Acoustic qualitative recognition method and network training method for mixed gas components based on deep learning network

Abstract

The invention belongs to the technical field of gas detection and recognition, and particularly relates to a mixed gas component acoustic qualitative recognition method based on a deep learning network and a network training method. Testing a plurality of groups of sound velocities and sound absorption coefficients corresponding to different sound wave frequencies of the to-be-identified gas under the conditions of preset temperature and pressure, and then calculating to obtain effective heat capacities corresponding to the plurality of groups of to-be-identified gas according to the plurality of groups of sound velocities and sound absorption coefficients; decomposing the effective heat capacity according to a mixed gas acoustic relaxation decoupling model to obtain a gas relaxation information parameter; and taking the gas relaxation information parameter as the input of the trained mixed gas vibration characteristic frequency detection network, namely outputting the gas type in the to-be-identified gas. The invention provides a new way for identifying gas types, and the model is high in identification accuracy and wide in application scene.

Description

Technical Field

[0001] This invention belongs to the field of gas detection and identification technology, specifically relating to an acoustic qualitative identification method for mixed gas components based on a deep learning network and a network training method. Background Technology

[0002] The detection and sensing of gas components is essential in many fields such as environmental monitoring, industrial production, and military aerospace. Acoustic detection and sensing technology, due to its advantages of low cost, strong robustness, non-invasiveness, and real-time capability, has been widely applied in gas monitoring across various scenarios. For example, by introducing attention mechanisms into acoustic relaxation data analysis and establishing a mapping relationship between relaxation time series and gas concentration through LSTM networks, gas identification can be achieved. However, this method is based on macroscopic acoustic measurements and cannot qualitatively determine the structure of gas molecules. Because existing machine learning models generally possess "black box" characteristics and lack deep integration with physical models, the generalization ability of the network models is insufficient. Furthermore, using acoustic propagation parameters such as sound velocity dispersion and acoustic relaxation absorption during the relaxation process of mixed gases to identify gas components cannot qualitatively analyze the internal structure of gas molecules. The process of identifying gas components usually requires changing the ambient temperature or pressure to achieve detection, which is difficult to implement in normal industrial scenarios. Summary of the Invention

[0003] The purpose of this invention is to provide an acoustic qualitative identification method and network training method for mixed gas components based on deep learning networks. Starting from the relaxation microscopic process of mixed gases, the effective heat capacity closely related to molecular structure is used to explore and detect gas components. Combined with deep learning networks, a method is given to qualitatively determine gas components using the effective heat capacity of the acoustic relaxation process. It has the characteristics of high identification accuracy and strong scene adaptability.

[0004] To achieve the above objectives, this invention provides an acoustic qualitative identification method for mixed gas components based on deep learning networks, comprising the following steps:

[0005] S1. Test the gas to be identified under preset temperature and pressure conditions, and obtain several sets of sound velocities and sound absorption coefficients corresponding to different sound wave frequencies. Then, calculate the effective heat capacity corresponding to several sets of the gas to be identified based on the several sets of sound velocities and sound absorption coefficients.

[0006] S2. Decompose the effective heat capacity according to the mixed gas acoustic relaxation decoupling model to obtain gas relaxation information parameters;

[0007] S3. Use the gas relaxation information parameters as input to the trained mixed gas vibration characteristic frequency detection network, that is, output the types of gases in the gas to be identified.

[0008] Furthermore, in step S2, the gas relaxation information parameters include the decomposition heat capacity, relaxation time, and external degree of freedom heat capacity of the relaxation process.

[0009] Furthermore, the acoustic relaxation decoupling model for the mixed gas is as follows:

[0010]

[0011] in, Indicates effective heat capacity, N represents the heat capacity of the external degrees of freedom, and N represents the number of vibration modes. This represents the decomposition heat capacity of the nth vibration mode. This represents the relaxation time of the nth vibration mode. Let a be the vibrational heat capacity of the internal degree of freedom of the j-th vibration mode. j Let Ξ be the mole fraction of the j-th vibration mode, and Ξ represent the acoustic angular frequency. λ n h is the eigenvalue of the nth vibration mode of R. k V represents the vector of the k-th vibration mode of the H matrix. jn V' represents the element in the j-th row and n-th column of the eigenvector matrix V of R. jk V represents the inverse matrix of the eigenvectors of R. -1 The element in the j-th row and k-th column is R, which is the energy transfer matrix calculated through the energy transfer rate between different vibration modes.

[0012] Furthermore, the mixed gas vibration characteristic frequency detection network consists of a KAN regression network and an MLkNN classification network;

[0013] The KAN regression network is used to obtain the characteristic vibrational frequencies of gas molecules based on the gas relaxation information parameters; the MLkNN classification network is used to classify the gas types based on the characteristic vibrational frequencies of gas molecules.

[0014] Furthermore, the mixed gas vibration characteristic frequency detection network is trained using a mixed gas relaxation information parameter dataset, which is obtained by simulation calculation using the mixed gas acoustic relaxation decoupling model.

[0015] The simulation calculation includes: selecting several groups of mixed gases from CH4, N2, O2, Cl2, CO2, and SO2, and using the mixed gas acoustic relaxation decoupling model to perform effective heat capacity decomposition, solving the equations at different acoustic frequencies, and obtaining a mixed gas relaxation information parameter dataset.

[0016] Furthermore, the mixture contains three or fewer types of gases.

