Industrial process modeling method for output binary quantization

Abstract

The invention discloses an output binary quantization-oriented industrial process modeling method, which comprises the following steps of: inputting pre-acquired ore pulp concentration data and quantization output data of an ore pulp concentration sensor into a four-order finite impulse response (FIR) system obtained by training to obtain model parameters; wherein the step of training to obtain the fourth-order finite impulse response system FIR comprises the following steps: step 1, constructing the fourth-order finite impulse response system FIR; step 2, obtaining an observation data set; step 3, initializing an estimation parameter of a fourth-order finite impulse response system FIR; 4, calculating to obtain estimation output, estimation quantization output and the like; and step 5, judging whether k reaches a preset number of iterations N, if not, repeating the step 4, and if not, obtaining an estimation parameter of the fourth-order finite impulse response system FIR.

Description

Technical Field

[0001] The invention relates to an industrial process modeling method oriented to output binary quantization, belonging to the technical field of industrial process modeling. Background Art

[0002] In recent years, coal preparation plants have achieved automated or semi-automated production, significantly improving efficiency and reducing costs. Sludge flotation, a key step in coal sorting, is a complex process that relies heavily on sensor-based monitoring of key variables. However, in actual industrial production, to reduce production costs, sensors have large quantization intervals and low precision, often resulting in inaccurate output data due to quantization errors. This inaccurate quantization error not only affects the monitoring and control of flotation parameters (such as foam layer thickness, gas-liquid ratio, and slurry concentration), but can also further impair flotation efficiency and sorting effectiveness.

[0003] In the coal slime flotation process, commonly used sensor quantified variables include optical signals for froth image analysis, instantaneous flow signals from gas flowmeters, and electrical output signals from slurry concentration meters. Inaccurate quantization errors in sensor outputs can cause deviations in the values ​​of these sensor quantified variables, affecting the control of key processes such as flotation reagent addition and agitation intensity adjustment. This information loss and noise amplification in the quantization process pose significant challenges to system modeling and control accuracy.

[0004] Currently, there is a lack of effective solutions to the modeling challenges caused by sensor quantization in coal slime flotation. Directly using quantized outputs for system identification can significantly reduce the accuracy of model parameter identification due to information loss and uncertainty accumulation. Summary of the Invention

[0005] The technical problem to be solved by the present invention is to overcome the shortcomings of the existing technology and provide an industrial process modeling method for binary output quantization. For FIR system models whose output is a binary quantized signal, the present invention designs a system identification algorithm based on the least squares criterion. By introducing weight terms into the error function, the error function remains differentiable under binary quantization conditions, thereby achieving optimal identification of model parameters. The present invention derives and defines an error function form that adapts to the characteristics of the quantized signal, ensuring that the error function can accurately describe the identification characteristics of the quantized output signal.

[0006] Preferably, the present invention provides an industrial process modeling method for output binary quantization, comprising:

[0007] Inputting the pre-acquired slurry concentration data and the quantitative output data of the slurry concentration sensor into the trained fourth-order finite impulse response system FIR to obtain model parameters;

[0008] Among them, the training obtains the fourth-order finite impulse response system FIR, including:

[0009] Step 1: Construct a fourth-order finite impulse response system FIR:

[0010] y(k)=a1u(k)+a2u(k-1)+a3u(k-2)+a4u(k-3)+v(k),

[0011] Where u(k) is the k-th system input sequence, y(k) is the k-th system output sequence; a1, a2, a3, a4 are the model parameters of the fourth-order finite impulse response system FIR, and v(k) is the measurement noise of the k-th fourth-order finite impulse response system FIR; v(k) is set to zero-mean Gaussian white noise, and v(k) obeys the distribution is the variance of the measurement noise v(k);

[0012] Step 2: Obtain an observation data set, which includes the slurry concentration u as the input signal of the fourth-order finite impulse response system FIR 1:N and the quantized output electrical signal s of the slurry concentration sensor as the output signal of the fourth-order finite impulse response system FIR 1:N ;

[0013] Step 3: Initialize the estimated parameters of the fourth-order finite impulse response system FIR α k , is the model parameter, α k is the learning rate;

