation coefficient between the candidate components and the original signal envelope, and retaining components with an absolute cross-correlation coefficient greater than 0.7 as valid components.

[0066] By leveraging the kurtosis index's ability to keenly capture non-Gaussian impact signals, the two most prominent modal components with the most significant impact characteristics are prioritized through descending order of these components. This ensures the preferential capture of transient pulse components generated by abrasive particles, effectively preventing the omission of weak but crucial signals due to noise overload. Subsequently, a retention threshold with a cross-correlation coefficient greater than 0.7 is set, mandating that candidate components maintain a high degree of consistency with the envelope of the original signal in terms of energy fluctuation trends. In this way, spurious pulse interference, which possesses high kurtosis but lacks physical correlation, is eliminated from both statistical characteristics and waveform morphology perspectives. This ensures that the final reconstructed signal possesses both distinct impact characteristics and faithfulness to the original waveform, maximizing the signal-to-noise ratio and fidelity of the signal enhancement.

[0067] Optionally, after step S5, an accuracy evaluation step for the identification results is also included, including: calculating the fitted waveform of the Gaussian mixture model using the optimal parameter set, and calculating the coefficient of determination between the fitted waveform and the electrostatic detection signal segment. If the coefficient of determination If the accuracy exceeds the preset accuracy threshold, the currently identified single abrasive grain feature information is deemed valid.

[0068] By quantitatively evaluating the statistical correlation between the fitted waveform of the Gaussian mixture model and the original monitoring signal, this step can automatically identify and intercept underfitting and overfitting phenomena caused by the algorithm getting stuck in local optima or noise interference, effectively eliminating false identification results that are mathematically convergent but physically distorted. This ensures that the final output abrasive particle feature information not only meets the convergence condition, but also has high fidelity in waveform energy distribution, improving the confidence and engineering usability of online monitoring data.

[0069] For example, after obtaining the optimal parameter set and completing signal reconstruction, this embodiment uses an automated accuracy verification step to ensure the reliability of the identification results. A preset accuracy threshold (e.g., 0.95) is set; if the calculated accuracy is... If the value is greater than the threshold, the current deconvolution identification result is deemed valid, and abrasive grain feature information is output; if... If the value is below the threshold, the current signal segment is determined to contain atypical interference or model mismatch, and the segment is marked for review or directly removed. This prevents mathematically convergent but physically distorted erroneous identification results from entering the subsequent data statistics stage.

[0070] To quantify and verify the identification accuracy of the method provided in this embodiment, the determination coefficient is used. As an evaluation indicator, its calculation formula is as follows: ; in, For observation data, These are the model's predicted values. This represents the average value of the observed data. The closer a value is to 1, the higher the model's interpretation of the signal and the better the fit.

[0071] In the simulation experiment of the double abrasive grain overlapping signal, the method provided in this embodiment was used for processing. Experimental results show that after processing according to this embodiment, the fitting determination coefficient of the signal is... The value achieved a significant improvement, from approximately 0.805 when using only the initial parameter estimates to over 0.998 after hybrid optimization (e.g. Figure 6 (As shown in the figure). This data proves that this embodiment has extremely high segmentation accuracy when processing complex overlapping signals, effectively solving the problem of low recognition rate of traditional methods under dense abrasive flow conditions.

[0072] Optionally, the method also introduces a signal timing matching verification mechanism based on a dual-probe structure. The specific process is as follows: acquire the monitoring signals synchronously collected by two electrostatic probes arranged before and after the flow channel, perform the deconvolution identification process of Gaussian mixture model on the signals of the two channels respectively, and obtain two sets of independent single Gaussian component parameters; calculate the time center difference of the single Gaussian component corresponding to the same abrasive grain in the two channels. If the difference matches the ratio of the physical distance between the two probes and the lubricating oil flow rate, the abrasive grain signal identification is confirmed to be effective; otherwise, it is regarded as an interference signal and discarded.

[0073] This embodiment rigorously verifies whether the time lag relationship of the same abrasive grain in the upstream and downstream probe induction waveforms conforms to the laws of fluid dynamics. This mechanism can strongly filter out common-mode electromagnetic interference (usually acting synchronously on both probes) or random pulse noise that do not have motion delay characteristics from a physical level. This dual-channel mutual verification strategy adds physical consistency constraints to the identification results of pure mathematical algorithms, enhancing the system's ability to capture real abrasive grain signals and its identification accuracy under complex and strong interference conditions.

