CN110989349A - Multivariate system model identification method - Google Patents
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- G05B13/00—Adaptive control systems, i.e. systems automatically adjusting themselves to have a performance which is optimum according to some preassigned criterion
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Abstract
The invention provides a multivariate system model identification method, aiming at the problem that a multivariate system is difficult to identify in engineering application, for the multivariate system with M inputs, the identification data under M groups of irrelevant excitation conditions are collected together, a transfer function matrix G(s) of the multivariate system is set, a particle swarm optimization algorithm is adopted to carry out model identification on a selected multivariate system structure model, the parameters of the transfer function matrix G(s) are solved to obtain a transfer function matrix G(s), and finally, the best fitted equivalent model of the tested system is obtained. The verification proves that the identification method is simple and easy to implement, high in identification precision and high in engineering application value.
Description
Technical Field
The invention belongs to the field of control science and engineering, and relates to a multivariate system model identification method.
Background
With the development of science and technology and social economy, modern industrial equipment is increasingly large and complex, and the production process consisting of a plurality of links is generally coupled and associated among the links. This coupling and association is manifested in that a certain input variable of the system will affect a plurality of output variables simultaneously, or a certain output variable will be affected by a plurality of input variables. This coupling and correlation has become a key difficult factor affecting multivariable system modeling and multivariable system control.
Currently, in the actual implementation of multivariate system identification engineering, a univariate identification method is also commonly used, which uses only one set of data for identification. Because the multiple input quantities of the multivariable system are not all artificially controllable, the result of using only the univariate identification method for the multivariable system identification is inevitably more failure than success, and the identification precision is difficult to improve.
In addition, the number of the manually controllable input quantities is often a small number of the total number of the input quantities of the multivariate system, which means that most of the identification data which can be recorded is multivariate excitation response data, multivariate excitation signals are different from univariate excitation signals, and whether the observed multivariate excitation signals are effective for system model identification needs to be judged before identification calculation.
Disclosure of Invention
In order to solve the above problems, the invention provides an effective identification method in engineering application aiming at the problem that multivariable system is difficult to identify, which adopts the following technical scheme:
the invention provides a multivariate system model identification method, which is characterized by comprising the following steps:
step S1, defining M dimension input vector of multivariable system as U (S) and Q dimension output vector Y (S), setting transfer function matrix G (S) of multivariable system, obtaining input and output relation Y (S) G (S) U (S), and determining transfer function matrix G (S) by carrying out model identification on multivariable system;
and step S2, solving parameters of a transfer function matrix G (S) by using an intelligent optimization algorithm on the M groups of data groups of input vectors and output vectors of the multivariable system under irrelevant excitation to obtain the transfer function matrix G (S), wherein the intelligent optimization algorithm comprises a particle swarm optimization algorithm, a differential evolution algorithm and a cuckoo algorithm.
In step S2, the process of solving the parameters of the transfer function matrix g (S) by using the intelligent optimization algorithm includes the following steps:
and step T1, taking the simulation program corresponding to the intelligent optimization algorithm as an identification program, and initializing.
Step T2, obtaining response data under the same excitation input through simulation calculation aiming at the transfer function matrix G(s)
Wherein N is the total number of sampled data.
Step T3, calculating the function formula of the optimized performance index:
step T4, adopting an identification procedure, adjusting the model parameters to:
{ai,j,k,i＝1,2,…,M；j＝1,2,…,Q；k＝1,2,…,nij}
{bi,j,k,i＝1,2,…,M；j＝1,2,…,Q；k＝1,2,…,mij}
wherein n isijFor the denominator order of the transfer function, mijIs the molecular order of the transfer function.
And step T5, repeating the steps from T2 to T4 until the preset counting times are reached.
And step T6, outputting the adjusted model parameters to obtain a transfer function matrix G(s).
