Dense medium suspension density robust soft measurement method based on mixed distribution

Abstract

The invention discloses a dense-medium suspension density robust soft measurement method based on mixed distribution, which comprises the following steps: inputting valve opening data into a dense-medium suspension density robust soft measurement model obtained by training, and outputting target dense-medium suspension density data; training to obtain a dense-medium suspension density robust soft measurement model: constructing a nonlinear state space model based on density control loop characteristics of a dense-medium coal separation process density loop system; historical operation data of the densimeter is collected, and an identification data set is constructed; the nonlinear state space model comprises a state transition equation and an output measurement equation; modeling the noise characteristics by using a mixed probability distribution theory to obtain a nonlinear state space robust probability model; an expectation maximization algorithm is adopted to carry out joint parameter identification and state estimation, an optimal parameter combination of a nonlinear state space robust probability model is determined through iterative optimization, a dense medium suspension density robust soft measurement model is obtained, and the problem that a traditional soft measurement method is poor in robustness is effectively solved.

Description

Technical Field

[0001] The invention relates to a robust soft measurement method for density of a heavy medium suspension based on mixed distribution, and belongs to the technical field of a robust soft measurement method for density of a heavy medium suspension based on mixed distribution. Background Art

[0002] In the dense medium coal preparation process, precise control of suspension density directly determines separation accuracy and product quality. Currently, coal preparation plants primarily rely on densitometers for online density measurement. However, the differential pressure densitometers widely used in coal preparation plants suffer from significant measurement errors, requiring daily manual sampling, testing, and calibration. These instruments cannot accurately and accurately provide real-time density values for the dense medium separation process. Furthermore, high-precision sensors rely on imported equipment, which is costly. With the advancement of intelligent coal preparation plants, the construction of soft measurement models based on manually measured density data is gaining popularity. However, manual density data suffers from slow detection speeds and delayed results. When product coal quality changes suddenly, model parameter updates often lag, easily leading to prediction errors. Using real-time density data from densitometers to build soft measurement models also presents significant measurement errors, making it difficult to establish 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 existing technology and provide a robust soft measurement method for the density of heavy medium suspension based on mixed distribution. The model detection accuracy reaches the level of manual testing, which effectively solves the problem of poor robustness of traditional soft measurement methods.

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

[0005] The valve opening data is input into the trained robust soft-sensing model of heavy medium suspension density, and the target heavy medium suspension density data is output;

[0006] Among them, the training of the robust soft-sensing model for the density of heavy medium suspensions includes:

[0007] Step 1: Based on the density control loop characteristics of the density loop system of the heavy medium coal preparation process, a nonlinear state space model is constructed; historical operation data of the densitometer is collected to construct an identification data set of the density loop system of the heavy medium coal preparation process;

[0008] The nonlinear state space model includes a state transfer equation and an output measurement equation;

[0009] Step 2: Use the mixed probability distribution theory to model the noise characteristics and obtain a nonlinear state space robust probability model;

[0010] Step 3: Use the expectation maximization algorithm to perform joint parameter identification and state estimation, determine the optimal parameter combination of the nonlinear state space robust probability model through iterative optimization, and obtain the optimized robust soft measurement model of heavy medium suspension density.

[0011] Preferably, in step 1, the density loop system of the heavy medium coal preparation process is simplified to a single-input-single-output system with the water supply valve opening as input and the density of the heavy medium suspension in the qualified medium barrel as output:

[0012]

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

[0014] Perform Taylor expansion at the operating point and 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) represents 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 transfer function; g(·) represents the nonlinear output measurement function; θ f and θ g represents the model parameters, 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] Among them, 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 water supply valve opening at sampling time k, a1 and b0 represent model parameters, f v (·) represents the nonlinear functional relationship, w(k) represents the system noise;

[0021] The output measurement equation 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:

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

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

[0027] Among them, x k+1 =x(k+1),x k =x(k),x k+1 、x k They represent the state quantity of the density loop system at time k+1 and time k respectively, x(k+1) is the density state at time k+1; x(k) represents the density state at time k; b0 represents the model parameter, u k =u(k),u k represents the input of the density loop system at time k, i.e., the opening of the water supply valve; y k =y(k),y k Represents the output data collected by the density loop system, that is, the data collected by the density meter; f v (x(k),a1) represents the nonlinear dynamics in the density loop, set w k ,e k are the state noise and measurement noise of the density loop system, respectively.

