A robust soft measurement method for density of dense medium suspension based on mixed distribution

Abstract

The application discloses a heavy medium suspension density robust soft measurement method based on a mixed distribution, valve opening data is input into a trained heavy medium suspension density robust soft measurement model, and target heavy medium suspension density data is output; the heavy medium suspension density robust soft measurement model is trained, and the method comprises the following steps: constructing a nonlinear state space model based on the density control loop characteristics of a density loop system in a heavy medium coal separation process; collecting historical operation data of a densimeter to construct an identification data set; the nonlinear state space model comprises a state transition equation and an output measurement equation; a noise characteristic is modeled by using a mixed probability distribution theory to obtain a nonlinear state space robust probability model; joint parameter identification and state estimation are performed by using an expectation maximization algorithm, optimal parameter combinations of the nonlinear state space robust probability model are determined by iterative optimization, a heavy medium suspension density robust soft measurement model is obtained, and the problem that a traditional soft measurement method has poor robustness is effectively solved.

Description

Technical Field

[0001] This invention relates to a robust soft measurement method for the density of heavy medium suspensions based on mixed distribution, belonging to the technical field of robust soft measurement methods for the density of heavy medium suspensions based on mixed distribution. Background Technology

[0002] In heavy media coal preparation processes, precise control of suspension density directly determines separation accuracy and product quality. Currently, coal preparation plants primarily rely on densitometers for online density detection. However, the widely used differential pressure densitometers in coal preparation plants suffer from large measurement errors, requiring daily manual sampling and calibration, and cannot provide real-time and accurate suspension density values ​​during heavy media separation. Furthermore, high-precision sensors rely on imported equipment, which is costly. With the advancement of intelligent coal preparation plants, methods for constructing soft measurement models based on manually analyzed density data are emerging. However, manual density analysis suffers from slow detection speed and delayed results; when coal quality changes abruptly, model parameter updates are often delayed, easily leading to prediction bias. Conversely, using real-time densitometer measurements for soft measurement model construction is difficult to achieve due to significant measurement errors, hindering the establishment of high-precision soft measurement models. Summary of the Invention

[0003] The technical problem to be solved by the present invention is to overcome the defects of the prior art and provide a robust soft measurement method for the density of heavy medium suspensions based on mixed distribution. The model detection accuracy reaches the level of manual laboratory testing, which effectively solves the problem of poor robustness of traditional soft measurement methods.

[0004] Preferably, the present invention provides a robust soft measurement method for the density of heavy medium suspensions based on mixed distribution, comprising:

[0005] Input the valve opening data into the trained robust soft measurement model of the heavy medium suspension density, and output the target heavy medium suspension density data.

[0006] Among them, the robust soft measurement model for the density of heavy medium suspensions was obtained through training, including:

[0007] Step 1: Based on the density control loop characteristics of the density loop system in the heavy medium coal preparation process, construct a nonlinear state-space model; collect historical operating data of the density meter to construct an identification dataset for the density loop system in the heavy medium coal preparation process.

[0008] The nonlinear state-space model includes state transition equations and output measurement equations;

[0009] Step 2: Model the noise characteristics using the mixed probability distribution theory to obtain a nonlinear state-space robust probabilistic model;

[0010] Step 3: Use the expectation-maximization algorithm to identify joint parameters and estimate the state. Determine the optimal parameter combination of the nonlinear state-space robust probabilistic model through iterative optimization, and obtain the optimized density robust soft measurement model of the heavy medium suspension.

[0011] Prioritize that, in step 1, the density loop system of the heavy medium coal preparation process is simplified into a single-input, single-output system with the feedwater valve opening as input and the density of the heavy medium suspension in the qualified medium tank as output:

[0012]

[0013] Among them, Q mf and ρ wf ρ represents the volumetric flow rate and density of the heavy medium suspension, respectively. w ρ represents the density of pure water. cf Q represents the density of the heavy medium recovered at the outlet of the magnetic separator. cf Q represents the volumetric flow rate of the heavy medium flowing into the qualified medium tank after passing through the magnetic separator; hm and ρ bm V represents the volumetric flow rate and density of the high-concentration medium added from the high-concentration medium tank to the qualified medium tank, respectively; cor Indicates the volume of the heavy medium suspension in the qualified medium tank; Q w This indicates the volumetric flow rate of clean water added to the qualified medium tank through the water supply valve;

[0014] A Taylor expansion is performed at the operating point to establish the following nonlinear state-space model:

[0015] x(k+1)=f(u(k),x(k),θ f )+w(k)

[0016] y(k)=g(x(k),θ g )+e(k),

[0017] Where k represents the sampling time, x(k+1) is the density state at time k+1, and x(k) represents the density state at time k; y(k) and y(k+1) represent the density meter measurement data at sampling time k and sampling time k+1, respectively; u(k) represents the water supply valve opening at sampling time k; f(·) represents the nonlinear state transition function; g(·) represents the nonlinear output measurement function; and θ f and θ g Let w(k) and e(k) represent the model parameters, and w(k) and e(k) represent the system noise.

