Metal dust concentration detection method based on physical constraint neural network

Abstract

The metal dust concentration detection method based on physical constraint neural network belongs to the technical field of dust concentration detection and dust explosion prevention. The method constructs a three-dimensional space sensitivity model described by a physical formula as a constraint condition to establish a neural network for the voltage change generated by a single dust particle moving around a rod-shaped induction electrode. An open space dust scattering platform and a rod-shaped electrostatic induction sensor are used to record voltage signals generated by different concentrations of dust as input data for training to realize dust concentration prediction. Compared with traditional ANN neural networks, sliding filter methods and median filter methods, the proposed method has higher accuracy, overcomes the poor interpretability of traditional neural networks, can extract key features in data faster, meets the needs of dust operation scenes, and has good popularization and application value.

Description

TECHNICAL FIELD

[0001] The present application relates to an improved dust concentration detection technology, in particular to a metal dust concentration detection method based on a physically constrained neural network, belonging to the technical field of dust concentration detection and dust explosion prevention. BACKGROUND

[0002] Metal dust is ubiquitous in many industrial fields, such as mining, metallurgy and material fields, etc. Not only is it directly related to the safety and health of personnel in the workplace, but it also plays an important role in causing serious accidents such as explosions and fires. Due to long-term exposure to a dust environment, inhaled inorganic dust cannot be degraded in the human body, accumulates in the lungs and causes inflammation and tissue fibrosis diseases, known as pneumoconiosis, which is the most serious and common occupational disease in China. Moreover, due to the small particle size of the dust, the surface area in contact with the air is large, when metal dust particles are dispersed in the air to form a dust cloud, due to the full contact of the particle surface with oxygen, the combustion and heat transfer effect of the fuel will be significantly enhanced, when encountering a fire, the dust will burn violently, causing an explosion, producing a shock wave and high temperature, causing casualties. In practical applications, metal dust explosions have been a threat to the production, processing, transportation and other aspects of China's metal processing and mining industry, with the characteristics of frequent accidents and serious consequences, posing a great threat to China's safety production.

[0003] When the metal dust concentration in the workplace exceeds the lower explosion limit, the sparks generated by operation and collision may ignite the dust, causing an explosion. When the dust concentration in the air of the workplace rises, the physical quantities such as the space transmittance, induced charge quantity and dust mass will also change, and by collecting and monitoring these dust concentration related factors, it is possible to determine whether the current dust concentration exceeds the critical value in time. For this reason, many researches have been conducted at home and abroad around different principles of metal dust concentration detection methods. In terms of dust detection technology and equipment, the current methods for monitoring dust cloud concentration include light scattering, filter membrane weight, beta ray absorption, micro-oscillation balance and charge induction, etc. The commonly used dust concentration monitoring technology parameters and their advantages and disadvantages are shown in Table 1.

[0004] Table 1 Comparison of advantages and disadvantages of dust cloud concentration detection technologies

[0005]

[0006] As can be seen from Table 1, the signal-to-noise ratio of optical detection technologies (such as scattering, transmission, beta rays, etc.) generally decreases significantly in high concentration scenarios; the micro-oscillation balance method (0-700 mg / m 3) high sensitivity, but high maintenance cost, poor high humidity environment stability; filter membrane weight method delay time is extremely long, it is difficult to meet the real-time monitoring demand, cannot timely alarm response. And electrostatic induction method has the advantages of passive signal, large measurement range, strong adaptability, long service life and so on, compared with traditional technology, the detection unit will not be affected by the bonding dust, so it does not need to be maintained frequently.

[0007] However, in the model complex industrial scene, there are interference factors, which lead to unstable voltage signal, so that the detection effect of electrostatic induction method is affected, especially in the industrial environment with unstable dust flow and large dust concentration change.

[0008] In recent years, with the continuous progress of industrial technology, various new schemes are applied to traditional dust concentration detection, machine learning technology shows strong potential in pattern recognition and prediction modeling field, can extract hidden feature trend in data by processing large amount of complex data set, dynamically predict dust concentration change, improve monitoring accuracy in different environmental conditions, provide new solution for real-time and accurate detection of metal dust concentration. However, the neural network has complex model structure, large number of nodes and poor interpretability. SUMMARY

[0009] In view of the problems of existing dust measurement technology, such as not applicable at high concentration, easy to be disturbed by noise and slow measurement speed, the present application proposes a dust concentration detection method based on physics-informed neural network (PINN), which constructs a three-dimensional sensitivity model described by physical formula by constructing the voltage change generated by the movement of dust particles around the rod-shaped induction electrode, establishes a neural network as a constraint condition, extracts key features in the experimental data set, and realizes accurate detection of dust concentration. While ensuring the interpretability of the model, the measurement accuracy and speed are improved, and the detection range of metal dust concentration in open space is expanded.