[0074] Specifically, the electrostatic monitoring sensor includes two sensing electrodes arranged at intervals along the front and rear of the lubricating oil flow path, with a physical distance between them of [missing information]. The system synchronously acquires monitoring signals from two channels and executes the aforementioned Gaussian mixture model deconvolution identification process in parallel to obtain two sets of independent single Gaussian component parameters.

[0075] The verification logic is as follows: For any abrasive grain signal identified by the upstream channel (time center is...) The system searches the downstream channel identification results for the existence of a time center. The matching signal. The matching criterion is: time difference. With theoretical lag time (in The deviation between the lubricating oil flow rate and the target signal is within the allowable tolerance range. If the matching criterion is met, the signal is confirmed as a genuine abrasive particle induction signal, and the average value of the dual-channel data can be further used to improve feature extraction accuracy. If a matching signal cannot be found, the isolated waveform is treated as a random electromagnetic pulse or local noise and discarded. This fully utilizes the spatiotemporal consistency of abrasive particle motion and reduces the false alarm rate.

[0076] Optionally, before constructing the initial parameter set in step S3, a statistical screening step for waveform geometric features is also included. Specifically, this involves: calculating the peak significance of all local peaks in the electrostatic detection signal segment and calculating the interquartile range of these peak significances; setting a screening threshold of 1.5 times the interquartile range, retaining only peaks with peak significance higher than the screening threshold as valid peaks, and estimating the initial parameters of the single Gaussian impulse component based solely on the geometric features of these valid peaks to suppress the interference of background noise on model initialization.

[0077] This step cleans the original signal at the beginning of model construction, which can intelligently distinguish between high-significance pulses generated by real abrasive particles and random spurious peaks caused by background noise. This avoids the initial redundancy or positional deviation of Gaussian components due to misjudgment of spurious peaks. This not only ensures the high purity and accuracy of the initial parameter set, but also reduces the search time of subsequent hybrid optimization algorithms in the invalid solution space, and greatly improves the initialization robustness and overall convergence efficiency of the algorithm in low signal-to-noise ratio environments.

[0078] Specifically, firstly, the electrostatic detection signal segments extracted in the time domain are browsed, all local maxima are identified, and their peak significance is calculated. Then, statistical analysis is performed on all identified peak significances, and their interquartile range (IQR) is calculated. An adaptive screening threshold is set to 1.5 times the IQR (i.e., ...). Only peaks with a significance level higher than the threshold are retained as valid peaks. Subsequent initial amplitude extraction and standard deviation estimation based on inflection points are performed only on the selected valid peaks. This step effectively eliminates spurious peaks through dynamic thresholding, resulting in a purer initial parameter set and significantly reducing the search time of subsequent hybrid optimization algorithms in the invalid solution space.

[0079] In some alternative embodiments, when constructing the initial parameter set of the Gaussian mixture model, in order to overcome the interference of background noise on peak identification, the initial time center ( ) and amplitude ( The estimation accuracy of ) is improved by a robust initialization method based on sliding window cross-correlation and peak significance statistics.

[0080] First, based on the sensor structural parameters and lubricating oil flow rate, a standard abrasive particle induced charge simulation signal is constructed as a sliding window template. The enhanced signal obtained in step S1 is integrated and converted into a charge signal form. The sliding window step size is set to 10 sampling points, and the cross-correlation sequence between the sliding window template and the local signal is calculated by traversing the entire signal. The cross-correlation function can effectively measure the similarity between two time series waveforms. When abrasive particles pass through, a clear peak appears in the cross-correlation curve.

[0081] Considering that the extreme values ​​of the cross-correlation peaks alone are insufficient to completely distinguish between real abrasive particles and random disturbances, this embodiment utilizes the physical property that the abrasive particle velocity is approximately equal to the oil flow velocity, indicating that the peaks formed by real abrasive particles on the cross-correlation curve should have specific steepness characteristics. Therefore, peak significance is selected as the core discrimination criterion, and interference peaks with flat shapes are filtered out by peak prominence.

[0082] Specifically, computational tools such as MATLAB are used to extract the significance of all local peaks in the cross-correlation function curve, and an adaptive threshold is set using the interquartile range (IQR) method. The decision threshold is set to 1.5 times the interquartile range of the significance of all peaks. Peaks with significance above this threshold are identified as "outliers" (i.e., valid abrasive signal points), while those below the threshold are considered background noise and discarded. Finally, using the specific locations of these filtered outliers in the cross-correlation function graph, the initial time centers of each component in the Gaussian mixture model are accurately located, and the corresponding peak heights are used as the initial amplitudes. This method effectively solves the problem of difficult model initialization under low signal-to-noise ratio conditions, providing high-quality initial values ​​for subsequent mixture optimization algorithms.

