CN106066608A - The modelling by mechanism of multivariate continuous process model merges discrimination method with Experimental modeling - Google Patents

Abstract

The modelling by mechanism that the present invention relates to a kind of multivariate continuous process model merges discrimination method with Experimental modeling, comprise the following steps: 1) under rational assumed condition sets, utilize Analysis on Mechanism modeling method to determine model structure and the parameter being identified multivariable process；2) the some groups of Identification Data being identified multivariable process are gathered；3) carry out modelling by mechanism and merge identification with Experimental modeling.Compared with prior art, the present invention has the advantage such as more accurately and reliably.

Description

The modelling by mechanism of multivariate continuous process model merges discrimination method with Experimental modeling

Technical field

The present invention relates to the multivariate continuous process identification technique in modeling and simulating field in Control Science and Engineering subject, The modelling by mechanism especially relating to a kind of multivariate continuous process model merges discrimination method with Experimental modeling.

Background technology

Along with socioeconomic development, modern industrial equipment increasingly maximizes, complicates, and whole production process is by numerous rings Joint composition, and generally there is coupling and associate between these links, this coupling shows as some input of system Variable affects multiple output variable simultaneously, or some output variable is affected by multiple input variables, such system It is referred to as multi-variable system.Extensive all the more for the utilization of multi-variable system, for ensureing security of system and stablizing, carry in every profession and trade High product quality, the energy consumption etc. of reducing need one the most accurately system model to be controlled the design of system.Therefore, many The modeling problem of variable system is always control theory and the focus of industrial application research.Being modeled as of system mathematic model Lose and affect the design of control system all the time, adjust and performance evaluation.

For a long time, mode based on Analysis on Mechanism carries out the modeling of system, to need the principle of modeling to determine accordingly One group of (partially) differential equation and the continuous time system of some restriction relations composition, have explicit physical meaning and reliability be high Advantage but have that computing is complicated and nonlinear model such as is difficult to resolve at the problem.So, Analysis on Mechanism modeling is considered as engineering always Disabled modeling method in application, especially for multivariate complication system.The method of application experiment modeling carries out many During the modeling of variable complication system, there is highly versatile and the feature pressing close to engineering actual there is also the model structure being difficult to overcome Uncertain and the insecure problem of identification model.But, under rational assumed condition sets, can effectively simplify and be set up Analysis on Mechanism model, and it is possible to obtain on difinite quality analysis significance can computation model.The structure of this model and spy Property parameter value can be exactly that the model structure of multivariate complication system Experimental modeling is uncertain and the unreliable difficulty of identification model Topic provides solution.

Summary of the invention

Defect that the purpose of the present invention is contemplated to overcome above-mentioned prior art to exist and provide one more accurately and reliably Modelling by mechanism and the Experimental modeling of multivariate continuous process model merge discrimination method.

The purpose of the present invention can be achieved through the following technical solutions:

The modelling by mechanism of a kind of multivariate continuous process model merges discrimination method with Experimental modeling, comprises the following steps:

1) under rational assumed condition sets, Analysis on Mechanism modeling method is utilized to determine the mould being identified multivariable process Type structure and parameter；

2) the some groups of Identification Data being identified multivariable process are gathered；

3) carry out modelling by mechanism and merge identification with Experimental modeling.

Described step 1) particularly as follows:

If being expressed as of obtained Analysis on Mechanism model available delivery functional form

$\mathrm{\Φ}\left(s\right)=\left[\begin{array}{cccc}{G}_{11}\left(s\right)& G_{12}\left(s\right)& ...& G_{1n}\left(s\right)\\ G_{21}\left(s\right)& G_{22}\left(s\right)& ...& G_{2n}\left(s\right)\\ \·& \·& \·& \·\\ \·& \·& \·& \·\\ \·& \·& \·& \·\\ G_{m1}\left(s\right)& G_{m2}\left(s\right)& ...& G_{mn}\left(s\right)\end{array}\right]---\left(1\right)$

In formula, Φ (s) is the transfer function model matrix being identified multivariable process；G_ijS () is jth input the i-th output Branch's transfer function model；