[0017] In step S1, the gas to be identified includes one or more of CH4, N2, O2, Cl2, CO2, and SO2, preferably three or fewer.

[0018] Furthermore, in step S1, the preset temperature and pressure are the same as those used in the simulation calculation;

[0019] The sound wave frequency f includes 0.5 × 10⁻⁶. 3 Hz, 3×10 3 Hz, 8×10 3 Hz, 10×10 3 Hz, 15×10 3 Hz, 20×10 3 Hz, 40×10 3 Hz.

[0020] Furthermore, in step S1, the effective heat capacity is related to the sound velocity c and the sound absorption coefficient α. r The relation is:

[0021]

[0022] P0 represents gas pressure, ρ0 represents gas density, and Ξ represents acoustic angular frequency.

[0023] This invention also provides a training method for a mixed gas vibration characteristic frequency detection network, comprising: constructing a KAN-MLkNN mixed gas vibration characteristic frequency detection network composed of a KAN regression network and an MLkNN classification network, wherein the input of the KAN regression network is a mixed gas relaxation information parameter dataset and the output is the characteristic vibration frequency of gas molecules; the input of the MLkNN classification network is the characteristic vibration frequency of gas molecules and the output is the gas type.

[0024] Several groups of mixed gases were selected from CH4, N2, O2, Cl2, CO2, and SO2. The effective heat capacity decomposition was performed using the acoustic relaxation decoupling model of the mixed gas, and the equations at different acoustic frequencies were solved to obtain a dataset of mixed gas relaxation information parameters.

[0025] The mixed gas relaxation information parameter dataset is used as the input to the KAN-MLkNN mixed gas vibration characteristic frequency detection network, and the gas type corresponding to each group of data in the mixed gas relaxation information parameter dataset is used as the output to train the KAN-MLkNN mixed gas vibration characteristic frequency detection network, thus obtaining the trained mixed gas vibration characteristic frequency detection network.

[0026] Furthermore, binary (two types) and ternary (three types) mixed gases are preferred for the mixed gas, and different concentration gas types are designed according to a certain concentration gradient. The concentration change of each component in the binary mixed gas relaxation information parameter dataset can be 0.1%, with a total of 14,985 data entries; the concentration change of each component in the ternary mixed gas relaxation information parameter dataset can be 1%, with a total of 103,020 data entries.

[0027] The training uses a five-fold cross-validation method, with a training set to test set ratio of 4:1.

[0028] The mixed gas contains three or fewer types of gases, and the sound wave frequency f includes 0.5 × 10⁻⁶. 3 Hz, 3×10 3 Hz, 8×10 3 Hz, 10×10 3 Hz, 15×10 3 Hz, 20×10 3 Hz, 40×10 3 Hz;

[0029] The KAN regression network contains three hidden layers with 256, 128, and 32 nodes respectively, a spline order of 4, and an initial grid value of 20.

[0030] In summary, compared with the prior art, the above-described technical solutions conceived by this invention mainly possess the following technical advantages:

[0031] 1. The acoustic qualitative identification method for mixed gas components based on deep learning networks provided by this invention starts from the relaxation microscopic process of mixed gas and uses the effective heat capacity closely related to molecular structure to explore and detect gas components. Based on the acoustic relaxation decoupling model of mixed gas, the effective heat capacity of mixed gas is decomposed into the effective heat capacity of single relaxation process. Combined with the deep learning network model, a method for qualitatively judging gas components using the effective heat capacity of acoustic relaxation process is given. It has the characteristics of high identification accuracy and strong scene adaptability, and can realize detection and identification at room temperature and normal pressure.

[0032] 2. This invention utilizes the vibrational coupling heat capacity and relaxation time parameters of each individual relaxation process to construct a training dataset. Based on the correspondence between these parameters and gas types, the gas relaxation information parameters are used as input, and the gas type is used as output to build a KAN-MLkNN deep learning network model. First, the relationship between the effective heat capacity of the individual relaxation process and the characteristic parameters of gas molecules (such as molecular vibrational frequency) is extracted through the KAN regression network. Then, the characteristic vibrational frequency is mapped one-to-one with the corresponding gas type through the MLkNN classification network. This results in an acoustic method for qualitatively determining gas composition using the effective heat capacity of the acoustic relaxation process of mixed gases, providing a new approach for the identification of mixed gases. Attached Figure Description

[0033] Figure 1 This is the overall structure of the detection network of the present invention.

[0034] Figure 2 The RMSE learning rate curves of three mixed gases under the same network structure are obtained by passing them through MLP network, ResNet network and KAN network respectively.

[0035] Figure 3 This is the confusion matrix of CH4 in the case of a binary gas mixture.

[0036] Figure 4 This is the confusion matrix of Cl2 in the case of a binary gas mixture.

[0037] Figure 5 This is the confusion matrix of CO2 in the case of a binary gas mixture.

[0038] Figure 6 This is the confusion matrix of N2 in the case of a binary gas mixture.

[0039] Figure 7 This is the confusion matrix of O2 in the case of a binary gas mixture.

[0040] Figure 8 This is the confusion matrix of SO2 in the case of a binary gas mixture.

[0041] Figure 9 This is the confusion matrix of CH4 in the case of a ternary gas mixture.

[0042] Figure 10 This is the confusion matrix of Cl2 in the case of a ternary gas mixture.

