Oxygen-enriched spray gun service life prediction technology based on digital-analog linkage

Abstract

The invention discloses an oxygen-enriched spray gun service life prediction technology based on digital-analog linkage, and belongs to the technical field of non-ferrous metal pyrogenic smelting, and the technology comprises the following steps: carrying out wavelet noise reduction processing on original oxygen-enriched spray gun data to reduce data noise, and normalizing the data by adopting a max-min method; a nonlinear MLPs network is adopted to extract a scalar composite health index from the high-dimensional features, and a Wiener process is used to parameterize the composite health index; deriving and obtaining a probability density function of the oxygen-enriched spray gun life based on a first arrival time concept, and further obtaining a mean value and a variance; adopting maximum likelihood estimation to obtain an optimal estimation value of a Wiener model parameter; an objective function of a training model is constructed based on historical oxygen-enriched spray gun data, and optimal model parameters are obtained by combining a particle swarm optimization algorithm and an Adam algorithm. According to the method, the reliable oxygen-enriched spray gun service life prediction value can be provided, then an operator is guided to replace the oxygen-enriched spray gun in time, and the method has important significance in reducing the use cost of the oxygen-enriched spray gun and improving the oxygen-enriched copper smelting efficiency and quality.

Description

Technical Field

[0001] The invention belongs to the technical field of nonferrous metal pyrometallurgy smelting, and in particular relates to a life prediction technology of an oxygen-enriched lance based on digital-analog linkage. Background Art

[0002] The oxygen-enriched top-blown copper smelting process has a long process flow and a complex reaction mechanism, and its normal operation is affected by many process steps. The oxygen-enriched lance not only provides the oxygen-enriched air and fuel necessary to support the smelting process, but also promotes the reaction by stirring the melt. It is the core component in the oxygen-enriched top-blown copper smelting process. At present, the service life of the oxygen-enriched lance can only be judged by manual experience, and it is very important to implement soft measurement of the life of the oxygen-enriched lance. The rapid development of sensor technology and data analysis technology has provided new possibilities for the prediction of the life of the oxygen-enriched lance. For life prediction, there are generally two approaches in the existing technology, namely data-driven modeling and mechanism knowledge modeling. Data-driven modeling collects real-time monitoring data during the operation of the oxygen-enriched lance, uses machine learning, deep learning and other algorithms to process and analyze the data, and constructs a prediction of the remaining life of the oxygen-enriched lance. Mechanism knowledge modeling is to deeply analyze the degradation mechanism of the equipment, build a degradation model of the equipment based on the existing physical knowledge, and then obtain the failure time of the equipment, that is, the service life of the equipment.

[0003] According to the survey, the existing technology still has many shortcomings. First, the existing data-driven modeling only relies on a large amount of data to discover the model, and it is difficult to establish a model with high credibility and good generalization for small sample data, and the constructed model has poor interpretability. Secondly, mechanism knowledge modeling requires a lot of manpower and material resources to deeply analyze the mechanism of equipment degradation, and for equipment with complex working conditions (such as oxygen-enriched spray guns), it is difficult to fully understand its degradation mechanism, which makes it almost impossible to obtain a degradation mechanism model with good practicality. Finally, according to the survey, few scholars have studied the prediction method of the life of oxygen-enriched spray guns. Some scholars have used SVM to establish an oxygen-enriched spray gun life prediction model, but its prediction accuracy is unsatisfactory. Therefore, in order to overcome the limitations of the prior art, the present invention proposes a life prediction technology for oxygen-enriched spray guns based on digital-analog linkage. Summary of the invention

[0004] In view of the above problems of the prior art, the present invention proposes a life prediction technology of an oxygen-enriched spray gun based on digital-analog linkage.

