An intelligent detection method for slurry density based on concept drift data stream

Abstract

The present invention discloses an intelligent detection method for ore pulp density oriented to concept drift data stream, including: obtaining artificial test value ore pulp density; obtaining linear model estimation value; obtaining data-driven model estimation value; obtaining estimation value and confidence interval of intelligent detection model; obtaining linear model estimation value and variance of estimation value; obtaining estimation value of density of nonlinear model; if estimation value is not within confidence interval, dynamic structural adjustment is performed to enhance generalization performance of model; otherwise, updating of overall model is completed; selecting a part of data to establish initial model according to Gaussian process regression and regularized random configuration method, respectively updating linear model and nonlinear model through stream data, combining detection results of two models to obtain final ore pulp density detection value. The present invention constructs an overall model composed of known linear model and unknown nonlinear model, and solves the accuracy and real-time problems existing in ore pulp density detection in industrial production process.

Description

Technical Field

[0001] The present invention relates to the technical field of detection of grinding and classification operations, and in particular to an intelligent detection method for ore pulp density oriented to concept drift data streams. Background Art

[0002] Slurry density is a key indicator of grinding and classification operations. It is crucial to metal recovery and concentrate grade, and also directly affects the efficiency and stability of the production process. At present, slurry density detection mainly adopts manual testing and densitometer detection methods, while artificial intelligence methods are rarely used in slurry density detection.

[0003] The most commonly used manual test method is the density pot method, which is to fill the density pot with slurry liquid, measure the weight with a spring balance or a platform scale, subtract the weight of the density pot, and finally calculate the density of the slurry manually according to the formula. The density meter detection method is a method of measuring the density of materials using precision instruments. The measurement principle of the density meter involves a series of physical concepts, and the density value is calculated based on the response of the medium to specific physical effects. According to different measurement principles, the density meter can be divided into ultrasonic density meter, gamma ray density meter, vibration tube density meter, electromagnetic density meter, etc.

[0004] However, changes in ore properties and fluctuations in mill loads make the slurry processing environment extremely complex. Traditional manual sampling and testing methods have problems such as high labor costs and slow response, and cannot monitor slurry density in real time, affecting processing efficiency and product quality. At the same time, existing density detection equipment based on acoustic, electromagnetic or radioactive principles is often costly and may pose environmental and safety risks. Summary of the invention

[0005] In view of the problems existing in the above-mentioned prior art, the present invention proposes an intelligent detection method for slurry density based on concept drift data stream, forming a set of slurry density measurement technology based on artificial intelligence algorithm, which can not only improve the detection accuracy and efficiency, but also reduce costs and environmental pollution. To achieve the above-mentioned purpose, the technical solution adopted by the present invention is as follows:

[0006] A method for intelligent detection of slurry density based on concept drift data stream includes the following steps:

[0007] S1: Analyze the mechanism of the slurry flow process in the pipeline, select auxiliary variables to establish the overall model of slurry density detection, and obtain the artificial test value slurry density ρ;

[0008] S2: Gaussian process regression is used to identify the linear part of the slurry density and obtain the linear model estimate

[0009] S3: The unknown nonlinear terms are fitted with a data-driven model, and the regularized random configuration is used as the data-driven algorithm to obtain the data-driven model estimate

[0010] S4: The results of linear regression estimation are combined with the results of nonlinear regression estimation to finally obtain the estimated value of the intelligent detection model. and the confidence interval

[0011] S5: Propose an online Gaussian process regression based on a sliding window to obtain the linear model estimate and the variance of the estimate σ 2 , and then get the mentor signal

[0012] S6: Update parameters online by combining regularization and forgetting mechanisms, dynamically adjust the model structure through network pruning and random configuration, and obtain the estimated value of the density of the nonlinear model

[0013] S7: When the estimate is not within the confidence interval In the process, the nonlinear model is dynamically adjusted through network pruning to enhance the generalization performance of the model; otherwise, the overall model is updated;

[0014] S8: A part of the data is selected to establish an initial model according to the Gaussian process regression and regularized random configuration methods, and then the linear model and the nonlinear model are updated respectively through the flow data, and the results of the two model detections are combined to obtain the final slurry density detection value.

