An industrial process modeling method oriented to output binary quantization

Abstract

The application discloses an industrial process modeling method for output binary quantization, and comprises the following steps: inputting pre-acquired slurry concentration data and quantization output data of a slurry concentration sensor into a fourth-order finite impulse response system (FIR) obtained through training to obtain model parameters; wherein the fourth-order finite impulse response system (FIR) is obtained through training, and the training 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 estimated parameters of the fourth-order finite impulse response system (FIR); step 4, calculating and obtaining estimated output and estimated quantization output; step 5, judging whether k reaches a preset iteration number N, if not, repeatedly executing the step 4, otherwise, obtaining the estimated parameters of the fourth-order finite impulse response system (FIR).

Description

An Industrial Process Modeling Method Oriented to Output Binary Quantization Technical Field

[0001] This invention relates to an industrial process modeling method oriented towards output binary quantization, belonging to the field of industrial process modeling technology. Background Technology

[0002] In recent years, coal preparation plants have achieved automated or semi-automated production, greatly improving production efficiency and significantly reducing production costs. Coal slime flotation, a crucial step in coal separation, involves a complex process and is highly dependent on key variables monitored by sensors. However, in actual industrial production, to reduce costs, sensors often have large quantization intervals and low accuracy. This results in inaccurate output data due to quantization errors. These inaccuracies not only affect the monitoring and control of flotation parameters (such as froth layer thickness, gas-liquid ratio, and slurry concentration) but may also further weaken flotation efficiency and separation effects.

[0003] In the coal slime flotation process, commonly used sensor quantification variables include optical signals required for foam image analysis, instantaneous flow signals from gas flow meters, and electrical signal outputs from slurry concentration meters. Inaccurate quantification errors in sensor outputs can cause numerical deviations in these quantified variables, thus affecting the control of critical processes such as reagent addition and agitation intensity adjustment. This information loss and noise amplification during quantification 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 the coal slime flotation process. Directly using quantization output for system identification will lead to a significant decrease in the accuracy of model parameter identification due to information loss and the accumulation of uncertainties. Summary of the Invention

[0005] The technical problem this invention aims to solve is to overcome the shortcomings of existing technologies and provide a method for industrial process modeling oriented towards output binary quantization. Specifically, for FIR system models with output binary quantized signals, this invention designs a system identification algorithm based on the least squares criterion. By introducing weight terms into the error function, the error function maintains differentiability under binary quantization conditions, thereby achieving optimized identification of model parameters. This invention derives and defines an error function form adapted 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] The pre-acquired slurry concentration data and quantized output data from the slurry concentration sensor are input into the trained fourth-order finite impulse response (FIR) system to obtain the model parameters.

[0008] The training yields a fourth-order finite impulse response (FIR) system, including:

[0009] Step 1, construct a fourth-order finite impulse response (FIR) system:

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

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

[0012] Step 2: Obtain the observation dataset, which includes the slurry concentration u, which serves as the input signal for the fourth-order finite impulse response (FIR) system. 1:N And the quantized output electrical signal s of the slurry concentration sensor as the output signal of a fourth-order finite impulse response (FIR) system. 1:N ;

[0013] Step 3: Initialize the estimated parameters of the fourth-order finite impulse response (FIR) system. α k , For model parameters, α k The learning rate;

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

[0015] Based on formula get

[0016] Based on the normalization formula get

[0017] Step 5: Determine if k has reached the preset iteration number N. If not, repeat step 4 above; otherwise, obtain the estimated parameters of the fourth-order finite impulse response (FIR) system. a 1,N Let a be the estimated value of parameter a1 obtained after the Nth iteration. 2,NLet a be the estimated value of parameter a2 obtained after the Nth iteration. 3,N Let a3 be the estimated value of parameter a3 obtained after the Nth iteration. 4,N This is the estimated value of parameter a4 obtained after the Nth iteration.

[0018] Prioritize, in step 2, acquiring the observation dataset, which includes the slurry concentration u as the input signal to the fourth-order finite impulse response (FIR) system. 1:N And the quantized output electrical signal s of the slurry concentration sensor as the output signal of a fourth-order finite impulse response (FIR) system. 1:N ,include:

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

[0020]

[0021] In the formula, d(k) is the desired output signal;

[0022] Based on the mean squared expected value of the error, the objective function J(θ) is calculated. k ):

[0023]

[0024] In the formula, E() represents the expected value of the expression within the parentheses.