[0018] Preferably, the state transition equation in step 1 is:

[0019] x(k+1)=b0u(k)+f v (x(k),a1)+w(k),

[0020] Where x(k+1) is the density state at time k+1; x(k) represents the density state at time k; k represents the sampling time; u(k) represents the opening degree of the water supply valve at sampling time k; a1 and b0 represent model parameters; and f v (·) represents a nonlinear functional relationship, and w(k) represents system noise;

[0021] The output measurement equation mentioned in step 1 is:

[0022] y(k) = x(k) + e(k),

[0023] Where y(k) represents the density meter measurement data at sampling time k, and e(k) represents the system noise;

[0024] In step 1, the discrete state-space model is as follows:

[0025] x k+1 =b0u k +f v (x k ,a1)+w k

[0026] y k =x k +e k ,

[0027] Where, x k+1 =x(k+1),x k =x(k), x k+1 x k Let x(k+1) and x(k) represent the state variables of the density loop system at time k+1 and time k, respectively, where x(k+1) is the density state at time k+1 and x(k) is the density state at time k; b0 represents the model parameters, and u... k =u(k), u k This represents the input to the density loop system at time k, i.e., the opening degree of the water supply valve; y k =y(k),y k This represents the output data collected by the density loop system, i.e., the data collected by the density meter; f v (x(k),a1) represents the nonlinear dynamics in the density loop, denoted as x(k),a1. w k ,e k These are the state noise and measurement noise of the density loop system, respectively.

[0028] Prioritize, in step 2, w k Set to zero-mean Gaussian white noise, following the distribution N(w k |0,R w ), Rw The variance is a Gaussian distribution; the noise e is modeled using a Gaussian-Student's t mixture distribution. k :

[0029] w k ~GStM(e k |τ1,τ2,μ en ,μ es ,R en ,R es ,v)=τ1N(e k |μ en ,R en )+τ2St(e k |μ es ,R es ,v),

[0030] Where GStM represents the Gaussian-Student's t-mixture distribution, and N(·) represents the Gaussian distribution; e k The measurement noise of the density loop system is given by: St represents the Student's t-distribution; τ1 and τ2 represent the mixed weights of the Gaussian and Student's t-distributions, respectively, and τ1 + τ2 = 1; μ en and R en Let μ represent the mean and variance of the Gaussian distribution, respectively; es R es v and v represent the mean, scale parameter, and degrees of freedom parameter of the Student's t-distribution, respectively;

[0031] The state variables and output variables of the density loop follow the following distribution:

[0032]

[0033] y k ~GStM(y k |x k ,τ1,τ2,μ en ,μ es ,R en ,R es ,v),

[0034] In the formula, x(k+1) is the density state at time k+1; x(k) represents the density state at time k; a1 and b0 represent the model parameters; y k This represents the output data collected by the density loop system, i.e., the data collected by the density meter;

[0035] In step 2, the auxiliary variable β is introduced. k The mixture distribution is decomposed into a mixture of Gaussian and gamma distributions, resulting in the following output variable distribution:

[0036] y k~GStM(y k |x k ,τ1,τ2,μ en ,μ es ,R en ,R es ,v)

[0037] =τ1N(e k |x k ,μ en ,R en )+τ2∫N(e k |x k ,μ es ,R es / β k )G(β k |v / 2,v / 2)dβ k ,

[0038] Where G(·) represents the gamma distribution, β k These are the auxiliary variables introduced.

[0039] Prioritize introducing the auxiliary variable β in step 2. k The mixture distribution is decomposed into a mixture of Gaussian and gamma distributions, resulting in the following output variable distribution:

[0040] y k ~GStM(y k |x k ,τ1,τ2,μ en ,μ es ,R en ,R es ,v)

[0041] =τ1N(e k |x k ,μ en ,R en )+τ2∫N(e k |x k ,μ es ,R es / β k )G(β k |v / 2,v / 2)dβ k ,

[0042] Where G(·) represents the gamma distribution;

[0043] In step 2, a Bernoulli random variable d is introduced. k ={d 1k ,d 2k}, d k The probability density function is:

[0044]

[0045] The probability density function of the output variable is:

[0046]

[0047] Where Θ={τ1,τ2,μ en ,μ es ,R w ,R en ,R es ,u} represents the noise parameter.