[0028] Preferably, in step 2, w k Set to zero-mean Gaussian white noise, obey the distribution N(w k |0,R w ), Rw is the variance of the Gaussian distribution; the Gaussian-Student's t mixture distribution is used to model the measurement noise e 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 Gaussian-Student's t mixture distribution, N(·) represents Gaussian distribution; e k is the measurement noise of the density loop system; St represents the Student's t distribution; τ1 and τ2 represent the mixed weights of the Gaussian distribution and the Student's t distribution, respectively, and τ1+τ2=1; μ en and R en Respectively represent the mean and variance of Gaussian distribution; μ es 、R es and v represent the mean, scale parameter, and degree of freedom parameter of Student’s t distribution, respectively;

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

[0032]

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

[0034] Where x(k+1) is the density state at time k+1; x(k) is the density state at time k; a1 and b0 are model parameters; y k Indicates the output data collected by the density loop system, that is, the data collected by the density meter;

[0035] In step 2, the auxiliary variable β is introduced k The mixed distribution is decomposed into a mixture of Gaussian distribution and gamma distribution, and the output variable distribution is obtained as follows:

[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 is the auxiliary variable introduced.

[0039] Prior to step 2, an auxiliary variable β is introduced k The mixed distribution is decomposed into a mixture of Gaussian distribution and gamma distribution, and the output variable distribution is obtained as follows:

[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, the 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] Prior to step 3, define the initial parameter Ω to be estimated 1 , the number of iterations s is set to 1; the E-step step under the EM algorithm framework includes calculating the cost function Q(Ω|Ω s ):

[0049]

[0050] in is the log-likelihood function of the identification data set and the latent data set; Ω s are the parameters of the current nonlinear state space model; To identify the data set, u 1:N Indicates that the water supply valve is open 1:N Degree, y 1:N Indicates the density data measured by the densitometer; is an implicit data set, where x 1:N represents the state quantity of the density loop system, represents the auxiliary variable introduced, and Ω={a1,b0,Θ} is the model parameter to be identified; express The conditional expectation of

[0051] In the E-step of the EM algorithm framework, the Q function is calculated by giving the identification data set M, and the log-likelihood function of the identification data set and the implicit data set is for:

[0052]

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

[0054] Based on the probability chain rule, the log-likelihood function is simplified is 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] Calculation of implicit data sets The conditional expectation of Q function Q(Ω|Ωs ) :

[0060]

[0061]

[0062] in, <d 1k > l and <d 2k > lIndicates d 1k and d 2k The corresponding mathematical expectations represent the output data y k The posterior probability of belonging to the Gaussian distribution and the Student's t distribution is calculated as the combined probability density function:

[0063]

[0064] Where, is the mean parameter of the Gaussian distribution in the mixed distribution at the sth iteration, is the variance parameter of the Gaussian distribution in the mixed distribution at the sth iteration, is the mean parameter of the Student's t distribution in the mixed distribution at the sth iteration, is the scale parameter of the Student's t distribution in the mixed distribution at the sth iteration, v s is the degrees of freedom parameter of the Student's t distribution in the mixture distribution at the sth iteration.

[0065] Preferably, in step 3, the Q function is calculated using a particle smoothing algorithm:

[0066]

[0067] Where N is the data length, Γ is the gamma function, and L represents the total number of particles; represents the state quantity represented by the lth particle at sampling time k+1 and sampling time k; represents the particle smoothing weights at sampling time k+1 and sampling time k; <β k > l and <log β k > l Represents 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] Where log() is the logarithmic function and Ψ() is the digamma function.