[0043] Figure 11 This is the confusion matrix of CO2 under the condition of a ternary gas mixture.

[0044] Figure 12 This is the confusion matrix of N2 in the case of a ternary gas mixture.

[0045] Figure 13 This is the confusion matrix of O2 in the case of a ternary gas mixture.

[0046] Figure 14 This is the confusion matrix of SO2 in the case of a ternary gas mixture. Detailed Implementation

[0047] To make the objectives, technical solutions, and advantages of this invention clearer, the invention will be further described in detail below with reference to embodiments. It should be understood that the specific embodiments described herein are merely illustrative and not intended to limit the invention. Furthermore, the technical features involved in the various embodiments of this invention described below can be combined with each other as long as they do not conflict with each other.

[0048] Starting from the acoustic physics model, although the effective heat capacity of the acoustic relaxation process of a mixed gas can be decoupled into multiple single relaxation process heat capacities, the effective heat capacity of a single relaxation process cannot correspond to a specific molecular vibration mode. This makes it difficult to qualitatively determine the gas composition based solely on the two acoustic parameters of sound velocity dispersion and acoustic relaxation absorption caused by the acoustic relaxation process. To address this problem, this invention decomposes the effective heat capacity of the mixed gas into the effective heat capacity of a single relaxation process based on the acoustic relaxation decoupling model of the mixed gas. A dataset is constructed using the obtained vibrational coupling heat capacity and relaxation time parameters of each single relaxation process. A KAN-MLkNN deep learning network model is then built to extract the relationship between the effective heat capacity of a single relaxation process and the characteristic vibrational frequencies of gas molecules, thus obtaining an acoustic method for qualitatively determining the gas composition using the effective heat capacity of the acoustic relaxation process of a mixed gas. The details are as follows:

[0049] This invention provides an acoustic qualitative identification method for mixed gas components based on deep learning networks, comprising the following steps:

[0050] S1. Test the gas to be identified under preset temperature and pressure conditions, and obtain several sets of sound velocities and sound absorption coefficients corresponding to different sound wave frequencies. Then, calculate the effective heat capacity corresponding to several sets of the gas to be identified based on the several sets of sound velocities and sound absorption coefficients.

[0051] S2. Decompose the effective heat capacity according to the mixed gas acoustic relaxation decoupling model to obtain gas relaxation information parameters;

[0052] S3. Use the gas relaxation information parameters as input to the trained mixed gas vibration characteristic frequency detection network, that is, output the types of gases in the gas to be identified.

[0053] Furthermore, in step S2, the gas relaxation information parameters include the decomposition heat capacity, relaxation time, and external degree of freedom heat capacity of the relaxation process.

[0054] In step S1, the preset temperature and pressure are typically room temperature (25°C) and normal pressure (1 atm). The speed of sound can be measured using methods such as TOF (Time-of-Flight), resonant cavity method, and phase comparison method. The sound absorption coefficient can be obtained by measuring sound intensity attenuation (sound pressure attenuation method), resonant cavity attenuation method, or pulse echo method.

[0055] The preferred sound wave frequency f is one of seven frequencies, including 0.5 × 10⁻⁶. 3Hz, 3×10 3 Hz, 8×10 3 Hz, 10×10 3 Hz, 15×10 3 Hz, 20×10 3 Hz, 40×10 3 Hz. This corresponds to seven sets of sound speeds and sound absorption coefficients.

[0056] The gas to be identified is selected from one or more of CH4, N2, O2, Cl2, CO2, and SO2, preferably a mixture of three or fewer gases. The identification accuracy will decrease as the number of gases increases.

[0057] Effective heat capacity, sound velocity c, and sound absorption coefficient α r The relation is:

[0058]

[0059] P0 represents gas pressure, ρ0 represents gas density, and ω = 2πf represents acoustic angular frequency.

[0060] In step S2, the acoustic relaxation decoupling model of the mixed gas is as follows:

[0061]

[0062] in, Indicates effective heat capacity, N represents the heat capacity of the external degrees of freedom, and N represents the number of vibration modes. This represents the decomposition heat capacity of the nth vibration mode. This represents the relaxation time of the nth vibration mode. Let a be the vibrational heat capacity of the internal degree of freedom of the j-th vibration mode. j Let ω represent the mole fraction of the j-th vibration mode, and ω represent the acoustic angular frequency. λ n h is the eigenvalue of the nth vibration mode of R. k V represents the vector of the k-th vibration mode of the H matrix. jn V' represents the element in the j-th row and n-th column of the eigenvector matrix V of R. jk V represents the inverse matrix of the eigenvectors of R. -1 The elements in the j-th row and k-th column are R and H, which are N×N energy transfer matrices calculated from the energy transfer rates between different vibration modes.

[0063] In step S3, the mixed gas vibration characteristic frequency detection network consists of a KAN regression network (Kolmogorov-Arnold Network) and an MLkNN classification network (Multi-Label k-Nearest Neighbors); the KAN regression network is used to obtain the characteristic vibration frequencies of gas molecules based on the gas relaxation information parameters; the MLkNN classification network is used to classify the gas types based on the characteristic vibration frequencies of gas molecules.

[0064] Several groups of mixed gases were selected from CH4, N2, O2, Cl2, CO2, and SO2. The effective heat capacity decomposition was performed using the acoustic relaxation decoupling model of the mixed gas, and the equations at different acoustic frequencies were solved to construct a mixed gas relaxation information parameter dataset.