[0048] Firstly, in step 3, the initial parameter Ω to be estimated is defined. 1 The iteration number s is set to 1; the E-step step under the EM algorithm framework includes calculating the cost function Q(Ω|Ω) of the density loop system in the heavy medium sorting process. s ):

[0049]

[0050] in To identify the log-likelihood function of the dataset and the latent dataset; Ω s These are the parameters of the current nonlinear state-space model; To identify the dataset, u 1:N Indicates that the water supply valve is open (β). 1:N Degree, y 1:N This represents the density data measured by the densitometer; For the hidden dataset, x 1:N The state variables of the density loop system are represented by Ω = {a1, b0, Θ}, which are the model parameters to be identified. express The expected value of the condition;

[0051] In the E-step step within the EM algorithm framework, the Q function is calculated given the identification dataset M, along with the log-likelihood functions of the identification dataset and the latent dataset. for:

[0052]

[0053] Where, const = log p(u 1:N |Ω) represents the constant term;

[0054] Based on the probability chain rule, the log-likelihood function is simplified. For log p(y) 1:N ,u 1:N ,x 1:N ,β 1:N ,d 1:N|Ω):

[0055]

[0056] log p(y 1:N ,u 1:N ,x 1:N ,β 1:N ,d 1:N |Ω) Joint distribution log p(y k ,d k |u k ,x k ,β k ,Ω) is further expressed as log p(y k ,d k |u k ,x k ,β k ,Ω):

[0057] log p(y k ,d k |u k ,x k ,β k ,Ω)=log(p(y k |u k ,d k ,x k ,β k ,Ω)p(d k |Ω))

[0058] =d 1k log[τ1N(y k |μ en ,x k ,R en )]+d 2k log[τ2St(y k |μ es ,x k ,R es ,v,β k )],

[0059] Calculate about the hidden dataset The conditional expectation is used to obtain the Q function Q(Ω|Ωs). ) :

[0060]

[0061]

[0062] in, <d 1k > l and <d 2k > ld 1k and d 2k The corresponding mathematical expectations represent the output data y. k Given the posterior probabilities belonging to both the Gaussian and Student's t-distributions, calculate the combined probability density function:

[0063]

[0064] In the formula, Let be the mean parameter of the Gaussian distribution in the mixture distribution at the s-th iteration. Let be the variance parameter of the Gaussian distribution in the mixture distribution at the s-th iteration. Let be the mean parameter of the Student's t-distribution in the mixed distribution at the s-th iteration. Let v be the scaling parameter of the Student's t-distribution in the mixed distribution at the s-th iteration. s Let be the degree of freedom parameter of the Student's t-distribution in the mixed distribution at the s-th iteration.

[0065] Prioritizes step 3, where the Q-function is calculated using the particle smoothing algorithm:

[0066]

[0067] Where N is the data length, Γ is the gamma function, and L represents the total number of particles; This represents the state quantity represented by the l-th particle at sampling time k+1 and sampling time k; This represents the particle smoothing weights at sampling time k+1 and sampling time k; <β k > l and <log β k > l Indicates β k and log β k The corresponding mathematical expectation; const1 is the constant term;

[0068] <β k > l and (log β) k > l for:

[0069]

[0070] In the formula, log() is the logarithmic function and Ψ() is the digamma function.

[0071] Firstly, in step 3, the Q-function is maximized to obtain the mixed weight estimate; the terms in the Q-function concerning the mixed weights are retained:

[0072]

[0073] Based on the terms related to the mixture weights in the Q-function, update the mixture weights and calculate the average posterior probability:

[0074]

[0075] Prior to this, the M-step step within the EM algorithm framework in step 3 includes calculating the derivative of the Q function with respect to the parameters and setting the derivative of the parameters equal to zero to obtain μ. en Iterative estimates μ es Iterative estimates R w Iterative estimates R en Iterative estimates and R es Iterative estimates

[0076]

[0077] In the formula, f v (·) represents a nonlinear functional relationship;

[0078] Calculate the iterative estimate of the degree-of-freedom parameter v, and set the partial derivative of the Q function with respect to the degree-of-freedom parameter v equal to 0, then we get:

[0079]

[0080] An iterative estimate of v is obtained by solving the above equation using a function solver;

[0081] The model parameter a1 is estimated by maximizing the Q function. and the estimate of b0

[0082]

[0083] In the formula, in the formula, For the l-th particle at the (k+1)-th sampling time, Let a1 be the parameter in the s-th iteration. Let b0 be the parameter in the s-th iteration. This refers to the l-th particle at the k-th sampling time.

[0084] Prioritize step 3 by repeatedly executing the E-step and M-step steps until the maximum number of iterations is reached; then obtain the final iteration result. The parameter a1 obtained in the last iteration, The parameter b0 is obtained from the last iteration. The parameter τ1 is obtained from the last iteration. The parameter τ2 is obtained from the last iteration. The parameter μ obtained in the last iteration en , The parameter μ obtained in the last iteration es , The parameter R obtained for the last iteration w , The parameter R obtained for the last iteration en , The parameter R obtained for the last iteration es v * For all parameters The final iterative results yielded a robust soft measurement model for the density of the heavy medium suspension.

[0085] 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.

[0086] 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 one of the first aspects.

