CN116821558A - Liquid saturated steam heat exchange system parameter identification method based on gradient algorithm - Google Patents
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Abstract
The invention provides a parameter identification method of a liquid saturated steam heat exchange system based on a gradient algorithm, belongs to the technical field of steam heat exchange system identification, and solves the technical problem of low parameter identification precision of the liquid saturated steam heat exchange system. The technical proposal is as follows: a liquid saturated steam heat exchange system parameter identification method based on a gradient algorithm comprises the following steps: step 1), establishing a fractional order Wiener OEARMA model of a liquid saturated steam heat exchange system; step 2) constructing an identification flow of a hierarchical multi-innovation random gradient algorithm. The beneficial effects of the invention are as follows: the hierarchical multi-innovation random gradient algorithm provided by the invention has higher convergence speed and higher convergence precision, and can be better suitable for parameter identification of a liquid saturated steam heat exchange system.
Description
Technical Field
The invention relates to the technical field of steam heat exchange system identification, in particular to a liquid saturated steam heat exchange system parameter identification method based on a gradient algorithm.
Background
With the rapid development of science and technology, industrial processes tend to put more stringent and urgent demands on control of actual production processes. In order to meet such control requirements, and achieve better control, an accurate and efficient mathematical model must be built for the actual production process. The liquid saturated steam heat exchange system belongs to the field of steam heat exchange, and has wide application in practical production and life. The heat exchange system for liquid saturated steam is a device for heating liquid by using steam as a heat source, and can fully replace a large amount of heat value in the steam for heating the liquid. Since the liquid saturated steam heat exchange system is a typical nonlinear system, modeling it becomes a serious difficulty in production control. In order to better analyze and predict the production process, it is necessary to build an accurate mathematical model for the liquid saturated steam heat exchange system while identifying the parameters of the built model. For this reason, researchers have also proposed different identification methods, such as: random gradient algorithm, newton iterative algorithm, particle swarm algorithm, etc.
The random gradient algorithm has the problems of low convergence speed and low identification precision in parameter identification; the Newton iterative algorithm is an iterative algorithm, each step needs to solve the inverse matrix of the Hessian matrix of the objective function, and the calculation is complex and the occupied memory is larger; particle swarm algorithm as swarm intelligence algorithm can be well applied to different working conditions, but genetic operators are sometimes troublesome to select, and the problem of low identification accuracy exists.
How to solve the technical problems is the subject of the present invention.
Disclosure of Invention
The invention aims to provide a parameter identification method of a liquid saturated steam heat exchange system based on a gradient algorithm, and the proposed hierarchical multi-information random gradient algorithm has higher convergence speed and higher convergence precision, and can be better suitable for modeling and parameter identification of the liquid saturated steam heat exchange system.
The invention is realized by the following measures: the parameter identification method of the liquid saturated steam heat exchange system based on the gradient algorithm specifically comprises the following steps:
step 1), establishing a fractional order Wiener OEARMA model of a liquid saturated steam heat exchange system;
step 2) constructing an identification flow of a hierarchical multi-innovation random gradient algorithm.
As a further optimization scheme of the liquid saturated steam heat exchange system parameter identification method based on the gradient algorithm, the specific modeling steps of the step 1) are as follows:
step 1-1) constructing a fractional order Wiener OEARMA model of the liquid saturated steam heat exchange system: given the general form of the fractional order Wiener OEARMA system, as in equation (4), u (t) is the system input signal, y (t) is the system output signal, v (t) is a mean of 0 and variance of σ 2 And white noise satisfying a gaussian distribution, the intermediate variables m (t), h (t) and e (t) are intermediate unmeasurable signals, where h (t) is a two-segment piecewise non-linear:
k 1 and k 2 Coefficients that are piecewise functions, introducing an auxiliary function:
formula (1) is rewritable:
h(t)＝k 1 m(t)+(k 2 -k 1 )m(t)k(t), (3)
the general form of the model is available:
h(t)＝k 1 m(t)+(k 2 -k 1 )m(t)k(t),
y(t)＝h(t)+e(t), (4)