[0010] The technical scheme adopted by the present application is: a physics-informed neural network dust concentration detection method based on dust particle induction signal physical model construction, a physics-informed neural network model is constructed with physical model as constraint condition, voltage signal data generated by different concentration dust collected by electrostatic induction sensor are collected through repeated experiments, and the neural network model is trained as data set to capture dust data hidden features and realize dust concentration prediction; specifically including the following steps:

[0011] S1, data acquisition: randomly select different concentration dust data, combine the measurement sequence and voltage signal Form a two-dimensional vector to form a data set as neural network input, the data set is divided into training set and validation set ;

[0012] S2, Network structure and mapping relationship:

[0013] Constructing physical constraint neural network with time as input; except input layer, hidden layer is composed of multiple fully connected units, tanh and ReLU activation functions are selected, and network output is average dust density in discrete space ;

[0014] S3, Sensitivity kernel convolution mechanism mapping and observation model: according to the electrostatic induction mechanism and the spatial sensitivity of the rod electrode, the contribution of the electrode induction charge at is represented by the sensitivity kernel ; The total predicted induction charge is:

[0015]

[0016] Where is the induction area, is the electrode radius and effective length;

[0017] The measured voltage standard deviation, which is equivalent to the voltage quantity, is linearly mapped with the induction charge;

[0018] S4, Constructing loss function: physical constraint neural network loss function is composed of three parts:

[0019]

[0020] Where, is the consistency term calculated by the least square number:

[0021]

[0022] Where, is the total number of sampling points in the corresponding sample, is the sampling time, is the predicted voltage signal strength of the model at that time, is the true voltage signal strength at that time;

[0023] The physical constraint term combined with weak form and prior constraint includes mass / density constraint, and peak time is selected to calculate the volume average Consistency constraint concentration-density-charge density relationship calculation:

[0024] ​

[0025]

[0026] where, is the equivalent uniform mass concentration after powdering, denotes the dust particle material density, denotes the dust particle average radius, represents the integration domain of the induction zone, denotes the volume fraction crossing the induction zone, is the single particle average charge;

[0027] denotes the smoothing and diffusion prior, used to characterize the cluster-dispersion characteristics of the dust cloud in open space, approximated by the Laplace calculation with isotropic second-order difference:

[0028]

[0029] far-field attenuation prior is calculated as:

[0030]

[0031] is the physical constraint term, calculated by superposition:

[0032]

[0033] where, is the weak form and prior constraint combined constraint term weight, is the smoothing and diffusion prior weight, is the far-field attenuation prior weight; is the physical constraint term weight, used to control the influence degree of the physical prior constraint on the loss function . The larger the value, the more the model prediction conforms to the physical trend.

[0034] is the regularization term, used to suppress false high frequency and sparse prior, calculated as:

[0035]

[0036] where, is the total trainable parameter, , are the weight and bias, respectively, is the L1 coefficient;

[0037] is the regularization constraint term weight, used to control the influence degree of the regularization term on the loss function The greater the value, the smoother the model, which is used to prevent model overfitting or output shock.

[0038] S5, back propagation and parameter update:

[0039] The Adam adaptive method is used for parameter update, following the gradient descent:

[0040]

[0041] where, is the learning rate, and the gradient of the weight according to the chain rule is shown as:

[0042]

[0043]

[0044] S6, model training: the training set is input into the network in batches, and the loss function is minimized .

[0045] Further, in step S1, the data collection is specifically: weighing a dust sample with a mass of , dividing it into groups, and uniformly spreading it in space through a powder spraying device to obtain a dust cloud with a concentration of ; using an electric inductive sensor to measure the voltage signal caused by the dust cloud passing through the inductive area, using a horizontal river oscilloscope to sample and record the voltage signal, and using it to construct the data set; for each sampling point , the corresponding time is , and the voltage signal strength is .