[0005] To achieve the above object, the technical solution adopted by the present invention is: a technology for predicting the life of an oxygen-enriched spray gun based on digital-analog linkage, comprising the following steps:

[0006] S1. Preprocess the original data of the oxygen-enriched spray gun and establish a database; the original data includes: operation process data and actual production data;

[0007] Preprocessing includes:

[0008] S1.1, using wavelet denoising based on sym4 wavelet basis function to process the original data;

[0009] S1.2. The modeling database is formed by max-min normalization; the expression is as follows:

[0010]

[0011] In the formula, is the normalized data of the ith sensor, x i '(t) is the raw data x of the i-th sensor i (t) Data after wavelet denoising;

[0012] S2. Construct a digital-analog linkage prediction model; the steps are as follows:

[0013] S2.1. Use MLPs to extract composite health indicators (composite health indicators are also called random degradation features); the expression is as follows:

[0014] y t =Uσ(Wx t + b);

[0015] In the formula, x t =[x1(t),x2(t),...,x n (t)] T is the normalized data of all sensors at time t; W∈R m ×n is the total weight of the input layer; b∈R m×1 is the input layer bias; σ(·) is the Sigmoid activation function; U∈R 1×m is the output layer weight;

[0016] S2.2. Use Wiener process to parameterize composite health index; the expression is as follows:

[0017]

[0018] In the formula, is the drift coefficient that characterizes the degradation rate, is the diffusion coefficient, w t is the standard Brownian motion representing the dynamics of the composite health indicator;

[0019] in, and It is obtained based on the maximum likelihood estimation theory;

[0020] S2.3, define the life of the oxygen-enriched spray gun based on the first arrival time;

[0021]

[0022] Where, L k is the life of the oxygen-enriched spray gun; inf{} is a mathematical operator, indicating the lower bound; l k Indicates that the composite health indicator meets the conditions , the value at time t; Indicates the composite health index at t k +l k The value at the time; v is the failure threshold corresponding to the composite health indicator; y t represents the value of the composite health index at sampling time t;

[0023] S2.4. Based on the Wiener process and the life of the oxygen-enriched spray gun, the probability density function of the oxygen-enriched spray gun life is defined and derived; the expression is as follows:

[0024]

[0025] In the formula, are the model parameters of the Wiener process; is the location parameter of the inverse Gaussian distribution; is the shape parameter of the inverse Gaussian distribution; y k represents the composite health index value at sampling time k;

[0026] S2.5. Calculate the mean and variance of the probability density function of the oxygen-enriched spray gun life, and use the mean as the predicted value of the oxygen-enriched spray gun life; the expression is as follows:

[0027]

[0028] In the formula, Indicates the life of the oxygen-enriched spray gun L k The mean under the model parameter Θ of the Wiener process, Indicates the life of the oxygen-enriched spray gun L k Variance under the model parameter Θ of the Wiener process;

[0029] S2.6. Obtain the model parameter estimates of the Wiener process based on the maximum likelihood estimation theory; the details are as follows:

[0030] S2.6.1. Construct the likelihood function for maximum likelihood estimation; the expression is as follows:

[0031]

[0032] In the formula, In[·] represents the natural logarithmic function; L(Θ) is the independent variable of the function, which represents the life under the model parameter Θ of the Wiener process; Δt is the sampling period; Δyk =y k -y k-1 It represents the increment of the composite health index extracted by the kth sampling, which is a time series. k and k-1 They represent the composite health index values ​​of the oxygen-enriched spray gun at the kth sampling and the k-1th sampling respectively; K represents the total number of sampling times of the sensor in the life cycle of an oxygen-enriched spray gun;

[0033] S2.6.2. Obtain model parameter estimates of the Wiener process based on maximum likelihood estimation theory;

[0034] The expression is as follows:

[0035]

[0036] Where, t K is the use time of the oxygen-enriched spray gun; tK The oxygen-enriched spray gun is used for a period of time t K y0 is the composite health index value of the oxygen-enriched spray gun at the initial moment;

[0037] The expression is as follows:

[0038]