Assume the i-th output Y of process_iS () is expressed as

$Y_i\left(s\right)=\underset{j=1}{\overset{n}{\Σ}}{Y}_{ij}\left(s\right)=\underset{j=1}{\overset{n}{\Σ}}{G}_{ij}\left(s\right)U_j\left(s\right),i=1,2,...,m---\left(2\right)$

In formula, U_jS () is the jth input being identified multivariable process；Y_ijS () is Y_iS () inputs U for jth_jThe sound of (s) Answer component；

Assume G_ijS () is expressed as with a kind of universal model

$G_{ij}\left(s\right)=\frac{K_{ij}({\mathrm{\β}}_{{\mathrm{ijq}}_{ij}}{s}^{q_{ij}}+{\mathrm{\β}}_{{\mathrm{ijq}}_{ij}-1}{s}^{q_{ij}-1}+...+{\mathrm{\β}}_{ij1}s+1)}{{\mathrm{\α}}_{{\mathrm{ijp}}_{ij}}{s}^{p_{ij}}+{\mathrm{\α}}_{{\mathrm{ijp}}_{ij}-1}{s}^{p_{ij}-1}+...+{\mathrm{\α}}_{ij1}s+1}{e}^{-{\mathrm{\τ}}_{ij}s}$

In formula, K_ijIt is G_ijThe gain of (s)；τ_ijIt is G_ijDelaying of (s)；q_ijIt is G_ijThe polynomial exponent number of molecule of (s)；p_ij It is G_ijThe exponent number of the denominator polynomials of (s)；{β_ijk, k=1,2 ..., q_ijIt is G_ijThe polynomial coefficient of molecule of (s)；{α_ijk,k =1,2 ..., p_ijIt is G_ijThe coefficient of the denominator polynomials of (s).

Described step 2) particularly as follows:

Assume that Identification Data length elects N as, collected and be identified the input data table of multivariable process and be shown as { u_j(k), K=1,2 ..., N；J=1,2 ... n}, collected and be identified the output tables of data of multivariable process and be shown as { y_i(k), k=1, 2,…,N；I=1,2 ... m}.

Described step 3) particularly as follows:

The gain of Experimental modeling model and exponent number directly take modelling by mechanism parameter, the time class parameter of Experimental modeling model Calculate with identification optimization and obtain, it may be assumed that

${\hat{K}}_{ij}=K_{ij}---\left(4\right)$

${\hat{q}}_{ij}=q_{ij}---\left(5\right)$

${\hat{p}}_{ij}=p_{ij}---\left(6\right)$

WithIt is calculated by the identification optimization according to Identification Data.

Described step 3) particularly as follows:

The model order of Experimental modeling directly takes modelling by mechanism model parameter, the gain of Experimental modeling model and time class Parameter calculates with identification optimization and obtains, it may be assumed that

${\hat{q}}_{ij}=q_{ij}---\left(7\right)$

${\hat{p}}_{ij}=p_{ij}---\left(8\right)$

WithCalculated by the identification optimization according to Identification Data Arrive.

Described step 3) particularly as follows:

The parameter optimization scope of Experimental modeling is according to modelling by mechanism parameter determination, it may be assumed that

WithBy the identification according to Identification Data Optimization is calculated.

But, the identification of each parameter optimizes codomain all can be centered by modelling by mechanism model parameter, left and right 10% to 50% For border.And for exponent number class parameter such asOrThe most desirableOr

The modeling problem of multivariate continuous process is always advanced control theory and the bottleneck problem of Technique Popularizing application, uses Analysis on Mechanism modeling method is set up multivariate continuous process model and is had explicit physical meaning and the high advantage of reliability, but exists Parameter difficulty to determine and equation complexity intractable problem.Set up multivariate continuous process model by the method for Experimental modeling and have logical Strong by property and press close to the feature that engineering is actual, but there is also that model structure is uncertain and the insecure problem of model characteristics.But, Two kinds of methods are merged and sets up multivariate continuous process model, then can learn from other's strong points to offset one's weaknesses, set up more accurately and more reliable Model.Compared with prior art, the Mathematical Models that the present invention is directed to a kind of general transfer function form proposes three kinds of machines Reason modeling merges discrimination method with Experimental modeling, and the essence of this fusion discrimination method is to utilize Analysis on Mechanism modeling method to obtain Being identified model structure and the initial parameter values of multivariable process, re-using experiment modeling method is asked for being identified multivariable process Concrete model parameter.