[0071] Prioritize, maximize the Q function in step 3 to obtain the mixture weight estimation formula; retain the terms related to the mixture weight in the Q function:

[0072]

[0073] Based on the terms of the mixing weights in the Q function, the mixing weights are updated and the average posterior probability is calculated:

[0074]

[0075] Prior to this, the M-step in the EM algorithm framework in step 3 involves finding the derivative of the Q function with respect to the parameter and setting the derivative of the parameter equal to zero, obtaining μ en Iterative estimate of μ es Iterative estimate of R w Iterative estimate of R en Iterative estimate of and R es Iterative estimate of

[0076]

[0077] Where, f v (·) indicates a nonlinear functional relationship;

[0078] Calculate the iterative estimate of the degrees of freedom parameter v, set the partial derivative of the Q function with respect to the degrees of freedom parameter v equal to 0, and obtain:

[0079]

[0080] Use the function solver to solve the above equation to obtain the iterative estimate of v;

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

[0082]

[0083] In the formula, in the formula, is the lth particle at the k+1th sampling moment, is the parameter a1 of the sth iteration, is the parameter b0 of the sth iteration, is the lth particle at the kth sampling moment.

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

[0085] Preferably, the present invention provides an electronic device comprising a memory, a processor, and a computer program stored in the memory and executable on the processor, wherein the processor implements the steps of any one of the methods described in the first aspect when executing the program.

[0086] Preferably, the present invention provides a computer-readable storage medium having a computer program stored thereon, which implements the steps of any one of the methods described in the first aspect when executed by a processor.

[0087] The beneficial effects achieved by the present invention are:

[0088] The method of the present invention takes into account the poor robustness of existing soft measurement methods caused by density meter measurement data errors and measurement errors, and proposes a robust identification method for nonlinear state space systems based on mixed distribution. It can effectively establish a robust soft measurement model for the density of heavy medium suspensions. Through systematic fusion of dynamic modeling, probabilistic robustness enhancement and adaptive parameter optimization, it achieves detection accuracy similar to that of manual testing, significantly improves the intelligent level of heavy medium separation density control, and provides theoretical support for coal preparation plants to realize unmanned density control throughout the entire process. BRIEF DESCRIPTION OF THE DRAWINGS

[0089] In order to more clearly illustrate the technical solution of the present application, the following is a brief introduction to the drawings required for use in the embodiments. Obviously, for ordinary technicians in this field, other drawings can be obtained based on these drawings without any creative work.

[0090] Figure 1 is a flow chart of the present invention;

[0091] Figure 2 This is the identification framework diagram 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 DESCRIPTION

[0093] See also Figure 1 The present application discloses a robust soft measurement method for density of a heavy medium suspension based on a mixed distribution, comprising:

[0094] The valve opening data is input into the trained robust soft-sensing model of heavy medium suspension density, and the target heavy medium suspension density data is output;

[0095] Among them, the training of the robust soft-sensing model for the density of heavy medium suspensions includes:

[0096] Step 1: Based on the density control loop characteristics of the density loop system of the heavy medium coal preparation process, a nonlinear state space model is constructed; historical operation data of the densitometer is collected to construct an identification data set of the density loop system of the heavy medium coal preparation process;

[0097] The nonlinear state space model includes a state transfer equation and an output measurement equation;

[0098] Step 2: Use the mixed probability distribution theory to model the noise characteristics and obtain a nonlinear state space robust probability model;

[0099] Step 3: Use the expectation maximization algorithm to perform joint parameter identification and state estimation, determine the optimal parameter combination of the nonlinear state space robust probability model through iterative optimization, and obtain the optimized robust soft measurement model of heavy medium suspension density.