[0083] The electrostatic sensor particle coupling signal deconvolution integration peak method provided in this embodiment first performs zero-mean processing on the acquired original electrostatic monitoring signal before acquiring the electrostatic detection signal segment containing multiple abrasive particle overlap features. This removes the DC component in the signal and eliminates the impact of baseline drift on the accuracy of subsequent analysis. Subsequently, a variational mode decomposition algorithm is used to process the signal. This algorithm is based on a constrained variational problem, whereby, under the constraint that the sum of the time-domain superposition of each intrinsic mode function component equals the input signal, the optimization objective is set to minimize the sum of the estimated bandwidths of each component, thereby obtaining several bandwidth-limited intrinsic mode function components. To accurately identify the effective components containing abrasive particle information, the kurtosis values ​​of each intrinsic mode function component are calculated and sorted in descending order. The top two components are selected as candidates. Simultaneously, the cross-correlation coefficients between these candidate components and the original signal envelope are calculated, and only components with an absolute cross-correlation coefficient greater than 0.7 are retained as effective components. Finally, the selected effective components are reconstructed to obtain an electrostatic detection signal segment with a significantly improved signal-to-noise ratio.

[0084] After signal preprocessing, a Gaussian mixture model is constructed based on the electrostatic induction mechanism of abrasive particles. This model represents overlapping electrostatic detection signal segments as a linear superposition of multiple single Gaussian components, and its mathematical expression consists of the summation of N Gaussian functions. Each single Gaussian component is described by three key parameters: amplitude, time center, and standard deviation. To address the sensitivity of initial values ​​in nonlinear optimization, this embodiment estimates the initial parameter set of the model based on waveform geometric features. Before estimation, a statistical screening step for waveform geometric features is performed, calculating the peak significance of all local peaks in the signal segment, statistically analyzing the interquartile range of these peak significances, and setting a screening threshold of 1.5 times the interquartile range; only peaks with peak significance higher than this threshold are retained as valid peaks to suppress background noise interference. Based on these valid peaks, the identified peak extrema are determined as the initial amplitude of the corresponding single Gaussian component, and the time point corresponding to the peak is determined as the initial time center. Simultaneously, the second derivative of the electrostatic detection signal segment is calculated to locate the waveform inflection point. The absolute value of the time difference between the waveform inflection point and the corresponding peak is used as the initial standard deviation of the corresponding single Gaussian component, thereby constructing an initial parameter set containing physical prior information.

[0085] In the parameter solving stage, a hierarchical optimization strategy coupling global search and local approximation is employed to iteratively refine the initial parameter set. First, a differential evolution algorithm is used to perform a random search within the global solution space. Leveraging its superior global optimization capabilities, the differential evolution algorithm can effectively traverse complex terrains with multi-peak objective functions, locking the convergence domain of the parameters and obtaining approximate solutions. Subsequently, this approximate solution is used as the initial value, and a nonlinear least squares method is switched to perform local fine-tuning. Here, the algorithm utilizes gradient information to rapidly approximate extreme points. The optimization process uses minimizing the mean square error between the calculated output value of the Gaussian mixture model and the actual observed value of the electrostatic detection signal segment as the objective function, until the model fitting residuals satisfy the preset convergence condition, ultimately obtaining the optimal parameter set.

[0086] After obtaining the optimal parameter set, the independent single Gaussian components are reconstructed using these parameters, thereby achieving deconvolution segmentation of the overlapping pulse waveform. To ensure the accuracy of the identification results, this embodiment introduces a multi-dimensional accuracy evaluation and verification mechanism. First, the fitted waveform is calculated using the optimal parameter set, and the coefficient of determination between it and the actual electrostatic detection signal segment is calculated. Only when The result is considered valid when the accuracy exceeds a preset threshold. Secondly, a signal timing matching verification mechanism based on a dual-probe structure is introduced. Monitoring signals synchronously acquired by two electrostatic probes arranged before and after the flow channel are obtained. The aforementioned deconvolution identification process is then executed to obtain two sets of parameters. The time center difference of the single Gaussian component corresponding to the same abrasive grain in the two channels is calculated. If this difference matches the ratio of the physical distance between the two probes to the lubricating oil flow rate, it is confirmed as a genuine abrasive grain signal; otherwise, it is considered interference and discarded. Finally, the characteristic information of a single abrasive grain is determined based on the verified valid independent component parameters: the time center parameter is extracted to characterize the moment the corresponding abrasive grain passes through the sensor, and the amplitude parameter is extracted to characterize the relative size or charge of the corresponding abrasive grain, thereby achieving accurate monitoring of continuous abrasive grain flow.