Detailed description of the invention

Below in conjunction with the embodiment of the present invention, technical scheme is clearly and completely described, it is clear that described enforcement Example is a part of embodiment of the present invention rather than whole embodiment.Based on the embodiment in the present invention, ordinary skill The every other embodiment that personnel are obtained on the premise of not making creative work, all should belong to the model of present invention protection Enclose.

It is identified process, it is assumed that its realistic model is for what certain known two input one exported:

$G_{11}\left(s\right)=\frac{2}{200s+1}$

$G_{12}\left(s\right)=\frac{895(90s+1)}{(2s+1)(45s+1)(230s+1)}$

The model of postulated mechanism modeling gained is very accurate, just the same with realistic model.

Tested by identification, it is thus achieved that 800 point process output response { y₁(k), k=1,2 ..., 800}, input data { u₁ (k), k=1,2 ..., 800} and input data { u₂(k), k=1,2 ..., 800}.

Directly take with the model order that Experimental modeling merges discrimination method, i.e. Experimental modeling according to the second modelling by mechanism Modelling by mechanism parameter, the recycling available identification model of population (PSO) identification program is:

${\hat{G}}_{11-2}\left(s\right)=\frac{2.191}{232.9s+1}$

${\hat{G}}_{12-2}\left(s\right)=\frac{951.1(97.11s+1)}{(1.995s+1)(45.79s+1)(259.3s+1)}$

Directly take according to gain and the exponent number of the first modelling by mechanism with Experimental modeling fusion discrimination method, i.e. Experimental modeling Using modelling by mechanism parameter, recycling the available identification model of population (PSO) identification program is:

${\hat{G}}_{11-1}\left(s\right)=\frac{2}{200.0000s+1}$

${\hat{G}}_{12-1}\left(s\right)=\frac{895(90.0001s+1)}{(2.0000s+1)(45.0001s+1)(230.0001s+1)}$

Contrast two kinds of modellings by mechanism and merge knowable to the model parameter that identification obtains with Experimental modeling, modelling by mechanism and experiment It is highly effective that discrimination method is merged in modeling, particularly merges discrimination method with the first modelling by mechanism with Experimental modeling.From Above case is it can be seen that merge distinguishing of time class parameter that discrimination method obtains with the first modelling by mechanism and Experimental modeling Know precision the highest, and the time class parameter obtained with the second modelling by mechanism and Experimental modeling fusion discrimination method exists significantly Identification Errors.

The above, the only detailed description of the invention of the present invention, but protection scope of the present invention is not limited thereto, and any Those familiar with the art, in the technical scope that the invention discloses, can readily occur in the amendment of various equivalence or replace Changing, these amendments or replacement all should be contained within protection scope of the present invention.Therefore, protection scope of the present invention should be with right The protection domain required is as the criterion.

Claims (6)

1. the modelling by mechanism of a multivariate continuous process model merges discrimination method with Experimental modeling, it is characterised in that include Following steps:

1) under rational assumed condition sets, Analysis on Mechanism modeling method is utilized to determine the model knot being identified multivariable process Structure and parameter；

2) the some groups of Identification Data being identified multivariable process are gathered；

3) carry out modelling by mechanism and merge identification with Experimental modeling.

The modelling by mechanism of a kind of multivariate continuous process model the most according to claim 1 merges identification side with Experimental modeling Method, it is characterised in that described step 1) particularly as follows:

If being expressed as of obtained Analysis on Mechanism model available delivery functional form

$\mathrm{\Φ}\left(s\right)=\left[\begin{array}{cccc}{G}_{11}\left(s\right)& G_{12}\left(s\right)& ...& G_{1n}\left(s\right)\\ G_{21}\left(s\right)& G_{22}\left(s\right)& ...& G_{2n}\left(s\right)\\ \·& \·& \·& \·\\ \·& \·& \·& \·\\ \·& \·& \·& \·\\ G_{m1}\left(s\right)& G_{m2}\left(s\right)& ...& G_{mn}\left(s\right)\end{array}\right]---\left(1\right)$

