Complex industrial process prediction method for mixed noise distribution

Abstract

The invention provides a mixed noise distribution-oriented complex industrial process prediction method, which comprises the following steps of: 1, collecting a data set with mixed noise characteristics in an offline state of a liquid excavator system, collecting the position of an operating rod as input data of a hydraulic excavator system model, and taking an actual displacement value of an oil cylinder as output data, constructing an ARX model of the liquid excavator system; 2, for an ARX model, introducing system noise distribution and prior distribution of model parameters, forming probability description of a liquid excavator system identification problem, and assuming that system noise obeys Gaussian distribution and K-1 Laplacian distributions with proper weights so as to improve system robustness; and step 3, based on the identification data set and the probability description of the liquid excavator system identification problem, iteratively updating under an expectation maximization algorithm framework to obtain a to-be-identified parameter. According to the method, system identification modeling of the complex industrial process is realized based on Gaussian-Laplacian mixed noise characteristics, and the identification accuracy is improved.

Description

Technical Field

[0001] The invention relates to a complex industrial process prediction method oriented to mixed noise distribution, belonging to the technical field of complex industrial process prediction method oriented to mixed noise distribution. Background Art

[0002] With the rapid development of intelligent manufacturing, industrial process modeling and optimization play an increasingly important role in improving production efficiency, reducing energy consumption and realizing intelligent control. As the core equipment in the field of engineering machinery, the dynamic characteristics modeling of hydraulic excavators is of great significance for optimizing control strategies, improving operating efficiency and reducing energy consumption. However, the hydraulic excavator system faces complex working conditions and multi-source interference in actual operation, which makes it difficult for traditional modeling methods to meet the needs of high-precision control.

[0003] Traditional hydraulic excavator system modeling is mostly based on the linear autoregressive exogenous model (ARX) framework, whose core assumption is that system noise obeys a single Gaussian distribution. However, in actual industrial scenarios, the complex working conditions of the hydraulic system lead to multi-source interference in the collected data: on the one hand, the displacement signal of the hydraulic cylinder is easily affected by mechanical vibration, hydraulic pulsation, sensor drift, etc., and the noise presents non-Gaussian characteristics; on the other hand, there is a strong nonlinear coupling between the operating lever command and the actuator response, and factors such as sudden load changes and oil temperature changes during operation may introduce outliers. When facing mixed noise distributions, the existing identification methods based on the single Gaussian noise assumption are prone to significant deviations in model parameter estimation, resulting in insufficient robustness. In addition, the presence of outliers will further destroy the convergence of the traditional maximum likelihood estimation, resulting in a decrease in model accuracy, making it difficult to meet the requirements of high dynamic and high precision control.

[0004] Combined with the current development of industrial processes, industrial systems are developing towards high complexity, high dynamics and high precision control, which puts forward higher requirements on the robustness and adaptability of modeling methods. Especially in complex industrial processes such as hydraulic excavators, the data acquisition environment is complex and the noise sources are diverse. Traditional modeling methods are difficult to effectively deal with mixed noise and outlier interference, which seriously restricts the further improvement of system performance. Therefore, there is an urgent need for an identification method that is compatible with mixed noise distribution and suppresses outlier interference, so as to improve the accuracy and reliability of hydraulic excavator system modeling and meet the needs of modern industrial processes for high-precision modeling. Summary of the invention

[0005] The technical problem to be solved by the present invention is to overcome the defects of the prior art and provide a complex industrial process prediction method for mixed noise distribution. In order to solve the problem that in the hydraulic excavator system, when there are noise and abnormal values in the data acquisition process in the prior art, the system identification accuracy will be reduced, the present invention proposes a system identification method based on Gaussian-Laplace mixed noise distribution.

[0006] Preferably, the present invention provides a prediction method for complex industrial processes facing mixed noise distributions, including:

[0007] Input the pre-acquired joystick position measurement values into the trained ARX model, and the ARX model predicts and outputs the cylinder displacement data; wherein, training the completed ARX model includes:

[0008] Step 1: Collect data with mixed noise characteristics in the offline state of the hydraulic excavator system and construct a data set. The data with mixed noise characteristics includes the joystick position and the actual cylinder displacement values;

[0009] Use the joystick position as the input data of the ARX model of the hydraulic excavator system, and use the actual cylinder displacement value as the output data of the ARX model of the hydraulic excavator system. Construct the mapping relationship between the joystick position and the actual cylinder displacement value in the ARX model of the hydraulic excavator system to obtain the ARX model of the hydraulic excavator system;

[0010] Step 2: Introduce the prior distributions of the system noise distribution and the model parameters into the ARX model to obtain a probabilistic description of the identification problem of the hydraulic excavator system. Set the system noise to follow a Gaussian distribution and K - 1 Laplace distributions with appropriate weights;

[0011] Step 3: Based on the data set and the probabilistic description of the identification problem of the hydraulic excavator system, iteratively update the ARX model parameters of the hydraulic excavator system within the framework of the expectation - maximization algorithm to obtain the ARX model parameters to be identified and obtain the trained ARX model.