[0039] In the formula, Δy k =y k -y k-1 It represents the increment of the composite health index extracted by the kth sampling, which is a time series;

[0040] S3, use PSO and Adma algorithm to train the digital-analog linkage model by minimizing the objective function to obtain the optimal model parameters; the steps are as follows:

[0041] S3.1. Construct the objective function of the optimization problem:

[0042]

[0043] In the formula, K is the predicted value of oxygen-enriched spray gun life; n’ is the final sampling time of the n'th oxygen-enriched spray gun; y Kn’,n’ Indicates that the n'th oxygen-enriched spray gun is at time K n’ Composite health index value; y 0,n’ represents the composite health index value of the n'th oxygen-enriched spray gun at the initial moment; T n’ is the true value of the life of the n'th oxygen-enriched spray gun; N is the sample capacity of the training set; n' represents the sample in the training set;

[0044] S3.2, use PSO algorithm to preliminarily optimize the objective function;

[0045] The particle position update formula is:

[0046]

[0047] In the formula, v o (j) is the velocity of particle o in the jth step; p o (j) is the position of particle o in the jth step; is the particle with the best fitness function in the particle swarm in the jth step; is the particle with the best global fitness value before the j+1th step; w is the inertia weight, which indicates the influence of the speed of the jth step on the speed of the j+1th step; c1 and c2 are the first acceleration factor and the second acceleration factor of the particles in the particle swarm; r1 and r2 are the first and second random numbers uniformly distributed in the interval [0,1];

[0048] S3.3, using the result of the preliminary optimization of the objective function as the initial value of the Adma algorithm to continue optimizing the objective function until the preset number of iterations reaches 20;

[0049] The update formula of the parameters to be optimized is:

[0050]

[0051] Where θ represents W, U, b and v; m θ and θ are the first and second order moment estimates of θ respectively; ▽θ represents the gradient of θ; β1 and β2 are the first exponential decay rate and the second exponential decay rate of the Adam algorithm; α is the learning rate; ∈ is a constant to maintain numerical stability; ⊙ represents the Hadamard product;

[0052] S4. Verify the effect of the digital-analog linkage model through performance indicators;

[0053] Performance indicators include: prediction score, root mean square error, and coefficient of determination;

[0054] The details are as follows:

[0055] S4.1. Calculate the prediction score ;

[0056] Prediction score The smaller the better, the theoretical value is 0; the expression is as follows:

[0057]

[0058] Where exp(·) represents an exponential function with e=2.718 as the base; N1 is the number of all samples (including the sample capacity of the training set and the test set); n” Represents samples of the training set and the test set;

[0059] S4.2, calculate the root mean square error RMSE;

[0060] The smaller the root mean square error, the better, and the theoretical value is 0; the expression is as follows:

[0061]

[0062] In the formula, K is the predicted value of oxygen-enriched spray gun life; n” For the n” The final sampling time of the oxygen-enriched lance; y kn”,n” Indicates n” The oxygen-enriched spray gun is at time K n” Composite health index value; y 0,n” Indicates n” The composite health index value of an oxygen-enriched spray gun at the initial moment; T n” For the n” The actual life of the oxygen-enriched spray gun; n” represents a sample among all samples;

[0063] S4.3. Calculation of the coefficient of determination R 2 ;

[0064] The larger the coefficient of determination, the better, and the theoretical value is 1; the expression is as follows:

[0065]

[0066] Beneficial effects of the present invention:

[0067] This method first uses MLPs to extract scalar random degradation features from high-dimensional data, and uses the random degradation features as the composite health index of the oxygen-enriched spray gun. Then, the composite health index is parameterized using the Wiener process, and the mean and variance of the oxygen-enriched spray gun life are derived in combination with mathematical statistics. Then, the model parameter estimation value of the Wiener process is given based on the maximum likelihood estimation. The present invention organically combines the data model and the mechanism model to construct the life prediction model of the oxygen-enriched spray gun, greatly giving play to the advantages of the two types of modeling methods, so that the constructed model has the characteristics of excellent effect, high credibility and good practicality.