[0065] The mixed gas relaxation information parameter dataset is used as the input to the KAN-MLkNN mixed gas vibration characteristic frequency detection network, and the gas type corresponding to each group of data in the mixed gas relaxation information parameter dataset is used as the output to train the KAN-MLkNN mixed gas vibration characteristic frequency detection network, thus obtaining the trained mixed gas vibration characteristic frequency detection network.

[0066] In constructing the mixed gas relaxation information parameter dataset, binary (two types) and ternary (three types) mixed gases were selected, and different concentration types of gases were designed according to a certain concentration gradient to increase the variety of the dataset and improve its recognition accuracy. Specifically, the binary mixed gas relaxation information parameter dataset has a concentration change of 0.1% for each component and a total of 14,985 data entries; the ternary mixed gas relaxation information parameter dataset has a concentration change of 1% for each component and a total of 103,020 data entries.

[0067] Specifically, in step S3, firstly, based on the acoustic relaxation decoupling model of the mixed gas, the effective heat capacity of the mixed gas relaxation process is decomposed into the effective heat capacity of multiple individual relaxation processes, obtaining relaxation information parameters such as vibrational coupling heat capacity and relaxation time of the individual relaxation processes closely related to the gas composition. Then, a dataset containing relaxation information parameters of binary and ternary mixed gases (CH4, N2, O2, Cl2, CO2, SO2) is constructed under room temperature and atmospheric pressure conditions. Next, based on the constructed dataset, a KAN-MLkNN deep learning network is built to complete the qualitative identification of the mixed gas composition. Specifically, the KAN regression network calculates the regression of characteristic vibrational frequencies of gas molecules; the MLkNN classification network utilizes the one-to-one physical relationship between characteristic vibrational frequencies and gas molecule types to map the regressed characteristic vibrational frequencies to specific gas types.

[0068] Experiments show that the recognition accuracy on the binary mixed gas dataset reaches 99.17%, and the recognition accuracy on the ternary mixed gas dataset is 95.05%.

[0069] Specifically, the mixed gas relaxation information parameter dataset is a parameter dataset obtained by decomposing the effective heat capacity of binary and ternary mixed gases containing six candidate gases according to the mixed gas acoustic relaxation decoupling model. The following is a brief introduction on how to use the mixed gas acoustic relaxation decoupling model to decompose the effective heat capacity of mixed gases.

[0070] The theoretical derivation process of the formula in this invention is as follows:

[0071] Effective per-unit molar heat capacity This reflects the relationship between temperature change and energy, and also the macroscopic footprint of molecular relaxation processes. The total thermodynamic energy change caused by sound propagation in a gas is the sum of the energy changes of each molecular degree of freedom. In different molecular external degrees of freedom (translation and rotation), the sound energy and sound wave are in phase, and the temperature change is considered the same. However, different vibrational modes have different characteristic frequencies, and the temperature changes of their internal degrees of freedom (vibration) differ. For a gas mixture, its effective heat capacity consists of the heat capacity of the external degrees of freedom and the heat capacity of the internal degrees of freedom, calculated using the following formula:

[0072]

[0073] It is the external degree of freedom heat capacity of the mixture. For the external degree of freedom heat capacity of vibration mode l, Let a be the vibrational heat capacity of the inner degrees of freedom of vibration mode j. l a j The mole fractions of vibration modes l and j, respectively, and y j Let be the ratio of the temperature change to the change in the external degrees of freedom of vibration mode j. Let represent the temperature change of vibration mode j. Where the vibrational heat capacity... Calculated from equation (2):

[0074]

[0075] Where h is Planck's constant, and k B Let θ be the Bolmann constant, T0 be the equilibrium temperature, and θ be the constant. vib v, g, and γ represent the characteristic temperature, characteristic frequency, and degeneracy, respectively, and R = 8.31 is the gas molar constant. The characteristic temperature and characteristic frequency differ for different vibrational modes. Table 1 shows the degeneracy of the six candidate gases studied in this invention, as well as the vibrational frequencies and vibrational heat capacities of gas molecules exhibiting significant relaxation at T = 298.15 K and P = 1 atm.

[0076] Table 1. Vibrational mode frequencies and vibrational heat capacities of the candidate gases

[0077]

[0078]

[0079] y j It is the ratio of the temperature change to the external degree of freedom change of vibration mode j. Since the excitable mixed gas contains two or more vibration modes, multimode relaxation occurs, and coupling occurs through the VV process (vibration-vibration). Therefore, y j The relaxation process, which relates to all vibrational modes of the mixture, can be calculated using the energy relaxation equation for the gas mixture. j The calculation is obtained from the energy relaxation matrix of the mixed gas:

[0080] (R+iωI)y=H (3)

[0081] Where R and H are energy transfer matrices calculated from the energy transfer rates between different vibration modes, R jj =k jj ,R jk =-k jk , k jj k represents the energy transfer rate of the j-th vibrational mode and the j-th vibrational mode itself. jk ω represents the energy transfer rate between the j-th vibration mode and the k-th vibration mode, and ω is the acoustic angular frequency.