Further, in the multivariate system model identification method provided by the present invention, the step S1 comprises the following steps:
step S1.1, let the input vector of the multivariate system be M-dimensional, and define the input vector of the multivariate system as U (S) ═ U1(s) U2(s) … UM(s)]T，Ui(s) (i ═ 1,2, …, M) is the ith input to the multivariate system, the output of the multivariate system is given by dimension Q, and the output vector of the multivariate system is defined as Y(s) ═ Y1(s) Y2(s) … YQ(s)]T，Yj(s) (j ═ 1,2, …, Q) is the jth output of the multivariable system;
step S1.2, setting a transfer function matrix of the multivariable system as G (S), and obtaining the input and output relation of the multivariable system as follows:
Y(s)＝G(s)U(s)
wherein G(s) is a transfer function matrix of the multivariate system, and is developed as follows:
the transfer function matrix g(s) is determined by model identification of the multivariate system.
Further, in the multivariate system model identification method provided by the present invention, the step S2 comprises the following steps:
s2.1, selecting M groups of data groups of input vectors and output vectors of the multivariate system under irrelevant excitation, and assuming that the sampling time is TsAnd the total number of the sampling data is N, and the acquired data group is as follows:
{ui,j,k,i＝1,2,…,M；j＝1,2,…,Q；k＝1,2,…,N}
{yi,j,k,i＝1,2,…,M；j＝1,2,…,Q；k＝1,2,…,N}
and S2.2, taking the data groups of the input vectors and the output vectors of the M groups of collected multivariable systems under irrelevant excitation as data to be identified, and solving parameters of a transfer function matrix G (S) by adopting an intelligent optimization algorithm to obtain a transfer function matrix G (S).
Action and Effect of the invention
According to the practical method for identifying the multivariate system model effectively applied to engineering, which is provided by the invention, aiming at the problem that the multivariate system is difficult to identify, for the multivariate system with M inputs, the identification data under M groups of irrelevant excitation conditions are gathered together, and the model identification is carried out on the selected multivariate system structure model by adopting an intelligent optimization algorithm, so that the best fitted equivalent model of the tested system is obtained. The verification proves that the identification method is simple and easy to implement, high in identification precision and high in engineering application value.
Drawings
FIG. 1 is a schematic diagram of a transfer function matrix of a multivariate system model of an embodiment of the invention;
FIG. 2 is a model of a low temperature reheater system of an embodiment of the present invention;
FIG. 3a) is a block diagram of the field operational data of 10:00-11:23 on 31 days 3/2015 of the distributed control system database of an embodiment of the invention, i.e., operational data 1;
FIG. 3b) is the field operational data of 15:30-16:53 on 31 days 3/2015 of the distributed control system database 2015 of an embodiment of the invention, i.e., operational data 2;
FIG. 3c) is the field operational data for distributed control system database 2015, 3, 31, 22:10-23:33, i.e., operational data 3, of an embodiment of the present invention;
FIG. 3d) is the field operation data of the centralized and distributed control system database 2016, 07:00-08:23, 1 month 4, of the present invention, i.e., operation data 4;
FIG. 4 shows the result of the multivariate system identification method of the present invention for the operation data 1-3 in the embodiment of the present invention;
FIG. 5 shows the result of identifying the running data 1 by a univariate identification method according to the embodiment of the present invention;
FIG. 6 is a model validation of the multivariate system identification method of the invention for operational data 4 in an embodiment of the invention;
FIG. 7 is a model verification for the operation data 4 identified by the univariate identification method according to the embodiment of the present invention.
Detailed Description
The following description of the embodiments of the present invention will be made with reference to the accompanying drawings and examples
< example >
FIG. 2 is a model of a low temperature reheater system of an embodiment of the present invention.