[0068] The present invention uses PSO algorithm and Adma optimization algorithm to optimize the objective function, initializes the initial value of Adma algorithm with the help of PSO's powerful search ability, avoids Adma algorithm from falling into local optimum, and then obtains more accurate model parameters with the help of the excellent performance of Adma algorithm. The organic combination of PSO algorithm and Adma optimization algorithm makes the trained model have superior performance, greatly increasing the credibility and practicality of the constructed model.

[0069] The method proposed in the present invention is applied to the measured data of a certain factory. The results show that the method proposed in the present invention can more accurately predict the life of the oxygen-enriched spray gun, which not only provides a new research idea for studying the life of the oxygen-enriched spray gun, but also provides a valuable reference for guiding workers to replace the spray gun in time, which is of great significance for ensuring the stable and reliable operation of the oxygen-enriched copper smelting equipment. BRIEF DESCRIPTION OF THE DRAWINGS

[0070] Figure 1 The flowchart of the present invention is:

[0071] Figure 2 This is a flow chart of the oxygen-enriched spray gun life prediction technology and system based on digital-analog linkage;

[0072] Figure 3 The original data is the data after wavelet denoising and normalization;

[0073] Figure 4 This is the flow chart of PSO+Adma algorithm;

[0074] Figure 5 It is the fitness function diagram of the PSO+Adma optimization model in Example 1;

[0075] Figure 6 The true value, training set predicted value and test set predicted value of the life of the oxygen-enriched lance in Example 1 are shown in FIG.

[0076] Figure 7 This is the prediction absolute error diagram on the test set and training set in Example 1. DETAILED DESCRIPTION

[0077] In order to better illustrate the purpose, technical solutions and advantages of the present invention, the present invention will be further described below in conjunction with specific embodiments.

[0078] In this embodiment, the day and night shift data of a factory from 2021 to 2023 is taken as an example. The collected raw data includes 12 characteristic variables: minimum temperature (℃): x1(t), maximum temperature (℃): x2(t), average oxygen-enriched spray gun air flow (Nm 3 / s): x3(t), minimum shaft load (t): x4(t), maximum shaft load (t): x5(t), maximum end pressure (kPa): x6(t), minimum end pressure (kPa): x7(t), maximum back pressure (kPa): x8(t), minimum back pressure (kPa) x9(t), thermocouple TE1602-2 (℃): x 10 (t), Thermocouple TE1602-3 (℃): x 11 (t), melt temperature (℃): x 12 (t);

[0079] like Figure 1 , Figure 2 As shown, a life prediction technology and system of oxygen-enriched spray gun based on digital-analog linkage, the steps are as follows:

[0080] S1. Preprocessing the original data of the oxygen-enriched spray gun and establishing a database;

[0081] The original data includes: operation process data and actual production data, which in this embodiment includes 12 characteristic variables;

[0082] Preprocessing includes:

[0083] S1.1, using wavelet denoising based on sym4 wavelet basis function to process the original data;

[0084] S1.2. The modeling database is formed by max-min normalization; the expression is as follows:

[0085]

[0086] In the formula, is the normalized data of the ith sensor, x i '(t) is the raw data x of the i-th sensor i (t) data after wavelet denoising, in this embodiment, i=1, 2, ..., 12; original data x i (t) After

[0087] Data after wavelet denoising and normalization See Figure 3 ;

[0088] S2. Construct a digital-analog linkage prediction model; the steps are as follows:

[0089] S2.1. Use MLPs to extract composite health indicators (composite health indicators are also called random degradation features); the expression is as follows:

[0090] y t =Uσ(Wx t + b);