[0087] The beneficial effects achieved by this invention are as follows:

[0088] This invention addresses the issue of poor robustness of existing soft measurement methods due to density meter measurement errors and other measurement errors. It proposes a robust identification method for nonlinear state-space systems based on mixed distribution, which can effectively establish a robust soft measurement model for the density of heavy medium suspensions. Through systematic integration of dynamic modeling, probabilistic robustness enhancement, and adaptive parameter optimization, it achieves detection accuracy similar to manual testing, significantly improving the intelligence level of density control in heavy medium separation and providing theoretical support for achieving unmanned density control throughout the entire coal preparation plant process. Attached Figure Description

[0089] 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.

[0090] Figure 1 This is a flowchart of the present invention;

[0091] Figure 2 This is a diagram illustrating the identification framework of the method of the present invention under mixed distribution.

[0092] Figure 3This is a schematic diagram of the density prediction results of the algorithm in the Matlab environment; Detailed Implementation

[0093] See Figure 1 This application discloses a robust soft measurement method for the density of heavy medium suspensions based on mixed distribution, comprising:

[0094] Input the valve opening data into the trained robust soft measurement model of the heavy medium suspension density, and output the target heavy medium suspension density data.

[0095] Among them, the robust soft measurement model for the density of heavy medium suspensions was obtained through training, including:

[0096] Step 1: Based on the density control loop characteristics of the density loop system in the heavy medium coal preparation process, construct a nonlinear state-space model; collect historical operating data of the density meter to construct an identification dataset for the density loop system in the heavy medium coal preparation process.

[0097] The nonlinear state-space model includes state transition equations and output measurement equations;

[0098] Step 2: Model the noise characteristics using the mixed probability distribution theory to obtain a nonlinear state-space robust probabilistic model;

[0099] Step 3: Use the expectation-maximization algorithm to identify joint parameters and estimate the state. Determine the optimal parameter combination of the nonlinear state-space robust probabilistic model through iterative optimization, and obtain the optimized density robust soft measurement model of the heavy medium suspension.

[0100] Furthermore, in step 1, the density loop system of the heavy medium coal preparation process is simplified into a single-input, single-output system with the feedwater valve opening as input and the density of the heavy medium suspension in the qualified medium tank as output:

[0101]

[0102] Among them, Q mf and ρ mf ρ represents the volumetric flow rate and density of the heavy medium suspension, respectively. w ρ represents the density of pure water. cf Q represents the density of the heavy medium recovered at the outlet of the magnetic separator. cf Q represents the volumetric flow rate of the heavy medium flowing into the qualified medium tank after passing through the magnetic separator; hm and ρ hm V represents the volumetric flow rate and density of the high-concentration medium added from the high-concentration medium tank to the qualified medium tank, respectively; cor Indicates the volume of the heavy medium suspension in the qualified medium tank; Q w This indicates the volumetric flow rate of clean water added to the qualified medium tank through the water supply valve;

[0103] A Taylor expansion is performed at the operating point to establish the following nonlinear state-space model:

[0104] x(k+1)=f(u(k),x(k),θ f )+w(k)

[0105] y(k)=g(x(k),θ g )+e(k),

[0106] Where k represents the sampling time, x(k+1) is the density state at time k+1, and x(k) represents the density state at time k; y(k) and y(k+1) represent the density meter measurement data at sampling time k and sampling time k+1, respectively; u(k) represents the water supply valve opening at sampling time k; f(·) represents the nonlinear state transition function; g(·) represents the nonlinear output measurement function; and θ f and θ g Let w(k) and e(k) represent the model parameters, and w(k) and e(k) represent the system noise.

[0107] Furthermore, the state transition equation described in step 1 is:

[0108] x(k+1)=b0u(k)+f v (x(k),a1)+w(k),

[0109] Where x(k+1) is the density state at time k+1; x(k) represents the density state at time k; k represents the sampling time; u(k) represents the opening degree of the water supply valve at sampling time k; a1 and b0 represent model parameters; and f v (·) represents a nonlinear functional relationship, and w(k) represents system noise;

[0110] The output measurement equation mentioned in step 1 is:

[0111] y(k) = x(k) + e(k),

[0112] Where y(k) represents the density meter measurement data at sampling time k, and e(k) represents the system noise;

[0113] In step 1, the discrete state-space model is as follows:

[0114] x k+1 =b0u k +f v (x k ,a1)+w k

[0115] y k =x k +e k ,

[0116] Where, x k+1 =x(k+1),x k =x(k), x k+1 x k Let x(k+1) and x(k) represent the state variables of the density loop system at time k+1 and time k, respectively, where x(k+1) is the density state at time k+1 and x(k) is the density state at time k; b0 represents the model parameters, and y k =u(k), y k This represents the input to the density loop system at time k, i.e., the opening degree of the water supply valve; y k =y(k),y k This represents the output data collected by the density loop system, i.e., the data collected by the density meter; f v (x(k),a1) represents the nonlinear dynamics in the density loop, denoted as x(k),a1. w k ,e k These are the state noise and measurement noise of the density loop system, respectively.