[0087] To verify the effectiveness and robustness of the decoupling integration peak method for the particle coupling signal of the electrostatic sensor in this embodiment, a simulation dataset containing various complex working conditions such as double abrasive grain overlap and triple abrasive grain dense overlap was constructed for testing and analysis.

[0088] First, the recognition effect of the overlapping signal of two abrasive grains was verified. Two charged abrasive grains were continuously passed through the sensor, with two typical operating conditions: the same charge and different charge amounts. Under the condition that the two abrasive grains had the same charge, as shown... Figure 8 As shown, the two Gaussian components obtained from the initial estimation deviate significantly from the original signal in the overlapping region; however, after processing by the hybrid optimization algorithm in this embodiment (such as...), Figure 9 As shown), the two independent Gaussian waveforms extracted achieved a high degree of fit to the original signal, successfully separating two abrasive grain signals with completely identical characteristics. Under asymmetric operating conditions with different abrasive grain charges, the small-charge abrasive grain signal is highly susceptible to tailing interference from the large-charge abrasive grain signal (e.g., ...). Figure 10 As shown), the initial fitting could not reproduce waveform details; after optimization (as shown), Figure 11 As shown in the figure, the algorithm accurately identified two Gaussian components with large amplitude differences, proving that the method has accurate deconvolution capability for asymmetric overlapping signals.

[0089] Furthermore, to verify the algorithm's performance under conditions of extremely high sampling frequency or high abrasive particle concentration, a scenario was simulated where three abrasive particles passed continuously. In the case where the three abrasive particles had the same charge, the three peaks overlapped, causing severe distortion of the middle peak's characteristics (e.g., ...). Figure 12 As shown); after optimization by this method (such as... Figure 13 As shown), the three independent Gaussian components are clearly and equidistantly restored, effectively solving the problem of low accuracy in extracting the "middle peak" parameter in dense abrasive grain identification. However, under the most complex operating conditions with different charges on the three abrasive grains, the interweaving of three signals with varying amplitudes results in an extremely irregular overall shape (as shown). Figure 14 As shown); after algorithmic optimization (such as... Figure 15 As shown in the figure, three Gaussian waveforms with distinct physical characteristics (amplitude, time center, and width) were successfully identified, and the reconstructed waveform almost completely overlapped with the original data.

[0090] Finally, to quantify the fitting accuracy, this embodiment uses the coefficient of determination. Statistical analysis was performed on the above four simulation conditions (results are shown below). Figure 16 (As shown). Experimental data show that, before optimization, the initial parameter fitting accuracy varies significantly for each working condition, especially for the initial parameters under the two-particle identical charge and three-particle complex working conditions. The values ​​are low, with the lowest being only about 0.80, indicating uncertainty in parameter initialization. However, after processing with the differential evolution and nonlinear least squares hybrid optimization algorithm in this embodiment, the final fitting accuracy of all test scenarios is significantly improved and remains highly stable. The values ​​all converged to above 0.998. This result fully demonstrates that the Gaussian mixture identification model and its hierarchical optimization strategy proposed in this embodiment can effectively cope with multiple complex waveform overlap interferences ranging from two-particle to multi-particle and from equal-electricity to variable-electricity, eliminate identification errors caused by parameter initialization deviations, and provide reliable technical support for accurate quantitative diagnosis of wear status in lubrication systems.

[0091] The foregoing description and accompanying drawings fully illustrate embodiments of the present disclosure to enable those skilled in the art to practice them. Other embodiments may include structural and other changes. The embodiments represent only possible variations. Individual components and functions are optional unless explicitly required, and the order of operation may vary. Parts and features of some embodiments may be included or substituted for parts and features of other embodiments. Embodiments of the present disclosure are not limited to the structures described above and shown in the accompanying drawings, and various modifications and changes may be made without departing from its scope. The scope of the present disclosure is limited only by the appended claims, and the foregoing embodiments should be considered exemplary and non-limiting.