[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 water supply valve opening as input and the density of the heavy medium suspension in the qualified medium barrel as output:

[0101]

[0102] Among them, Q mf and ρ mf Respectively represent the volume flow rate and density of the heavy medium suspension; ρ w represents the density of clean water; ρ cf Indicates the density of the heavy medium recovered at the outlet of the magnetic separator; Q cf Indicates the volume flow of heavy medium flowing through the magnetic separator into the qualified medium barrel; Q hm and ρ hm Respectively represent the volume flow rate and density of the high-concentration medium added from the high-concentration medium barrel to the qualified medium barrel; V cor Indicates the volume of heavy medium suspension in the qualified medium barrel; Q w Indicates the volume flow of clean water added to the qualified medium barrel through the water supply valve;

[0103] Perform Taylor expansion at the operating point and 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) represents 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 transfer function; g(·) represents the nonlinear output measurement function; θ f and θ g represents the model parameters, w(k) and e(k) represent the system noise.

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

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

[0109] Among them, 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 water supply valve opening at sampling time k, a1 and b0 represent model parameters, f v (·) represents the nonlinear functional relationship, w(k) represents the system noise;

[0110] The output measurement equation 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:

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

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

[0116] Among them, x k+1 =x(k+1),x k =x(k),x k+1 、x k They represent the state quantity of the density loop system at time k+1 and time k respectively, x(k+1) is the density state at time k+1; x(k) represents the density state at time k; b0 represents the model parameter, y k =u(k),y k represents the input of the density loop system at time k, i.e., the opening of the water supply valve; y k =y(k),y k Represents the output data collected by the density loop system, that is, the data collected by the density meter; f v (x(k),a1) represents the nonlinear dynamics in the density loop, set w k ,e k 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, obey the distribution N(w k |0,R w ), R w is the variance of the Gaussian distribution; the Gaussian-Student's t mixture distribution is used to model the measurement noise e 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 Gaussian-Student's t mixture distribution, N(·) represents Gaussian distribution; e k is the measurement noise of the density loop system; St represents the Student's t distribution; τ1 and τ2 represent the mixed weights of the Gaussian distribution and the Student's t distribution, respectively, and τ1+τ2=1; μ en and R en Respectively represent the mean and variance of Gaussian distribution; μ es 、R es and v represent the mean, scale parameter, and degree of freedom parameter of Student’s t distribution, respectively;

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

[0121]

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

[0123] Where x(k+1) is the density state at time k+1; x(k) is the density state at time k; a1 and b0 are model parameters; y k Indicates the output data collected by the density loop system, that is, the data collected by the density meter;

[0124] In step 2, the auxiliary variable β is introduced k The mixed distribution is decomposed into a mixture of Gaussian distribution and gamma distribution, and the output variable distribution is obtained as follows:

[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 is the auxiliary variable introduced.

[0128] Furthermore, in step 2, an auxiliary variable β is introduced k The mixed distribution is decomposed into a mixture of Gaussian distribution and gamma distribution, and the output variable distribution is obtained as follows:

[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, the 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 as 1 , the number of iterations s is set to 1; the E-step step under the EM algorithm framework includes calculating the cost function Q(Ω|Ω s ):

[0139]

[0140] in is the log-likelihood function of the identification data set and the latent data set; Ω s are the parameters of the current nonlinear state space model; To identify the data set, u 1:N Indicates that the water supply valve is open 1:N Degree, y 1:N Indicates the density data measured by the densitometer; is an implicit data set, where x 1:N represents the state quantity of the density loop system, represents the auxiliary variable introduced, and Ω={a1,b0,Θ} is the model parameter to be identified; express The conditional expectation of

[0141] In the E-step of the EM algorithm framework, the Q function is calculated by giving the identification data set M, and the log-likelihood function of the identification data set and the implicit data set is for:

[0142]

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

[0144] Based on the probability chain rule, the log-likelihood function is simplified is 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] Calculation of implicit data sets The conditional expectation of Q function Q(Ω|Ω s ):

[0150]

[0151] in, <d 1k > l and <d 2k > l Indicates d 1k and d 2k The corresponding mathematical expectations represent the output data y k The posterior probability of belonging to the Gaussian distribution and the Student's t distribution is calculated as the combined probability density function:

[0152]

[0153] Where, is the mean parameter of the Gaussian distribution in the mixed distribution at the sth iteration, is the variance parameter of the Gaussian distribution in the mixed distribution at the sth iteration, is the mean parameter of the Student's t distribution in the mixed distribution at the sth iteration, is the scale parameter of the Student's t distribution in the mixed distribution at the sth iteration, v s is the degrees of freedom parameter of the Student's t distribution in the mixture distribution at the sth iteration.