[0117] Furthermore, in step 2, w k Set to zero-mean Gaussian white noise, following the distribution N(w k |0,R w ), R w The variance is a Gaussian distribution; the noise e is modeled using a Gaussian-Student's t mixture distribution. k :

[0118] w k ~GStM(e k |τ1,τ2,μ en ,μ es ,R en ,R es ,v)=τ1N(e k |μ en ,R en )+τ2St(e k |μ es ,R es ,v),

[0119] Where GStM represents the Gaussian-Student's t-mixture distribution, and N(·) represents the Gaussian distribution; e k The measurement noise of the density loop system is given by: St represents the Student's t-distribution; τ1 and τ2 represent the mixed weights of the Gaussian and Student's t-distributions, respectively, and τ1 + τ2 = 1; μ en and R en Let μ represent the mean and variance of the Gaussian distribution, respectively; es R es v and v represent the mean, scale parameter, and degrees of freedom parameter of the Student's t-distribution, respectively;

[0120] The state variables and output variables of the density loop follow the following distribution:

[0121]

[0122] y k ~GStM(y k |x k ,τ1,τ2,μ en ,μ es ,R en ,R es ,v),

[0123] In the formula, x(k+1) is the density state at time k+1; x(k) represents the density state at time k; a1 and b0 represent the model parameters; y k This represents the output data collected by the density loop system, i.e., the data collected by the density meter;

[0124] In step 2, the auxiliary variable β is introduced. k The mixture distribution is decomposed into a mixture of Gaussian and gamma distributions, resulting in the following output variable distribution:

[0125] y k ~GStM(y k |x k ,τ1,τ2,μ en ,μ es ,R en ,R es ,v)

[0126] =τ1N(e k |x k ,μ en ,R en )+τ2∫N(e k |x k ,μ es ,R es / β k )G(β k |v / 2,v / 2)dβ k ,

[0127] Where G(·) represents the gamma distribution, β k These are the auxiliary variables introduced.

[0128] Furthermore, in step 2, an auxiliary variable β is introduced. k The mixture distribution is decomposed into a mixture of Gaussian and gamma distributions, resulting in the following output variable distribution:

[0129] y k ~GStM(yk |x k ,τ1,τ2,μ en ,μ es ,R en ,R es ,v)

[0130] =τ1N(e k |x k ,μ en ,R en )+τ2∫N(e k |x k ,μ es ,R es / β k )G(β k |v / 2,v / 2)dβ k ,

[0131] Where G(·) represents the gamma distribution;

[0132] In step 2, a Bernoulli random variable d is introduced. k ={d 1k ,d 2k}, d k The probability density function is:

[0133]

[0134] The probability density function of the output variable is:

[0135]

[0136]

[0137] Where Θ={τ1,τ2,μ es ,μ es ,R w ,R en ,R es ,v} represents the noise parameter.

[0138] Furthermore, in step 3, the initial parameter Ω to be estimated is defined. 1 The iteration number s is set to 1; the E-step step under the EM algorithm framework includes calculating the cost function Q(Ω|Ω) of the density loop system in the heavy medium sorting process. s ):

[0139]

[0140] in To identify the log-likelihood function of the dataset and the latent dataset; Ω s These are the parameters of the current nonlinear state-space model; To identify the dataset, u 1:N Indicates that the water supply valve is open (β). 1:N Degree, y 1:N This represents the density data measured by the densitometer; For the hidden dataset, x 1:N The state variables of the density loop system are represented by Ω = {a1, b0, Θ}, which are the model parameters to be identified. express The expected value of the condition;

[0141] In the E-step step within the EM algorithm framework, the Q function is calculated given the identification dataset M, along with the log-likelihood functions of the identification dataset and the latent dataset. for:

[0142]

[0143] Where, const = log p(u 1:N |Ω) represents the constant term;

[0144] Based on the probability chain rule, the log-likelihood function is simplified. For log p(y) 1:N ,u 1:N ,x 1:N ,β 1:N ,d 1:N |Ω):

[0145]

[0146] log p(y 1:N ,u 1:N ,x 1:N ,β 1:N ,d 1:N |Ω) Joint distribution log p(y k ,d k |u k ,x k ,β k ,Ω) is further expressed as log p(y k ,d k |u k ,x k ,β k ,Ω):

[0147] log p(y k ,d k |u k ,x k ,β k ,Ω)=log(p(y k |u k,d k ,x k ,β k ,Ω)p(d k |Ω))

[0148] =d 1k log[τ1N(y k |μ en ,x k ,R en )]+d 2k log[τ2St(y k |μ es ,x k ,R es ,v,β k )],

[0149] Calculate about the hidden dataset The conditional expectation is obtained by deriving the Q function Q(Ω|Ω). s ):

[0150]

[0151] in, <d 1k > l and <d 2k > l d 1k and d 2k The corresponding mathematical expectations represent the output data y. k Given the posterior probabilities belonging to both the Gaussian and Student's t-distributions, calculate the combined probability density function:

[0152]

[0153] In the formula, Let be the mean parameter of the Gaussian distribution in the mixture distribution at the s-th iteration. Let be the variance parameter of the Gaussian distribution in the mixture distribution at the s-th iteration. Let be the mean parameter of the Student's t-distribution in the mixed distribution at the s-th iteration. Let v be the scaling parameter of the Student's t-distribution in the mixed distribution at the s-th iteration. s Let be the degree of freedom parameter of the Student's t-distribution in the mixed distribution at the s-th iteration.