[0082] By solving for the analytical expression of y and substituting it into equation (1), we can obtain the decoupled expression for the effective heat capacity of the gas mixture:

[0083]

[0084] in, λ n h is the eigenvalue of the nth vibration mode of matrix R. k V represents the vector of the k-th vibration mode of the H matrix. jn V' represents the element in the j-th row and n-th column of the eigenvector matrix V of R. jk V represents the inverse matrix of the eigenvectors of R. -1 The elements in the j-th row and k-th column are R and H, which are N×N energy transfer matrices calculated from the energy transfer rates between different vibration modes. As can be seen from equation (4), for a mixed gas with N vibration modes, N single relaxation processes can be formed through decoupling, each with a different vibration coupling heat capacity. Between relaxation time quantity sets Its parameter values ​​are calculated from the characteristic vibrational frequencies of N gas molecules and the coupling effects between different modes, using the relaxation matrix, and are functions of the gas composition. The relaxation parameters of the 2N decomposition processes of N single relaxation processes are related to the heat capacity of one external degree of freedom. This constitutes the effective heat capacity of the gas mixture. Although the effective heat capacity of a gas mixture containing N vibrational modes can be decoupled into N single relaxation process heat capacities, the vibrational coupling heat capacity value of a single relaxation process cannot be attributed to the vibrational mode of a specific gas molecule, i.e., it cannot be mapped to a specific gas component. This leads to the fact that existing gas sensing methods based on acoustic relaxation, which rely solely on physical models, cannot qualitatively determine the type of gas molecules through measurements of sound velocity and acoustic relaxation absorption.

[0085] The effective heat capacity of a gas is related to the vibrational modes of its individual molecules at the microscopic level, and is reflected macroscopically in the sound velocity c and the sound absorption coefficient α. r The measured values ​​are as follows. Formula (5) below is the analytical expression of effective heat capacity, sound velocity, and sound absorption.

[0086]

[0087] P0 represents gas pressure, ρ0 represents gas density, and i represents an imaginary number.

[0088] Table 2 shows the decomposition heat capacity and relaxation time of several relaxation processes after decoupling of mixed gases with different components. The number of decoupling processes with different decomposition heat capacities and relaxation times is the same as the number of vibrational modes in the mixed gas. For example, a 70% SO2-20% N2-10% O2 mixed gas has five vibrational modes, forming five decoupling processes. It can be found that the heat capacity of these single relaxation processes is different from the molar heat capacity of any gas itself. The decoupling calculation of this relaxation process is essentially a redistribution of the vibrational energy of a series of gas molecules. Multimode relaxation is determined by two types of energy transfer: VV energy exchange and VT transfer (vibrational-translational). The VV process couples the stored energy of all vibrational modes, while the VT process provides a de-excitation path for energy to the translational kinetic energy of molecules. Therefore, the vibrational coupling heat capacity and relaxation time of each single relaxation process include the contributions of all vibrational modes.

[0089] Table 2 shows the heat capacity and relaxation time of each relaxation process after decoupling the mixed gas of different components using formula (4).

[0090]

[0091] The data in Table 2 shows the decomposition heat capacity of the first decoupling process. The decomposition heat capacity is much larger than that of other processes, and is almost equal to the sum of the relaxation heat capacity contributions of all vibrational modes, i.e. This is called the main relaxation process. Since the energy gap between higher modes is usually much smaller than the energy level of the lowest mode, almost all vibrational energy is relaxed through the VT process of the lowest mode. The heat capacity of the main relaxation process is almost equal to the contribution of all relaxed vibrational modes, followed by the second and third relaxation processes. The later non-main relaxation processes usually provide smaller relaxation contributions. For the effective heat capacity decomposition of an unknown gas mixture, it is often unknown in advance how many molecular vibrational modes exist in the gas mixture. When using equation (4) for decomposition, it is impossible to determine how many relaxation processes will be decomposed. Since the later non-main relaxation processes contribute very little to the overall relaxation, and considering too many non-main relaxation processes will make solving equation (4) more difficult, it is sufficient to take only the first 3 relaxation processes to contain most of the relaxation information of the gas mixture.

[0092] This invention utilizes the aforementioned decoupling model to perform effective thermal capacity decomposition on binary and ternary gas mixtures containing six candidate gases: CH4, N2, O2, Cl2, CO2, and SO2. The acoustic relaxation process is simulated using MATLAB, employing seven frequency points at f = [0.5 3 8 10 15 20 40] × 10⁻⁶. 3 Hz Solve the relaxation decomposition equation and construct a mixed gas relaxation information parameter dataset for network model learning. The binary mixed gas relaxation information parameter dataset has a component concentration change of 0.1% and a total of 14,985 data entries; the ternary mixed gas relaxation information parameter dataset has a component concentration change of 1% and a total of 103,020 data entries.

[0093] The KAN-MLkNN network for detecting vibrational characteristic frequencies of mixed gases is as follows:

[0094] The machine learning network task of this invention can be decomposed into two parts: a regression task and a classification task network. The regression network, through training, fits the relaxation information parameters obtained from the effective heat capacity decomposition and the inverse relationship between them and the vibrational modes of gas molecules. Based on the input relaxation blind decomposition data, it can regress and calculate the characteristic vibrational frequencies of gas molecules. The classification network, based on the characteristic vibrational frequencies obtained from the regression, uses the one-to-one correspondence between the characteristic vibrational frequencies and the types of gas molecules to map them to the gas types. The regression task and classification task of this invention are completed using KAN (Kolmogorov-Arnold Network) and MLkNN (Multi-Label k-Nearest Neighbors) networks, respectively.