[0154] Furthermore, in step 3, the particle smoothing algorithm is used to calculate the Q function:

[0155]

[0156] Where N is the data length, Γ is the gamma function, and L represents the total number of particles; represents the state quantity represented by the lth particle at sampling time k+1 and sampling time k; represents the particle smoothing weights at sampling time k+1 and sampling time k; <β k > l and <log β k > l Represents 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] Where log() is the logarithmic function and Ψ() is the digamma function.

[0161] Furthermore, in step 3, the Q function is maximized to obtain the mixture weight estimation formula; the terms related to the mixture weight in the Q function are retained:

[0162]

[0163] Based on the terms of the mixing weights in the Q function, the mixing weights are updated and the average posterior probability is calculated:

[0164]

[0165] Furthermore, the M-step in the EM algorithm framework in step 3 includes finding the derivative of the Q function with respect to the parameter and setting the derivative of the parameter equal to zero, and obtaining μ en Iterative estimate of μ es Iterative estimate of R w Iterative estimate of R en Iterative estimate of and R es Iterative estimate of

[0166]

[0167] Where, f v (·) indicates a nonlinear functional relationship;

[0168] Calculate the iterative estimate of the degrees of freedom parameter v, set the partial derivative of the Q function with respect to the degrees of freedom parameter v equal to 0, and obtain:

[0169]

[0170] Use the function solver to solve the above equation to obtain the iterative estimate of v;

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

[0172]

[0173] In the formula, in the formula, is the lth particle at the k+1th sampling moment, is the parameter a1 of the sth iteration, is the parameter b0 of the sth iteration, is the lth particle at the kth sampling moment.

[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 obtained is the parameter a1 obtained in the last iteration, is the parameter b0 obtained in the last iteration, is the parameter τ1 obtained in the last iteration, is the parameter τ2 obtained in the last iteration, is the parameter μ obtained in the last iteration en , is the parameter μ obtained in the last iteration es , The parameter R obtained in the last iteration w , The parameter R obtained in the last iteration en , The parameter R obtained in the last iteration es , v * For all parameters The final iterative result is a robust soft-sensing model for the density of heavy medium suspensions.

[0175] In an embodiment of the present application, the present invention provides an electronic device, comprising a memory, a processor, and a computer program stored in the memory and executable on the processor, wherein the processor implements the steps of any of the above methods when executing the program.

[0176] In an embodiment of the present application, the present invention provides a computer-readable storage medium having a computer program stored thereon, which implements the steps of any of the above methods when executed by a processor.

[0177] Example

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

[0179] Step 1: Collect the water valve opening and density meter data of the density loop system of the heavy medium separation process as the identification data set and perform data preprocessing, that is,

[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 particle smoothing algorithm is used to calculate the smoothed probability density function p(x k |y 1:N ,Ω s ),p(x k ,x k-1 |y 1:N ,Ω s ) and the expectations at each sampling moment <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: Increase the value of s by 1 until the maximum number of iterations S is reached.

[0186] Collect the water valve opening and densitometer data of the density loop system of the dense medium separation process as the identification data set and perform data preprocessing; set simulation parameters; and perform simulation verification:

[0187] For the convenience of description, the method of the present invention is abbreviated as NSSM-GStM. A simulation experiment was conducted in Matlab environment using the method proposed in the present invention to verify the performance of the algorithm. Figure 2 500 test results of the algorithm NSSM-GStM are shown. The error band in the figure represents the acceptable error range of density measurement in the actual field of heavy medium separation, and the circle represents the predicted value of the algorithm NSSM-GStM. As can be seen from the figure, most of the predicted values fall within the error band, indicating that the estimated value of the algorithm NSSM-GStM is closer to the true value and can meet the soft measurement requirements of the heavy medium suspension density index at the coal preparation site. Table 1 records the results of NSSM-GStM and the existing robust identification algorithm NSSM-Student in 50 independent experiments. Table 1 shows the comparison results of the mean ± standard deviation of the NSSM-GStM algorithm. The NSSM-Student algorithm failed to meet the accuracy requirements. This is primarily due to the positive offset error of the field differential pressure density meter, which was not considered in the NSSM-Student algorithm's design, thus affecting identification accuracy. This result further confirms that the robust soft sensor model constructed using 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, and the same or similar parts between the various embodiments can be referred to each other. Each embodiment focuses on the differences from other embodiments.