[0046] Further, in step S2, the network forward propagation is:

[0047]

[0048] where, is the output of the layer, , are the weights and biases respectively; the parameters are initialized with Gaussian random:

[0049]

[0050] To ensure the non-negativity of the charged density, the output layer applies Softplus nonlinearity to the linear output :

[0051] .

[0052] Furthermore, the linear observation mapping between the equivalent voltage and the induced charge is as follows:

[0053]

[0054] in, and These are learnable equivalent gain and bias coefficients used for the equivalent preamplifier gain and calibration factor.

[0055] Furthermore, in step S5, monitoring is performed during the training process. and If the convergence status of the validation set loss no longer decreases or oscillates, early stopping is triggered and the weight file is exported. ;

[0056] During the training process, input is used Linear scaling to [0,1]; measurement Perform zero-mean / unit-variance standardization, train the system, and then inverse normalize; use appropriate methods. L1 canonical inhibition Non-physical oscillations and excessive sparsity and divergence.

[0057] The physical constraint neural network constructs a three-dimensional spatial sensitivity model described by physical formulas based on the voltage change generated when a single dust particle moves around a rod-shaped sensing electrode. It can accurately predict the concentration while providing key features in the concentration prediction process, and has good interpretability.

[0058] The advantages of this invention compared to existing technologies are as follows: This invention employs a Physically Informed Neural Network (PINN) method, constructing a physical model based on the spatial sensitivity of the induction signal of dust on a conductor metal rod in three-dimensional space. Then, the neural network captures the mapping relationship between the fluctuation characteristics of voltage intensity and the average dust concentration. When applied to the data processing system of an electrostatic induction sensor, compared to other traditional dust concentration detection methods, it can predict the average dust concentration more quickly, providing rapid and accurate dust concentration detection with good interpretability. Attached Figure Description

[0059] To more clearly illustrate the technical solutions in the embodiments of this application or the prior art, the drawings used in the description of the embodiments or the prior art will be briefly introduced below. Obviously, the drawings described below are only some embodiments of this application. For those skilled in the art, other drawings can be obtained based on these drawings without creative effort.

[0060] Figure 1 A schematic model of the charged dust and electrode space.

[0061] Figure 2 A schematic model of the charged dust and electrode space. A plot of the radial charge-induced spatial sensitivity.

[0062] Figure 3 A plot of the axial charge-induced spatial sensitivity.

[0063] Figure 4 A plot of the induced alternating signal from a unit charge.

[0064] Figure 5 A schematic diagram of the dust detection experiment procedure.

[0065] Figure 6 A plot of the accuracy and loss function of the physically constrained neural network as a function of the number of iterations.

[0066] Figure 7 A plot of the 200-1800 g / m 3 A plot of the prediction performance of the physically constrained neural network, conventional ANN neural network, sliding filter method, and median filter method for metal dust concentrations.

[0067] Figure 8 A plot of the MSE of the physically constrained neural network, conventional ANN neural network, sliding filter method, and median filter method. DETAILED DESCRIPTION

[0068] In the following, certain example embodiments are described. As will be realized by one of ordinary skill in the art, the described embodiments can be modified in various different ways without departing from the spirit or scope thereof. Accordingly, the drawings and descriptions are to be regarded as illustrative in nature and not as restrictive.

[0069] Embodiments of the present application will be described below in detail with reference to the accompanying drawings.

[0070] When the electrostatic object approaches the metal electrode, according to the principle of charge induction, the opposite charge will be induced on the surface of the metal electrode near the charged object. When the electrode is grounded, the same phase charge flows into the ground; when the electrode is not grounded, the same phase charge moves to the end of the metal electrode away from the static source. The design of the electrostatic induction sensor is based on this principle. There is a metal sensing electrode inside the sensor. When the sensor is powered on, the metal sensing electrode is given a voltage, forming an electric field around the sensing electrode and forming an induction area. In an ideal situation, when there is no moving dust particle in the induction area and there is no electromagnetic interference in the environment, the charge accumulation on the metal sensing electrode will remain balanced. However, since the dust particles naturally carry a small amount of charge, when the charged particles enter and move in the induction area, their electric field will superimpose on the original electric field of the electrode plate, thereby disturbing the distribution of accumulated charge on the electrode plate and causing dynamic changes in equivalent charge and equivalent current. When the dust particle approaches the electrostatic detection electrode, the induced charge on the surface of the electrostatic detection electrode gradually increases; as the dust particle moves away from the electrostatic detection electrode, the induced charge on the surface of the electrostatic detection electrode gradually decreases. Therefore, the dynamic induced charge produced by the moving dust particle first increases and then decreases, generating an alternating current signal. The fluctuation of the signal is positively correlated with the particle concentration, so the fluctuation characteristics of the induced signal can be extracted based on the method, and the sampler can be used for calibration to realize real-time detection of dust concentration.