[0095] Among them, the KAN regression network is a network model proposed based on the Kolmogorov-Arnold representation theorem. Its core advantage lies in its ability to decompose complex high-dimensional functions into a combination of simple one-dimensional functions, giving KAN a significant advantage in handling the fitting problem of complex data relationships and enabling it to more accurately simulate complex phenomena in the real world. KAN is proposed based on the Kolmogorov-Arnold representation theorem, which states that any continuous multivariable function can be decomposed into a combination of several univariable functions and addition operations. Specifically, it is expressed as (6), where φ q,p and Φ q It is a single-variable function.

[0096]

[0097] KAN extends the Kolmogorov-Arnold representation theorem to simulate the structure of a neural network. For an L-layer KAN network, the structure is [n0, n1, ... nn]. L (The number of nodes in layer L is n) L If we add one more layer to the base layer L, resulting in layer L+1, then the activation functions between layer L and layer L+1 are n. L ×n L+1 Each layer of nodes receives a KAN structure where the input is the sum of values ​​mapped from the nodes of the previous layer through an activation function. Therefore, the relationship between nodes in two layers can be represented by a matrix. A complete KAN structure can be expressed as the following formula, where Φ... L It is a matrix composed of unary functions:

[0098]

[0099] KAN performs function fitting in the following way. First, the activation function represented by each edge is initialized using a B-spline function (a function that can smoothly connect discrete points through partial polynomials; the higher the order, the better the smooth fitting effect). The activation function is expressed as φ(x) = w b b(x)+w s spline(x), where w b and w s Let b(x) be the weight, and b(x) be the basis function, which can be a nonlinear silu function, i.e. B-spline functions are piecewise polynomial functions that are smoothly connected at the nodes and possess high-order continuity. Their shape is determined by the nodes t. i and control point c i The decision, which can be used to fit complex data distributions, is calculated in the following way:

[0100] spline(x) = ∑ ic i B i (x) (8)

[0101] Where c i B is the coefficient optimized when training the network. i (x)(hereinafter referred to as N) i p(x), where p is the order, is a spline basis function defined by a recursive formula:

[0102] Zero-order (p=0) basis functions (step functions): Where [t0,t1,...,t N ] represents the node vector.

[0103] Higher-order (p>0) basis functions are obtained through recursive formulas:

[0104] N i,p (x)=w i,p (x)·N i,p-1 (x)+(1-w i+1,p (x))·N i+1,p-1 (x)

[0105]

[0106] Specifically, this invention improves the efficiency of KAN network data processing by optimizing the original KAN model: It introduces an adaptive grid size adjustment strategy, combining data distribution information, and calculates a new grid by weighting the adaptive grid and the uniform grid, then recalculates the spline weights. This adaptive grid update mechanism better adapts to different data distributions, improving the model's expressive power. Furthermore, the model's regularization term is improved by not only calculating the L1 regularization loss of the spline weights but also introducing an entropy regularization term to make the model parameters more sparse, thus improving the model's generalization ability. In calculating the regularization loss, a simple statistical mean operation on the spline weights replaces the complex calculation process of the original model, improving computational efficiency. In the calculation of the B-spline basis functions, the matrix tensor function is called, avoiding explicit loops and manual adjustment of the tensor's shape and dimensions, further improving computational efficiency compared to the original KAN model.

[0107] The task of the classification network is to map the frequency of gas features obtained from regression to specific gas components. Since there are one to three possible mixed gases, there are six candidate gases. If 0 / 1 represents the presence or absence of a gas, a six-dimensional 0 / 1 sequence can be used as the output, meaning the classification network belongs to the multi-label classification task. MLkNN is a simple, efficient, and highly interpretable multi-label classification algorithm. Its main advantages are its ease of implementation, lack of training process, high interpretability, and multi-label processing capability. The core idea of ​​MLkNN is to transform the multi-label classification problem into multiple binary classification problems and predict the label of the current sample using the label information of the nearest neighbor samples. For each test sample, the distance to all samples in the training set is calculated, and the k nearest training samples are found as the nearest neighbors. For each gas label l in the output, the number of samples containing that gas label, freq(l), is calculated in the k nearest neighbor samples, and then the posterior probability is calculated. If the posterior probability is greater than 0.5, the test sample x is considered to contain that gas. In the network task of this invention, the classification network is input with the gas feature frequencies obtained by the regression network. The results often have a small range of error compared with the true values. The classification network can be used to correct the small range of prediction errors to the true gas composition.

[0108] Figure 1 The diagram shows the overall network structure of this invention. First, the effective heat capacity values ​​at several frequency points are obtained from the sound velocity and sound absorption coefficient at several frequency points in the mixed gas. Second, the effective heat capacity decoupling equations are solved to obtain a dataset of relaxation information parameters for the mixed gas. Third, the dataset is used as network input data, and regression calculation is performed using the KAN algorithm to obtain the characteristic vibrational frequencies of the molecules contained in the mixed gas. Fourth, the MLkNN classification network algorithm is used to map the regressed gas vibrational frequencies to the specific types of gas molecules contained, thereby realizing the function of identifying the components of the mixed gas.