[0012] Preferably, the expression of the ARX model of the hydraulic excavator system is:

[0013]

[0014] Wherein, represents the predicted cylinder displacement value, ε n is the random noise of the hydraulic excavator system, x n is the joystick position collected by the input data matrix, n a is the order of the autoregressive part, n b is the order of the input part, β is the ARX model parameter to be identified, is the pre - acquired data set, x n is the nth joystick position, y n is the nth actual cylinder displacement value, and N is the total number of joystick positions.

[0015] Preferably, Step 2 includes:

[0016] Step 2-1: Set the system noise to follow a Gaussian distribution and K-1 Laplace distributions with appropriate weights:

[0017]

[0018] where τ k ≥0, K≥2, τ k is the Laplace distribution weight, τ1 is the Gaussian distribution weight,

[0019] is the probability density function of the noise following a Gaussian distribution, L(ε|0, σ L；k ) is the probability density function of the noise following a Laplace distribution, and the set of mixed noise weights is Γ={τ1,τ2…,τ K} with variance

[0020] Set the prior probability of the ARX model parameters to be identified to follow a Gaussian distribution:

[0021]

[0022] Preferably, in Step 2-2: The random variable following a Laplace distribution is represented as a random variable following a normal distribution and an exponential distribution, and the expression of the probability density function of the exponential distribution:

[0023]

[0024] In the formula, g(v) is the probability density function of the exponential distribution, and v is the random variable related to the exponential distribution;

[0025] Given v, the conditional distribution of the random variable x is a normal distribution:

[0026]

[0027] In the formula, is the probability density function of the exponential distribution, η is the mathematical expectation of the normal distribution, i.e., the mean, and μ is the standard deviation of the normal distribution;

[0028] The probability density function of the random variable of the Laplace distribution is:

[0029]

[0030] In the formula, is the decomposed form of the probability density function of the Laplace distribution, x is the random variable, μ is the location parameter, η is the scale parameter, and v is the random variable related to the exponential distribution;

[0031] The actual value of the cylinder displacement y nThe probability density function is as follows:

[0032]

[0033] In the formula, p(y n |x n , β, Γ, ∑) is the probability density function of the actual value y of the cylinder displacement n , and is the Gaussian distribution component, and L(y n |h(x n )β, σ L；k ) is the Laplace distribution component;

[0034] By introducing variables related to the exponential distribution, the probability density function of the actual value of the cylinder displacement is obtained:

[0035]

[0036] In the formula, p(y n , v n |x n , β, Γ, ∑) is the probability density function of the actual value of the cylinder displacement obtained by introducing variables related to the exponential distribution.

[0037] Preferably, step 2-3: Introduce latent variables When y n comes from the k-th component, z kn =1; otherwise, z kn =0. Therefore, the prior distribution of z n is as follows:

[0038]

[0039] Based on the complete data (x n , y n , v n , z n ), the joint probability density function is obtained:

[0040]

[0041] In the formula, p(y n , v n , z n |x n , β, Γ, ∑) is the joint probability density function based on the complete data (x n , y n , v n , z n ), and p(y n , v n |x n , β, Γ, ∑) is the joint probability density function based on the data without the latent variable z nThe joint probability density function, p(z n ) is the prior distribution of the latent variable z n .

[0042] Given the complete data set T = {X, y, v, Z}, where X is the set of all joystick positions, y is the set of all cylinder displacement data, v is a random variable related to the exponential distribution, and Z is the introduced latent variable, the likelihood function is determined as:

[0043]

[0044] where p(y, v, Z|X, β, Γ, ∑) is the expression of the likelihood function after introducing the latent variable;

[0045] According to Bayes' theorem, the posterior probability density of the model parameter β is determined as:

[0046]

[0047] where is the posterior probability density of the model parameter β, is the prior probability density of the model parameter β;

[0048] Taking the logarithm gives:

[0049]

[0050] where σ g is the variance of the Gaussian distribution, is the variance of the k-th Laplace distribution, P is the model order, and c is a constant.