[0071] A dust particle induction signal physical model based on electrostatic field theory, by setting the dust concentration, induction electrode distance, shape, charge density and other state parameters of a single dust particle moving near the induction electrode, the voltage signal strength induced is calculated, and the physical constraint condition is constructed for subsequent neural network model training.

[0072] The charge induction space sensitivity of the rod-shaped electrode is defined as the absolute value of the induced charge on the electrode under the action of a unit charge at a certain point in space. By establishing a physical model of charged dust particles and electrodes, the charge induction space sensitivity of the rod-shaped electrode is derived using the Gaussian electrostatic field theory.

[0073] The rod-shaped electrode is connected to a charge amplifier. When the charged dust particle approaches the electrode, a certain amount of reverse charge is induced on the surface of the electrode, and the same direction charge moves to the capacitor at the edge for charging. When the charged dust particle moves away from the electrode, the same direction charge returns to the electrode from the capacitor, thereby discharging. The charging and discharging process generates an alternating signal at the reverse end of the charge amplifier.

[0074] A physical model of charged dust particles and rod-shaped electrodes is established to study the alternating signal variation, thereby deriving the charge induction space sensitivity of the rod-shaped electrode, as shown in Figure 1 M is a charged q dust particle, which can be regarded as a mass point; the rod-shaped electrode can be simplified to a cylinder with radius , the axis coincides with the cylinder axis, a horizontal axis perpendicular to the axis, the axis of the cylinder, the intersection of the axis of the cylinder and the axis of the cylinder, the intersection of the axis of the cylinder and the axis of the cylinder, the intersection of the axis of the cylinder and the axis of the cylinder, a vertical axis upward through point M and point , the line connecting point M and point lies in the plane and is tangent to the cylinder surface, the angle between the axis of the cylinder and the axis of the cylinder, the angle between the axis of the cylinder and the axis of the cylinder, the angle between the axis of the cylinder and the axis of the cylinder. the angle between the axis of the cylinder and the axis of the cylinder, the angle between the axis of the cylinder and the axis of the cylinder, the angle between the axis of the cylinder and the axis of the cylinder. According to symmetry, the charge-induced spatial sensitivity of the electrode is only related to the axial position and the radial position

[0075] , and is independent of the tangential position , so the charge-induced spatial sensitivity is a function of and . First, calculate the charge-induced spatial sensitivity as the radial position changes when the dust particle is in the middle of the electrode axis. Since the electrode is not grounded, the electric field of the dust particle remains spherical. According to Gauss's electrostatic theory, the total amount of charge induced on the surface of the electrode is equal to the electric flux passing through the closed surface multiplied by the dielectric constant. Let the electric field at the electrode be , then:

[0076]

[0077] In the formula, is the dielectric constant in air. Therefore, the electric field component pointing to the axis direction is , which can be calculated by the following formula:

[0078]

[0079] From the above two formulas, the electric field strength at point on the electrode is:

[0080]

[0081] According to Gauss's electrostatic field theory, the amount of charge induced on the surface of the electrode is:

[0082] ​​

[0083]

[0084]

[0085] The spatial sensitivity of the rod electrode to the charge can be obtained :

[0086]

[0087] Substitute the geometric size of the electrode, and the charge induction spatial sensitivity curve obtained with the change of can be calculated by the program, as shown in x , where the origin represents the electrode surface, and positive and negative represent the direction of the two sides of the electrode. Figure 2 The distance of the charged particles at different radial positions from the electrode surface is different, and the axial position

[0088] changes to obtain the charge induction spatial sensitivity curve, as shown in . From the curve change, it can be seen that the change of the axial position has a weak effect on the charge induction spatial sensitivity, and the induced charge rapidly decreases only near the end of the electrode, and the falling part corresponds to the length of the electrode, which can be ignored. Therefore, it can be considered that the charge induction spatial sensitivity in the axial direction is equal everywhere when the radial position of the electrode is the same; in the radial direction, the induced charge rapidly increases as the charged particles approach the electrode, and rapidly decreases as the charged particles move away from the electrode. Therefore, it can be concluded that the charge induction spatial sensitivity of the electrode is independent of the axial position, and only related to the radial position. Figure 3 From the above analysis, it can be obtained that the output signal of the charge amplifier is only related to the charged particles moving along the radial direction of the electrode, and the charged particles with a charge of