[0015] In view of the problem that the slurry density detection model in the industrial environment faces the concept drift that leads to the degradation of model performance, the present invention proposes an intelligent slurry density detection method for concept drift data stream. This method uses an online Gaussian process regression method based on a sliding window to update the linear model parameters, introduces a forgetting mechanism to construct an online update recursive formula for the parameters of the nonlinear model, and uses network pruning and random configuration methods to dynamically adjust the nonlinear model structure, wherein the random configuration process combines weighted least squares and regularization methods to evaluate the model output weights. This method can improve the ability of the mechanism model to depict the dynamic relationship of the process, reduce the dependence of the data-driven model on old data, and use the latest data to describe the dynamic information of the current working conditions, thereby solving the concept drift problem of complex process data.

[0016] Compared with the prior art, the present invention has the following beneficial effects:

[0017] (1) The present invention proposes an intelligent detection method for slurry density based on concept drift data stream. By deeply analyzing the mechanism of slurry flow in the grinding process, an overall model consisting of a known linear model and an unknown nonlinear model is constructed to solve the accuracy and real-time problems existing in slurry density detection in the industrial production process.

[0018] (2) By applying the sliding window mechanism in the linear model and deriving the recursive formula of the model parameters, real-time online updating of the model is achieved.

[0019] (3) In order to enhance the adaptability of the nonlinear model to the new data distribution, a forgetting mechanism is introduced in the online update process of the neural network output weights, which reduces the weight of old data in the model update process and reduces the negative gain of historical data on the constructed model.

[0020] (4) Network pruning and random configuration techniques are used to dynamically optimize the model structure. At the same time, the weighted least squares method and regularization techniques are combined to evaluate the output weights to ensure that the degree of forgetting of historical data is maintained when the model structure is adjusted. BRIEF DESCRIPTION OF THE DRAWINGS

[0021] In order to more clearly illustrate the embodiments of the present invention or the technical solutions of the prior art, the following briefly introduces the drawings required for use in the embodiments or the description of the prior art. Obviously, the drawings described below are some embodiments of the present invention. For ordinary technicians in this field, other drawings can be obtained based on these drawings without paying creative work.

[0022] Figure 1 It is a closed circuit grinding process flow chart of the present invention;

[0023] Figure 2 is a flow chart of the method of the present invention;

[0024] Figure 3 Different models R 2 , comparison chart of minimum frequency of estimation error, TPR, TNR and δ<1.0%;

[0025] Figure 4 This is a comparison chart of RMSE and MAE of different models;

[0026] Figure 5 This is a comparison chart of the estimation error PDF of different models;

[0027] Figure 6 is the autocorrelation function of the estimation error of the OGPRSWM-FMRSC model. DETAILED DESCRIPTION

[0028] The following will be combined with the drawings in the embodiments of the present invention to clearly and completely describe the technical solutions in the embodiments of the present invention. Obviously, the described embodiments are only part of the embodiments of the present invention, not all of the embodiments. Based on the embodiments of the present invention, all other embodiments obtained by ordinary technicians in this field without creative work are within the scope of protection of the present invention.

[0029] Example

[0030] like Figure 1 As shown in the figure, a first-stage ball mill and a spiral classifier form a first-stage grinding closed circuit, and a second-stage ball mill, a cyclone and a pump pool form a second-stage grinding closed circuit. After the ore is treated to a certain extent, an appropriate amount of water is added to the first-stage ball mill for grinding, and a certain amount of water is added to the obtained slurry for classification through a classifier. The classifier returns the ore particles with larger particle size to the first-stage grinding machine for grinding, and the ore particles with smaller particle size enter the pump pool for second-stage grinding. A certain amount of water is added to the pump pool, and the slurry is sent to the cyclone through the slurry pump. The slurry is classified by the action of centrifugal force. The coarse-grained slurry is discharged from the bottom of the cyclone and enters the second-stage grinding machine for grinding. The fine-grained slurry overflows from the top of the cyclone and enters the subsequent selection process.