[0191] Those skilled in the art will readily appreciate other embodiments of the present invention after considering the specification and practicing the invention as disclosed herein. This application is intended to cover any variations, uses, or adaptations of the present invention that follow the general principles of the invention and include common knowledge or customary techniques in the art not invented herein, and the description and examples are to be considered merely as exemplary.

[0192] The above specific implementation methods further illustrate the purpose, technical solutions and beneficial effects of this application in detail. It should be understood that the above are only specific implementation methods of this application and are not intended to limit the scope of protection of this application. Any modifications, equivalent replacements, improvements, etc. made on the basis of the technical solutions of this application should be included in the scope of protection of this application.

Claims

1. A robust soft measurement method for density of heavy medium suspension based on mixed distribution, characterized in that: include: The valve opening data is input into the trained robust soft-sensing model of heavy medium suspension density, and the target heavy medium suspension density data is output; Among them, the training of the robust soft-sensing model for the density of heavy medium suspensions includes: Step 1: Based on the density control loop characteristics of the density loop system of the heavy medium coal preparation process, a nonlinear state space model is constructed; historical operation data of the densitometer is collected to construct an identification data set of the density loop system of the heavy medium coal preparation process; The nonlinear state space model includes a state transfer equation and an output measurement equation; Step 2: Use the mixed probability distribution theory to model the noise characteristics and obtain a nonlinear state space robust probability model; Step 3: Use the expectation maximization algorithm to perform joint parameter identification and state estimation, determine the optimal parameter combination of the nonlinear state space robust probability model through iterative optimization, and obtain the optimized robust soft measurement model of heavy medium suspension density.

2. The method for robust soft measurement of density of a heavy medium suspension based on mixed distribution according to claim 1, characterized in that: In step 1, the density loop system of the heavy medium coal preparation process is simplified to a single-input-single-output system with the water valve opening as input and the density of the heavy medium suspension in the qualified medium barrel as output: Among them, Q mf and ρ mf Respectively represent the volume flow rate and density of the heavy medium suspension; ρ w represents the density of clean water; ρ cf Indicates the density of the heavy medium recovered at the outlet of the magnetic separator; Q cf Indicates the volume flow of heavy medium flowing through the magnetic separator into the qualified medium barrel; Q hm and ρ hm Respectively represent the volume flow rate and density of the high-concentration medium added from the high-concentration medium barrel to the qualified medium barrel; V cor Indicates the volume of heavy medium suspension in the qualified medium barrel; Q w Indicates the volume flow of clean water added to the qualified medium barrel through the water supply valve; Perform Taylor expansion at the operating point and establish the following nonlinear state space model: x(k+1)=f(u(k),x(k),θ f )+w(k) y(k)=g(x(k),θ g )+e(k), Where k represents the sampling time, x(k+1) represents 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 transfer function; g(·) represents the nonlinear output measurement function; θ f and θ g represents the model parameters, w(k) and w(k) represent the system noise.