[0154] Furthermore, in step 3, the Q-function is calculated using the particle smoothing algorithm:

[0155]

[0156] Where N is the data length, Γ is the gamma function, and L represents the total number of particles; This represents the state quantity represented by the l-th particle at sampling time k+1 and sampling time k; This represents the particle smoothing weights at sampling time k+1 and sampling time k; <β k > l and <log β k > l Indicates β k and log β k The corresponding mathematical expectation; const1 is the constant term;

[0157] <β k > l and <log β k > l for:

[0158]

[0159]

[0160] In the formula, log() is the logarithmic function and Ψ() is the digamma function.

[0161] Furthermore, in step 3, the Q-function is maximized to obtain the mixed weight estimate; the terms in the Q-function concerning the mixed weights are retained:

[0162]

[0163] Based on the terms related to the mixture weights in the Q-function, update the mixture weights and calculate the average posterior probability:

[0164]

[0165] Furthermore, in step 3, the M-step step within the EM algorithm framework includes calculating the derivative of the Q function with respect to the parameters and setting the derivative of the parameters equal to zero to obtain μ. en Iterative estimates μ es Iterative estimates R w Iterative estimates R en Iterative estimates and R es Iterative estimates

[0166]

[0167] In the formula, f v (·) represents a nonlinear functional relationship;

[0168] Calculate the iterative estimate of the degree-of-freedom parameter v, and set the partial derivative of the Q function with respect to the degree-of-freedom parameter v equal to 0, then we get:

[0169]

[0170] An iterative estimate of v is obtained by solving the above equation using a function solver;

[0171] The model parameter a1 is estimated by maximizing the Q function. and the estimate of b0

[0172]

[0173] In the formula, in the formula, For the l-th particle at the (k+1)-th sampling time, Let a1 be the parameter in the s-th iteration. Let b0 be the parameter in the s-th iteration. This refers to the l-th particle at the k-th sampling time.

[0174] Furthermore, in step 3, the E-step and M-step steps are repeatedly executed until the maximum number of iterations is reached; the final iteration result is then obtained. The parameter a1 obtained in the last iteration, The parameter b0 is obtained from the last iteration. The parameter τ1 is obtained from the last iteration. The parameter τ2 is obtained from the last iteration. The parameter μ obtained in the last iteration en , The parameter μ obtained in the last iteration es , The parameter R obtained for the last iteration w , The parameter R obtained for the last iteration en , The parameter R obtained for the last iteration es v * For all parameters The final iterative results yielded a robust soft measurement model for the density of the heavy medium suspension.

[0175] 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.

[0176] 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.

[0177] Example

[0178] In this embodiment, the robust soft measurement method for the density of heavy medium suspensions based on mixed distribution is implemented according to the following steps:

[0179] Step 1: Collect the water supply valve opening and density meter data of the density loop system in the heavy medium separation process as the identification dataset and perform data preprocessing, i.e.

[0180] Step 2: Initialize parameter set Ω s And set s = 1;

[0181] Step 3: Update the posterior probability distribution and expectation:

[0182] Using the formula given in E-step, the smoothing probability density function p(x) is calculated using the particle smoothing algorithm. k |y 1:N ,Ω s ),p(x k ,x k-1 |y 1:N ,Ω s and the expected values ​​at each sampling time. <d 1k > l , <d 2k > l ,<β k > l , <log β k > l ;

[0183] Step 4: Update model parameter estimates:

[0184] Update model parameters a0, b1 and noise parameters τ1, τ2, μ en ,μ es ,R w ,R en ,R es ,vR w ,σ;

[0185] Step 5: Increment the value of s by 1 until the maximum number of iterations S is reached.

[0186] Data on the opening degree of the feedwater valves and the density meter data of the density loop system in the heavy medium separation process were collected as identification datasets and preprocessed; simulation parameters were set; simulation verification was performed.

