Fractional order fluid control valve system parameter identification method based on gradient iteration algorithm

Abstract

The application provides a fractional order fluid control valve system parameter identification method based on a gradient iteration algorithm, belongs to the technical field of fluid control valve system identification, and solves the problem of low identification precision of the fractional order fluid control valve system parameter. The technical scheme is as follows: a fractional order fluid control valve system identification method based on a gradient iteration algorithm, comprising the following steps: step 1) establishing a fractional order fluid control valve system Wiener nonlinear model; and step 2) constructing an identification process of the gradient iteration algorithm. The application has the beneficial effects that the gradient iteration algorithm has a faster convergence speed and higher convergence precision, and can be better applied to modeling and parameter identification of the fractional order fluid control valve system.

Description

Technical Field

[0001] This invention relates to the field of fluid control valve system identification technology, and in particular to a method for identifying parameters of fractional-order fluid control valve systems based on gradient iteration algorithms. Background Technology

[0002] With the rapid development of science and technology, industrial processes inevitably place more stringent and urgent demands on the control of actual production processes. To meet these control requirements and achieve better control effects, it is essential to establish accurate and effective mathematical models of the actual production processes. Since almost all actual production processes involve the control of gases or liquids, fluid control valves are indispensable in control systems and are a crucial component of industrial automation systems. Fluid control valves are mechanical devices used to control the flow state of fluids (pressure, flow rate, shut-off / opening). Due to the nonlinear flow characteristics of fluid control valves, modeling them becomes a key challenge in production control. To better analyze and predict the production process, it is necessary to establish accurate system models for fluid control valves and identify the parameters of the established models. Researchers have proposed different identification methods, such as stochastic gradient descent, Newton's iteration algorithm, and particle swarm optimization.

[0003] The stochastic gradient algorithm suffers from slow convergence and low accuracy in parameter identification; the Newton iteration algorithm is an iterative algorithm that requires solving the inverse of the Hessian matrix of the objective function at each step, which is computationally complex and consumes a lot of memory; the particle swarm optimization algorithm, as a swarm intelligence algorithm, can be well applied to different working conditions, but the selection of genetic operators is sometimes troublesome, resulting in low identification accuracy.

[0004] How to solve the above-mentioned technical problems is the challenge facing this invention. Summary of the Invention

[0005] The purpose of this invention is to provide a parameter identification method for fractional-order fluid control valve systems based on gradient iteration algorithm. It has a fast convergence speed and high convergence accuracy, and can be well applied to the modeling and parameter identification of fractional-order fluid control valve systems.

[0006] This invention is achieved through the following measures: a parameter identification method for fractional-order fluid control valve systems based on a gradient iteration algorithm, specifically including the following steps:

[0007] Step 1) Establish the input and output mathematical model of the fractional-order fluid control valve system.

[0008] Step 2) Construct the identification process for gradient iteration algorithms.

[0009] As a further optimization scheme for the fractional-order fluid control valve system parameter identification method based on gradient iteration algorithm provided by the present invention, the specific modeling steps of step 1) are as follows:

[0010] (1-1) Construct the structure of a Wiener nonlinear model of a fractional-order fluid control valve system.

[0011] (1-2) Based on this model, the Wiener nonlinear model expression for the fractional-order fluid control valve system is constructed as follows:

[0012]

[0013]

[0014] e(t)=D(z)v(t), (3)

[0015] y(t)=x(t)+e(t), (4)

[0016] The symbols in the above formulas have the following meanings: u(t) is the model input signal, y(t) is the model output signal, and v(t) is a signal with a mean of 0 and a variance of σ. 2 Furthermore, the noise follows a Gaussian distribution and is white noise. The intermediate variables u(t), x(t), and e(t) are intermediate, unmeasurable signals, and z... -1 It is the unit delay symbol: z -1 y(t) = y(t-1), A(z), B(z), and D(z) are constant polynomials with the following definitions:

[0017]

[0018]

[0019]

[0020] Wherein, the polynomial factor a i b j and d l The parameter to be estimated is α. i ,β j and γ l It is the fractional order of the denominator of the polynomial. This invention considers fractional symmetry systems, i.e., fractional orders that are multiples of the same basis and are known:

[0021]