3. The method for robust soft measurement of density of a heavy medium suspension based on mixed distribution according to claim 1, characterized in that: The state transition equation in step 1 is: x(k+1)=b0u(k)+f v (x(k),a1)+w(k), Among them, 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 water supply valve opening at sampling time k, a1 and b0 represent model parameters, f v (·) represents the nonlinear functional relationship, w(k) represents the system noise; The output measurement equation in step 1 is: y(k)=x(k)+e(k), Where y(k), y(k+1) represent the density meter measurement data at sampling time k, and e(k) represents the system noise; In step 1, the discrete state space model is: x k+1 =b0u k +f v (x k ,a1)+w k and k =x k +e k , Among them, x k+1 =x(k+1),x k =x(k),x k+1 、x k They represent the state quantity of the density loop system at time k+1 and time k respectively, x(k+1) is the density state at time k+1; x(k) represents the density state at time k; b0 represents the model parameter, u k =u(k),u k represents the input of the density loop system at time k, i.e., the opening of the water supply valve; y k =y(k),y k Represents the output data collected by the density loop system, that is, the data collected by the density meter; f v (x(k),a1) represents the nonlinear dynamics in the density loop, set w k ,e k are the state noise and measurement noise of the density loop system, respectively.

4. The method for robust soft measurement of density of heavy medium suspension based on mixed distribution according to claim 1, characterized in that: In step 2, w k Set to zero-mean Gaussian white noise, obey the distribution N(w k |0,R w ), R w is the variance of the Gaussian distribution; the Gaussian-Student's t mixture distribution is used to model the measurement noise e k : w k ~GStM(e k |τ1,τ2,μ en ,m es ,R en ,R es ,v)=τ1N(e k |m en ,R en )+τ2St(e k |m es ,R es ,v), Where GStM represents Gaussian-Student's t mixture distribution, N(·) represents Gaussian distribution; e k is the measurement noise of the density loop system; St represents the Student's t distribution; τ1 and τ2 represent the mixed weights of the Gaussian distribution and the Student's t distribution, respectively, and τ1+τ2=1; μ en and R en Respectively represent the mean and variance of Gaussian distribution; μ es 、R es and v represent the mean, scale parameter, and degree of freedom parameter of Student’s t distribution, respectively; The density loop state variables and output variables obey the following distribution: y k ~GStM(y k |x k ,τ1,τ2,μ en ,m es ,R en ,R es ,v), Where x(k+1) is the density state at time k+1; x(k) is the density state at time k; a1 and b0 are model parameters; y k Indicates the output data collected by the density loop system, that is, the data collected by the density meter; In step 2, the auxiliary variable β is introduced k The mixed distribution is decomposed into a mixture of Gaussian distribution and gamma distribution, and the output variable distribution is obtained as follows: y k ~GStM(y k |x k ,τ1,τ2,μ en ,m es ,R en ,R es ,v) =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 , Where G(·) represents the gamma distribution, β k is the auxiliary variable introduced.

5. The method for robust soft measurement of density of heavy medium suspension based on mixed distribution according to claim 4, characterized in that: In step 2, the auxiliary variable β is introduced k The mixed distribution is decomposed into a mixture of Gaussian distribution and gamma distribution, and the output variable distribution is obtained as follows: y k ~GStM(y k |x k ,τ1,τ2,μ en ,m es ,R en ,R es ,v) =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 , Where G(·) represents the gamma distribution; In step 2, the Bernoulli random variable d is introduced k ={d 1k ,d 2k }, d k The probability density function is: The probability density function of the output variable is: Where Θ={τ1,τ2,μ en ,μ es ,R w ,R en ,R es ,v} represents the noise parameter.