wherein A (z), B (z), C (z) and D (z) are constant polynomials, polynomial factors a i ,b j ,c l And d q Is the parameter to be estimated, alpha i ，β j ，γ l And omega q The present invention considers a fractional phase-fit system, which is a fractional order of a polynomial denominator, i.e., the fractional order is a multiple of the same radix and is known:
step 1-2) then the intermediate signals m (t) and e (t) are expressed as:
the invention adopts Grunwald Letnikov (GL) definition to solve fractional derivatives, and GL is defined as:
where Δ is the discrete fractional order difference operator, Δ α x (kh) is the alpha-order fractional derivative of the function x (k), let t=kh, where h is the sampling interval and k is the number of samples for which the calculated derivative approximates, substituting equation (7) into equations (5), (6), and the discretized intermediate signals m (t) and e (t) are rewritten as:
the key term separation technique is used to separate the key term m (t) for the two-segment nonlinear portion of the system, then the two-segment nonlinear portion can be described as:
h(t)＝m(t)+(k 1 -1)m(t)+(k 2 -k 1 )m(t)k(t), (10)
step 1-3) obtaining an identification model of a fractional order Wiener OEARMA model of the liquid saturated steam heat exchange system:
in the above formula, ψ (t) is an information vector of the system, expressed as:
ψ(t)＝[φ mu T (t),φ evm T (t)] T ,
wherein phi is mu (t)，φ evm (t) is defined as:
φ mu (t)＝[-Δ α m(t-1),…,-Δ α m(t-n a ),Δ α u(t-1),…,Δ α u(t-n b )] T ,
φ evm (t)＝[-Δ α e(t-1),…,-Δ α e(t-n c ),Δ α v(t-1),…,Δ α v(t-n d ),m(t),m(t)k(t)] T ,
the parameter vector of the system is expressed as: />Wherein θ ab ，θ cdk Respectively defined as:
as a further optimization scheme of the liquid saturated steam heat exchange system parameter identification method based on the gradient algorithm, the model in the step 1) is a fractional order Wiener OEARMA model.
As a further optimization scheme of the liquid saturated steam heat exchange system parameter identification method based on the gradient algorithm, the specific flow of the algorithm in the step 2) comprises the following steps:
step 2-1) initializing, defining a data length L, defining an output vector Y (p, t), defining a pile-up information matrix phi, given a number of loops h mu (p,t),Φ evm (p, t) as in formula (12), wherein p is the innovation length;
step 2-2), taking the liquid flow of the liquid saturated steam heat exchange system as input data u (t), taking the outlet liquid temperature as output data y (t), and recording data;
step 2-3) combining the intermediate variables m (t), e (t), and the fractional derivative delta in the information vector α m(t),Δ α e(t),Δ α v (t) and the auxiliary function k (t) are replaced by their estimated valuesAnd->Constructing an estimate of the information vector according to equations (13) and (14)>
ThenExpressed as:
step 2-4) introducing scalar innovation:
wherein the method comprises the steps ofAnd->Respectively is theta cdk And theta cdk The estimated value of the parameter vector is expressed as
Simultaneously introducing an innovation vector E (p, t) as shown in a formula (16), wherein p is the innovation length;
step 2-5) selection of an appropriate convergence factor r according to formulas (17) and (18) 1 (t),r 2 (t)；
Step 2-6) calculating the estimated value θ of the parameter vector according to equations (19) and (20) ab (t),θ cdk (t)；
Step 2-7) calculation according to formulas (21) - (24)And->
Step 2-8) calculation of fractional derivative from GL definition of formula (7)
Step 2-9) judging whether the maximum cycle number is reached, if not, jumping the program to step 2-3), and if so, entering step 2-10);
step 2-10) outputting the identification resultAnd (5) completing identification.
Compared with the prior art, the invention has the beneficial effects that:
(1) The invention establishes a fractional order Wiener OEARMA model aiming at a liquid saturated steam heat exchange system, wherein the model is formed by connecting a linear dynamic system in series with a static nonlinear system; the invention establishes a model with fractional order when describing a system, and establishes a fractional order model more accurately than an integer order model when describing a real system. It can be seen from fig. 4 that the algorithm can well identify the internal parameters of the model.
(2) Compared with a random gradient algorithm, the hierarchical multi-innovation random gradient algorithm introduces a hierarchical identification theory and a multi-innovation identification idea, so that the convergence speed is improved, the hierarchical multi-innovation random gradient algorithm can better identify a nonlinear system, the identification accuracy is higher, and the obtained estimation error is smaller; meanwhile, the identification method is also proved to have better applicability to a liquid saturated steam heat exchange system.
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The accompanying drawings are included to provide a further understanding of the invention and are incorporated in and constitute a part of this specification, illustrate the invention and together with the embodiments of the invention, serve to explain the invention.