[0089] move at a speed q along the radial direction near the electrode, and according to the charge induction spatial sensitivity function, the function of the induced charge on the electrode with time can be obtained as:

[0090]

[0091]

[0092]

[0093] The current induced on the electrode is:

[0094]

[0095] The voltage output by the charge amplifier​u t ) is:

[0096]

[0097] When the unit charge particle approaches and leaves the electrode at a speed v , the alternating signal generated at the output end of the charge amplifier can be represented by Figure 4 , the abscissa is the time axis, and the ordinate is the voltage value of the charge amplifier output. x The unit dust particle is closest to the electrode surface at 0, and the ordinate is the voltage value of the charge amplifier output.

[0098] By calculating each physical quantity in the experiment, the corresponding relationship between the voltage signal sequence and the concentration is established. Since the volume of the powder tank and the mass of the weighed dust are known during the experiment, the equivalent uniform mass concentration after spraying can be calculated.

[0099]

[0100] Combined with the average radius of the particle , the material density of the dust particle , the number density of the dust particle can be calculated .

[0101]

[0102] Combined with the average charge of a single particle q p , the charge density p q can be calculated.

[0103]

[0104] Since the volume of the gas cylinder , the cross-sectional area of the nozzle , and the internal and external pressure difference are known, the gas flow injection time after the valve is opened can be calculated:

[0105]

[0106] where is the flow coefficient, and the gas density before the valve is taken. The time taken by the generated dust cloud to pass through the induction area conforms to the Gaussian distribution. When the upper part of the powder tank is opened, the dust cloud passes through the induction area of the electrostatic induction sensor in an open state. The equivalent cross-sectional area of the induction area and the main flow cross-sectional area of the powder tank can be calculated.​​The specific flow of dust through the induction area is calculated according to the ratio. Corresponding to the static induction signal collection time, the calculation can be carried out:

[0107]

[0108]

[0109]

[0110] wherein, is the diffusion backflow correction coefficient, , indicates the volume fraction passing through the induction area, indicates the arrival time, indicates the spread, which is used to describe the time distribution of the dust cloud passing through the induction area.

[0111] The space charge density field change caused by the space sensitivity change can be represented by the window function

[0112]

[0113] The time-varying induction charge obtained from the space sensitivity change is:

[0114]

[0115] wherein, represents the integral domain of the induction area. Example 1

[0116] A physical constraint neural network dust concentration detection method is constructed according to a physical model of dust particle induction signals. The physical constraint neural network model is constructed with the physical model as a constraint condition. Through multiple repeated experiments, the voltage signal data generated by the different concentration dust collected by the electrostatic induction sensor is collected as a data set to train the neural network model, capture the hidden features of the dust data, and realize the dust concentration prediction.

[0117] Taking aluminum dust as the research object, a dust cloud is prepared in an open space to simulate the production scene in the actual production place. The electrostatic induction sensor is used to measure the voltage signal intensity value caused by the dust cloud flowing through the induction area. By comparing with the traditional ANN neural network, the sliding filter algorithm and the median filter algorithm, the convergence speed, the steady-state deviation and the robustness under different dust concentrations are evaluated, and it is verified that the proposed algorithm has higher precision. The data processing and network model construction process are as follows:

[0118] 1. Data collection:

[0119] First, take a dust sample with a mass of , and divide it into ​The dust is evenly spread in the space by the powder spraying device to obtain a dust cloud with a concentration of 0.1 g / m3. The voltage signal caused by the dust cloud passing through the induction area is measured using an electric induction sensor. The voltage signal is sampled and recorded using a Yokogawa oscilloscope for data set construction. For each sampling point , the corresponding time is , and the voltage signal strength is .

[0120] Randomly select different concentration dust data, combine the measurement sequence with the voltage signal to form a two-dimensional vector as the input of the neural network, and set the dust concentration as the target value, and divide it into a training set and a validation set according to a certain proportion.

[0121] The experimental process can be mainly divided into the following five steps: experimental preparation, dust weighing, dust spraying, data collection, cleaning and repetition, as shown in Figure 5 .