[0025] Prior to this, step 2 includes:

[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] In the formula, μ is the learning rate of the gradient descent method;

[0031] The update rule for the parameter vector is determined as follows:

[0032]

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

[0034] Prior to this, step 2 includes:

[0035] Minimize criterion function Obtain the parameter estimates for the (k+1)th iteration. for:

[0036]

[0037] Will As We obtain the weights from the given values:

[0038]

[0039] Normalization get

[0040] Prior to this, step 3 includes:

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

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

[0043] Step 3-2, use the known output data {y} 1:N The input quantizer produces quantized output data {s}. 1:N}, construct the identification dataset C obs ={u 1:N ,s 1:N};

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

[0045] Steps 3-4, using the formula get By normalization formula get

[0046] Step 3-5 iterates through steps 3-3 and 3-4 to obtain the model parameters of the fourth-order finite impulse response (FIR) system. 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 including a memory, a processor, and a computer program stored in the memory and executable on the processor, wherein the processor executes the program to implement the steps of the method described in any of the first aspects.

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

[0049] The beneficial effects achieved by this invention are as follows:

[0050] This invention addresses FIR system models whose output is a binary quantized signal. Based on the least squares criterion, a system identification method is designed. By introducing weight terms into the error function, the error function remains differentiable under binary quantization conditions, thereby achieving optimized identification of model parameters. This invention derives and defines an error function form adapted to the characteristics of the quantized signal, ensuring that the error function accurately describes the identification characteristics of the quantized output signal. Attached Figure Description

[0051] To more clearly illustrate the technical solution of this application, the drawings used in the embodiments will be briefly introduced below. Obviously, for those skilled in the art, other drawings can be obtained based on these drawings without creative effort.

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

[0053] Figure 2 shows the estimation curves of parameters a1 and a2 of the BRLS method of the present invention and the traditional RLS method after the output is binary quantized by {-1, 1}.

[0054] Figure 3 shows the estimation curves of parameters a3 and a4 of the BRLS method of the present invention and the traditional RLS method after the output is binary quantized by {-1, 1}.

[0055] Figure 4 is a flowchart of the fourth-order finite impulse response (FIR) system obtained by the method of the present invention. Detailed Implementation

[0056] Referring to Figure 1, this invention is divided into a training phase and an application phase. The training phase includes the following steps:

[0057] Training yields a fourth-order finite impulse response (FIR) system, including:

[0058] As shown in Figure 4, step 1 involves constructing a fourth-order finite impulse response (FIR) system:

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

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

[0061] Step 2: Obtain the observation dataset, which includes the slurry concentration u, which serves as the input signal for the fourth-order finite impulse response (FIR) system. 1:N And the quantized output electrical signal s of the slurry concentration sensor as the output signal of a fourth-order finite impulse response (FIR) system. 1:N ;

[0062] Step 3: Initialize the estimated parameters of the fourth-order finite impulse response (FIR) system. α k ;in For the estimated model parameters, α k The learning rate;

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

[0064] Based on formula get

[0065] According to the normalization formula get

[0066] Step 5: Determine if k has reached the preset iteration number N. If not, repeat step 4 above; otherwise, obtain the estimated parameters of the fourth-order finite impulse response (FIR) system. a 1,N Let a be the estimated value of parameter a1 obtained after the Nth iteration. 2,N Let a be the estimated value of parameter a2 obtained after the Nth iteration. 3,N Let a3 be the estimated value of parameter a3 obtained after the Nth iteration. 4,N This is the estimated value of parameter a4 obtained after the Nth iteration.

[0067] The application phase includes the following steps:

[0068] The process of coal slime flotation involves acquiring slurry concentration data and quantized output data from slurry concentration sensors, which are then input into a fourth-order finite impulse response (FIR) system obtained through training to obtain model parameters.

[0069] Example

[0070] This invention provides an industrial process modeling method oriented towards 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 includes the following steps:

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

[0072] Step 2: For a fourth-order finite impulse response (FIR) system whose output is a binary quantized signal, this invention designs a system identification algorithm based on the least squares criterion. By introducing a weight term into the error function, the error function remains differentiable under binary quantization conditions, thereby achieving optimized identification of model parameters. This invention defines an error function form adapted 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 dataset and the error function with weighted terms, iteratively update the parameters to be identified within the framework of the recursive least squares algorithm.

[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 (FIR) system, and v(k) is the measurement noise of the fourth-order finite impulse response (FIR) system; v(k) is set to zero-mean Gaussian white noise, following the distribution... in Let v(k) be the variance of the noise.