[0091] In the formula, x t =[x1(t),x2(t),...,x n (t)] T is the normalized data of all sensors at time t, n is 12 in this embodiment; W∈R m×n is the total weight of the input layer, m is 4 in this embodiment; b∈R m×1 is the input layer bias; σ(·) is the Sigmoid activation function; U∈R 1×m is the output layer weight; the values ​​of the input layer full weight W, input layer bias b and output layer weight U obtained by training the model are as follows:

[0092]

[0093] b=[-42.21 51.72 33.70 5.26] T ;

[0094] U=[-7.72 4.56 -59.25 43.08];

[0095] The Sigmoid activation function expression is:

[0096]

[0097] Wherein, z represents the independent variable of the Sigmoid function, and e=2.718 is a natural constant.

[0098] S2.2. Use Wiener process to parameterize composite health index; the expression is as follows:

[0099]

[0100] In the formula, is the drift coefficient that characterizes the degradation rate, is the diffusion coefficient, w t is the standard Brownian motion representing the dynamics of the composite health indicator;

[0101] in, and It is obtained based on the maximum likelihood estimation theory;

[0102] S2.3, define the life of the oxygen-enriched spray gun based on the first arrival time;

[0103]

[0104] Where, L k is the life of the oxygen-enriched spray gun; inf{} is a mathematical operator, indicating the lower bound; l k Indicates that the composite health indicator meets the conditions , the value at time t; Indicates the composite health index at t k +l k The value at the moment; v is the failure threshold corresponding to the composite health indicator, and the failure threshold obtained by training the model is v = -59.25; y t represents the value of the composite health index at sampling time t;

[0105] S2.4. Based on the Wiener process and the life of the oxygen-enriched spray gun, the probability density function of the oxygen-enriched spray gun life is defined and derived; the expression is as follows:

[0106]

[0107] In the formula, is the model parameter of the Wiener process, which is automatically generated by the software according to different oxygen-enriched spray guns; is the position parameter of the inverse Gaussian distribution, which is automatically generated by the software according to different oxygen-enriched spray guns; is the shape parameter of the inverse Gaussian distribution, which is automatically generated by the software according to different oxygen-enriched spray guns; k represents the composite health index value at sampling time k;

[0108] S2.5. Calculate the mean and variance of the probability density function of the oxygen-enriched spray gun life, and use the mean as the predicted value of the oxygen-enriched spray gun life; the expression is as follows:

[0109]

[0110] In the formula, Indicates the life of the oxygen-enriched spray gun L k The mean under the model parameter Θ of the Wiener process, Indicates the life of the oxygen-enriched spray gun L k Variance under the model parameter Θ of the Wiener process;

[0111] S2.6. Obtain the model parameter estimates of the Wiener process based on the maximum likelihood estimation theory; the details are as follows:

[0112] S2.6.1. Construct the likelihood function for maximum likelihood estimation; the expression is as follows:

[0113]

[0114] Where, In[·] represents the natural logarithmic function; L(Θ) is the independent variable of the function, which represents the life under the condition of the model parameter Θ of the Wiener process; Δt is the sampling period, in this embodiment, Δt = 0.5 day; Δy k =y k -yk-1 It represents the increment of the composite health index extracted by the kth sampling, which is a time series. k and k-1 They represent the composite health index values ​​of the oxygen-enriched spray gun at the kth sampling and the k-1th sampling respectively; K represents the total number of sampling times of the sensor in the life cycle of an oxygen-enriched spray gun;

[0115] S2.6.2. Obtain model parameter estimates of the Wiener process based on maximum likelihood estimation theory;

[0116] The expression is as follows:

[0117]

[0118] Where, t K The usage time of the oxygen-enriched spray gun; The oxygen-enriched spray gun is used for a period of time t K y0 is the composite health index value of the oxygen-enriched spray gun at the initial moment;

[0119] The expression is as follows:

[0120]

[0121] In the formula, Δy k =y k -y k-1 It represents the increment of the composite health index extracted by the kth sampling, which is a time series;