6. The method for robust soft measurement of density of heavy medium suspension based on mixed distribution according to claim 5, characterized in that: In step 3, define the initial parameter Ω to be estimated 1 , the number of iterations s is set to 1; the E-step step under the EM algorithm framework includes calculating the cost function Q(Ω|Ω s ): in is the log-likelihood function of the identification data set and the latent data set; Ω s are the parameters of the current nonlinear state space model; To identify the data set, u 1:N Indicates that the water supply valve is open 1:N Degree, y 1:N Indicates the density data measured by the densitometer; is an implicit data set, where x 1:N represents the state quantity of the density loop system, represents the auxiliary variable introduced, and Ω={a1,n0,Θ} is the model parameter to be identified; express The conditional expectation of In the E-step of the EM algorithm framework, the Q function is calculated by giving the identification data set M, and the log-likelihood function of the identification data set and the implicit data set is for: +logp(β 1:N |Ω)+const, Where, const = log p(u 1:N |Ω) represents a constant term; Based on the probability chain rule, the log-likelihood function is simplified is log p(y 1:N ,u 1:N ,x 1:N ,β 1:N ,d 1:N |Ω): 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): log p(y k ,d k |u k ,x k ,b k ,Ω)=log(p(y k |u k ,d k ,x k ,b k ,Ω)p(d k |Oh)) =d 1k log[τ1N(y k |m en ,x k ,R en )]+d 2k log[τ2St(y k |m es ,x k ,R es ,v,b k )], Calculation of implicit data sets The conditional expectation of Q function Q(Ω|Ω s ): in, <d 1k > l and <d 2k > l Indicates d 1k and d 2k The corresponding mathematical expectations represent the output data y k The posterior probability of belonging to the Gaussian distribution and the Student's t distribution is calculated as the combined probability density function: Where, is the mean parameter of the Gaussian distribution in the mixed distribution at the sth iteration, is the variance parameter of the Gaussian distribution in the mixed distribution at the sth iteration, is the mean parameter of the Student's t distribution in the mixed distribution at the sth iteration, is the scale parameter of the Student's t distribution in the mixed distribution at the sth iteration, v s is the degrees of freedom parameter of the Student's t distribution in the mixture distribution at the sth iteration.

7. The method for robust soft measurement of density of heavy medium suspension based on mixed distribution according to claim 6, characterized in that: In step 3, the particle smoothing algorithm is used to calculate the Q function: Where N is the data length, Γ is the gamma function, and L represents the total number of particles; represents the state quantity represented by the lth particle at sampling time k+1 and sampling time k; represents the particle smoothing weights at sampling time k+1 and sampling time k; <β k > l and <log β k > l Represents β k and log β k The corresponding mathematical expectation; const1 is the constant term; <β k > l and <log β k > l for: Where log() is the logarithmic function and Ψ() is the digamma function.

8. The method for robust soft measurement of density of heavy medium suspension based on mixed distribution according to claim 7, characterized in that: In step 3, the Q function is maximized to obtain the mixture weight estimation formula; the terms related to the mixture weight in the Q function are retained: Based on the terms of the mixing weights in the Q function, the mixing weights are updated and the average posterior probability is calculated:

9. The method for robust soft measurement of density of heavy medium suspension based on mixed distribution according to claim 8, characterized in that: The M-step in the EM algorithm framework in step 3 involves finding the derivative of the Q function with respect to the parameter and setting the derivative of the parameter equal to zero, obtaining μ en Iterative estimate of μ es Iterative estimate of R w Iterative estimate of R en Iterative estimate of and R es Iterative estimate of Where, f v (·) indicates a nonlinear functional relationship; Calculate the iterative estimate of the degrees of freedom parameter v, set the partial derivative of the Q function with respect to the degrees of freedom parameter v equal to 0, and obtain: Use the function solver to solve the above equation to obtain the iterative estimate of v; The estimation of the model parameter a1 is obtained by maximizing the Q function and the estimate of b0 Where, is the lth particle at the k+1th sampling moment, is the parameter a1 of the sth iteration, is the parameter b0 of the sth iteration, is the lth particle at the kth sampling moment.

10. The method for robust soft measurement of density of heavy medium suspension based on mixed distribution according to claim 9, characterized in that: In step 3, the E-step and M-step steps are repeated until the maximum number of iterations is reached; the final iteration result is obtained is the parameter a1 obtained in the last iteration, is the parameter b0 obtained in the last iteration, is the parameter τ1 obtained in the last iteration, is the parameter τ2 obtained in the last iteration, is the parameter μ obtained in the last iteration en , is the parameter μ obtained in the last iteration es , The parameter R obtained in the last iteration w , The parameter R obtained in the last iteration en , The parameter R obtained in the last iteration es , v * For all parameters The final iterative result is a robust soft-sensing model for the density of heavy medium suspensions.

Images