The 660MW once-through boiler of a certain power plant is taken as an embodiment object, and the structure diagram is shown in FIG. 2. Divide the reheat air temperature model into an inlet temperature T13 transfer function channels of feed water flow D and baffle opening degree F are subjected to system identification, and the output is the outlet temperature T of the low-temperature reheater2。
Screening out four sections according to field operation data of a plurality of days stored in a distributed control system databaseAs shown in the figure, 3a) is the field operation data of 10:00-11:23 on 31 days 3 and 31 months in 2015, 3b) is the field operation data of 15:30-16:53 on 31 days 3 and 31 months in 2015, 3c) is the field operation data of 22:10-23:33 on 31 days 3 and 31 months in 2015, and 3d) is the field operation data of 07:00-08:23 on 1 day 1 and 1 month in 2016. The sampling period is 5s and the sampling duration is 5000 s. Wherein: t is2Is the outlet temperature, T, of the low-temperature reheater1Is the inlet temperature of the low temperature reheater; d is water supply flow; f is the opening degree of the flue damper.
Fig. 3a) is the field operational data of 10:00-11:23 on 31 days 3/2015 of the distributed control system database 2015, i.e., operational data 1, according to an embodiment of the invention.
Fig. 3b) is the field operational data of 15:30-16:53 on 31 days 3/2015 of the distributed control system database 2015, i.e. operational data 2, according to an embodiment of the invention.
Fig. 3c) is the field operational data of 22:10-23:33 on 31/3/2015 of the distributed control system database 2015, i.e., operational data 3, according to an embodiment of the invention.
Fig. 3d) is the field operation data of 07:00-08:23 on 1/4/2016 of the distributed control system database of the embodiment of the present invention, i.e., operation data 4.
The data shown in fig. 3a), 3b), 3c) are used for model recognition and the data shown in fig. 3d) are used for model verification. According to the multivariate system model identification method provided by the embodiment, the following steps are carried out:
step S1, defining M-dimensional input vector and Q-dimensional output vector y (S) of the multivariate system, setting the transfer function matrix g (S) of the multivariate system, obtaining the input/output relational expression y (S) ═ g (S) u (S), and determining the transfer function matrix g (S) by performing model identification on the multivariate system, which is the specific steps from step S1.1 to S1.2.
Step S1.1, let the input vector of the multivariate system be M-dimensional, and define the input vector of the multivariate system as U (S) ═ U1(s) U2(s) … UM(s)]T，Ui(s) (i ═ 1,2, …, M) is the ith input to the multivariate system, the output of the multivariate system is given by dimension Q, and the output vector of the multivariate system is defined as Y(s) ═ Y1(s) Y2(s) … YQ(s)]T，Yj(s) (j ═ 1,2, …, Q) is the jth output of the multivariable system;
step S1.2, the defined input and output relationship of the multivariable system is as follows:
Y(s)＝G(s)U(s)
wherein G(s) is expanded to:
FIG. 1 is a schematic diagram of a transfer function matrix of a multivariate system model according to an embodiment of the invention.
As shown in fig. 1, the multivariate system is modeled to determine the transfer function matrix g(s).
The most widely applied transfer function model in the process control of the power plant is generally a multi-order inertia link, and the transfer function of the model is as follows:
wherein: k is an amplification factor; t is a time constant; n is the order of the system.
And step S2, selecting M groups of data groups of input vectors and output vectors of the multivariable system under irrelevant excitation, solving parameters of a transfer function matrix G (S) by using an intelligent optimization algorithm to obtain a transfer function matrix G (S), and the specific steps are as described in steps S2.1-S2.2.
S2.1, selecting M groups of data groups of input vectors and output vectors of the multivariate system under irrelevant excitation, and assuming that the sampling time is TsAnd the total number of the sampling data is N, and the acquired data group is as follows:
{ui,j,k,i＝1,2,…,M；j＝1,2,…,Q；k＝1,2,…,N}
{yi,j,k,i＝1,2,…,M；j＝1,2,…,Q；k＝1,2,…,N}
step S2.2, using the data sets of the input vectors and the output vectors of the M groups of multivariate systems under irrelevant excitation as data to be identified, and solving parameters of a transfer function matrix g (S) by using an intelligent optimization algorithm to obtain a transfer function matrix g (S), wherein the intelligent optimization algorithm includes a particle swarm optimization algorithm, a differential evolution algorithm, and a cuckoo algorithm, and the embodiment uses the particle swarm optimization algorithm, and the specific steps are as described in steps T1 to T6.