[0122] S3, use PSO and Adma algorithm to train the digital-analog linkage model by minimizing the objective function to obtain the optimal model parameters; the steps are as follows:

[0123] S3.1. Construct the objective function of the optimization problem:

[0124]

[0125] In the formula, K is the predicted value of oxygen-enriched spray gun life; n’ is the final sampling time of the n'th oxygen-enriched spray gun; y Kn’,n’ Indicates the nth ’ The oxygen-enriched spray gun is at time K n’ Composite health index value; y 0,n’ represents the composite health index value of the n'th oxygen-enriched spray gun at the initial moment; T n’ is the true value of the life of the n'th oxygen-enriched spray gun; N is the sample capacity of the training set, N = 26; n' represents the sample in the training set; the fitness function diagram of the PSO+Adma optimization model is shown in Figure 5 ;

[0126] S3.2, use PSO algorithm to preliminarily optimize the objective function;

[0127] The particle position update formula is:

[0128]

[0129] In the formula, v o (j) is the velocity of particle o in the jth step; p o (j) is the position of particle o in the jth step; is the particle with the best fitness function in the particle swarm in the jth step; is the particle with the best global fitness value before the j+1th step; w=0.95 is the inertia weight, which indicates the influence of the speed of the jth step on the speed of the j+1th step; c1=2.5 and c2=1.2 are the first acceleration factor and the second acceleration factor of the particle in the particle swarm; r1 and r2 are the first random number and the second random number uniformly distributed in the interval [0,1]; in this embodiment, a particle in this application refers to a set of feasible solutions in the search space, specifically a set of values ​​of the model parameters W, U, b and v; the step size of j is 1, and in this embodiment, j∈[1,2,...,15], which is an integer; each particle in the particle swarm can calculate a scalar objective function value using the S3.1 formula, and the particle corresponding to the minimum objective function is the best particle;

[0130] S3.3, using the result of the preliminary optimization of the objective function as the initial value of the Adma algorithm to continue optimizing the objective function until the preset number of iterations reaches 20;

[0131] The update formula of the parameters to be optimized is:

[0132]

[0133] Where θ represents W, U, b and v; m θ and θ are the first-order and second-order moment estimates of θ, respectively; ▽θ represents the gradient of θ; β1 and β2 are the first exponential decay rate and the second exponential decay rate of the Adam algorithm, with default values ​​of 0.9 and 0.999, respectively; α is the learning rate, with a default value of 0.001; ∈ is a constant for maintaining numerical stability, with a default value of 10 -8 ;PSO+Adma algorithm flow chart see Figure 4 ; ⊙ represents the Hadamard product;

[0134] S4. Verify the effect of the digital-analog linkage model through performance indicators;

[0135] Performance indicators include: prediction score, root mean square error, and coefficient of determination;

[0136] The details are as follows:

[0137] S4.1. Calculate the prediction score ;

[0138] Prediction score The smaller the better, the theoretical value is 0; the expression is as follows:

[0139]

[0140] Where exp(·) represents an exponential function with e=2.718 as the base; N1=53 is the number of all samples (including the sample capacity of the training set and the test set); n” Represents samples of the training set and the test set;

[0141] S4.2, calculate the root mean square error RMSE;

[0142] The smaller the root mean square error, the better, and the theoretical value is 0; the expression is as follows:

[0143]

[0144] In the formula, K is the predicted value of oxygen-enriched spray gun life; n” For the n "The final sampling time of the oxygen-enriched lance; y kn”,n” Indicates n "An oxygen-enriched spray gun at time K n” Composite health index value; y 0,n” Indicates n” The composite health index value of an oxygen-enriched spray gun at the initial moment; T n” For the n” The actual life of the oxygen-enriched spray gun; n” represents a sample among all samples;

[0145] S4.3. Calculation of the coefficient of determination R 2 ;

[0146] The larger the coefficient of determination, the better, and the theoretical value is 1; the expression is as follows:

[0147]

[0148] Table 1 shows the performance index values ​​of the algorithm proposed in the present invention; the actual value of the oxygen-enriched lance life, the training set predicted value and the test set predicted value are shown in FIG. Figure 6 , and the prediction absolute error graphs on the test set and training set are shown in Figure 7 ;

[0149] Table 1 Performance index values ​​of the proposed method

[0150]

[0151] It can be seen from Table 1 that compared with the prior art, the prediction score of the method proposed in the present invention can reach 0.9460, RMSE can reach 1.2476h, R 2 It reaches 0.9996, which is very close to the expected performance index value, which is enough to show that the method proposed in the present invention has good modeling effect on the problem of oxygen-enriched lance life prediction, high credibility and good practicality, and can fully meet the actual production needs of the factory;

[0152] In summary, the oxygen-enriched spray gun life prediction technology based on digital-analog linkage proposed in the present invention not only provides a new idea for studying the life of oxygen-enriched spray guns, but also can provide decision-making guidance for on-site operators to replace spray guns in a timely manner.

[0153] Finally, it should be noted that the above embodiments are only used to illustrate the technical solution of the present invention rather than to limit the scope of protection of the present invention. Although the present invention has been described in detail with reference to the preferred embodiments, those skilled in the art should understand that the technical solution of the present invention can be modified or replaced by equivalents without departing from the essence and scope of the technical solution of the present invention.

Claims

1. A technology for predicting the life of an oxygen-enriched spray gun based on digital-analog linkage, characterized in that: The steps include: S1. Preprocess the original data of the oxygen-enriched spray gun and establish a database; The original data includes: operation process and actual production data The pre-processing comprises: S1.1, using wavelet denoising based on sym4 wavelet basis function to process the original data; S1.2, forming a modeling database through maximum and minimum normalization; S2, build a digital-analog linkage prediction model; S3, using particle swarm and deep learning optimization algorithms to train the digital-analog linkage model by minimizing the objective function to obtain the optimal model parameters; S4. Verify the effect of the digital-analog linkage model under the optimal model parameters through performance indicators; Performance indicators include: prediction score, root mean square error, and coefficient of determination.

2. The oxygen-enriched spray gun life prediction technology based on digital-analog linkage according to claim 1 is characterized in that: The steps of constructing the digital-analog linkage prediction model are as follows: S2.

1. Use MLPs to extract composite health indicators; the expression is as follows: y t =Uσ(Wx t +b); In the formula, x t =[x1(t),x2(t),...,x n (t)] T is the normalized data of all sensors at time t; W∈R m×n is the total weight of the input layer; b∈R m×1 is the input layer bias; σ(·) is the Sigmoid activation function; U∈R 1×m is the output layer weight; S2.

2. Use Wiener process to parameterize composite health index; the expression is as follows: In the formula, is the drift coefficient that characterizes the degradation rate, is the diffusion coefficient, w t is the standard Brownian motion representing the dynamics of the composite health indicator; in, and It is obtained based on the maximum likelihood estimation theory; S2.

3. Define the oxygen-enriched spray gun life based on the first arrival time. The expression is as follows: Where, L k is the life of the oxygen-enriched spray gun; inf{} is a mathematical operator, indicating the lower bound; l k Indicates that the composite health indicator meets the conditions , the value at time t; Indicates the composite health index at t k +l k The value at the time; v is the failure threshold corresponding to the composite health indicator; y t represents the value of the composite health index at sampling time t; S2.

4. Based on the Wiener process and the life of the oxygen-enriched spray gun, the probability density function of the oxygen-enriched spray gun life is defined and derived. The expression is as follows: In the formula, are the model parameters of the Wiener process; is the location parameter of the inverse Gaussian distribution; is the shape parameter of the inverse Gaussian distribution; is the drift coefficient that characterizes the degradation rate, is the diffusion coefficient, y k represents the composite health index at sampling time k; S2.