[0051] Preferably, step 3 includes:

[0052] Step 3-1, initialize the model parameter β to be estimated, and set the iteration count s to 1;

[0053] Step 3-2, perform step E-step, and calculate the conditional expectation of the posterior distribution for the data set D = {x n , y n}, omitting the terms irrelevant to the parameter and containing the terms with v to obtain the Q-function: n

[0054]

[0055] Step 3-3, perform step M-step, and obtain a new parameter estimate by optimizing the Q-function such that the parameter satisfies the constraint condition:​

[0056]

[0057] Step 3-4: Increase the value of s by 1, and return to Step 3-2. Continuously repeat Step E-step and Step M-step until the parameters of the ARX model to be identified meet the convergence condition. The convergence condition is:

[0058]

[0059] where q is the number of iterations.

[0060] Preferably, in Step 3-2, the Step E-step includes:

[0061] Calculate the conditional expectation of the posterior distribution for the data set D = {x n , y n}, remove the terms irrelevant to the parameter , that is, the terms containing v , and determine the Q-function: n

[0062]

[0063] where represents the expectation operator, c1 represents a constant independent of the parameter , P = n a + n b is the sum of the orders of the autoregressive and input parts;

[0064] When k = 1, determine

[0065]

[0066] where is the probability density function of the Laplace distribution component,

[0067] is the probability density function of the Gaussian distribution component;

[0068] When k ≥ 2, determine

[0069]

[0070] where γ kn is a defined value;

[0071] Determine

[0072]

[0073] ​Q - function:

[0074]

[0075] where γ 1n is a defined value.

[0076] Preferably, in step 3 - 3, the step M - step includes:

[0077] Calculating Maximizing the cost loss function

[0078]

[0079] Let The following iterative formula is obtained:

[0080]

[0081] where is the variance of the (q + 1)-th iteration of the Gaussian distribution, is the variance of the (q + 1)-th iteration of the k-th Laplace distribution, β (q+1) is the model parameter of the (q + 1)-th iteration, is the prior of β of the (q + 1)-th iteration, Ψ is a diagonal matrix composed of I p is a P-dimensional identity matrix;

[0082] By iteratively looping through step 3 - 2 and step 3 - 3, the convergence condition for the ARX model parameter β to be identified is:

[0083]

[0084] Preferably, the present invention provides an electronic device, including a memory, a processor, and a computer program stored on the memory and executable on the processor. When the processor executes the program, the steps of the method according to any one of the first aspect are implemented.

[0085] Preferably, the present invention provides a computer-readable storage medium, on which a computer program is stored. When the computer program is executed by a processor, the steps of the method according to any one of the first aspect are implemented.

[0086] The beneficial effects achieved by the present invention:

[0087] The present invention provides a complex industrial process modeling method for a hybrid noise distribution. Step 1: Collect a dataset with hybrid noise characteristics in the offline state of the liquid excavator system. Collect the position of the joystick as the input data of the hydraulic excavator system model, and the cylinder displacement as the output data of the hydraulic excavator system model, and construct an ARX model of the liquid excavator system. Step 2: For the ARX model, introduce the prior distributions of the system noise distribution and model parameters to form a probabilistic description of the liquid excavator system identification problem. Since the data collected from the liquid excavator system is affected by unknown noise and outliers, it is assumed that the system noise follows a Gaussian distribution and K-1 Laplace distributions with appropriate weights, which improves the system robustness. Step 3: Based on the identification dataset and the probabilistic description of the liquid excavator system identification problem, iteratively update under the framework of the expectation maximization algorithm to obtain the parameters to be identified. The present invention uses the characteristics of Gaussian-Laplace hybrid noise to realize the identification modeling of complex industrial process systems, proposes an identification method that can be compatible with hybrid noise distributions and suppress the interference of outliers, improves the accuracy of identification, enhances the accuracy and reliability of the hydraulic excavator system modeling, and meets the requirements of modern industrial processes for high-precision modeling. BRIEF DESCRIPTION OF THE DRAWINGS

[0088] In order to more clearly illustrate the technical solutions of the present application, the drawings required for use in the embodiments will be briefly introduced below. Obviously, for those of ordinary skill in the art, other drawings can also be obtained based on these drawings without creative efforts.