[0109] The machine learning network was trained using a five-fold cross-validation method, with a training set to test set ratio of 4:1. All programs ran on a server with the following configuration: Intel(R) Core(TM) i9-12900KF CPU, NVIDIA GeForce RTX3090Ti (24G) GPU, Windows 10, CUDA 11.6, and PyTorch 1.10.0.

[0110] (1) Performance of regression networks

[0111] The performance of the KAN-MLkNN network is evaluated below. First, the KAN regression network is compared with other classic regression networks: the KAN network contains three hidden layers with 256, 128, and 32 nodes respectively, a spline order of 4, and an initial grid value of 20. It is compared with the classic regression network MLP network model and the seven-dimensional single-channel deep residual network ResNet. Both models are optimized to the network structure best suited to the dataset of this invention. The MLP has four hidden layers with 256, 128, 64, and 16 nodes. The ResNet network increases the dimensionality to 256 through a fully connected layer, then reduces the dimensionality through two residual layers (256, 128) and (128, 32), and finally connects to the output layer through a fully connected layer.

[0112] The network performance is evaluated using the root mean square error (RMSE). RMSE is a commonly used parameter for evaluating the performance of regression networks; here, it is calculated as the deviation between the predicted gas vibration frequencies and the actual gas vibration frequencies.

[0113]

[0114] Where S represents the total number of samples. This represents the predicted and actual values ​​of the vibrational frequency of the k-th mode molecule in the i-th sample gas mixture. For the binary gas mixture dataset, the RMSE values ​​of MLP, ResNet, and KAN on the test set are 0.0613, 0.0497, and 0.0296, respectively. For the ternary gas mixture dataset, the RMSE values ​​of MLP, ResNet, and KAN on the test set are 0.1358, 0.1196, and 0.0521, respectively. Figure 2 The diagram shows the learning curves of three regression networks, which converge to the minimum network error after several rounds.

[0115] from Figure 2 It is evident that the KAN network has a significantly stronger fitting and regression ability than the MLP and ResNet networks when processing mixed gas relaxation information datasets. The mean square error decays much faster than other networks and remains at a low level. The final mean square error convergence value of KAN is more than half that of other networks.

[0116] (2) Classification of network performance

[0117] Next, the characteristic vibrational frequencies of gas molecules output from the regression network are input into the ML-KNN classification network for gas type identification. The k-value of the ML-KNN network ranges from 1 to 100, searching for the highest accuracy. Here, the accuracy of the multi-label classification network refers to the sample-level accuracy, that is, the proportion of samples that correctly predict the presence or absence of all six gases out of the total samples. For the mixture of two gases, the accuracy is highest when the k-value is 1, with a test set accuracy of 99.17%; for the mixture of three gases, the accuracy is highest when the k-value is 46, with a test set accuracy of 95.05%. Compared with the other two regression networks, the output results of the KAN network regression network improved by this invention show a significant improvement in accuracy on the same classification network (see Table 3).

[0118] Table 3. Classification accuracy of different regression networks after processing by classification networks.

[0119]

[0120] Furthermore, the Hamming loss, recall, precision, and F1 score of different regression networks were compared. Table 4 shows the network performance of the three different regression networks after passing them through the MLkNN classification network. Regardless of whether it is a mixture of two or three gases, the KAN network provided in this invention shows high reliability and effectiveness.

[0121] Table 4. Classification network performance on the KAN-MLkNN classification network for test sets of two and three mixed gases.

[0122]

[0123] The network's ability to identify individual gases was analyzed. Figure 3-14 The image shows the confusion matrix for a single gas generated by the classification network. The numbers on the diagonal represent the number of correct predictions (positive or negative). Those not on the diagonal are incorrect predictions. Positive examples indicate the presence of this gas.

[0124] Table 5 shows the recognition accuracy of the KAN-MLkNN neural network algorithm for each gas given in this invention. The recognition accuracy for each gas in the two mixed gas recognition networks is above 99.5%, and the recognition accuracy for each gas in the three mixed gas recognition networks is above 96.9%, which shows good recognition effect.

[0125] Table 5. Accuracy of machine learning network in identifying individual gases in a gas mixture.

[0126]

[0127] In summary, this invention decomposes the effective heat capacity of a gas mixture containing six candidate gases (CH4, N2, O2, Cl2, CO2, and SO2) based on a mixed gas acoustic relaxation decoupling model, and constructs binary and ternary mixed gas relaxation information parameter datasets respectively. A deep learning network for mixed gas vibration frequency detection is built, and the mixed gas relaxation information parameter data is regressed using a KAN network to obtain the characteristic vibration frequencies of gas molecules contained in the mixed gas. Then, an MLkNN network is used to obtain the correspondence between the characteristic vibration frequencies of gas molecules and the gas components, enabling the network to identify the gas components of a multi-component mixed gas.

[0128] Those skilled in the art will readily understand that the above description is merely a preferred embodiment of the present invention and is not intended to limit the present invention. Any modifications, equivalent substitutions, and improvements made within the spirit and principles of the present invention should be included within the scope of protection of the present invention.

Claims

1. A method for acoustic qualitative identification of mixed gas components based on deep learning networks, characterized in that, Includes the following steps: S1. Test the gas to be identified under preset temperature and pressure conditions, and obtain several sets of sound velocities and sound absorption coefficients corresponding to different sound wave frequencies. Then, calculate the effective heat capacity corresponding to several sets of the gas to be identified based on the several sets of sound velocities and sound absorption coefficients. S2. Decompose the effective heat capacity according to the mixed gas acoustic relaxation decoupling model to obtain gas relaxation information parameters; S3. Use the gas relaxation information parameters as input to the trained mixed gas vibration characteristic frequency detection network, that is, output the types of gases in the gas to be identified.