[0031] like Figure 2 As shown, the present invention provides a method for intelligent detection of slurry density based on concept drift data stream, comprising the following steps:

[0032] S1: Analyze the mechanism of the slurry flow process in the pipeline, select auxiliary variables to establish the overall model of slurry density detection, and obtain the artificial test value slurry density ρ; the details are as follows:

[0033] Ideally, if there is no resistance loss, the pressure difference is:

[0034] Δp=ρgΔH

[0035] Where ρ is the slurry density, g is the gravitational acceleration, and ΔH is the liquid level height difference. During the slurry flow, there will be resistance loss along the way, and the calculation formula is:

[0036]

[0037] Among them, γ is the resistance coefficient along the way, L is the pipe length, D is the pipe diameter, V is the average flow velocity of the section, and g is the gravitational acceleration; in the actual industrial process, the total pressure difference Δp = ρgΔH-H f , we can get:

[0038]

[0039] The common parameter for measuring density in industrial production is the differential pressure signal measured by pressure sensors placed at different heights, but directly using the differential pressure signal as the input of the detection model will affect the detection result. According to Bernoulli's law, the overall pressure of the fluid is constant. As the flow rate increases, the static pressure of the fluid will decrease, but the slurry pressure gauge can only measure the static pressure.

[0040] As the flow rate at the fluid inlet gradually increases, the dynamic pressure difference between the two points will also expand accordingly. The working principle of the traditional pressure sensor is to use the pressure of the liquid to induce compression deformation of the force-sensitive element, which will cause the resistance of the bridge to change, thereby generating a potential difference and outputting it, converting the pressure into an electrical signal output. This method can measure the static pressure difference of the liquid, but cannot measure the dynamic pressure difference. Therefore, directly using the pressure difference signal as the input of the density measurement model may affect the measurement results to some extent. In addition, when using a pressure instrument for pressure measurement, systematic errors and random errors will occur. Therefore, it is necessary to measure the measured absolute pressure p on the high-pressure side. H And low pressure side absolute pressure p L Make corresponding corrections, and the pressure difference measured at time t is Δp(t) = p H (t)-p L (t) is rewritten as:

[0041] Δp(t)=Ap H (t)-Bp L (t)+C+l1(p H (t),p L (t))

[0042] Among them, A and B are the correction coefficients of high pressure and low pressure, C is the offset term, l1(·) represents the unknown nonlinear error when measuring pressure; the unknown nonlinear expression of the average flow velocity V and the current i and frequency f of the slurry pump is as follows:

[0043] V(t)=l2(f(t),i(t))

[0044] Arranged:

[0045] ρ(t)=ρ0(t)+Δρ(t)

[0046] in,

[0047] ρ0(t)=k1p H (t)+k2p L (t)+k3

[0048] Δρ(t)=l(p H (t),p L (t),f(t),i(t))

[0049]

[0050] Where l(·) represents the unknown nonlinear term including instrument measurement error and slurry flow process.

[0051] S2: Gaussian process regression is used to identify the linear part of the slurry density and obtain the linear model estimate The details are as follows:

[0052] According to the acquisition time sequence observation point t=k-1,...,kN t Get the training data set, represented as {X off,lin (k-1),Y off,lin (k-1)};

[0053] definition Then we have:

[0054]

[0055] ε represents the noise that follows a Gaussian distribution, and The likelihood function of the target observation sample is obtained as:

[0056]

[0057] In the formula, E is the unit matrix; assuming the parameters The prior probability distribution of According to the Bayesian formula:

[0058]

[0059] in, When t = k, the data When input, the probability distribution of the output value of the mechanism model is:

[0060]

[0061] is the linear model estimation result, Variance estimated for Gaussian process regression.

[0062] S3: The unknown nonlinear terms are fitted with a data-driven model, and the regularized random configuration is used as the data-driven algorithm to obtain the data-driven model estimate The details are as follows:

[0063] Given a training dataset {X off,non (k-1),Y off,non (k-1)}, given the objective function Assuming that the number of nodes in the current hidden layer is L-1, the output of the neural network is:

[0064]

[0065] In the formula, β j represents the output weight of hidden layer node j; g j (·) represents the jth activation function; ω j and b j Respectively represent the input weight and bias of the jth hidden node in the hidden layer; calculate the network output residual:

[0066]

[0067] The maximum number of hidden layer nodes is L max , the expected accuracy is ∈; if L≤L max ,‖e L-1 ‖ 2 >∈, then add the Lth hidden layer node and let e L-1 =[e L-1,1 ,e L-1,2 ], the output h of the hidden layer node L is obtained by the following two equations respectively L and supervision mechanism L,q ,q=1,2;

[0068]

[0069] In the formula, Given 1-∈<r<1, let μ L =(1-r) / (L+1), C is the regularization coefficient. Random configuration T max Each time, the input weight ω of the Lth hidden layer node will be randomly selected within a certain range. L and bias b L , and calculate ξ L,q ,q=1,2; if minξ L,1 ,ξ L,2 ≥0, then ω L , b L , L,q Store; if all ξ L,q If none of them meet the conditions, a larger r value will be selected for reconfiguration; after the random configuration is completed, the largest The corresponding ω L , b L As the input weight and bias of the Lth node;