[0014] Step 4, according to Calculate the estimated output and estimate the quantized output Where Φ(k)=[u(k),u(k-1),u(k-2),u(k-3)] T represents the input column vector for the kth iteration;

[0015] Based on the formula get

[0016] Based on the normalization formula get

[0017] Step 5: Determine whether k reaches the preset number of iterations N. If not, repeat step 4 above. Otherwise, obtain the estimated parameters of the fourth-order finite impulse response system FIR. a 1,N is the estimated value of parameter a1 obtained after the Nth iteration, a 2,N is the estimated value of parameter a2 obtained after the Nth iteration, a 3,Nis the estimated value of parameter a3 obtained after the Nth iteration, a 4,N is the estimated value of parameter a4 obtained after the Nth iteration.

[0018] Preferably, in step 2, an observation data set is obtained, the observation data set including the slurry concentration u as the input signal of the fourth-order finite impulse response system FIR 1:N and the quantized output electrical signal s of the slurry concentration sensor as the output signal of the fourth-order finite impulse response system FIR 1:N ,include:

[0019] Determine the error signal E(k) of the fourth-order finite impulse response system FIR:

[0020]

[0021] Where d(k) is the desired output signal;

[0022] Based on the mean square expectation value of the error, calculate the objective function J(θ k ):

[0023]

[0024] In the formula, E() represents the mathematical expectation of the formula in the brackets.

[0025] Preferably, step 2 comprises:

[0026] Calculate the objective function with respect to the parameter vector θ k Gradient

[0027]

[0028] Based on the principle of gradient descent, the update rule for the parameter vector is determined as follows:

[0029]

[0030] Where μ is the learning rate of the gradient descent method;

[0031] The update rule for determining the parameter vector is:

[0032]

[0033] Among them, α k =-2μ is the learning rate.

[0034] Preferably, step 2 comprises:

[0035] Minimize the criterion function Get the parameter estimate for the k+1th iteration for:

[0036]

[0037] Will As The weight of , we get:

[0038]

[0039] Normalization get

[0040] Preferably, step 3 comprises:

[0041] Initialize the parameters to be estimated and learning rate α k , the number of iterations k is set to 1;

[0042] Get the known input data {u 1:N};

[0043] Step 3-2, the known output data {y 1:N} Input quantizer to get quantized output data {s 1:N}, build recognition data set C obs ={u 1:N ,s 1:N};

[0044] Step 3-3, according to Calculate the estimated output Will After quantization by the quantizer, the estimated quantized output is obtained

[0045] Step 3-4, by formula get By normalization formula get

[0046] Step 3-5, iterate steps 3-3 and 3-4 to obtain the model parameters of the fourth-order finite impulse response system FIR The convergence condition of the iterative loop is k=N, where N is the preset number of iterations.

[0047] Preferably, the present invention provides an electronic device comprising a memory, a processor, and a computer program stored in the memory and executable on the processor, wherein the processor implements the steps of any one of the methods described in the first aspect when executing the program.

[0048] Preferably, the present invention provides a computer-readable storage medium having a computer program stored thereon, which implements the steps of any one of the methods described in the first aspect when executed by a processor.

[0049] The beneficial effects achieved by the present invention are:

[0050] This paper designs a system identification method based on the least squares criterion for FIR system models whose output is a binary quantized signal. By introducing weight terms into the error function, the error function remains differentiable under binary quantization conditions, thereby achieving optimal identification of model parameters. The present invention derives and defines an error function form that adapts to the characteristics of the quantized signal, ensuring that the error function accurately describes the identification characteristics of the quantized output signal. BRIEF DESCRIPTION OF THE DRAWINGS

[0051] In order to more clearly illustrate the technical solution of the present application, the following is a brief introduction to the drawings required for use in the embodiments. Obviously, for ordinary technicians in this field, other drawings can be obtained based on these drawings without any creative work.

[0052] Figure 1 This is a principle block diagram of the present invention.

[0053] Figure 2 This is a curve diagram of the estimated parameters a1 and a2 of the BRLS method of the present invention and the traditional RLS method when the output is binary quantized to {-1, 1}.