[0022] (1-3) The intermediate signal And e(t) can be expressed as:

[0023]

[0024]

[0025] Simplifying, we get:

[0026]

[0027]

[0028] This invention uses Grünwald Letnikov's (GL) definition to solve fractional derivatives. The GL definition can be expressed as:

[0029]

[0030] Where Δ is the discrete fractional difference operator, Δ α m(kh) is the α-order fractional derivative of the function m(k), which can be expressed as t = kh, where h is the sampling interval and k is the number of samples used to approximate the derivative. Substituting equation (7) into equations (5) and (6), the discretized intermediate signal... And e(t) can be rewritten as:

[0031]

[0032]

[0033] The output of the nonlinear element in the model is in polynomial form, which can be expressed as:

[0034]

[0035] Where, p i These are the unknown coefficients that need to be identified, while the order r of the polynomial function is known. To ensure the uniqueness of the parameters, let the first modulus p1 of the nonlinear component be 1.

[0036] (1-4) The identified model of the Wiener nonlinear model of the fractional-order fluid control valve system is obtained:

[0037]

[0038] In the above formula, The information vector of the system is represented as:

[0039]

[0040] in, Defined respectively

[0041]

[0042]

[0043]

[0044] θ is the system's parameter vector, expressed as: θ = [θ1] T ,θ2 T ,θ3 T ] T ,

[0045] Wherein, θ1, θ2, and θ3 are defined as:

[0046]

[0047] θ2=[p2,p3,…,p r ] T ,

[0048]

[0049] A further design of the Wiener nonlinear model parameter identification method for fractional-order fluid control valve systems based on gradient iteration algorithm is that step 2) specifically includes:

[0050] Step 2-1) Initialization, given the number of iterations k max Data length N;

[0051] Step 2-2) Use the pneumatic control signal of the valve as the input data u(t) of the fractional-order fluid control valve system model, the fluid flow rate as the output data y(t), and the valve plug position as the intermediate signal.

[0052] Steps 2-3) Define the stacked output vector Y(N) and the stacked information matrix Ψ(N) according to the input and output data, as shown in equation (12);

[0053]

[0054] Step 2-4) Define the criterion function J(θ) as follows:

[0055]

[0056] in, It is an estimate of the stacked information matrix. It is an estimate of the parameter vector;

[0057] Steps 2-5) The intermediate variables in the information vector Fractional derivative of intermediate variable Fractional derivative Δ of unmeasurable noise α v(t) is replaced by its estimated value. and The information vector is estimated according to equation (14). Construct according to equation (15)

[0058]

[0059]

[0060] Step 2-6) Select an appropriate convergence factor μ according to equation (16) k ;

[0061]

[0062] Step 2-7) Calculate the estimated value of the parameter vector according to equation (17).

[0063]

[0064] Step 2-8) Calculate the estimated intermediate variables according to equations (8) and (18). and estimated noise The fractional derivatives of the estimated intermediate variables and noise are calculated using the GL definition in equation (7).

[0065]

[0066] Step 2-9) Determine if the maximum number of iterations has been reached. If not, the program jumps to step 2-5. If it has been reached, proceed to step 2-10.

[0067] Step 2-10) Output the results to complete the identification.

[0068] Compared with the prior art, the beneficial effects of the present invention are as follows:

[0069] (1) This invention establishes a model for parameter identification of a fractional-order fluid control valve Wiener nonlinear system. The pneumatic control signal of the valve is used as input data, and a gradient iteration algorithm is employed to identify the parameters of the model. Figure 4 It can be seen that the algorithm can effectively identify the internal parameters of the model.

[0070] (2) Compared with the stochastic gradient algorithm, the gradient iteration algorithm uses all available data in the system in each iteration, updates the intermediate variables and noise in each iteration to obtain the estimated information vector, thereby improving the convergence speed. The gradient iteration algorithm can better identify nonlinear systems and has higher identification accuracy and smaller estimation error. At the same time, it also shows that this identification method has good applicability to the Wiener nonlinear model of fractional fluid control valve. Attached Figure Description

[0071] The accompanying drawings are provided to further illustrate the invention and form part of the specification. They are used together with the embodiments of the invention to explain the invention and do not constitute a limitation thereof.