[0089] Figure 1 is the algorithm block diagram of the method of the present invention;

[0090] Figure 2 is a comparison chart of the system parameter estimation curves of the ARX-Lap method and the ARX-Mix method when the outlier ratio is 10% and the mixture Gaussian noise is included during the output measurement process;

[0091] Figure 3 is a comparison chart of the system parameter estimation curves of the ARX-Lap method and the ARX-Mix method when the outlier ratio is 10% and the mixture Gaussian noise is included during the output measurement process;

[0092] Figure 4 is a comparison chart of the system parameter estimation curves of the ARX-Lap method and the ARX-Mix method when the outlier ratio is 10% and the mixture Gaussian noise is included during the output measurement process;

[0093] Figure 5 is a comparison chart of the system parameter estimation curves of the ARX-Lap method and the ARX-Mix method when the outlier ratio is 10% and the mixture Gaussian noise is included during the output measurement process;

[0094] Figure 6 This is the algorithm flowchart of the method of the present invention. Detailed implementation manners

[0095] Refer to Figure 1 , this application discloses a robust identification method for a nonlinear state space system based on heavy-tailed noise, including a training stage and an application stage;

[0096] The training stage includes the following steps:

[0097] Step 1: Collect data with mixed noise characteristics in the offline state of the liquid excavator system and construct a data set. The data with mixed noise characteristics includes the joystick position and the cylinder displacement. Take the joystick position as the input data of the ARX model of the hydraulic excavator system, and take the cylinder displacement as the output data of the ARX model of the hydraulic excavator system. Construct the mapping relationship between the joystick position and the cylinder displacement data in the ARX model of the liquid excavator system, and construct the ARX model of the liquid excavator system;

[0098] Step 2: Introduce the prior distributions of the system noise distribution and the model parameters into the ARX model to obtain the probability description of the identification problem of the liquid excavator system. Since the data collected from the liquid excavator system is affected by unknown noise and outliers, in order to improve the system robustness, it is set that the system noise follows a Gaussian distribution and K - 1 Laplace distributions with appropriate weights;

[0099] Step 3: Based on the data set and the probability description of the identification problem of the liquid excavator system, iteratively update the ARX model of the liquid excavator system under the framework of the expectation - maximization algorithm to obtain the ARX model parameters to be identified, and obtain the trained ARX model.

[0100] The application stage includes the following steps:

[0101] Input the pre - obtained joystick position to be measured into the trained ARX model, and the ARX model predicts and outputs the cylinder displacement data.

[0102] In Step 1, the ARX model of the liquid excavator system is expressed as:

[0103]

[0104] Wherein, represents the predicted value of the cylinder displacement, ε n is the random noise of the hydraulic excavator system, x n is the joystick position collected by the input data matrix, n a is the order of the autoregressive part, n bis the order of the input part, β is the parameter of the ARX model to be identified, is the pre-acquired data set, x n is the position of the nth joystick, y n is the displacement data of the nth oil cylinder, and N is the total number of joystick positions.

[0105] Step 2 includes:

[0106] Step 2-1: Assume that the system noise ε follows a Gaussian distribution and K-1 Laplace distributions with appropriate weights, that is, the probability density function of the system noise is:

[0107]

[0108] where, τ k ≥ 0, K ≥ 2, τ k is the Laplace distribution weight, τ1 is the Gaussian distribution weight,

[0109] is the probability density function of the noise following a Gaussian distribution, is the probability density function of the noise following a Laplace distribution, and the set of mixed noise weights is Γ = {τ1, τ2…, τ K}, and the variance is

[0110] There is less prior empirical knowledge about the ARX model parameters to be identified. Assume that the prior probability of the ARX model parameters to be identified follows a Gaussian distribution, that is, the prior probability density of the ARX model parameters to be identified is:

[0111]

[0112] Step 2-2: A random variable following a Laplace distribution can be expressed as a random variable following a normal distribution and an exponential distribution. Introduce a random variable v related to the exponential distribution. The probability density function of the exponential distribution is:

[0113]

[0114] In the formula, g(v) is the probability density function of the exponential distribution, and v is the random variable related to the exponential distribution;

[0115] Given v, the conditional distribution of the random variable x is a normal distribution:

[0116]

[0117] In the formula, is the probability density function of the exponential distribution, η is the mathematical expectation (i.e., the mean) of the normal distribution, and μ is the standard deviation of the normal distribution;

[0118] The probability density function of a random variable following the Laplace distribution can be decomposed as follows:

[0119]

[0120] where is the decomposed form of the probability density function of the Laplace distribution;

[0121] where x is the random variable, μ is the location parameter, η is the scale parameter, and v is the random variable related to the exponential distribution.