[0054] Figure 3 This is a curve diagram of the estimated parameters a3 and a4 of the BRLS method of the present invention and the traditional RLS method when the output is binary quantized to {-1, 1}.

[0055] Figure 4 The present invention provides a flow chart for obtaining a fourth-order finite impulse response (FIR) system through training using the method of the present invention. DETAILED DESCRIPTION

[0056] See also Figure 1 The present invention is divided into a training phase and an application phase. The training phase includes the following steps:

[0057] The training obtains the fourth-order finite impulse response system FIR, including:

[0058] like Figure 4 As shown, step 1, construct a fourth-order finite impulse response system FIR:

[0059] y(k)=a1u(k)+a2u(k-1)+a3u(k-2)+a4u(k-3)+v(k),

[0060] Where u(k) is the k-th system input sequence, y(k) is the k-th system output sequence; a1, a2, a3, a4 are the model parameters of the fourth-order finite impulse response system FIR, and v(k) is the measurement noise of the k-th fourth-order finite impulse response system FIR; v(k) is set to zero-mean Gaussian white noise, obeying the distribution in is the variance of the measurement noise v(k);

[0061] Step 2: Obtain an observation data set, which includes the slurry concentration u as the input signal of the fourth-order finite impulse response system FIR 1:N and the quantized output electrical signal s of the slurry concentration sensor as the output signal of the fourth-order finite impulse response system FIR 1:N ;

[0062] Step 3: Initialize the estimated parameters of the fourth-order finite impulse response system FIR α k ;in is the estimated model parameter, α k is the learning rate;

[0063] Step 4, according to Calculate the estimated output and estimate the quantized output Where Φ(k)=[u(k),u(k-1),u(k-2),u(k-3)] T represents the input column vector for the kth iteration;

[0064] Based on the formula get

[0065] According to the normalization formula get

[0066] Step 5: Determine whether k reaches the preset number of iterations N. If not, repeat step 4 above. Otherwise, obtain the estimated parameters of the fourth-order finite impulse response system FIR. a 1,N is the estimated value of parameter a1 obtained after the Nth iteration, a 2,N is the estimated value of parameter a2 obtained after the Nth iteration, a 3,N is the estimated value of parameter a3 obtained after the Nth iteration, a 4,N is the estimated value of parameter a4 obtained after the Nth iteration.

[0067] The application phase includes the following steps:

[0068] The slurry concentration data and the quantitative output data of the slurry concentration sensor in the coal slime flotation process are obtained, and the trained fourth-order finite impulse response system FIR is input to obtain the model parameters.

[0069] Example

[0070] The present invention provides an industrial process modeling method for output binary quantization, which reduces the impact of quantization errors on the modeling process and improves the reliability and accuracy of system identification. The method comprises the following steps:

[0071] Step 1: The present invention uses the slurry concentration during the coal slime flotation process as the system input signal and the quantized output electrical signal of the slurry concentration sensor as the system output. This system is modeled as a fourth-order finite impulse response (FIR) system. Specifically, the system input signal is generated through the fourth-order finite impulse response (FIR) system to generate an output signal. The sensor quantizer then quantizes the output signal to obtain a binary quantized signal of {1, -1}, which ultimately constitutes the identification data set used for model identification.

[0072] Step 2: For a fourth-order finite impulse response (FIR) system whose output is a binary quantized signal, the present invention designs a system identification algorithm based on the least squares criterion. By introducing weight terms into the error function, the error function remains differentiable under binary quantization conditions, thereby achieving optimal identification of the model parameters. The present invention defines an error function form that adapts to the characteristics of the quantized signal, ensuring that it can accurately describe the identification characteristics of the quantized output signal.

[0073] Step 3: Based on the identification data set and the error function with weight terms, iteratively update under the framework of recursive least squares algorithm to obtain the parameters to be identified.

[0074] In step 1, the fourth-order finite impulse response system FIR model is expressed as:

[0075] y(k)=a1u(k)+a2u(k-1)+a3u(k-2)+a4u(k-3)+v(k),

[0076] Where u(k) is the system input sequence, y(k) is the system output sequence; a1, a2, a3, a4 are the model parameters of the fourth-order finite impulse response system FIR, and v(k) is the measurement noise of the fourth-order finite impulse response system FIR; v(k) is set to zero-mean Gaussian white noise, obeying the distribution in is the variance of the noise v(k).