[0072] Figure 1 The overall flowchart of the Wiener nonlinear system identification method for fractional-order fluid control valves based on gradient iteration algorithm provided by the present invention is shown in the figure.

[0073] Figure 2 The schematic diagram of the fractional-stage fluid control valve provided by the present invention mainly includes a displacement sensor, a magnet, an electromagnetic linear actuator, a mushroom valve, a valve seat, and a valve body cover fixed on the central axis. A fluid inlet connected to an external gas supply pipeline is provided on one side of the valve body.

[0074] Figure 3 A schematic diagram of the general model of the input-output system of the fractional-order fluid control valve parameter identification method based on gradient iteration algorithm provided by the present invention.

[0075] Figure 4 This is a schematic diagram illustrating the error between the identification parameters and the true values ​​in this invention. Detailed Implementation

[0076] To make the objectives, technical solutions, and advantages of this invention clearer, the invention will be further described in detail below with reference to the accompanying drawings and embodiments. Of course, the specific embodiments described herein are merely illustrative and not intended to limit the invention.

[0077] Example 1

[0078] See Figures 1 to 4 This embodiment provides a technical solution: a method for parameter identification of a fractional-order fluid control valve system based on a gradient iteration algorithm, the specific steps of which are as follows:

[0079] Step 1) Establish the input and output mathematical model of the fractional-order fluid control valve system.

[0080] Step 2) Construct the identification process for gradient iteration algorithms.

[0081] As a further optimization scheme for the fractional-order fluid control valve system identification method based on gradient iteration algorithm provided in this embodiment, the specific modeling steps of step 1) are as follows:

[0082] (1-1) Construct the structure of a Wiener nonlinear model of a fractional-order fluid control valve system.

[0083] (1-2) Based on this model, the Wiener nonlinear model expression for the fractional-order fluid control valve system is constructed as follows:

[0084]

[0085]

[0086] e(t)=D(z)v(t), (3)

[0087] y(t)=x(t)+e(t), (4)

[0088] The symbols in the above formulas have the following meanings: u(t) is the model input signal, y(t) is the model output signal, and v(t) is a signal with a mean of 0 and a variance of σ. 2 And white noise that follows a Gaussian distribution, intermediate variable x(t) and e(t) are intermediate, unmeasurable signals, z -1 It is the unit delay symbol: z -1 y(t) = y(t-1), A(z), B(z), and D(z) are constant polynomials with the following definitions:

[0089]

[0090]

[0091]

[0092] Wherein, the polynomial factor a i b j and d l The parameter to be estimated is α. i ,β j and γ l This is the fractional order of the polynomial denominator. This embodiment considers a fractional symmetry system, where the fractional order is a multiple of the same basis and is known:

[0093]

[0094] (1-3) The intermediate signal And e(t) can be expressed as:

[0095]

[0096]

[0097] Simplifying, we get:

[0098]

[0099]

[0100] This embodiment uses Grünwald Letnikov's (GL) definition to solve for fractional derivatives. The GL definition can be expressed as:

[0101]

[0102] Where Δ is the discrete fractional difference operator, Δ α m(kh) is the α-order fractional derivative of the function m(k), which can be expressed as t = kh, where h is the sampling interval and k is the number of samples used to approximate the derivative. Substituting equation (7) into equations (5) and (6), the discretized intermediate signal... And e(t) can be rewritten as:

[0103]

[0104]

[0105] The output of the nonlinear element in the model is in polynomial form, which can be expressed as:

[0106]

[0107] Where, p i These are the unknown coefficients that need to be identified, while the order r of the polynomial function is known. To ensure the uniqueness of the parameters, let the first modulus p1 of the nonlinear component be 1.

[0108] (1-4) The identified model of the Wiener nonlinear model of the fractional-order fluid control valve system is obtained:

[0109]

[0110] In the above formula, The information vector of the system is represented as:

[0111]

[0112] in, Defined respectively

[0113]

[0114]

[0115]

[0116] θ is the system's parameter vector, expressed as: θ = [θ1] T ,θ2 T ,θ3 T ] T ,

[0117] Wherein, θ1, θ2, and θ3 are defined as:

[0118]

[0119] θ2=[p2,p3,…,p r ] T ,

[0120]

[0121] Preferably, the model in step 1) is a fractional-order Wiener nonlinear model.