[0122] The actual value of the cylinder displacement y n has the probability density function:

[0123]

[0124] where p(y n |x n , β, Γ, ∑) is the probability density function of the actual value of the cylinder displacement y n , is the Gaussian distribution component, and L(y n |h(x n )β, σ L；k ) is the Laplace distribution component;

[0125] By introducing a variable related to the exponential distribution, the probability density function of the actual value of the cylinder displacement is:

[0126]

[0127] where p(y n , v n |x n , β, Γ, ∑) is the probability density function of the actual value of the cylinder displacement obtained by introducing a variable related to the exponential distribution;

[0128] All samples in the dataset are independently sampled, and the following likelihood function can be obtained:

[0129]

[0130] where p(y, v|X, β, Γ, ∑) is the likelihood function of the variable to be estimated;

[0131] Step 2 - 3: To implement the EM algorithm, introduce the latent variable When y n comes from the k - th component, z kn = 1, otherwise z kn = 0. Therefore, the prior distribution of z n is:

[0132]

[0133] For the complete data (x n , y n , v n , z n ), the following joint probability density function can be obtained:

[0134]

[0135] In the formula, p(y n , v n , z n |x n , β, Γ, ∑) is the joint probability density function based on the complete data (x n , y n , v n , z n ), p(y n , v n |x n , β, Γ, ∑) is the joint probability density function based on the data without the latent variable z n , and p(z n ) is the prior distribution of the latent variable z n ;

[0136] Given the complete data set T = {X, y, v, Z}, where X is the set of joystick positions, y is the set of cylinder displacement data, v is a random variable related to the exponential distribution, being the introduced latent variable, the likelihood function can be re-expressed as follows:

[0137]

[0138] In the formula, p(y, v, Z|X, β, Γ, ∑) is the expression of the likelihood function after introducing the latent variable;

[0139] According to Bayes' theorem, the posterior probability density of the model parameter β can be calculated using the following formula:

[0140]

[0141] In the formula, is the posterior probability density of the model parameter β, is the prior probability density of the model parameter β;

[0142] Then take the logarithm of:

[0143]

[0144] In the formula, σ g is the variance of the Gaussian distribution, is the variance of the k-th Laplace distribution, P is the model order, and c is a constant;

[0145] Step 3 includes:

[0146] Step 3-1, Initialization: Initialize the parameter β to be estimated, and set the iteration number s to 1;

[0147] Step 3-2, Perform Step E-step. For the data set D = {x n , y n}, calculate the conditional expectation of the posterior distribution, omitting the terms irrelevant to the parameter , that is, the terms containing v n , and derive the objective cost function of the hydraulic excavator system, that is, the Q-function:

[0148]

[0149] Step 3-3, Perform Step M-step. By optimizing the Q-function, obtain a new parameter estimate such that the parameter satisfies the following constraint conditions:

[0150]

[0151] Step 3-4, Increase the value of s by 1, return to Step 3-2, and continuously repeat Step E-step and Step M-step until the parameters of the ARX model to be identified satisfy the convergence condition. The convergence condition is:

[0152]

[0153] where q is the iteration number.

[0154] In Step 3-2, the Step E-step includes:

[0155] For the data set D = {x n , y n}, calculate the conditional expectation of the posterior distribution, omitting the terms irrelevant to the parameter , that is, the terms containing v n , and derive the objective cost function of the hydraulic excavator system, that is, the Q-function:

[0156]

[0157] where represents the expectation operator, c1 represents a constant independent of the parameter , P = n a + n bis the sum of the autoregressive and input orders;

[0158] When k = 1, the calculation is as follows:

[0159]

[0160] wherein, is the probability density function of the Laplace distribution component,

[0161] is the probability density function of the Gaussian distribution component;

[0162] When k ≥ 2, the calculation is as follows:

[0163]

[0164] wherein, γ kn is a defined value;

[0165] The calculation is as follows:

[0166]

[0167] Therefore, the Q function can be expressed as follows:

[0168]

[0169] wherein, γ 1n is a defined value;

[0170] In step 3-3, the said step M-step includes:

[0171] Maximize the cost loss function The expression of which is:

[0172]

[0173] Let The following iterative formula can be obtained:

[0174]

[0175]

[0176] wherein, is the variance of the (q + 1)-th iteration of the Gaussian distribution, is the variance of the (q + 1)-th iteration of the k-th Laplace distribution, β (q+1) is the model parameter of the (q + 1)-th iteration, is the prior of β of the (q + 1)-th iteration, H(X) is, Ψ is from The composed diagonal matrix, I p is a P-dimensional identity matrix;