[0122] (a) Experimental preparation: Before the experiment, the equipment is checked comprehensively to ensure the normal operation of the system and the safety of the experiment. The operator needs to ensure that there is no abnormality in each part, including checking the dust supply device, confirming that the powder tank is sealed well, the gas connection is correct, the nozzle is not blocked, and the dust sample is dry, without lump condensation; check the sensor status to ensure that the electrostatic induction sensor, PLC industrial electrical control system line connection is correct, and the power supply is normal; check the data acquisition system to ensure that the Yokogawa DL950 oscilloscope is started normally, the channel and sensor connection are correct; check the safety device to ensure that the emergency stop button function is normal, and the safety equipment is working properly.

[0123] (b) Dust weighing: According to the pre-set dust type and concentration, calculate the corresponding dust mass combined with the space volume of the powder spraying device, and use a Sartorius electronic balance to accurately weigh. Pour the weighed dust into the experimental device, and evenly spread the dust around the nozzle with a dust-free brush to ensure that the dust is fully lifted when the air flow is sprayed, forming a uniformly dispersed dust cloud.

[0124] (c) Dusting operation: First, adjust the air source, adjust the JCF4-300 air compressor to 500 kPa to ensure uniform and stable jet flow. Then, through the manual switch, start the PLC industrial electrical control system to start the dusting device, control the jet flow, and the jet time is accurately controlled by the Siemens S7-1200CP PLC module, lasting 0.1 s ± 1 ms. At the same time, the air valve is opened, and the gas enters the dust generator through the pipeline and is sprayed through the nozzle to the umbrella-shaped top cover, raising the dust and making it evenly spread, and the airflow evenly distributes the dust cloud in the test space. Because the jet time is short, the dust is quickly and evenly distributed, avoiding agglomeration or settling, filling the measurement area, and facilitating subsequent signal acquisition.

[0125] (d) Data acquisition: When the manual switch is started, the Yokogawa DL950 oscilloscope is triggered by the PLC industrial electrical control system, and the static induction sensor real-time acquisition dust cloud static induction voltage signal is measured and recorded. The voltage signal is converted to a digital signal by an ADC digital-to-analog converter. The acquisition time is set to 10 s, the sampling frequency is 1000 Hz, 10000 data points are collected for each experiment, the resolution is 16 bits, and the dust concentration change can be accurately recorded. All collected data are stored in CSV and MAT formats for subsequent offline processing using Python and MATLAB.

[0126] (e) Cleaning and repetition: After the experiment is completed, save the data, turn off the Yokogawa DL950 oscilloscope, turn off the air source, empty the gas pipeline, and clean the residual dust. Check if the static induction sensor and other equipment have dust deposition and clean them in time, reset the PLC industrial electrical control system, check the equipment status, and ensure smooth development of the next experiment. For each specified concentration and type of dust working condition, 20 experiments are repeated to ensure the reliability of the results, and multiple sets of control experiment data are collected for subsequent method training and verification.

[0127] 2. Model construction:

[0128] a. Network structure and mapping relationship: To predict the evolution of dust concentration over time, a physically constrained neural network is constructed with time as input. In addition to the input layer, the hidden layer is composed of multiple layers of fully connected units, using tanh and ReLU activation functions, and the network output is the average dust density in the discrete space. The network forward propagation formula can be written as:

[0129]

[0130] where a (l) is the output of the layer, W (l) , b (l)respectively, are the weights and biases. The parameters are initialized with Gaussian random values:

[0131]

[0132] To ensure non-negativity of the charge density, the output layer applies a linear output with a Softplus nonlinearity:

[0133]

[0134] b. Sensitivity kernel convolution mechanism mapping and observation model: Based on the electrostatic induction mechanism and the spatial sensitivity of the rod electrode, the contribution of the unit cell at to the electrode induced charge can be represented by the sensitivity kernel . The total predicted induced charge is written as:

[0135]

[0136] where is the induction area, is the electrode radius and effective length. The measured voltage standard deviation, i.e., the equivalent voltage quantity, is mapped to the induced charge using a linear observation mapping:

[0137]

[0138] where: and are learnable amplification bias parameters used to equivalently absorb preamplifier gain and calibration factors.