[0122] Preferably, the specific steps of step 2) in constructing the identification process of the gradient iteration algorithm are as follows:

[0123] Step 2-1) Initialization, given the number of iterations k max Data length N;

[0124] Step 2-2) Use the pneumatic control signal of the valve as the input data u(t) of the fractional-order fluid control valve system model, the fluid flow rate as the output data y(t), and the valve plug position as the intermediate signal.

[0125] Steps 2-3) Define the stacked output vector Y(N) and the stacked information matrix Ψ(N) according to the input and output data, as shown in equation (12);

[0126]

[0127] Step 2-4) Define the criterion function J(θ) as follows:

[0128]

[0129] in, It is an estimate of the stacked information matrix. It is an estimate of the parameter vector;

[0130] Steps 2-5) The intermediate variables in the information vector Fractional derivative of intermediate variable Fractional derivative Δ of unmeasurable noise α v(t) is replaced by its estimated value. and The information vector is estimated according to equation (14). Construct according to equation (15)

[0131]

[0132]

[0133] Step 2-6) Select an appropriate convergence factor μ according to equation (16) k ;

[0134]

[0135] Step 2-7) Calculate the estimated value of the parameter vector according to equation (17).

[0136]

[0137] Step 2-8) Calculate the estimated intermediate variables according to equations (8) and (18). and estimated noise The fractional derivatives of the estimated intermediate variables and noise are calculated using the GL definition in equation (7).

[0138]

[0139] Step 2-9) Determine if the maximum number of iterations has been reached. If not, the program jumps to step 2-5. If it has been reached, proceed to step 2-10.

[0140] Step 2-10) Output the results to complete the identification.

[0141] A simplified diagram of the fractional-order fluid control valve system used in this embodiment is shown below. Figure 2 As shown. Where u(t) is the pneumatic control signal for the valve. Here, x(t) is the valve plug position, x(t) is the estimated fluid flow rate, and y(t) is the actual fluid flow rate.

[0142] Using the fractional Wiener model mentioned above, the following model can be established for this embodiment:

[0143]

[0144]

[0145] e(t)=(1+d1z -α v(t)=(1+0.1z) -0.3 v(t),

[0146] y(t)=x(t)+e(t),

[0147] Comparing the above model with step 1), we can obtain

[0148] a1=0.2, a2=0.4, b1=0.3, b2=0.5, p2=1, d1=0.1,

[0149] For the above model, a criterion function J(θ) is determined for use in the gradient iteration algorithm. This criterion function is defined as follows:

[0150]

[0151] Where Y(N) is the stacked output vector, It is an estimate of the stacked information matrix. It is an estimate of the parameter vector;

[0152] To facilitate substituting the parameters to be identified into the gradient iteration algorithm, the parameters to be identified are grouped into a parameter vector θ, as follows:

[0153] θ = [a1,a2,b1,b2,p2,d1] T ,

[0154] Based on the initialization in step 2-1), given the number of iterations k... max Data length N;

[0155] Based on the input and output data of the fractional-order fluid control valve system model obtained in step 2-2), calculate the valve plug position.

[0156] Define the stacked output vector Y(N) and the stacked information matrix Ψ(N) according to steps 2-3);

[0157] The criterion function J(θ) is obtained according to steps 2-4).

[0158] Calculate the estimated value of the information vector based on steps 2-5). Constructing the estimated value of the stacked information matrix

[0159] Select an appropriate convergence factor μ according to steps 2-6). k ;

[0160] Update the estimated values ​​of the parameter vector according to steps 2-7).

[0161] Calculate the estimated intermediate variables according to steps 2-8). and estimated noise Calculate the fractional derivatives of the estimated intermediate variables and noise.

[0162] Complete the loop according to steps 2-9) and 2-10) and output the result.

[0163] Among them, when setting the convergence factor μ kSeveral issues need to be considered when dealing with data length N: A convergence factor that is too small will result in excessive identification errors, making accurate identification impossible; a convergence factor that is too large will lead to fluctuating identification results and non-convergence. A data length that is too small will result in unsatisfactory identification results, leading to low identification accuracy; a data length that is too large will result in excessive computation.