FIG. 1 is an overall flow chart of a hierarchical multi-information random gradient algorithm provided by the invention.
Fig. 2 is a schematic diagram of a liquid saturated steam heat exchange system provided by the invention.
FIG. 3 is a general schematic of the Wiener OEARMA fractional order system of the present invention.
FIG. 4 is a diagram illustrating the error between the identification parameters and the true values according to the present invention.
Detailed Description
The present invention will be described in further detail with reference to the drawings and examples, in order to make the objects, technical solutions and advantages of the present invention more apparent. Of course, the specific embodiments described herein are for purposes of illustration only and are not intended to limit the invention.
Example 1
Referring to fig. 1 to 4, the present embodiment provides a method for identifying parameters of a liquid saturated steam heat exchange system based on a gradient algorithm, which specifically includes the following steps:
step 1), establishing a fractional order Wiener OEARMA model of a liquid saturated steam heat exchange system;
step 2) constructing an identification flow of a hierarchical multi-innovation random gradient algorithm.
Specifically, the specific modeling step of the step 1) is as follows:
step 1-1) constructing a fractional order Wiener OEARMA model of the liquid saturated steam heat exchange system: given the general form of the fractional order Wiener OEARMA system, as in equation (4), u (t) is the system input signal, y (t) is the system output signal, v (t) is a mean of 0 and variance of σ 2 And white noise satisfying a gaussian distribution, the intermediate variables m (t), h (t) and e (t) are intermediate unmeasurable signals, where h (t) is a two-segment piecewise non-linear:
k 1 and k 2 Coefficients that are piecewise functions, introducing an auxiliary function:
formula (1) is rewritable:
h(t)＝k 1 m(t)+(k 2 -k 1 )m(t)k(t), (3)
the general form of the model is available:
h(t)＝k 1 m(t)+(k 2 -k 1 )m(t)k(t),
y(t)＝h(t)+e(t), (4)
wherein A (z), B (z), C (z) and D (z) are constant polynomials, polynomial factors a i ,b j ,c l And d q Is the parameter to be estimated, alpha i ，β j ，γ l And omega q The present invention considers a fractional phase-fit system, which is a fractional order of a polynomial denominator, i.e., the fractional order is a multiple of the same radix and is known:
step 1-2) then the intermediate signals m (t) and e (t) are expressed as:
the invention adopts Grunwald Letnikov (GL) definition to solve fractional derivatives, and GL is defined as:
where Δ is the discrete fractional order difference operator, Δ α x (kh) is the alpha-order fractional derivative of the function x (k), let t=kh, where h is the sampling interval and k is the number of samples for which the calculated derivative approximates, substituting equation (7) into equations (5), (6), the discretized intermediate signal m (t) ande (t) is rewritten as:
the key term separation technique is used to separate the key term m (t) for the two-segment nonlinear portion of the system, then the two-segment nonlinear portion can be described as:
h(t)＝m(t)+(k 1 -1)m(t)+(k 2 -k 1 )m(t)k(t), (10)
step 1-3) obtaining an identification model of a fractional order Wiener OEARMA model of the liquid saturated steam heat exchange system:
in the above formula, ψ (t) is an information vector of the system, expressed as:
ψ(t)＝[φ mu T (t),φ evm T (t)] T ,
wherein phi is mu (t)，φ evm (t) is defined as:
φ mu (t)＝[-Δ α m(t-1),…,-Δ α m(t-n a ),Δ α u(t-1),…,Δ α u(t-n b )] T ,
φ evm (t)＝[-Δ α e(t-1),…,-Δ α e(t-n c ),Δ α v(t-1),…,Δ α v(t-n d ),m(t),m(t)k(t)] T ,
the parameter vector of the system is expressed as: />
Wherein θ ab ，θ cdk Respectively defined as:
specifically, the model in the step 1) is a fractional order Wiener OEARMA model.