[0070] After determining the model structure and input weights, calculate the output weight β:

[0071]

[0072] In the formula, HL =[h1,h2,...,h L ], E is the unit matrix;

[0073] Finally, the estimated value of the data-driven model at time t=k is obtained, which is expressed as:

[0074]

[0075] S4: The results of linear regression estimation are combined with the results of nonlinear regression estimation to finally obtain the estimated value of the intelligent detection model. and the confidence interval

[0076] S5: Propose an online Gaussian process regression based on a sliding window to obtain the linear model estimate and the variance of the estimate σ 2 ; The details are as follows:

[0077] Given a dataset {X on,lin (k+N str -1),Y on,lin (k+N str -1)}, linear model initialization stage, {X on,lin (k-1),Y on,lin (k-1)} is used to construct the initial linear model; the posterior distribution of the parameters estimated based on this N0 set of training data is obtained as:

[0078]

[0079] in,

[0080]

[0081] After adding new samples and discarding earlier historical data, the dataset Updated to The newly added samples are The discarded samples are recorded as After the data sample is updated, Updated to The key issue in updating the linear model is to convert A -1 (k-1) is updated to A -1 (k), A(k) is:

[0082]

[0083] The computational complexity of A(k) mainly comes from matrix multiplication. According to the original formula, the computational complexity is N w represents the sliding window size, and the recursive calculation complexity is because Therefore, the derived recursive formula is used for online updating of the linear model to reduce the amount of calculation and improve the calculation efficiency; the inverse operation of A(k) is performed to obtain the updated parameters and calculate the new incoming flow data samples The density estimate and variance of are:

[0084]

[0085] S6: Update parameters online by combining regularization and forgetting mechanisms, dynamically adjust the model structure through network pruning and random configuration, and obtain the estimated value of the density of the nonlinear model The details are as follows:

[0086] Given a dataset {X on,non (k+N str -1),Y on,non (k+N str -1)}, nonlinear model initialization stage, {X on,non (k-1),Y on,non (k-1)} is used to construct the initial nonlinear model; if a regularized random configuration network with L hidden nodes is constructed based on this N0 set of training data, the output layer weight β k-1 The optimization goal is:

[0087]

[0088] H k-1 Indicates that the output of the hidden layer node of the nonlinear model is initialized with N0 sets of training data, and C represents the regularization term coefficient. The solution is:

[0089]

[0090] When the N0+1th group of data arrives at the model, the weights need to be updated with the latest data. In order to reduce the impact of past data on the update of model parameters, a forgetting mechanism is introduced to achieve this goal. When the neural network structure and the input layer weights remain unchanged, the new output layer weights β are obtained. k Optimization goal:

[0091]

[0092] θ k represents the forgetting factor, h k represents the hidden layer node output calculated from the N0+1th group of data, and there is Written in the following form:

[0093]

[0094] in,

[0095]

[0096] The solution is:

[0097]

[0098] In order to satisfy the requirement that the parameters can be updated online, it is required to pass β k-1 Recursive calculation of β k , the formula is derived as follows:

[0099]

[0100] make We can get:

[0101]

[0102] From this, we can get the output weight recursion formula with forgetting mechanism; by analogy, when the N0+i2th group of data reaches the model, we have:

[0103]

[0104] in,

[0105]

[0106] The recursive formula is:

[0107]

[0108] in,

[0109]

[0110] S7: When the estimate is not within the confidence interval In the process, the nonlinear model is dynamically adjusted through network pruning to enhance the generalization performance of the model; otherwise, the overall model is updated; the details are as follows:

[0111] Online adjustment of the output layer parameters can achieve the purpose of adapting the model to new data. However, as the working conditions change and the data distribution changes, the learning ability of the neural network is not enough to cope with the new data characteristics. At this time, adjusting the model structure can effectively enhance the model's ability to adapt to data. The present invention proposes a model dynamic structure adjustment strategy based on network pruning to optimize the model structure, and optimizes parameters for the random configuration network characteristics; assuming that a regularized random configuration network with L hidden layer nodes has been constructed based on N0 groups of training data, the neural network output is:

[0112]