[0164] The parameter identification results using the fractional-order fluid control valve system parameter identification method based on gradient iteration algorithm in this embodiment are as follows: Figure 4 As shown, the method has high identification accuracy, and the estimated values ​​of the parameters to be identified are very close to the true values. This also shows that the method has good applicability to parameter identification of fractional-order fluid control valve models.

[0165] The above description is only a preferred embodiment of the present invention and is not intended to limit the present invention. Any modifications, equivalent substitutions, improvements, etc., made within the spirit and principles of the present invention should be included within the protection scope of the present invention.

Claims

1. A method for parameter identification of fractional-order fluid control valve systems based on gradient iterative algorithm, characterized in that, Includes the following steps: Step 1) Establish the input-output mathematical model of the fractional-order fluid control valve system; Step 2) Construct the identification process for gradient iteration algorithms; Step 2) includes the following steps: Step 2-1) Initialization, given the number of iterations Data length N; Step 2-2) Use the pneumatic control signal of the valve as the input data u(t) of the fractional-order fluid control valve system model, the fluid flow rate as the output data y(t), and the valve plug position as the intermediate signal. ; Steps 2-3) Define the stacked output vector based on the input and output data. Define the stacked information matrix As shown in equation (12); (12)； Steps 2-4) Define the criterion function for (13)； in, It is an estimate of the stacked information matrix. It is an estimate of the parameter vector; Steps 2-5) The intermediate variables in the information vector Fractional derivatives of intermediate variables Fractional derivatives of unmeasurable noise Replace with its estimated value , and The information vector is estimated according to equation (14). Construct according to equation (15) ; (14)； (15)； Steps 2-6) Select an appropriate convergence factor according to equation (16) ; (16)； Step 2-7) Calculate the estimated value of the parameter vector according to equation (17). ; (17)； Step 2-8) Calculate the estimated intermediate variables according to equations (8) and (18). and estimated noise The fractional derivatives of the estimated intermediate variables and noise are calculated using the GL definition in equation (7). , ; (18)； Step 2-9) Determine if the maximum number of iterations has been reached. If not, the program jumps to step 2-5. If it has been reached, proceed to step 2-10. Step 2-10) Output the results to complete the identification.

2. The parameter identification method for fractional-order fluid control valve systems based on gradient iteration algorithm according to claim 1, characterized in that, Step 1) includes the following steps: (1-1) Construct the structure of a Wiener nonlinear model of a fractional-order fluid control valve system; (1-2) Based on the Wiener nonlinear model obtained in step (1-1), the expression of the Wiener nonlinear model of the fractional-order fluid control valve system is constructed as follows: (1)； (2)； (3)； ,(4)； Where u(t) is the model input signal, y(t) is the model output signal, and v(t) is a signal with a mean of 0 and a variance of 0. And white noise that follows a Gaussian distribution, intermediate variable x(t) and e(t) are intermediate, unmeasurable signals. It is a unit delay symbol: , , and It is a constant polynomial, defined as follows: ； ； ； Wherein, the polynomial factor a i b j and d l These are the parameters to be estimated. , and Let be the fractional order of the denominator of a polynomial. Consider a fractional commensurability system, where the fractional order is a multiple of the same basis and is known: ； (1-3) then the intermediate signal And e(t) is represented as: ； ； Simplifying, we get: (5)； (6)； The fractional derivative is solved using the Grünwald-Letnikov (GL) definition, where GL is defined as: (7)； in It is a discrete fractional difference operator. It is a function of fractional derivative, let ,in It is the sampling interval. The number of samples approximated by the derivative is calculated. Substituting equation (7) into equations (5) and (6), the discretized intermediate signal is obtained. And e(t) can be rewritten as: (8)； (9)； The output of the nonlinear element in the model is in polynomial form, expressed as: (10)； in, These are the unknown coefficients that need to be identified, while the order r of the polynomial function is known. To ensure the uniqueness of the parameters, let the first modulus of the nonlinear component be... ; (1-4) The identified model of the Wiener nonlinear model of the fractional-order fluid control valve system is obtained: (11)； In the above formula, The information vector of the system is represented as: ； in, , , They are defined as follows: ； ； ； Let the system's parameter vector be represented as: ; in, , , They are defined as follows: ； ； 。

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