Specifically, the specific steps of the identification flow for constructing the hierarchical multi-innovation random gradient algorithm in the step 2) are as follows:
step 2-1) initializing, defining a data length L, defining an output vector Y (p, t), defining a pile-up information matrix phi, given a number of loops h mu (p,t),Φ evm (p, t) as in formula (12), wherein p is the innovation length;
step 2-2), taking the liquid flow of the liquid saturated steam heat exchange system as input data u (t), taking the outlet liquid temperature as output data y (t), and recording data;
step 2-3) combining the intermediate variables m (t), e (t), and the fractional derivative delta in the information vector α m(t),Δ α e(t),Δ α v (t) and the auxiliary function k (t) are replaced by their estimated valuesAnd->Constructing an estimate of the information vector according to equations (13) and (14)>
ThenExpressed as:
step 2-4) introducing scalar innovation:
wherein the method comprises the steps ofAnd->Respectively is theta cdk And theta cdk The estimated value of the parameter vector is expressed as
Simultaneously introducing an innovation vector E (p, t) as shown in a formula (16), wherein p is the innovation length;
step 2-5) selection of an appropriate convergence factor r according to formulas (17) and (18) 1 (t),r 2 (t)；
Step 2-6) calculating the estimated value θ of the parameter vector according to equations (19) and (20) ab (t),θ cdk (t)；
Step 2-7) calculation according to formulas (21) - (24)And->
Step 2-8) calculation by GL definition of formula (7)Fractional order derivative
Step 2-9) judging whether the maximum cycle number is reached, if not, jumping the program to step 2-3), and if so, entering step 2-10);
step 2-10) outputting the identification resultAnd (5) completing identification.
A schematic diagram of a liquid saturated steam heat exchange system used in this embodiment is shown in fig. 2. Wherein the input signal u (t) is a liquid flow signal and the output signal y (t) is an outlet liquid temperature.
By the fractional order Wiener OEARMA model mentioned above, the present embodiment can be modeled as follows:
y(t)＝-0.29Δ 0.3 m(t-1)-0.5Δ 0.3 m(t-2)+1.35Δ 0.3 u(t-1)+1.17Δ 0.3 u(t-2)-0.74Δ 0.3 e(t-1)+0.76Δ 0.3 v(t-1)-0.2m(t)+0.6m(t)k(t)+v(t),
comparing the model with the model in the step 1), and obtaining
a 1 ＝0.29,a 2 ＝0.3,b 1 ＝1.35,b 2 ＝1.17,c 1 ＝0.74,d 1 ＝0.76,k 1 ＝0.8,k 2 ＝1.4
In order to conveniently substitute the parameters to be identified into the gradient iterative algorithm, the parameters to be identified form a parameter vectorThe parameters to be identified are as follows:
according to step 2-1) a given number of loops h, defining a data length L, defining an output vector Y (p, t), defining a pile-up information matrix Φ mu (p,t),Φ evm (p,t)；
Collecting input and output data according to step 2-2);
constructing an estimate of the information vector according to step 2-3)
Determining an innovation length p according to the step 2-4), and introducing an innovation vector E (p, t);
calculating the convergence factor r according to step 2-5) 1 (t),r 2 (t)；
Calculating the estimated value θ of the parameter vector according to steps 2-6) ab (t),θ cdk (t)；
According to steps 2-7) calculationAnd->
Calculating fractional order derivatives according to steps 2-8)
And (3) completing the cycle according to the steps 2-9) and 2-10), and outputting a result.
Wherein several problems need to be considered when setting the innovation length p and the data length L: too small innovation length can cause too large identification error, and an accurate identification result cannot be obtained; too long of a new message can cause fluctuation of the identification result, and the identification result is not converged. Too small data length can lead to non-ideal identification results, thereby causing the problem of low identification accuracy; the data length is too large, which causes a problem of large calculation amount.
The result of parameter identification performed by using the gradient algorithm-based parameter identification method of the liquid saturated steam heat exchange system in this embodiment is shown in fig. 4; it can be seen that the identification accuracy of the method is higher, the estimated value of the parameter to be identified is very close to the true value, and meanwhile, the method also shows that the method has better applicability to the parameter identification of the liquid saturated steam heat exchange system.
The foregoing description of the preferred embodiments of the invention is not intended to limit the invention to the precise form disclosed, and any such modifications, equivalents, and alternatives falling within the spirit and scope of the invention are intended to be included within the scope of the invention.
Claims (4)
1. The parameter identification method of the liquid saturated steam heat exchange system based on the gradient algorithm is characterized by comprising the following steps of:
step 1), establishing a fractional order Wiener OEARMA model of a liquid saturated steam heat exchange system;
step 2) constructing an identification flow of a hierarchical multi-innovation random gradient algorithm.