Claims

1. A method for deconvolve integration peak of particle-coupled signal from an electrostatic sensor, characterized in that, Includes the following steps: S1: Acquire an electrostatic detection signal segment containing multiple abrasive grain overlap features; S2: Construct a Gaussian mixture model for the electrostatic detection signal segment, wherein the Gaussian mixture model is composed of multiple single Gaussian components superimposed. S3: Based on the waveform geometric features of the electrostatic detection signal segment, estimate the initial parameter set of the Gaussian mixture model; S4: Use a global optimization algorithm to perform a global search on the initial parameter set to obtain an approximate solution for the parameters, and use the approximate solution for the parameters as the initial value. Use a local optimization algorithm to find the optimal parameter set until the preset convergence condition is met. S5: Reconstruct each independent single Gaussian component based on the optimal parameter set, and determine the characteristic information of each individual abrasive grain based on each independent single Gaussian component.

2. The method for decoupling and integrating peaks of particle-coupled signals from electrostatic sensors according to claim 1, characterized in that, The process of obtaining the electrostatic detection signal segment containing the overlapping features of multiple abrasive grains in step S1 includes: The acquired raw signal is decomposed using a variational mode decomposition algorithm to obtain several bandwidth-limited intrinsic mode function components. Then, effective components containing abrasive impact characteristics are selected from the intrinsic mode function components for signal reconstruction.

3. The method for decoupling and integrating peaks of particle-coupled signals in electrostatic sensors according to claim 2, characterized in that, The process of filtering out effective components containing abrasive impact characteristics includes: Calculate the kurtosis value of each intrinsic mode function component and the cross-correlation coefficient between each intrinsic mode function component and the original signal envelope, and select the components with a kurtosis value greater than a preset first threshold and a cross-correlation coefficient greater than a preset second threshold as valid components.

4. The method for decoupling and integrating peaks of particle-coupled signals from electrostatic sensors according to claim 1, characterized in that, In step S2, the Gaussian mixture model is represented as follows: The linear combination of a single Gaussian component is expressed mathematically as follows: ; in, The fitting function representing the electrostatic detection signal segment, For time variables, 、 and Representing the first The amplitude, time center, and standard deviation of a single Gaussian component.

5. The method for decoupling and integrating peaks of particle-coupled signals in an electrostatic sensor according to claim 1, characterized in that, The initial parameter set in step S3 includes the initial amplitude and the initial time center. The method for estimating the initial amplitude and the initial time center is as follows: A waveform peak finding operation is performed on the electrostatic detection signal segment, and the identified peak extreme value is determined as the initial amplitude of the corresponding single Gaussian component, and the time point corresponding to the peak extreme value is determined as the initial time center of the corresponding single Gaussian component.

6. The method for decoupling and integrating peaks of particle-coupled signals in an electrostatic sensor according to claim 1, characterized in that, The initial parameter set in step S3 also includes the initial standard deviation, wherein the method for estimating the initial standard deviation is as follows: Calculate the second derivative of the electrostatic detection signal segment, determine the waveform inflection point based on the position of the zero-crossing point of the second derivative, and use the absolute value of the time difference between the waveform inflection point and the corresponding peak as the initial standard deviation of the corresponding single Gaussian component.

7. The method for decoupling and integrating peaks of particle-coupled signals in electrostatic sensors according to claim 1, characterized in that, In step S4, the global optimization algorithm adopts the differential evolution algorithm, and the local optimization algorithm adopts the nonlinear least squares method.

8. The method for decoupling and integrating peaks of particle-coupled signals from electrostatic sensors according to claim 1, characterized in that, In step S4, the convergence condition is constructed based on an objective function, which is configured to minimize the mean square error between the calculated output value of the Gaussian mixture model and the actual observed value of the electrostatic detection signal segment.

9. The method for decoupling and integrating peaks of particle-coupled signals from electrostatic sensors according to claim 1, characterized in that, The specific steps in step S5 for determining the characteristic information of a single abrasive grain include: Extracting the time center parameters of each independent Gaussian component after reconstruction Characterize the time when the corresponding abrasive grain passes through the sensor and extract the amplitude parameter. It characterizes the relative size or charge of the corresponding abrasive grains.

10. The method for decoupling and integrating peaks of particle-coupled signals in an electrostatic sensor according to claim 1, characterized in that, Following step S5, an accuracy evaluation step for the identification results is also included, comprising: The fitted waveform of the Gaussian mixture model is calculated using the optimal parameter set, and the coefficient of determination between the fitted waveform and the electrostatic detection signal segment is calculated. If the determination coefficient If the accuracy exceeds the preset accuracy threshold, the currently identified single abrasive grain feature information is deemed valid.

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