[0113] is the regularized random configuration network output with L hidden layer nodes without network structure adjustment, β j,0 ,g j,0 ,ω j,0 ,b j,0 They are respectively represented as the output weight of hidden node j, the jth activation function, the input weight of the jth hidden node, and the bias of the jth hidden node before the network structure is adjusted; when the new data stream arrives at the model and the accuracy still cannot meet the requirements after updating the parameters of the linear model and the nonlinear model, the nonlinear model structure needs to be adjusted. The adjustment discriminant formula is described as:

[0114]

[0115] When the difference between the value estimated by the nonlinear model and the nonlinear label is greater than three standard deviations, the model structure needs to be dynamically adjusted; after pruning the I-th hidden layer node, the model output is:

[0116]

[0117] Then, the network residual change can be expressed as:

[0118]

[0119] Compare the impact of each hidden layer node on the change of model output residual, according to ΔF (1) <ΔF (2) <...<ΔF (L) Sort and select the N with the least impact prun nodes and prune them, N prun satisfy and where σ p The clipping factor is used to determine the number of clipped nodes; the output of the nonlinear model after clipping is expressed as The current network residual size is as follows:

[0120]

[0121] Add nodes based on the supervision mechanism:

[0122]

[0123] in,

[0124]

[0125] Indicates the LNth training with N0+1 group data prun +1 hidden layer node nonlinear model hidden layer output; given 1-∈<r<1, let C is the regular term coefficient; then calculate the output weight:

[0126]

[0127] After adding the node, the network output is:

[0128]

[0129] Then, it is determined whether the network output error meets the preset error requirements; if so, the model construction is completed; otherwise, new hidden layer nodes are added according to the supervision mechanism to build the network to minimize the output error of the model until the termination condition is met.

[0130] S8: A part of the data is selected to establish an initial model according to the Gaussian process regression and regularized random configuration methods, and then the linear model and the nonlinear model are updated respectively through the flow data, and the results of the two model detections are combined to obtain the final slurry density detection value.

[0131] S9: 800 data sets are selected and divided into 1:3. The first 1 / 4 of the data sets are used for initial model training, and the last 3 / 4 of the data sets are streaming data. After each set of data reaches the model, the estimation error is calculated. After the model is updated according to this set of data, the next set of data reaches the model, and the cumulative RMSE and MAE and evaluation indicators are calculated to compare the performance of different models. In order to illustrate the effectiveness and superiority of the intelligent detection method for concept drift data streams proposed in the present invention, the method of the present invention is compared with some models, and the model introduction is as follows:

[0132] (1) OGPRSWM-FMRSC is a new algorithm proposed by the present invention. The linear model is an online Gaussian process regression based on a sliding window, and the nonlinear model is a regularized random configuration network based on a forgetting mechanism.

[0133] (2) OGPR-FMRSC, the linear model is an ordinary online Gaussian process regression, no sliding window is used, and historical data is not discarded. Then the update formula of the key parameters should be as shown above, and the nonlinear model is the same as the algorithm proposed in the present invention.

[0134]

[0135] (3) OGPRSWM-OSSC: the linear model is the same as the algorithm proposed in the present invention, and the nonlinear model is updated online using an online sequence random configuration method.

[0136] (4) OGPRSWM-OSRSC, the linear model is the same as the algorithm proposed in the present invention, and the nonlinear model is updated online using the online sequence regularization random configuration method. The online recursive formula of the output weight is as follows:

[0137]

[0138] in,

[0139] (5) OGPRSWM-FWRSC: The linear model is the same as the algorithm proposed in the present invention, and the nonlinear model updates the output weights according to the model parameter online updating method proposed in the present invention, without dynamically adjusting the model structure.

[0140] The R of five models was calculated. 2 , estimated minimum error frequency, δ<1.0%, MAE, RMSE, and also introduced the upward trend estimation accuracy (True positive rate, TPR) and downward trend estimation accuracy (True negative rate, TNR). The mathematical expressions of the newly introduced indicators are as follows:

[0141]

[0142] TP, FP, TN, and FN are the number of samples with correct upward trend estimation, the number of samples with incorrect upward trend estimation, the number of samples with correct downward trend estimation, and the number of samples with incorrect downward trend estimation, respectively.