[0077] In step 1, the input signal u(k) passes through a discrete-time invariant linear system H(z).-1 ) is filtered to produce the scalar output y(k) of the fourth-order finite impulse response (FIR) system; the discrete-time invariant linear system H(z) is filtered to produce the scalar output y(k) of the FIR system. -1 The impulse response of a given length L = 4 is a column vector θ = [a1, a2, a3, a4]. T Then the output y(k) of the discrete-time invariant linear system is different from the estimated output. It can be represented as:

[0078] y(k)=θ T Φ(k)

[0079]

[0080] in, Let Φ(k) represent the estimated parameters for the k-th iteration; Φ(k) = [u(k), u(k-1), u(k-2), u(k-3)] T Let represent the input column vector for the k-th iteration. The FIR output of the fourth-order finite impulse response system is quantized by a one-bit A / D converter, defined as follows: Where s k This represents the quantized output of the system output sequence y(k) after being quantized by the quantizer; Indicates estimated output The estimated quantized output after quantization by the quantizer; S(x) represents the quantizer, defined as:

[0081]

[0082] Step 2 includes:

[0083] Step 2-1: Starting from the general Least Mean Square (LMS) algorithm, a practical LMS-like method is derived to solve the FIR identification problem of output-quantized fourth-order finite impulse response (FIR) systems. 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 (FIR) system 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 is such that the mean square value of the error E(k) is minimized. To achieve the above objective, N is defined as the data length, and the objective function J(θ) is... k Let ) be the mean squared expected value of the error:

[0087]

[0088] Step 2-1-3: In order to minimize the objective function J(θ) k The gradient descent method is used. First, the objective function is calculated 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 for the parameter vector is as follows:

[0091]

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

[0093]

[0094] Step 2-1-6: In practical applications, since the expected value E{E(k)Φ(k)} cannot be accurately calculated, stochastic gradient descent (SGD) is usually used, that is, the expected value is replaced by the sample at the current time step. 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 makes the criterion function Minimize. Therefore, we can obtain the parameter estimates for the (k+1)th iteration. for:

[0098]

[0099] Steps 2-3: Due to the quantization effect, the system's true output y(k) is unknown; only the quantized output s is known. k Available at this time Its value is a constant, at this time Since it is always equal to zero, it cannot serve the purpose of updating the parameter vector. To solve this problem, consider using... As The weights, because for If it is differentiable, then we can obtain:

[0100]

[0101] Steps 2-3: ... Normalization yields

[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 ; Obtain system input data {u 1:N};

[0104] Step 3-2, convert the unknown output data {y} 1:N The input quantizer produces quantized output data {s}. 1:N}, construct the identification dataset C obs ={u 1:N ,s 1:N};

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

[0106] Steps 3-4, using the formula get Then after normalization formula get

[0107] Step 3-5 iterates through steps 3-3 and 3-4 to obtain the model parameters of the fourth-order finite impulse response (FIR) system. 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 oriented towards output binary quantization is implemented according to the following steps:

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

[0111] Step 2: Initialize the estimated parameters α k ,in For the estimated model parameters, α k The learning rate proposed in this invention is k, which 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 the estimated quantized output is obtained. Through formula get Then after normalization formula get

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

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

[0116] <2> Set simulation parameters;

[0117] <3> Simulation verification:

[0118] For ease of description, the method of this invention is abbreviated as BRLS. In comparison, the same simulation model was simulated using the traditional method RLS, and the comparison of simulation results effectively demonstrates the effectiveness of the method of this invention. To further verify the method of this invention, system model parameters were estimated for both BRLS and RLS methods after the output was binarized to {-1, 1}. Specific simulation results are shown in Figures 2 and 3, which are the system parameter estimation curves for BRLS and RLS methods respectively after the output has been binarized to {-1, 1}. The solid curve represents the estimated parameter value, and the dashed curve represents the actual parameter value. The closer the solid curve is to the dashed curve, the better the parameter estimation effect.

[0119] When the output is binarized to {-1, 1}, the relative parameter estimation error (RPEE) of the BRLS and RLS methods is... The root mean square error (RMSE) is shown in Table 1:

[0120] Table 1

[0121]

[0122] Simulation results summary: When the output is binary quantized to {-1, 1}, the parameter estimation performance of the BRLS method of this 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 the RLS method has larger RPEE and RMSE values ​​compared with the method of the present invention, indicating that the method of the present invention can achieve better parameter identification effect when the output is binary quantized by {-1, 1}.