[0187] For ease of description, the method of this invention is abbreviated as NSSM-GStM. Simulation experiments were conducted in the Matlab environment using the method proposed in this invention to verify the algorithm's performance. Figure 2 The figure presents 500 test results for the NSSM-GStM algorithm. The error bands in the figure represent the acceptable error range for density measurements in actual field conditions during heavy medium separation, and the circles represent the predicted values ​​of the NSSM-GStM algorithm. As can be seen from the figure, most predicted values ​​fall within the error bands, indicating that the estimates of the NSSM-GStM algorithm are closer to the true values ​​and can meet the soft measurement requirements for the density index of heavy medium suspensions in coal preparation fields. Table 1 records the results of 50 independent experiments comparing NSSM-GStM and the existing robust identification algorithm NSSM-Student. The comparison results of the mean ± standard deviation are shown in Table 1. As can be seen from Table 1, the NSSM-GStM algorithm has better overall performance. The NSSM-Student algorithm failed to meet the accuracy requirements, mainly because the differential pressure density meter in the field has a positive offset error, which the NSSM-Student algorithm did not consider in its design, thus affecting its identification accuracy. This result further verifies that the robust soft measurement model constructed by the NSSM-GStM algorithm has the best overall performance.

[0188] Table 1

[0189]

[0190] 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.

[0191] 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.

[0192] 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 robust soft measurement method for the density of heavy medium suspensions based on mixed distribution, characterized in that, include: Input the valve opening data into the trained robust soft measurement model of the heavy medium suspension density, and output the target heavy medium suspension density data. Among them, the robust soft measurement model for the density of heavy medium suspensions was obtained through training, including: Step 1: Based on the density control loop characteristics of the density loop system in the heavy medium coal preparation process, construct a nonlinear state-space model; collect historical operating data of the density meter to construct an identification dataset for the density loop system in the heavy medium coal preparation process. The nonlinear state-space model includes state transition equations and output measurement equations; Step 2: Model the noise characteristics using the mixed probability distribution theory to obtain a nonlinear state-space robust probabilistic model; Step 3: Use the expectation-maximization algorithm to identify joint parameters and estimate the state. Determine the optimal parameter combination of the nonlinear state-space robust probabilistic model through iterative optimization to obtain the optimized density robust soft measurement model of the heavy medium suspension. In step 1, the density loop system of the heavy medium coal preparation process is simplified into a single-input, single-output system with the feedwater valve opening as input and the density of the heavy medium suspension in the qualified medium tank as output: ， in, and These represent the volumetric flow rate and density of the heavy medium suspension, respectively. Indicates the density of pure water; This indicates the density of the heavy medium recovered at the outlet of the magnetic separator; This indicates the volumetric flow rate of the heavy medium flowing into the qualified medium tank after passing through the magnetic separator; and V represents the volumetric flow rate and density of the high-concentration medium added from the high-concentration medium tank to the qualified medium tank, respectively; cor Indicates the volume of heavy medium suspension in the qualified medium tank; This indicates the volumetric flow rate of clean water added to the qualified medium tank through the water supply valve; A Taylor expansion is performed at the operating point to establish the following nonlinear state-space model: ， in, Indicates the sampling time. for The density state at time k, x(k) represents the density state at time k; These represent the sampling times. and sampling time Densitometer measurement data, Indicates the sampling time The opening degree of the water supply valve, Represents a nonlinear state transition function. This represents a nonlinear output measurement function. and Indicates model parameters, and Indicates system noise; In step 2, Set to zero-mean Gaussian white noise, following the distribution R w The variance is a Gaussian distribution; a Gaussian-Student's t-mixture distribution is used to model the measurement noise. : ， Where GStM represents the Gaussian-Student's t-mixture distribution, Indicates a Gaussian distribution; e k The measurement noise of the density loop system; St represents the Student's t-distribution; and Let represent the mixed weights of the Gaussian distribution and the Student's t-distribution, respectively. ; and Let represent the mean and variance of the Gaussian distribution, respectively. , and Let represent the mean, scale parameter, and degrees of freedom parameter of the Student's t-distribution, respectively; The state variables and output variables of the density loop follow the following distribution: ， In the formula, for The density state at time k; x(k) represents the density state at time k. and Indicates model parameters, and Indicates model parameters; This represents the output data collected by the density loop system, i.e., the data collected by the density meter; In step 2, auxiliary variables are introduced. The mixture distribution is decomposed into a mixture of Gaussian and gamma distributions, resulting in the following output variable distribution: ， in, Represents the gamma distribution, β k Auxiliary variables introduced; In step 2, auxiliary variables are introduced. The mixture distribution is decomposed into a mixture of Gaussian and gamma distributions, resulting in the following output variable distribution: ， in, Indicates the gamma distribution; In step 2, a Bernoulli random variable is introduced. d k The probability density function is: ， The probability density function of the output variable is: ， in, This represents noise parameters.