[0139] c. Constructing the loss function: Physics-constrained neural network loss function is composed of three parts:

[0140]

[0141] where, is the consistency term calculated by the least square number:

[0142]

[0143] where, is the total number of sampling points within the corresponding sample, is the sampling time, is the predicted voltage signal strength of the model at that time, is the true voltage signal strength at that time.

[0144] is the physical constraint term combined with the weak form and prior constraints, including the mass / density constraints, and the peak time , where Consistency constraint concentration-number density-charge density relation calculation:

[0145]

[0146]

[0147] where, represents the dust particle material density, represents the average radius of the dust particles.

[0148] represents the smoothing and diffusion prior, used to characterize the cluster-dispersion characteristics of the dust cloud in the open space, which can be approximated by the Laplace calculation of the isotropic second-order difference:

[0149]

[0150] Far-field attenuation prior The calculation method is:

[0151]

[0152] It can be calculated by superposition:

[0153]

[0154] is the regularization term, used to suppress false high frequency and sparse prior, and its calculation method is:

[0155]

[0156] where, is all trainable parameters, is the L1 coefficient.

[0157] d. Backpropagation and parameter update: use the Adam adaptive method to update the parameters, follow the gradient descent:

[0158]

[0159] where, gamma is the learning rate, according to the chain rule, the gradient of the weight is shown as:

[0160]

[0161]

[0162] 3. Model training:

[0163] The training set Input the data into the network in batches and minimize the loss function. Monitoring during training and If the validation set loss stops decreasing or oscillates after several rounds, early stopping is triggered and the weight file is exported. To enhance stability, input methods are used during training. Linear scaling to [0,1]; measurement Perform zero-mean / unit-variance standardization, train the system, and then inverse normalize; use appropriate methods. L1 canonical inhibition Non-physical oscillations and excessive sparsity and divergence.

[0164] 4. Effect Verification:

[0165] Predict the dust concentration sequence for untrained conditions, weigh dust according to the target concentration, complete the dust spraying experiment, and obtain the corresponding voltage standard deviation sequence. Using an FFT preprocessing and normalization process, the test sequence is input into PINN to obtain... With inversion ;Calculate the error index MSE:

[0166]

[0167] By comparing with traditional ANN neural networks, sliding filter methods, and median filter methods, the convergence speed, steady-state deviation, and robustness under different dust concentrations are evaluated, verifying that the proposed method has higher accuracy.

[0168] Voltage intensity signal data is uploaded to a computer and smoothed. Using voltage intensity and time as input values ​​and average dust concentration as the predicted value, a dataset is constructed. The constructed physical constraint neural network model is then trained. The model's accuracy is measured by calculating the difference between the predicted and actual dust concentration values. The model is then compared with traditional ANN neural networks, sliding filter methods, and median filter methods to check the consistency between the predicted results and the actual concentration, thus evaluating the model's accuracy and generalization ability. Figure 6 The results demonstrate how the accuracy and loss function of the physically constrained neural network change with the number of iterations. The iterations lasted for 1500 rounds, and the model with the best training performance was selected as the final result. The final accuracy was 88.3% and the loss function was 0.432. Figure 3The results of the data of the induction signals of different concentrations of aluminum metal powder after being processed by the physical constraint neural network, the traditional ANN neural network, the sliding filter method and the median filter method are shown. As can be seen from the figure, the curve processed by the physical constraint neural network converges to the average dust concentration after an average of 1.5s of prediction, compared with the traditional ANN neural network which needs an average of 3s to converge, and the sliding filter method and the median filter method are difficult to converge, and the physical constraint neural network has better performance. In order to make this deviation more obvious, the deviations of different curves from the target value are accumulated in Figure 7 The results show that the relative deviation MSE of the prediction of the physical constraint neural network method is 0.19, compared with the traditional ANN neural network whose MSE is 0.28, and the MSE of the conventional sliding filter method and the median filter method is 0.79 and 0.86 respectively, so it can be judged that the physical constraint neural network has better processing effect on the data of the induction signal intensity caused by different concentrations of metal dust concentration compared with the traditional ANN neural network, the sliding filter method and the median filter method, and can quickly and accurately predict the dust concentration. The above embodiments are only used to illustrate the present application, and any equivalent transformation and improvement based on the technical scheme of the present application should not be excluded from the protection scope of the present application.