[0077] In step 1, the input signal u(k) is passed through a discrete time invariant linear system H(z -1) is filtered to generate the scalar output y(k) of the fourth-order finite impulse response system FIR; the discrete time invariant linear system H(z -1 ) has a finite length L = 4 impulse response, that is, the impulse response can be expressed as a column vector θ = [a1, a2, a3, a4] T , then the output y(k) of the discrete time invariant linear system is related to the estimated output It can be expressed as:

[0078] y(k)=θ T Φ(k)

[0079]

[0080] in, represents the estimated parameters of the kth iteration; Φ(k)=[u(k),u(k-1),u(k-2),u(k-3)] T Represents the input column vector of the kth iteration. The output of the fourth-order finite impulse response system FIR is quantized by a one-bit AD converter and defined as where s k Represents the quantized output of the system output sequence y(k) after quantization by the quantizer; Represents the estimated output The estimated quantized output after quantization by the quantizer; S(x) represents the quantizer and is defined as:

[0081]

[0082] Step 2 includes:

[0083] Step 2-1: Starting from the general least mean square algorithm (LMS), derive a practical LMS-like method that can solve the FIR identification problem of a fourth-order finite impulse response system with quantized output. The derivation process is as follows:

[0084] Step 2-1-1: Define the desired output signal as d(k), then the error signal E(k) of the fourth-order finite impulse response system FIR is defined as:

[0085]

[0086] Step 2-1-2: The goal of the algorithm is to adjust the parameter vector θ k The value of , makes the mean square value of the error E(k) minimum. In order to achieve the above goal, define N as the data length, the objective function J(θ k ) is the mean square expected value of the error:

[0087]

[0088] Step 2-1-3: To minimize the objective function J(θ k ), using the gradient descent method. First, calculate the objective function with respect to the parameter vector θ k Gradient:

[0089]

[0090] Step 2-1-4: Based on the principle of gradient descent, the update rule of the parameter vector is:

[0091]

[0092] Step 2-1-5: Substitute the gradient expression into the update rule of the parameter vector to obtain:

[0093]

[0094] Step 2-1-6: In practical applications, since it is impossible to accurately calculate the expected value E{E(k)Φ(k)}, stochastic gradient descent (SGD) is usually used, that is, the current sample is used instead of the expected value. Therefore, the update rule of the parameter vector is simplified to:

[0095]

[0096] where α k =-2μ is the learning rate.

[0097] Step 2-2: In the context of the current problem, since the least squares method is used, the criterion function is E(k)*E(k)=E 2 (k), the goal of the LMS algorithm is to adjust the parameter vector The value of , so that the criterion function Minimize. Therefore, the parameter estimate for the k+1th iteration can be obtained for:

[0098]

[0099] Step 2-3: Since the output is quantized, the true output y(k) of the system is unknown, only the quantized output s k Available, at this time Its value is a constant. is always equal to zero and cannot play a role in updating the parameter vector. To solve this problem, consider using As The weight of for Differentiable, then we can get:

[0100]

[0101] Step 2-3: Normalized to get

[0102] Step 3 includes:

[0103] Step 3-1, Initialization: Initialize the parameters to be estimated The number of iterations k is set to 1, and the learning rate α is initialized k ; Get the input data of the system {u 1:N};

[0104] Step 3-2, the unknown output data {y 1:N} Input quantizer to get quantized output data {s 1:N}, build recognition data set C obs ={u 1:N ,s 1:N};

[0105] Step 3-3, according to Calculate the estimated output Will After quantization by the quantizer, the estimated quantized output is obtained

[0106] Step 3-4, by formula get Then through the normalization formula get

[0107] Step 3-5, iterate steps 3-3 and 3-4 to obtain the model parameters of the fourth-order finite impulse response system FIR The convergence condition of the iterative loop is k=N, where N is the preset number of iterations.