In formula, Φ (s) is the transfer function model matrix being identified multivariable process；G_ijS () is dividing of jth input the i-th output Prop up transfer function model；

Assume the i-th output Y of process_iS () is expressed as

$Y_i\left(s\right)=\underset{j=1}{\overset{n}{\Σ}}{Y}_{ij}\left(s\right)=\underset{j=1}{\overset{n}{\Σ}}{G}_{ij}\left(s\right)U_j\left(s\right),i=1,2,...,m---\left(2\right)$

In formula, U_jS () is the jth input being identified multivariable process；Y_ijS () is Y_iS () inputs U for jth_jS the response of () divides Amount；

Assume G_ijS () is expressed as with a kind of universal model

$G_{ij}\left(s\right)=\frac{K_{ij}({\mathrm{\β}}_{{\mathrm{ijq}}_{ij}}{s}^{q_{ij}}+{\mathrm{\β}}_{{\mathrm{ijq}}_{ij}-1}{s}^{q_{ij}-1}+...+{\mathrm{\β}}_{ij1}s+1)}{{\mathrm{\α}}_{{\mathrm{ijp}}_{ij}}{s}^{p_{ij}}+{\mathrm{\α}}_{{\mathrm{ijp}}_{ij}-1}{s}^{p_{ij}-1}+...+{\mathrm{\α}}_{ij1}s+1}{e}^{-{\mathrm{\τ}}_{ij}s}---\left(3\right)$

In formula, K_ijIt is G_ijThe gain of (s)；τ_ijIt is G_ijDelaying of (s)；q_ijIt is G_ijThe polynomial exponent number of molecule of (s)；p_ijIt is G_ij The exponent number of the denominator polynomials of (s)；{β_ijk, k=1,2 ..., q_ijIt is G_ijThe polynomial coefficient of molecule of (s)；{α_ijk, k=1, 2,…,p_ijIt is G_ijThe coefficient of the denominator polynomials of (s).

The modelling by mechanism of a kind of multivariate continuous process model the most according to claim 2 merges identification side with Experimental modeling Method, it is characterised in that described step 2) particularly as follows:

Assume that Identification Data length elects N as, collected and be identified the input data table of multivariable process and be shown as { u_j(k), k=1, 2,…,N；J=1,2 ... n}, collected and be identified the output tables of data of multivariable process and be shown as { y_i(k), k=1,2 ..., N；I=1,2 ... m}.

The modelling by mechanism of a kind of multivariate continuous process model the most according to claim 3 merges identification side with Experimental modeling Method, it is characterised in that described step 3) particularly as follows:

The gain of Experimental modeling model and exponent number directly take modelling by mechanism parameter, and the time class parameter of Experimental modeling model is with distinguishing Know to optimize to calculate and obtain, it may be assumed that

${\hat{K}}_{ij}=K_{ij}---\left(4\right)$

${\hat{q}}_{ij}=q_{ij}---\left(5\right)$

${\hat{p}}_{ij}=p_{ij}---\left(6\right)$

WithIt is calculated by the identification optimization according to Identification Data.

The modelling by mechanism of a kind of multivariate continuous process model the most according to claim 3 merges identification side with Experimental modeling Method, it is characterised in that described step 3) particularly as follows:

The model order of Experimental modeling directly takes modelling by mechanism model parameter, the gain of Experimental modeling model and time class parameter Calculate with identification optimization and obtain, it may be assumed that

${\hat{q}}_{ij}=q_{ij}---\left(7\right)$

${\hat{p}}_{ij}=p_{ij}---\left(8\right)$

WithIt is calculated by the identification optimization according to Identification Data.

The modelling by mechanism of a kind of multivariate continuous process model the most according to claim 3 merges identification side with Experimental modeling Method, it is characterised in that described step 3) particularly as follows:

The parameter optimization scope of Experimental modeling is according to modelling by mechanism parameter determination, it may be assumed that

WithBy the identification optimization meter according to Identification Data Obtain.