[0177] Through the iterative loop from step 3-2 to step 3-3, the convergence condition for the parameters β of the ARX model to be identified is:

[0178]

[0179] The present invention provides a complex industrial process modeling method for a mixed noise distribution, including: Step 1: Collect a data set with mixed noise characteristics in the offline state of the hydraulic excavator system, collect the position of the joystick as the input data of the hydraulic excavator system model, and the cylinder displacement as the output data of the hydraulic excavator system model, and construct an ARX model of the hydraulic excavator system; Step 2: For the ARX model, introduce the prior distributions of the system noise distribution and model parameters to form a probabilistic description of the hydraulic excavator system identification problem. Since the data collected from the hydraulic excavator system is affected by unknown noise and outliers, in order to improve the system robustness, it is assumed that the system noise follows a Gaussian distribution and K-1 Laplace distributions with appropriate weights; Step 3: Based on the identification data set and the probabilistic description of the hydraulic excavator system identification problem, iteratively update under the framework of the expectation-maximization algorithm to obtain the parameters to be identified. The present invention uses the characteristics of Gaussian-Laplace mixed noise to realize the identification and modeling of complex industrial process systems, improving the accuracy of identification.

[0180] Embodiment

[0181] In this embodiment, the complex industrial process modeling method for a mixed noise distribution is specifically implemented according to the following steps:

[0182] Input of the algorithm: The position of the joystick of the hydraulic excavator system model Output of the algorithm includes: Cylinder displacement data

[0183] Step 1: Obtain the position of the joystick and cylinder displacement data in advance, and construct a data set:

[0184] Step 2: Initialize the parameters Model parameters β, mixed noise weights Γ = {τ1, τ2…, τ K}, mixed noise variances and model parameter variances and set s = 1;

[0185] Step 3: Update the posterior probability distribution and expectation:

[0186] Use the formula given in the E-step to calculate the loss cost function;

[0187] Step 4: Update the model parameter estimation:

[0188] Update the model parameters β, the mixture noise weights Γ = {τ1, τ2…, τ K}, the mixture noise variances and the model parameter variances

[0189] Step 5: Increase the value of s by 1 until the parameters of the ARX model to be identified converge.

[0190] <1>Collect a dataset with the characteristics of mixed noise in the offline state of the hydraulic excavator system. Collect the position of the joystick as the input data of the hydraulic excavator system model, and the cylinder displacement as the output data of the ARX model and perform preprocessing to construct the ARX model of the hydraulic excavator system;

[0191] <2>Set the simulation parameters:

[0192] To verify the effectiveness of the method of the present invention for problems such as noise and outliers in the collected data, assume that the output data contains 10% outliers and mixed Gaussian noise.

[0193] <3>Simulation verification:

[0194] For the sake of convenient description, the method of the present invention is abbreviated as: ARX-Mix. As a comparison, the traditional method ARX-Lap is used to simulate the same simulation model. The comparison of the simulation results can well prove the effectiveness of the method of the present invention. To better verify the method of the present invention, for the ARX-Mix and ARX-Lap methods, when the outlier ratio is 10% and there is mixed Gaussian noise in the output measurement process, the system model parameters are estimated respectively. The specific simulation results are shown in Figures 2 to 5 . Figures 2 to 5 Figure 1 is a comparison diagram of the system parameter estimation curves of the method ARX-Mix of the present invention and the prior art ARX-Lap method when the outlier ratio is 10% and there is mixed Gaussian noise in the output measurement process. The solid curve represents the curve of the parameter estimation of the ARX-Mix method, the dashed curve represents the curve of the parameter estimation of the ARX-Lap method, and the dotted line represents the true value of the system parameters. The closer to the dotted line, the better the parameter estimation effect.

[0195] When the outlier ratio is 10% in the state update process and the output measurement process, the relative parameter estimation errors and the root mean square error RMSE of the parameter estimation of the ARX-Mix and ARX-Lap methods are shown in Table 1:

[0196] Table 1

[0197]

[0198] Summary of simulation results:

[0199] When the proportion of outliers increases, the standard deviation of each parameter continuously decreases. The smaller the standard deviation, the better the estimation effect.

[0200] Under the condition of the same outlier proportion, the parameter estimation effect of the ARX-Mix method of the present invention is significantly better than that of the ARX-Lap method as a comparison.

[0201] According to the simulation results in Table 1, it can be seen that compared with the method of the present invention, the RPEE value of the ARX-Lap method differs greatly from that of the ARX-Mix method, indicating that the method of the present invention has strong robustness in the case of outliers and mixed noise in the output measurement process.