[0143] Figure 3 For different models R 2 , the minimum frequency of estimation error, TPR, TNR and δ<1.0%, Figure 4 Comparison of RMSE and MAE of different models. From the overall detection effect, the method OGPRSWM-FMRSC of the present invention performs better than other models in all indicators. Specifically, the performance of the OGPRSWM-FMRSC model exceeds that of the OGPR-FMRSC model, indicating the effectiveness of the sliding window mechanism in the linear model in dealing with concept drift. At the same time, the overall detection effects of the four models OGPRSWM-FMRSC, OGPRSWM-FWRSC, OGPRSWM-OSRSC, and OGPRSWM-OSSC weakened in turn, indicating that the dynamic structural adjustment of the model proposed in this chapter, the output weight update strategy combining the forgetting mechanism and the regularized least squares method are all feasible.

[0144] Table 1 Evaluation of model detection results

[0145]

[0146] In Table 1, the performance evaluation indicators of the models constructed by the five algorithms in slurry density detection are compared. The OGPRSWM-FMRSC model proposed in this invention shows relatively good performance, which is specifically manifested in lower MAE and RMSE, which are 6.11 and 7.56 respectively. 2 It reaches 99.40%, which is close to 1, indicating that the model prediction has a high degree of fit with the actual data. In terms of the proportion of sample relative error less than δ<1.0%, the OGPRSWM-FMRSC model reaches 91%, while its TPR and TNR are 75.88% and 76.39% respectively, which are slightly better than the other four comparison algorithms. This result shows that the OGPRSWM-FMRSC model has high accuracy and generalization performance in the task of slurry density detection.

[0147] like Figure 5 The error probability density functions of the five models are shown in Table 2. The error distribution of the OGPRSWM-FMRSC model is close to 0 compared with other models, and the distribution curves mostly show a single peak, which is consistent with the characteristics of the Gaussian distribution, indicating that the error sequence is close to randomness. Figure 6 As shown in the figure, the error autocorrelation function diagram of the OGPRSWM-FMRSC model shows that it is close to the white noise level, and the estimation error is mainly a random error, rather than a deviation caused by the poor generalization performance of the model itself, indicating that the model has better estimation performance and generalization ability. It shows that the OGPRSWM-FMRSC model is more suitable for application in a changing industrial production environment, and compared with other models, it may show more stable performance under specific working conditions.