Claims

1. A method for detecting metal dust concentration based on a physically constrained neural network, characterized in that: Using a physical model as a constraint, a physically constrained neural network model is constructed. Voltage signal data generated by dust at different concentrations, collected by an electrostatic induction sensor, are used as the dataset to train the neural network model, capturing hidden features of the dust data to achieve dust concentration prediction. The specific steps include: S1. Data Collection: Randomly select dust data of different concentrations and measure the sequence. With voltage signal The data is composed of two-dimensional vectors, which are used as input to the neural network. The dataset is divided into a training set according to the specified proportions. and verification set ; S2. Network Structure and Mapping Relationships: Constructing a time-based network structure. The input is a physically constrained neural network; apart from the input layer, the hidden layers consist of multiple fully connected units, using tanh and ReLU activation functions. The network output is the average dust density in discrete space. ; S3. Sensitivity Kernel Convolution Mechanism Mapping and Observation Model: Based on the electrostatic induction mechanism and the spatial sensitivity derivation of the rod electrode, unit cell... exist The contribution of the induced charge at the electrode is expressed by the sensitivity nucleus. The predicted total induced charge is: ； in The sensing area The electrode radius and effective length; The measured standard deviation of voltage, i.e., the equivalent voltage, is linearly mapped to the induced charge. S4. Constructing the loss function: Physically constrained neural network loss function It consists of three parts: ； in, For data consistency terms calculated using least squares: ； in, This represents the total number of sampling points within the corresponding sample. Sampling time, The predicted voltage signal strength of the model at that time. This represents the actual voltage signal strength at that time. For physical constraint terms that combine weak forms and prior constraints, including mass / number density constraints, the peak time is selected. average body Consistency constraint: Calculation of concentration-number density-charge density relationship: ； ； in, This represents the equivalent uniform mass concentration after powder spraying. Indicates the density of particulate matter. Indicates the average radius of dust particles. The integral domain representing the sensing area, , representing the volume fraction passing through the sensing zone. The average charge of a single particle; Representing smoothness and diffusion priors, this is used to characterize the clustering-diffusion properties of dust clouds in open space, calculated using an isotropic second-order difference approximation of the Laplace: ； Far-field attenuation prior The calculation method is as follows: ； These are physical constraint terms, calculated by superposition: ； in, The weights of the constraint terms are a combination of weak form and prior constraints. To smooth and diffuse prior weights, For far-field attenuation prior weights; These are the weights of the physical constraint terms, used to control the physical prior constraints. For loss function The degree of impact; This is a regularization term used to suppress spurious high-frequency and sparse priors; its calculation method is as follows: ； in, For all trainable parameters, , These are weights and biases, respectively. The L1 coefficient; These are the weights of the regularization constraint terms, used to control the regularization terms. For loss function The degree of impact; S5, Backpropagation and Parameter Update: Parameter updates are performed using the Adam adaptive method, following gradient descent: ； in, Let be the learning rate. The gradient of the weights according to the chain rule is illustrated as follows: ； ； S6. Model Training: The training set... Input the data into the network in batches and minimize the loss function. .

2. The detection method according to claim 1, characterized in that: In step S1, data acquisition specifically involves weighing a mass of... The dust samples were divided into The powder is evenly distributed in space using a powder spraying device to achieve a concentration of [missing information]. The dust cloud was measured using an inductive sensor. The voltage signal generated when the dust cloud passed through the sensing area was measured, and the voltage signal was sampled and recorded using an oscilloscope to construct a dataset. For each sampling point... The corresponding time is The voltage signal strength is .

3. The detection method according to claim 2, characterized in that: In step S2, the network forward propagation is as follows: ； in, For the first Layer output, , These are the weights and biases, respectively; the parameters are initialized using Gaussian randomization. ； To ensure the non-negativity of charge density, the output layer is for linear output. Applying Softplus nonlinearity: 。 4. The detection method according to claim 3, characterized in that: The linear observation mapping between the equivalent voltage and the induced charge is: ； in: and These are learnable amplification bias parameters used to equivalently absorb the preamplifier gain and calibration factor.

5. The detection method according to claim 4, characterized in that: In step S5, monitoring during training and If the convergence status of the validation set loss no longer decreases or oscillates, early stopping is triggered and the weight file is exported. ; During the training process, input is used Linear scaling to [0,1]; measurement Perform zero-mean / unit-variance standardization, train the system, and then inverse normalize; use appropriate methods. With L1 regularized inhibition Non-physical oscillations and excessive sparsity and divergence.

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