2. The acoustic qualitative identification method for mixed gas components based on deep learning networks according to claim 1, characterized in that, In step S2, the gas relaxation information parameters include the decomposition heat capacity, relaxation time, and external degree of freedom heat capacity of the relaxation process.

3. The acoustic qualitative identification method for mixed gas components based on deep learning networks according to claim 2, characterized in that, The acoustic relaxation decoupling model for the mixed gas is as follows: in, Indicates effective heat capacity, N represents the heat capacity of the external degrees of freedom, and N represents the number of vibration modes. This represents the decomposition heat capacity of the nth vibration mode. This represents the relaxation time of the nth vibration mode. Let a be the vibrational heat capacity of the internal degree of freedom of the j-th vibration mode. j Let ω represent the mole fraction of the j-th vibration mode, and ω represent the acoustic angular frequency. λ n h is the eigenvalue of the nth vibration mode of R. k V represents the vector of the k-th vibration mode of the H matrix. jn V' represents the element in the j-th row and n-th column of the eigenvector matrix V of R. jk V represents the inverse matrix of the eigenvectors of R. -1 The elements in the j-th row and k-th column are R and H, which are N×N energy transfer matrices calculated from the energy transfer rates between different vibration modes.

4. The acoustic qualitative identification method for mixed gas components based on deep learning networks according to claim 1, characterized in that, The mixed gas vibration characteristic frequency detection network consists of a KAN regression network and an MLkNN classification network. The KAN regression network is used to obtain the characteristic vibrational frequencies of gas molecules based on the gas relaxation information parameters; the MLkNN classification network is used to classify the gas types based on the characteristic vibrational frequencies of gas molecules.

5. The acoustic qualitative identification method for mixed gas components based on deep learning networks according to claim 4, characterized in that, The mixed gas vibration characteristic frequency detection network is trained using a mixed gas relaxation information parameter dataset, which is obtained by simulation calculation using the mixed gas acoustic relaxation decoupling model. The simulation calculation includes: selecting several groups of mixed gases from CH4, N2, O2, Cl2, CO2, and SO2, and using the mixed gas acoustic relaxation decoupling model to perform effective heat capacity decomposition, solving the equations at different acoustic frequencies, and obtaining a mixed gas relaxation information parameter dataset.

6. The acoustic qualitative identification method for mixed gas components based on deep learning networks according to claim 5, characterized in that, The mixed gas contains three or fewer types of gases. In step S1, the gas to be identified includes one or more of CH4, N2, O2, Cl2, CO2, and SO2, preferably three or fewer.

7. The acoustic qualitative identification method for mixed gas components based on deep learning networks according to claim 6, characterized in that, In step S1, the preset temperature and pressure are the same as those used in the simulation calculation; The sound wave frequency f includes 0.5 × 10⁻⁶. 3 Hz, 3×10 3 Hz, 8×10 3 Hz, 10×10 3 Hz, 15×10 3 Hz, 20×10 3 Hz and 40×10 3 Hz.

8. The acoustic qualitative identification method for mixed gas components based on deep learning networks according to claim 1, characterized in that, In step S1, the effective heat capacity is related to the sound velocity c and the sound absorption coefficient α. r The relation is: P0 represents gas pressure, ρ0 represents gas density, Ξ represents acoustic angular frequency, R = 8.31 is the gas molar constant, and i represents an imaginary number.

9. A training method for a mixed gas vibration characteristic frequency detection network, characterized in that, include: A KAN-MLkNN mixed gas vibrational characteristic frequency detection network was constructed, consisting of a KAN regression network and an MLkNN classification network. The input of the KAN regression network is the mixed gas relaxation information parameter dataset, and the output is the characteristic vibrational frequency of gas molecules; the input of the MLkNN classification network is the characteristic vibrational frequency of gas molecules, and the output is the gas type. Several groups of mixed gases were selected from CH4, N2, O2, Cl2, CO2, and SO2. The effective heat capacity decomposition was performed using the acoustic relaxation decoupling model of the mixed gas, and the equations at different acoustic frequencies were solved to obtain a dataset of mixed gas relaxation information parameters. The mixed gas relaxation information parameter dataset is used as the input to the KAN-MLkNN mixed gas vibration characteristic frequency detection network, and the gas type corresponding to each group of data in the mixed gas relaxation information parameter dataset is used as the output to train the KAN-MLkNN mixed gas vibration characteristic frequency detection network, thus obtaining the trained mixed gas vibration characteristic frequency detection network.

10. The training method for the mixed gas vibration characteristic frequency detection network according to claim 9, characterized in that, The training uses a five-fold cross-validation method, with a training set to test set ratio of 4:

1. The mixed gas contains three or fewer types of gases, and the sound wave frequency f includes 0.5 × 10⁻⁶. 3 Hz, 3×10 3 Hz, 8×10 3 Hz, 10×10 3 Hz, 15×10 3 Hz, 20×10 3 Hz, 40×10 3 Hz; The KAN regression network contains three hidden layers with 256, 128, and 32 nodes respectively, a spline order of 4, and an initial grid value of 20.

Images