5. Calculate the mean and variance of the probability density function of the oxygen-enriched spray gun life, and use the mean as the predicted value of the oxygen-enriched spray gun life; the expression is as follows: In the formula, Indicates the life of the oxygen-enriched spray gun L k The mean under the model parameter Θ of the Wiener process, Indicates the life of the oxygen-enriched spray gun L k Variance under the model parameter Θ of the Wiener process; S2.

6. Obtain the model parameter estimates of the Wiener process based on the maximum likelihood estimation theory; the details are as follows: S2.6.

1. Construct the likelihood function for maximum likelihood estimation; the expression is as follows: In the formula, In[·] represents the natural logarithmic function; L(Θ) is the independent variable of the function, which represents the life under the model parameter Θ of the Wiener process; Δt is the sampling period; Δy k =y k -y k-1 It represents the increment of the composite health index extracted by the kth sampling, which is a time series. k and k-1 They represent the composite health index values ​​of the oxygen-enriched spray gun at the kth sampling and the k-1th sampling respectively; K represents the total number of sampling times of the sensor in the life cycle of an oxygen-enriched spray gun; S2.6.

2. Calculate the model parameters of the Wiener process based on the maximum likelihood estimation theory; The expression is as follows: Where, t K is the use time of the oxygen-enriched spray gun; tK is the composite health index value of the oxygen-enriched spray gun during its use time; y0 is the composite health index value of the oxygen-enriched spray gun at the initial moment; The expression is as follows: In the formula, Δy k =y k -y k-1 It represents the increment of the composite health indicator extracted by the kth sampling, which is a time series.

3. The oxygen-enriched spray gun life prediction technology based on digital-analog linkage according to claim 1 is characterized in that: The steps of using the particle swarm algorithm and the deep learning optimization algorithm to train the digital-analog linkage model by minimizing the objective function and obtaining the optimal model parameters are as follows: S3.

1. Construct the objective function of the optimization problem, which is expressed as follows: In the formula, K is the predicted value of oxygen-enriched spray gun life; n’ is the final sampling time of the n'th oxygen-enriched spray gun; y Kn’,n’ Indicates that the n'th oxygen-enriched spray gun is at time K n’ Composite health index value; y 0,n’ represents the composite health index value of the n'th oxygen-enriched spray gun at the initial moment; T n’ is the true value of the life of the n'th oxygen-enriched spray gun; N is the sample capacity of the training set; S3.2, use PSO algorithm to preliminarily optimize the objective function; The particle position update formula is: p o (j+1)=p o (j)+v o (j+1); In the formula, v o (j) is the velocity of particle o in the jth step; p o (j) is the position of particle o in the jth step; is the particle with the best fitness function in the particle swarm in the jth step; is the particle with the best global fitness value before the j+1th step; w is the inertia weight, which indicates the influence of the speed of the jth step on the speed of the j+1th step; c1 and c2 are the first acceleration factor and the second acceleration factor of the particles in the particle swarm; r1 and r2 are the first and second random numbers uniformly distributed in the interval [0,1]; S3.3, using the result of the preliminary optimization of the objective function as the initial value of the Adma algorithm to continue optimizing the objective function until the preset number of iterations reaches 20; The update formula of the parameters to be optimized is: Where θ represents W, U, b and v; m θ and θ are the first-order and second-order moment estimates of parameter θ, respectively; ▽θ represents the gradient of parameter θ; β1 and β2 are the first exponential decay rate and the second exponential decay rate of the Adam algorithm; α is the learning rate; ε is a constant for maintaining numerical stability.

4. The oxygen-enriched spray gun life prediction technology based on digital-analog linkage according to claim 1 is characterized in that: The steps for verifying the effect of the digital-analog linkage model through performance indicators are as follows: S4.

1. Calculate prediction scores S4.2, calculate the root mean square error RMSE; S4.

3. Calculation of the coefficient of determination R 2 .

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