And step T1, taking a simulation program corresponding to the particle swarm optimization algorithm as an identification program, and initializing.
Step T2, obtaining response data under the same excitation input through simulation calculation aiming at the transfer function matrix G(s)
Where N is the total number of sampled data.
Step T3, calculating the function formula of the optimized performance index:
step T4, adopting a particle swarm optimization algorithm to adjust model parameters:
{ai,j,k,i＝1,2,…,M；j＝1,2,…,Q；k＝1,2,…,nij}
{bi,j,k,i＝1,2,…,M；j＝1,2,…,Q；k＝1,2,…,mij}
wherein n isijFor the denominator order of the transfer function, mijIs the molecular order of the transfer function.
And step T5, repeating the steps from T2 to T4 until the preset counting times are reached.
And step T6, outputting the adjusted model parameters to obtain a transfer function matrix G(s).
FIG. 4 shows the result of the multivariate system identification method of the present invention for the operation data 1-3 in the embodiment of the present invention.
As shown in fig. 4, a) operation data 1, b) operation data 2, and c) operation data 3 in the figure represent the results of identification of the outlet temperature of the low-temperature reheater in the data shown in fig. 3a), 3b), and 3c), respectively, and the dotted line in the figure represents the output of the model obtained by the identification, and the solid line represents the actual output of the low-temperature reheater. The identified model parameters are shown in table 1.
| Parameter(s) | G1(s) | G2(s) | G3(s) |
| K | 2.295 | -0.042 | 0.439 |
| T | 409.478 | 163.685 | 401.581 |
| n | 4 | 1 | 3 |
TABLE 1
FIG. 5 shows the result of the identification of the operation data 1 by the univariate identification method according to the embodiment of the present invention.
In contrast, as shown in fig. 5, the line represents the output of the identified model, and the solid line represents the actual output of the unit. The identified model parameters are shown in table 2.
TABLE 2
As shown in fig. 4 and 5, the response curve of the output value of the model identified by the univariate identification method and the method of the present invention is very close to the response curve of the true value of the actual unit, but the parameters of the model identified by the univariate identification method and the method of the present invention are very different.
Analyzing the model parameter data shown in table 1, it can be known that the outlet temperature of the reheater increases with the increase of the inlet steam temperature, decreases with the increase of the feedwater flow, and increases with the increase of the baffle opening, which completely conforms to the dynamic characteristics between the outlet temperature of the reheater and the three inputs obtained by the mechanism analysis; the model parameter data shown in table 2 is just contrary to the reheat air temperature dynamics obtained by the mechanism analysis, and therefore, the model parameters identified in table 2 are qualitatively incorrect.
FIG. 6 is a model validation of the multivariate system identification method of the present invention for operational data 4 in an embodiment of the present invention.
As shown in fig. 6, the output response curve of the identification model identified by the method of the present invention can be well fitted to the actual output response curve, and the mean square error is 0.9878.
FIG. 7 is a model verification for the operation data 4 identified by the univariate identification method according to the embodiment of the present invention.
As shown in fig. 7, the output curve of the identification model obtained by identification using the univariate identification method is greatly different from the actual output curve of the unit, and the mean square error is 3.2002. Therefore, the model identified by the method has higher reliability.
Examples effects and effects
According to the multivariate system model identification method provided by the invention, identification data under M groups of uncorrelated excitation conditions are collected together, and then an intelligent optimization algorithm is adopted to carry out model identification on the selected multivariate system structure model. In the embodiment, three groups of operation data are identified, the obtained model parameter data conform to the dynamic characteristics between the outlet temperature of the reheater and three inputs obtained through mechanism analysis, and in addition, the verification of one group of operation data proves that the method is simple and easy to implement, high in identification precision and high in engineering application value.