2. The robust soft measurement method for the density of heavy medium suspensions based on mixed distribution according to claim 1, characterized in that, The state transition equation mentioned in step 1 is: ， in, for The density state at time k; x(k) represents the density state at time k; Indicates the sampling time. Indicates the sampling time The opening degree of the water supply valve, and Indicates model parameters, Represents a nonlinear functional relationship. Indicates system noise; The output measurement equation mentioned in step 1 is: ， in, Indicates the sampling time Densitometer measurement data, Indicates system noise; In step 1, the discrete state-space model is as follows: ， in, , , Representing density loop systems State quantity at time and State quantity at any given time. for The density state at time k; x(k) represents the density state at time k; Indicates model parameters, , Density loop system The input at any given time is the opening degree of the water supply valve; , This represents the output data collected by the density loop system, i.e., the data collected by the density meter; Let the nonlinear dynamics in the density loop be represented by . ; These are the state noise and measurement noise of the density loop system, respectively.

3. The robust soft measurement method for the density of heavy medium suspensions based on mixed distribution according to claim 1, characterized in that, In step 3, the initial parameters to be estimated are defined. The iteration number s is set to 1; the E-step step under the EM algorithm framework includes calculating the cost function of the density loop system in the heavy medium sorting process. : ， in To identify the log-likelihood function of the dataset and the implicit dataset; These are the parameters of the current nonlinear state-space model; To identify the dataset, Indicates that the water supply valve is open. Spend, This represents the density data measured by the densitometer; For the hidden dataset, where Represents the state variables of the density loop system, and represents the introduced auxiliary variables. These are the model parameters to be identified; express The expected value of the condition; In the E-step step within the EM algorithm framework, the Q function is calculated given the identification dataset M, along with the log-likelihood functions of the identification dataset and the latent dataset. for: ， in, Represents a constant term; Based on the probability chain rule, the log-likelihood function is simplified. for : ， Joint distribution Further expressed as : ， Calculate about the hidden dataset The conditional expectation is used to obtain the Q function. : ， in, and express and The corresponding mathematical expectations represent the output data. Given the posterior probabilities belonging to both the Gaussian and Student's t-distributions, calculate the combined probability density function: ， ， In the formula, Let be the mean parameter of the Gaussian distribution in the mixture distribution at the s-th iteration. Let be the variance parameter of the Gaussian distribution in the mixture distribution at the s-th iteration. Let be the mean parameter of the Student's t-distribution in the mixed distribution at the s-th iteration. Let v be the scaling parameter of the Student's t-distribution in the mixed distribution at the s-th iteration. s Let be the degree of freedom parameter of the Student's t-distribution in the mixed distribution at the s-th iteration.

4. The robust soft measurement method for the density of heavy medium suspensions based on mixed distribution according to claim 3, characterized in that, In step 3, the Q-function is calculated using the particle smoothing algorithm: ， Where N is the data length, Γ is the gamma function, and L represents the total number of particles; Indicates the sampling time and sampling time The Each particle represents a state quantity; Indicates the sampling time and sampling time Particle smoothing weights; and express and The corresponding mathematical expectation; For constant terms; and for: ， ， In the formula, log() is the logarithmic function and Ψ() is the digamma function.

5. The robust soft measurement method for the density of heavy medium suspensions based on mixed distribution according to claim 4, characterized in that, In step 3, maximize the Q function to obtain the mixed weight estimate; retain the terms in the Q function related to the mixed weights: ， Based on the terms related to the mixture weights in the Q-function, update the mixture weights and calculate the average posterior probability: ， 。 6. The robust soft measurement method for the density of heavy medium suspensions based on mixed distribution according to claim 5, characterized in that, Step 3, within the EM algorithm framework, involves the M-step step, which involves calculating the derivative of the Q function with respect to the parameters and setting the derivative of the parameters to zero, to obtain... Iterative estimates , Iterative estimates , Iterative estimates , Iterative estimates and Iterative estimates : ， ， ， ， ， In the formula, Represents a nonlinear functional relationship; Calculate the degree of freedom parameters The iterative estimation of the Q function with respect to the degree of freedom parameters Since the partial derivatives are equal to 0, we get: ， Solving the above equation using a function solver yields the following results. Iterative estimation; The model parameters are obtained by maximizing the Q function. Estimate and Estimate : ， ， In the formula, For the first The l-th particle at the sampling time, The parameters for the s-th iteration , The parameters for the s-th iteration , For the first The l-th particle at the sampling time.

7. The robust soft measurement method for the density of heavy medium suspensions based on mixed distribution according to claim 6, characterized in that, In step 3, the E-step and M-step steps are repeatedly executed until the maximum number of iterations is reached; the final iteration result is then obtained. , The parameter a1 obtained in the last iteration, The parameter b0 is obtained from the last iteration. The parameter τ1 is obtained from the last iteration. The parameter τ2 is obtained from the last iteration. The parameter μ obtained in the last iteration en , The parameter μ obtained in the last iteration es , The parameter R obtained for the last iteration w , The parameter R obtained for the last iteration en , The parameter R obtained for the last iteration es , For all parameters The final iterative results yielded a robust soft measurement model for the density of the heavy medium suspension.

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