Claims

1. An intelligent detection method for slurry density based on concept drift data stream, characterized in that: The steps include: S1: Analyze the mechanism of the slurry flow process in the pipeline, select auxiliary variables to establish the overall model of slurry density detection, and obtain the artificial test value slurry density ρ; S2: Gaussian process regression is used to identify the linear part of the slurry density and obtain the linear model estimate S3: The unknown nonlinear terms are fitted with a data-driven model, and the regularized random configuration is used as the data-driven algorithm to obtain the data-driven model estimate S4: The results of linear regression estimation are combined with the results of nonlinear regression estimation to finally obtain the estimated value of the intelligent detection model. and the confidence interval S5: Propose an online Gaussian process regression based on a sliding window to obtain the linear model estimate and the variance of the estimate σ 2 , and then get the mentor signal Step S5 is specifically as follows: Given a dataset {X on,lin (k+N str -1),Y on,lin (k+N str -1)}, linear model initialization stage, {X on,lin (k-1),Y on,lin (k-1)} is used to construct the initial linear model; the posterior distribution of the parameters estimated based on the N0 sets of training data is obtained as follows, where N0 represents the number of training samples in the data pool, and N str Indicates the number of stream data, i2 indicates the index, and X on,lin (k+i2) represents the first k+i2 input data for linear model training, Y on,lin (k+i2) represents the output data for the first k+i2 hours of linear model training, y on,lin (k+i2) represents the k+i2th output data for linear model training: in, After adding new samples and discarding earlier historical data, the dataset Updated to The newly added samples are The discarded samples are recorded as After the data sample is updated, Updated to The key issue in updating the linear model is to convert A -1 (k-1) is updated to A -1 (k), A(k) is: The computational complexity of A(k) mainly comes from matrix multiplication. According to the original formula, the computational complexity is N w represents the sliding window size, and the recursive calculation complexity is because Therefore, the derived recursive formula is used for online updating of the linear model to reduce the amount of calculation and improve the calculation efficiency; the inverse operation of A(k) is performed to obtain the updated parameters and calculate the new incoming flow data samples The density estimate and variance of are: S6: Update parameters online by combining regularization and forgetting mechanisms, dynamically adjust the model structure through network pruning and random configuration, and obtain the estimated value of the density of the nonlinear model Step S6 is specifically as follows: Given a dataset {X on,non (k+N str -1),Y on,non (k+N str -1)}, nonlinear model initialization stage, {X on,non (k-1),Y on,non (k-1)} is used to construct the initial nonlinear model, where X on,non (k+i2) represents the first k+i2 hours of input data used for nonlinear model training, Y on,non (k+i2) represents the output data for the first k+i2 hours of nonlinear model training, y on,non (k+i2) represents the k+i2th output data for nonlinear model training; if a regularized random configuration network with L hidden nodes is constructed based on this N0 set of training data, the output layer weight β k-1 The optimization goal is: H k-1 Indicates that the output of the hidden layer node of the nonlinear model is initialized with N0 sets of training data, and C represents the regularization term coefficient. The solution is: When the N0+1th group of data arrives at the model, the weights need to be updated with the latest data. In order to reduce the impact of past data on the update of model parameters, a forgetting mechanism is introduced to achieve this goal. When the neural network structure and the input layer weights remain unchanged, the new output layer weights β are obtained. k Optimization goal: θ k represents the forgetting factor, h k represents the hidden layer node output calculated from the N0+1th group of data, and there is Written in the following form: in, The solution is: In order to satisfy the requirement that the parameters can be updated online, it is required to pass β k-1 Recursive calculation of β k , the formula is derived as follows: make We can get: This gives us the recursive formula for the output weights with a forgetting mechanism. Similarly, when the N0+i2th group of data reaches the model, we have: in, The recursive formula is: in, S7: When the estimate is not within the confidence interval In the process, the nonlinear model is dynamically adjusted through network pruning to enhance the generalization performance of the model; otherwise, the overall model is updated; Step S7 is specifically as follows: Assume that a regularized random configuration network with L hidden nodes has been constructed based on N0 sets of training data, x on,non (k+i2) represents the k+i2th input data for nonlinear model training, and the neural network output is: is the regularized random configuration network output with L hidden nodes without network structure adjustment, β j,0 ,g j,0 ,ω j,0 ,b j,0 They are respectively represented as the output weight of hidden node j, the jth activation function, the input weight of the jth hidden node, and the bias of the jth hidden node before the network structure is adjusted; when the new data stream arrives at the model and the accuracy still cannot meet the requirements after updating the parameters of the linear model and the nonlinear model, the nonlinear model structure needs to be adjusted. The adjustment discriminant formula is described as: When the difference between the value estimated by the nonlinear model and the nonlinear label is greater than three standard deviations, the model structure needs to be dynamically adjusted; after pruning the I-th hidden layer node, the model output is: Then, the network residual change is expressed as: Compare the impact of each hidden layer node on the change of model output residual, according to ΔF (1) <ΔF (2) <...<ΔF (L) Sort and select the N with the least impact prun nodes and prune, N prun satisfy where σ p The clipping factor is used to determine the number of clipped nodes; the output of the nonlinear model after clipping is expressed as The current network residual size is as follows: Add new nodes based on the supervision mechanism: in, Indicates the LNth training with N0+1 group data prun +1 hidden layer node nonlinear model hidden layer output; the expected accuracy is ψ, given 1-ψ<r<1, let C is the regular term coefficient; then calculate the output weight: After adding the node, the network output is: Then, determine whether the network output error meets the preset error requirements; if so, the model construction is completed; otherwise, add new hidden layer nodes according to the supervision mechanism to build the network to minimize the output error of the model until the termination condition is met; S8: A part of the data is selected to establish an initial model according to the Gaussian process regression and regularized random configuration methods, and then the linear model and the nonlinear model are updated respectively through the flow data, and the results of the two model detections are combined to obtain the final slurry density detection value.