The above embodiments only describe the implementation and operation results of the practical method for multi-variable system identification provided by the present invention, but the present invention is not limited to the above embodiments, and the method provided by the present invention is effective for other multi-variable systems.
Claims (4)
1. A multivariate system model identification method is used for carrying out model identification on a multivariate system, and is characterized by comprising the following steps:
step S1, defining M-dimensional input vectors and Q-dimensional output vectors of the multivariate system as u (S) and y (S), setting a transfer function matrix g (S) of the multivariate system to obtain an input-output relational expression y (S) ═ g (S) u (S), and determining the transfer function matrix g (S) by performing the model identification on the multivariate system;
step S2, solving parameters of the transfer function matrix g (S) by using an intelligent optimization algorithm on M groups of data sets of the input vector and the output vector of the multivariate system under uncorrelated excitation to obtain the transfer function matrix g (S).
In step S2, the process of solving the parameters of the transfer function matrix g (S) by using the intelligent optimization algorithm includes the following steps:
step T1, taking the simulation program corresponding to the intelligent optimization algorithm as an identification program, and initializing;
step T2, obtaining response data under the same excitation input through simulation calculation aiming at the transfer function matrix G(s)
Wherein N is the total number of the sampling data;
step T3, calculating the function formula of the optimized performance index:
step T4, adopting the identification procedure to adjust model parameters:
{ai,j,k,i＝1,2,…,M；j＝1,2,…,Q；k＝1,2,…,nij}
{bi,j,k,i＝1,2,…,M；j＝1,2,…,Q；k＝1,2,…,mij}
wherein n isijFor the denominator order of the transfer function, mijIs the molecular order of the transfer function;
step T5, repeating the steps from T2 to T4 until reaching the preset counting times;
and T6, outputting the adjusted model parameters to obtain the transfer function matrix G(s).
2. The multivariate system model identification method as defined in claim 1, wherein the step S1 comprises the steps of:
step S1.1, assuming that the input vector of the multivariate system is M-dimensional, defining the input vector of the multivariate system as U (S) ═ U1(s) U2(s) … UM(s)]T，Ui(s) (i ═ 1,2, …, M) is the ith input to the multivariable system, assuming that the output quantities of the multivariable system are in dimension Q, the output vector defining the multivariable system is Y(s) ═ Y1(s) Y2(s) … YQ(s)]T，Yj(s) (j ═ 1,2, …, Q) is the jth output of the multivariable system;
s1.2, setting a transfer function matrix of the multivariable system as G (S), and obtaining the input and output relation of the multivariable system as follows:
Y(s)＝G(s)U(s)
wherein G(s) is expanded to:
the model identification of the multivariate system is the determination of the transfer function matrix g(s).
3. The multivariate system model identification method as defined in claim 1, wherein the step S2 comprises the steps of:
step S2.1, assuming a sampling time T for the data sets of the input and output vectors of the multivariate system model under uncorrelated excitationsAnd the total number of the sampling data is N, and the acquired data group is as follows:
{ui,j,k,i＝1,2,…,M；j＝1,2,…,Q；k＝1,2,…,N}
{yi,j,k,i＝1,2,…,M；j＝1,2,…,Q；k＝1,2,…,N}
s2.2, using the acquired data groups of the input vectors and the output vectors of the M groups of multivariable systems under irrelevant excitation as data to be identified, and solving parameters of the transfer function matrix G (S) by adopting an intelligent optimization algorithm to obtain the transfer function matrix G (S).
4. The multivariate system model identification method as defined in claim 1, wherein:
the intelligent optimization algorithm comprises a particle swarm optimization algorithm, a differential evolution algorithm and a cuckoo algorithm.
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