[0108] Example

[0109] In this embodiment, the industrial process modeling method for output binary quantization is specifically implemented according to the following steps:

[0110] Step 1: Construct observation dataset C obs Specifically, the input of the fourth-order finite impulse response system FIR is C obs ={u 1:N ,s 1:N}, where u 1:N is the slurry concentration, which serves as the system input signal; s 1:N It is the quantitative output electrical signal of the slurry concentration sensor, which is the output of the fourth-order finite impulse response system FIR. The output of the fourth-order finite impulse response system FIR is the model parameter

[0111] Step 2: Initialize the estimated parameters α k ,in is the estimated model parameter, α k The learning rate proposed in the present invention, k is the number of iterations, and k=1 is set;

[0112] Step 3: Update model parameter estimates

[0113] according to Calculate the estimated output Then we get the estimated quantized output By formula get Then through the normalization formula get

[0114] Step 4: Increase the value of k by 1, and iterate step 3 until the iterative loop reaches the convergence condition.

[0115] <1> Collect input and output data;

[0116] <2> Set simulation parameters;

[0117] <3> Simulation verification:

[0118] For the convenience of description, the method of the present invention is abbreviated as: BRLS. As a comparison, the same simulation model is simulated using the traditional method RLS. The comparison of simulation results can well demonstrate the effectiveness of the method of the present invention. In order to better verify the method of the present invention, the system model parameters are estimated for the BRLS and RLS methods respectively when the output is binary quantized to {-1, 1}. The specific simulation results are shown in Figure 2 and Figure 3 , Figure 2 and Figure 3 These are the system parameter estimation curves of the BRLS and RLS methods when the output undergoes binary quantization of {-1, 1}. The solid curves represent the parameter estimates, and the dotted curves represent the true values ​​of the parameters. The closer the solid curves are to the dotted curves, the better the parameter estimation effect.

[0119] When the output is binary quantized to {-1, 1}, the relative parameter estimation error RPEE of the BRLS and RLS methods is And the root mean square error RMSE are shown in Table 1:

[0120] Table 1

[0121]

[0122] Summary of simulation results: When the output is binary quantized to {-1, 1}, the parameter estimation effect of the BRLS method of the present invention is significantly better than that of the RLS method used for comparison;

[0123] According to the simulation results in Table 1, it can be seen that compared with the method of the present invention, the RPEE value and RMSE value of the RLS method are larger, indicating that the method of the present invention can achieve better parameter identification effect when the output is binary quantized to {-1, 1}.

[0124] This invention provides an industrial process modeling method for output binary quantization. While there are numerous methods and approaches for implementing this technical solution, the above-described preferred embodiments of the invention are merely exemplary. It should be noted that those skilled in the art may make numerous improvements and modifications without departing from the principles of the invention, and such improvements and modifications are considered within the scope of protection of the invention. Any components not specified in this embodiment may be implemented using existing technologies.

[0125] In an embodiment of the present application, the present invention provides an electronic device, comprising a memory, a processor, and a computer program stored in the memory and executable on the processor, wherein the processor implements the steps of any of the above methods when executing the program.

[0126] In an embodiment of the present application, the present invention provides a computer-readable storage medium having a computer program stored thereon, which implements the steps of any of the above methods when executed by a processor.

[0127] The various embodiments in this specification are described in a progressive manner, and the same or similar parts between the various embodiments can be referred to each other. Each embodiment focuses on the differences from other embodiments.

[0128] Those skilled in the art will readily appreciate other embodiments of the present invention after considering the specification and practicing the invention as disclosed herein. This application is intended to cover any variations, uses, or adaptations of the present invention that follow the general principles of the invention and include common knowledge or customary techniques in the art not invented herein, and the description and examples are to be considered merely as exemplary.

[0129] The above specific implementation methods further illustrate the purpose, technical solutions and beneficial effects of this application in detail. It should be understood that the above are only specific implementation methods of this application and are not intended to limit the scope of protection of this application. Any modifications, equivalent replacements, improvements, etc. made on the basis of the technical solutions of this application should be included in the scope of protection of this application.