[0124] This invention provides a method for industrial process modeling oriented towards output binary quantization. Many methods and approaches exist for implementing this technical solution; the above description is merely a preferred embodiment of the invention. It should be noted that those skilled in the art can make various improvements and modifications without departing from the principles of this invention, and these improvements and modifications should also be considered within the scope of protection of this invention. All components not explicitly stated in this embodiment can be implemented using existing technologies.

[0125] In this embodiment of the application, the present invention provides an electronic device, including a memory, a processor, and a computer program stored in the memory and executable on the processor, wherein the processor executes the program to implement the steps of any of the methods described above.

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

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

[0128] Other embodiments of the invention will readily occur to those skilled in the art upon consideration of the specification and practice of the invention described herein. This application is intended to cover any variations, uses, or adaptations of the invention that follow the general principles of the invention and include common knowledge or customary techniques in the art not invented herein. The specification and embodiments are to be considered exemplary only.

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

Claims

1. A method for industrial process modeling oriented towards output binary quantization, characterized in that, include: The pre-acquired slurry concentration data and quantized output data from the slurry concentration sensor are input into the trained fourth-order finite impulse response (FIR) system to obtain model parameters. The training of the fourth-order FIR system includes: Step 1, constructing the fourth-order FIR system: y(k) = a1u(k) + a2u(k-1) + a3u(k-2) + a4u(k-3) + v(k), where u(k) is the input sequence of the k-th system, y(k) is the output sequence of the k-th system; a1, a2, a3, a4 are the model parameters of the fourth-order FIR system, and v(k) is the measurement noise of the k-th fourth-order FIR system; v(k) is set to zero-mean Gaussian white noise, and v(k) follows a distribution. To measure the variance of the noise v(k); Step 2, acquire the observation dataset, which includes the slurry concentration u as the input signal to the fourth-order finite impulse response (FIR) system. 1:N And the quantized output electrical signal s of the slurry concentration sensor as the output signal of a fourth-order finite impulse response (FIR) system. 1:N Step 3: Initialize the estimated parameters of the fourth-order finite impulse response (FIR) system. α k ， For model parameters, α k The learning rate; Step 4, based on Calculate the estimated output and estimated quantized output Where Φ(k)=[u(k),u(k-1),u(k-2),u(k-3)] T Represents the input column vector for the k-th iteration; based on the formula get Based on the normalization formula get Step 5: Determine if k has reached the preset iteration number N. If not, repeat step 4 above; otherwise, obtain the estimated parameters of the fourth-order finite impulse response (FIR) system. a 1,N Let a be the estimated value of parameter a1 obtained after the Nth iteration. 2,N Let a be the estimated value of parameter a2 obtained after the Nth iteration. 3,N Let a3 be the estimated value of parameter a3 obtained after the Nth iteration. 4,N This is the estimated value of parameter a4 obtained after the Nth iteration.

2. The industrial process modeling method oriented towards output binary quantization according to claim 1, characterized in that, Step 2: Obtain the observation dataset, which includes the slurry concentration u, which serves as the input signal for the fourth-order finite impulse response (FIR) system. 1:N And the quantized output electrical signal s of the slurry concentration sensor as the output signal of a fourth-order finite impulse response (FIR) system. 1:N This includes: determining the error signal E(k) of the fourth-order finite impulse response (FIR) system: In the formula, d(k) is the desired output signal; the objective function J(θ) is calculated based on the mean square expectation of the error. k ): In the formula, E() represents the expected value of the expression within the parentheses.

3. The industrial process modeling method oriented towards output binary quantization according to claim 2, characterized in that, Step 2 includes: calculating 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: In the formula, μ is the learning rate of gradient descent; the update rule for determining the parameter vector is: Where, 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: minimizing the criterion function E(k)*E(k)=E 2 (k), to obtain the parameter estimates for the (k+1)th iteration. for: Will As We obtain the weights from the given values: Normalization get 5. The industrial process modeling method for output binary quantization according to claim 1, characterized in that, Step 3 includes: initializing the parameters to be estimated. and learning rate α k The iteration count k is set to 1; the known input data {u} is obtained. 1:N Step 3-2, use the known output data {y} 1:N The input quantizer produces quantized output data {s}. 1:N }, construct the identification dataset C obs ={u 1:N ,s 1:N }; Step 3-3, according to Calculate the estimated output Will The estimated quantized output is obtained after quantization by a quantizer. Steps 3-4, using the formula get By normalization formula get Step 3-5 iterates through steps 3-3 and 3-4 to obtain the model parameters of the fourth-order finite impulse response (FIR) system. 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, characterized in that, When the processor executes the program, it implements the steps of the method according to any one of claims 1 to 5.

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

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