2. The method for identifying parameters of a liquid saturated steam heat exchange system based on a gradient algorithm according to claim 1, wherein the step 1) comprises the following steps:
step 1-1) constructing a fractional order Wiener OEARMA model of the liquid saturated steam heat exchange system: given the general form of the fractional order Wiener OEARMA system, as in equation (4), u (t) is the system input signal, y (t) is the system output signal, v (t) is a mean of 0 and variance of σ 2 And white noise satisfying a gaussian distribution, the intermediate variables m (t), h (t) and e (t) are intermediate unmeasurable signals, where h (t) is a two-segment piecewise non-linear:
k 1 and k 2 Coefficients that are piecewise functions, introducing an auxiliary function:
formula (1) is rewritten as:
h(t)＝k 1 m(t)+(k 2 -k 1 )m(t)k(t), (3)
the general form of the model is obtained:
h(t)＝k 1 m(t)+(k 2 -k 1 )m(t)k(t),
y(t)＝h(t)+e(t), (4)
wherein A (z), B (z), C (z) and D (z) are constant polynomials, polynomial factors a i ,b j ,c l And d q Is the parameter to be estimated, alpha i ，β j ，γ l And omega q The present invention considers a fractional phase-fit system, which is a fractional order of a polynomial denominator, i.e., the fractional order is a multiple of the same radix and is known:
step 1-2) then the intermediate signals m (t) and e (t) are expressed as:
the invention adopts Grunwald Letnikov (GL) definition to solve fractional derivatives, and GL is defined as:
where Δ is the discrete fractional order difference operator, Δ α x (kh) is the alpha-order fractional derivative of the function x (k), let t=kh, where h is the sampling interval and k is the number of samples for which the calculated derivative approximates, substituting equation (7) into equations (5), (6), and the discretized intermediate signals m (t) and e (t) are rewritten as:
the key term separation technique is used to separate the key term m (t) for the two-section nonlinear part of the system, and then the two-section nonlinear part is described as:
h(t)＝m(t)+(k 1 -1)m(t)+(k 2 -k 1 )m(t)k(t), (10)
step 1-3) obtaining an identification model of a fractional order Wiener OEARMA model of the liquid saturated steam heat exchange system:
in the above formula, ψ (t) is an information vector of the system, expressed as:
ψ(t)＝[φ mu T (t),φ evm T (t)] T ,
wherein phi is mu (t)，φ evm (t) is defined as:
φ mu (t)＝[-Δ α m(t-1),…,-Δ α m(t-n a ),Δ α u(t-1),…,Δ α u(t-n b )] T ,
φ evm (t)＝[-Δ α e(t-1),…,-Δ α e(t-n c ),Δ α v(t-1),…,Δ α v(t-n d ),m(t),m(t)k(t)] T ,
the parameter vector of the system is expressed as: />
Wherein θ ab ，θ cdk Respectively defined as:
3. the gradient algorithm-based liquid saturated vapor heat exchange system of claim 1, wherein the model of step 1) is a fractional order Wiener OEARMA model.
4. The method for identifying parameters of a liquid saturated steam heat exchange system based on a gradient algorithm according to claim 1, wherein the specific flow of the algorithm in step 2) comprises the following steps:
step 2-1) initializing, defining data given the number of loops hLength L, defining output vector Y (p, t), defining pile-up information matrix Φ mu (p,t),Φ evm (p, t) as in formula (12), wherein p is the innovation length;
step 2-2), taking the liquid flow of the liquid saturated steam heat exchange system as input data u (t), taking the outlet liquid temperature as output data y (t), and recording data;
step 2-3) combining the intermediate variables m (t), e (t), and the fractional derivative delta in the information vector α m(t),Δ α e(t),Δ α v (t) and the auxiliary function k (t) are replaced by their estimated valuesAnd->Constructing an estimate of the information vector according to equations (13) and (14)>
ThenExpressed as:
step 2-4) introducing scalar innovation:
wherein the method comprises the steps ofAnd->Respectively is theta cdk And theta cdk The estimated value of the parameter vector is expressed as
Simultaneously introducing an innovation vector E (p, t) as shown in a formula (16), wherein p is the innovation length;
step 2-5) selection of an appropriate convergence factor r according to formulas (17) and (18) 1 (t),r 2 (t)；
Step 2-6) calculating the estimated value θ of the parameter vector according to equations (19) and (20) ab (t),θ cdk (t)；
Step 2-7) calculation according to formulas (21) - (24)And->
Step 2-8) calculation of fractional derivative from GL definition of formula (7)
Step 2-9) judging whether the maximum cycle number is reached, if not, jumping the program to step 2-3), and if so, entering step 2-10);
step 2-10) outputting the identification resultAnd (5) completing identification.
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