Claims

1. An industrial process modeling method for output binary quantization, characterized in that: include: Inputting the pre-acquired slurry concentration data and the quantitative output data of the slurry concentration sensor into the trained fourth-order finite impulse response system FIR to obtain model parameters; Among them, the training obtains the fourth-order finite impulse response system FIR, including: Step 1: Construct a fourth-order finite impulse response system FIR: y(k)=a1u(k)+a2u(k-1)+a3u(k-2)+a4u(k-3)+v(k), Where u(k) is the k-th system input sequence, y(k) is the k-th system output sequence; a1, a2, a3, a4 are the model parameters of the fourth-order finite impulse response system FIR, and v(k) is the measurement noise of the k-th fourth-order finite impulse response system FIR; v(k) is set to zero-mean Gaussian white noise, and v(k) obeys the distribution is the variance of the measurement noise v(k); Step 2: Obtain an observation data set, which includes the slurry concentration u as the input signal of the fourth-order finite impulse response system FIR 1:N and the quantized output electrical signal s of the slurry concentration sensor as the output signal of the fourth-order finite impulse response system FIR 1:N ; Step 3: Initialize the estimated parameters of the fourth-order finite impulse response system FIR α k , is the model parameter, α k is the learning rate; Step 4, according to Calculate the estimated output and estimate the quantized output Where Φ(k)=[u(k),u(k-1),u(k-2),u(k-3)] T represents the input column vector for the kth iteration; Based on the formula get Based on the normalization formula get Step 5: Determine whether k reaches the preset number of iterations N. If not, repeat step 4 above. Otherwise, obtain the estimated parameters of the fourth-order finite impulse response system FIR. a 1,N is the estimated value of parameter a1 obtained after the Nth iteration, a 2,N is the estimated value of parameter a2 obtained after the Nth iteration, a 3,N is the estimated value of parameter a3 obtained after the Nth iteration, a 4,N is the estimated value of parameter a4 obtained after the Nth iteration.

2. The industrial process modeling method for output binary quantization according to claim 1, characterized in that: Step 2: Obtain an observation data set, which includes the slurry concentration u as the input signal of the fourth-order finite impulse response system FIR 1:N and the quantized output electrical signal s of the slurry concentration sensor as the output signal of the fourth-order finite impulse response system FIR 1:N ,include: Determine the error signal E(k) of the fourth-order finite impulse response system FIR: Where d(k) is the desired output signal; Based on the mean square expectation value of the error, calculate the objective function J(θ k ): In the formula, E() represents the mathematical expectation of the formula in the brackets.

3. The industrial process modeling method for output binary quantization according to claim 2, characterized in that: Step 2 includes: Calculate the objective function with respect to the parameter vector θ k Gradient Based on the principle of gradient descent, the update rule for the parameter vector is determined as follows: Where μ is the learning rate of the gradient descent method; The update rule for determining the parameter vector is: Among them, α k =-2μ is the learning rate.

4. The industrial process modeling method for output binary quantization according to claim 3, characterized in that: Step 2 includes: Minimize the criterion function E(k)*E(k)=E 2 (k), get the parameter estimate for the k+1th iteration for: Will As The weight of , we get: Normalization get 5. The industrial process modeling method for output binary quantization according to claim 1, characterized in that: Step 3 includes: Initialize the parameters to be estimated and learning rate α k , the number of iterations k is set to 1; Get the known input data {u 1:N }; Step 3-2, the known output data {y 1:N } Input quantizer to get quantized output data {s 1:N }, build recognition data set C obs ={u 1:N ,s 1:N }; Step 3-3, according to Calculate the estimated output Will After quantization by the quantizer, the estimated quantized output is obtained Step 3-4, by formula get By normalization formula get Step 3-5, iterate steps 3-3 and 3-4 to obtain the model parameters of the fourth-order finite impulse response system FIR The convergence condition of the iterative loop is k=N, where N is the preset number of iterations.

6. An electronic device comprising a memory, a processor, and a computer program stored in the memory and executable on the processor, wherein: When the processor executes the program, the steps of the method according to any one of claims 1 to 5 are implemented.

7. A computer-readable storage medium having a computer program stored thereon, characterized in that: When the computer program is executed by a processor, the steps of the method according to any one of claims 1 to 5 are implemented.

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