2. The intelligent detection method for slurry density based on concept drift data stream according to claim 1 is characterized in that: Step S1 is specifically as follows: Ideally, if there is no resistance loss, the pressure difference is: Δp=ρgΔH Where ρ is the slurry density, g is the gravitational acceleration, and ΔH is the liquid level height difference. During the slurry flow, there will be resistance loss along the way, and the calculation formula is: Among them, γ is the resistance coefficient along the way, L is the pipe length, D is the pipe diameter, V is the average flow velocity of the section, and g is the gravitational acceleration; in the actual industrial process, the total pressure difference Δp = ρgΔH-H f , we can get: In addition, when using pressure instruments to measure pressure, systematic errors and random errors will occur, so the measured absolute pressure p on the high-pressure side H And low pressure side absolute pressure p L Make corresponding corrections, and the pressure difference measured at time t is Δp(t) = p H (t)-p L (t) is rewritten as: Δp(t)=Ap H (t)-Bp L (t)+C+l1(p H (t),p L (t)) Among them, A and B are the correction coefficients of high pressure and low pressure, C is the offset term, l1(·) represents the unknown nonlinear error when measuring pressure; the unknown nonlinear expression of the average flow velocity V and the current i and frequency f of the slurry pump is as follows: V(t)=l2(f(t),i(t)) Arranged: ρ(t)=ρ0(t)+Δρ(t) in, ρ0(t)=k1p H (t)+k2p L (t)+k3 Δρ(t)=l(p H (t),p L (t),f(t),i(t)) Where l(·) represents the unknown nonlinear term including instrument measurement error and slurry flow process.

3. The intelligent detection method for slurry density based on concept drift data stream according to claim 2 is characterized in that: Step S2 is specifically as follows: According to the acquisition time sequence observation point t=k-1,...,kN t Get the training data set, represented as {X off,lin (k-1),Y off,lin (k-1)}, where N t represents the number of training samples in the data pool, X off,lin (k-1) represents the first k-i1 input data in the data pool for linear model training, Y off,lin (k-1) represents the output data of the first k-i1 seconds in the data pool for linear model training, where i1 represents the index; definition Then we have: ε represents the noise that follows a Gaussian distribution, and The likelihood function of the target observation sample is obtained as: Where E is the unit matrix, x off,lin (k-i1) represents the k-i1th moment input data in the data pool for linear model training, y off,lin (k-i1) represents the k-i1th moment output data in the data pool for linear model training; assuming the parameters The prior probability distribution of According to the Bayesian formula, we can get: in, When t = k, the data When input, the probability distribution of the output value of the mechanism model is: is the linear model estimation result, Variance estimated for Gaussian process regression.

4. The intelligent detection method for slurry density based on concept drift data stream according to claim 1 is characterized in that: Step S3 is as follows: Given a training dataset {X off,non (k-1),Y off,non (k-1)}, where X off,non (k-i1) represents the first k-i1 input data in the data pool for nonlinear model training, Y off,non (k-i1) represents the first k-i1 output data in the data pool for nonlinear model training; given the objective function F: Assuming that the number of nodes in the current hidden layer is L-1, the output of the neural network is: In the formula, β j represents the output weight of hidden layer node j; g j (·) represents the jth activation function; ω j and b j They represent the input weight and bias of the jth hidden node in the hidden layer respectively; Calculate the network output residual: The maximum number of hidden layer nodes is L max , the expected accuracy is ψ; if L≤L max ,‖e L-1 ‖ 2 >ψ, then add the Lth hidden layer node and let e L-1 =[e L-1,1 ,e L-1,2 ], the output h of the hidden layer node L is obtained by the following two equations respectively L and supervision mechanism L,q ,q=1,2; In the formula, x off,non (k-i1) represents the k-i1th input data in the data pool for nonlinear model training. Given 1-ψ<r<1, let μ L =(1-r) / (L+1), C is the regularization coefficient, and T is randomly configured max Each time, the input weight ω of the Lth hidden layer node will be randomly selected within a certain range. L and bias b L , and calculate ξ L,q ,q=1,2;if minξ L,1 ,ξ L,2 ≥0, then ω L , b L , L,q Store; if all ξ L,q If none of them meet the conditions, a larger r value will be selected for reconfiguration; after the random configuration is completed, the largest The corresponding ω L , b L As the input weight and bias of the Lth node; After determining the model structure and input weights, calculate the output weight β: In the formula, H L =[h1,h2,...,h L ], E is the unit matrix; Finally, the estimated value of the data-driven model at time t=k is obtained, which is expressed as:

5. The intelligent detection method for slurry density based on concept drift data stream according to claim 1 is characterized in that: The method also includes step S9: selecting 800 sets of data sets and dividing them into 1:3, with the first 1 / 4 of the data sets used for initial model training and the last 3 / 4 of the data sets used as streaming data; after each set of data reaches the model, the estimation error is calculated, and after the model is updated based on the set of data, the next set of data reaches the model, thereby calculating the cumulative RMSE, MAE and evaluation indicators for comparing the performance of different models.

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