[0202] The present invention provides a complex industrial process modeling method for a mixed noise distribution. There are many methods and ways to specifically implement this technical solution. The above is only the preferred embodiment of the present invention. It should be noted that for those of ordinary skill in the art, without departing from the principle of the present invention, several improvements and refinements can be made, and these improvements and refinements should also be regarded as the protection scope of the present invention. Each component not clearly defined in this embodiment can be implemented by the prior art.

[0203] In an embodiment of the present application, the present invention provides an electronic device, including a memory, a processor, and a computer program stored on the memory and executable on the processor. When the processor executes the program, the steps of the method described in any one of the above are implemented.

[0204] In an embodiment of the present application, the present invention provides a computer-readable storage medium, on which a computer program is stored. When the computer program is executed by a processor, the steps of the method described in any one of the above are implemented.

[0205] Each embodiment in this specification is described in a progressive manner. The same or similar parts between each embodiment can be referred to each other, and the key points of each embodiment are the differences from other embodiments.

[0206] Other embodiments of the present invention will be readily contemplated by those skilled in the art after considering the specification and practicing the invention herein. This application is intended to cover any variations, uses, or adaptations of the present invention that follow the general principles of the present invention and include known common general knowledge or conventional technical means in the technical field not invented by the present invention. The specification and examples are only regarded as exemplary. The above specific embodiments have further detailed the purpose, technical solution, and beneficial effects of this application. It should be understood that the above are only the specific embodiments of this application and are not used to limit the protection scope of this application. Any modifications, equivalent replacements, improvements, etc. made on the basis of the technical solution of this application shall be included in the protection scope of this application.

Claims

1. A prediction method for complex industrial processes facing mixed noise distributions, characterized in that, Including: Input the pre-acquired joystick position measurement values into the trained ARX model, and the ARX model predicts and outputs the cylinder displacement data; Among them, training the completed ARX model includes: Step 1: Collect data with mixed noise characteristics in the offline state of the hydraulic excavator system and construct a data set. The data with mixed noise characteristics includes the joystick position and the actual cylinder displacement value; Take the joystick position as the input data of the ARX model of the hydraulic excavator system, and take the actual cylinder displacement value as the output data of the ARX model of the hydraulic excavator system. Construct the mapping relationship between the joystick position and the actual cylinder displacement value in the ARX model of the hydraulic excavator system to obtain the ARX model of the hydraulic excavator system; Step 2: Introduce the prior distributions of the system noise distribution and the model parameters into the ARX model to obtain the probability description of the hydraulic excavator system identification problem. Set the system noise to follow a Gaussian distribution and K-1 Laplace distributions with appropriate weights; Step 3: Based on the data set and the probability description of the hydraulic excavator system identification problem, iteratively update the ARX model parameters of the hydraulic excavator system within the framework of the expectation maximization algorithm to obtain the ARX model parameters to be identified, and obtain the trained ARX model.

2. A complex industrial process prediction method for a mixed noise distribution according to claim 1, characterized in that The expression of the ARX model of the hydraulic excavator system is: Among them, represents the predicted value of the cylinder displacement, and ε n is the random noise of the hydraulic excavator system, x n is the joystick position collected by the input data matrix, n a is the order of the autoregressive part, n b is the order of the input part, and β is the parameter of the ARX model to be identified. is the pre-acquired data set, x n is the nth joystick position, y n is the actual value of the nth cylinder displacement, and N is the total number of joystick positions.

3. A complex industrial process prediction method for a mixed noise distribution according to claim 1, characterized in that Step 2 includes: Step 2-1: Set the system noise to follow a Gaussian distribution and K-1 Laplace distributions with appropriate weights: Among them, τ k is the Laplace distribution weight, and τ1 is the Gaussian distribution weight. is the probability density function of the noise following a Gaussian distribution, and L(ε|0, σ L；k ) is the probability density function of the noise following a Laplace distribution. The set of mixed noise weights is Γ = {τ1, τ2…, τ K}}, and the variance is Set the prior probability of the ARX model parameters to be identified to follow a Gaussian distribution:

4. A complex industrial process prediction method for a mixed noise distribution according to claim 3, characterized in that Step 2-2: The random variable following the Laplace distribution is expressed as a random variable following the normal distribution and the exponential distribution. The expression of the probability density function of the exponential distribution: In the formula, g(v) is the probability density function of the exponential distribution, and v is the random variable related to the exponential distribution; Given v, the conditional distribution of the random variable x is a normal distribution: In the formula, is the probability density function of the exponential distribution, η is the mathematical expectation of the normal distribution, i.e., the mean value, and μ is the standard deviation of the normal distribution; The probability density function of the random variable of the Laplace distribution is: wherein, is the decomposed form of the probability density function of the Laplace distribution, x is a random variable, μ is the location parameter, η is the scale parameter, and v is a random variable related to the exponential distribution; Actual value y of the cylinder displacement n The probability density function of which is as follows: where p(y n |x n , β, Γ, ∑) is the probability density function of the actual value y n of the cylinder displacement, is the Gaussian distribution component, and L(y n |h(x n )β, σ L；k ) is the Laplace distribution component; Obtain the probability density function of the actual cylinder displacement value by introducing the exponential distribution-related variable: where p(y n , v n |x n , β, Γ, ∑) is the probability density function for obtaining the actual value of the cylinder displacement by introducing variables related to the exponential distribution.

5. A complex industrial process prediction method for a mixed noise distribution according to claim 4, characterized in that Step 2-3: Introduce latent variables When y n comes from the k-th component, z kn = 1; otherwise z kn = 0. Therefore, the prior distribution of z n is as follows: Based on the complete data (x n , y n , v n , z n ), the joint probability density function is obtained as follows: where p(y n , v n , z n | x n , β, Γ, Σ) is the joint probability density function based on the complete data (x n , y n , v n , z n ), p(y n , v n | x n , β, Γ, Σ) is the joint probability density function based on the data without the latent variable z n , and p(z n ) is the prior distribution of the latent variable z n . Given a complete data set $T = \{X, y, v, Z\}$, where $X$ is the set of all joystick positions, $y$ is the set of all cylinder displacement data, and $v$ is a random variable related to the exponential distribution, which is the introduced latent variable, the likelihood function is determined as follows: In the formula, p(y, v, Z|X, β, Γ, Σ) is the expression of the likelihood function after introducing the latent variable; According to Bayes' theorem, determine the posterior probability density of the model parameter β; In the formula, is the posterior probability density of the model parameter β, is the prior probability density of the model parameter β; Take the logarithm of: where σ g is the variance of the Gaussian distribution, is the variance of the k-th Laplace distribution, P is the model order, and c is a constant.

6. A complex industrial process prediction method for a mixed noise distribution according to claim 1, characterized in that Step 3 includes: Step 3-1, Initialize the model parameter β to be estimated, and set the iteration number s to 1; Step 3-2, execute step E-step, for the data set D = {x n ,y n }calculate Conditional expectation of the posterior distribution, omitting parameters Irrelevant terms contain v n , we obtain the Q-function: Step 3-3, perform the M-step, and obtain new parameter estimates by optimizing the Q-function such that the parameter satisfies the constraint condition: Step 3-4: Increase the value of s by 1, and return to Step 3-2. Continuously repeat the execution of Step E-step and Step M-step until the parameters of the ARX model to be identified meet the convergence condition. The convergence condition is: where q is the number of iterations.

7. A complex industrial process prediction method for a hybrid noise distribution according to claim 6, characterized in that: In Step 3-2, the Step E-step includes: For the data set D = {x n ,y n }calculate The conditional expectation of the posterior distribution, removing the n The term determines the Q-function: Among them, represents the expectation operator, and c1 represents a constant independent of the parameter , P = n a + n b is the sum of the orders of the autoregressive and input parts; When k = 1, determine In the formula, is the probability density function of the Laplace distribution component is the probability density function of the Gaussian distribution component; When k ≥ 2, determine where γ kn is a defined value; Determine Determine the Q-function: where γ 1n is a defined value.

8. A complex industrial process prediction method for a hybrid noise distribution according to claim 6, characterized in that: In Step 3-3, the Step M-step includes: Calculation Maximize the cost loss function Let The following iterative formula is obtained: wherein, is the variance of the (q + 1)-th iteration of the Gaussian distribution, is the variance of the (q + 1)-th iteration of the k-th Laplace distribution, and β (q+1) is the model parameter of the (q + 1)-th iteration, is the prior of β of the (q + 1)-th iteration, Ψ is a diagonal matrix composed of , and I p is a P-dimensional identity matrix; By iteratively looping through Step 3-2 and Step 3-3, the convergence condition for the parameters β of the ARX model to be identified is:

9. An electronic device, comprising a memory, a processor, and a computer program stored on 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 8.

10. A computer-readable storage medium having a computer program stored thereon, characterized in that, When the computer program is executed by the processor, it implements the steps of the method according to any one of claims 1 to 8.

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