CN106970533A - A kind of nonlinear system modeling method estimated based on RBF ARX models steadiness parameter - Google Patents
A kind of nonlinear system modeling method estimated based on RBF ARX models steadiness parameter Download PDFInfo
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Abstract
, should comprising the following steps that based on the nonlinear system modeling method of RBF ARX models steadiness parameter estimation the invention discloses engineering design and a kind of nonlinear system modeling method estimated based on RBF ARX models steadiness parameter in optimisation technique field：S1：The structure of RBF neural is represented in the form of Gaussian function；S2：Build ARX model structure A (z‑1) Y (k)=z‑dB(z‑1)U(k)+e(k)；S3：Using gaussian network come the model coefficient in approximation step S1 and step S2；S4：The performance indications of model coefficient in step S3 are calculated using quadratic form adjuster；S5：The optimal solution that output error and controlling increment are weighted is exported, the present invention has the ability of adaptive and self study, the long-term forecast precision and robustness of RBF ARX models can be increased substantially, with higher practical value and market prospects.
Description
Technical field
It is specially that one kind is estimated based on RBF-ARX model stability parameters the present invention relates to engineering design and optimisation technique field
The nonlinear system modeling method of meter.
Background technology
Generally existing Nonlinear Dynamic and physical model are difficult to situation about obtaining in actual industrial process, are driven using data
Description of the dynamic modeling method to realize its characteristic is the premise analyzed it and controlled.RBF neural is with its simple knot
The ability of structure, higher None-linear approximation precision and Fast Learning, is widely used in pattern-recognition, function approximation, signal
The fields such as processing, nonlinear system modeling, it has also become one of most popular feedforward neural network.But due to actual industrial process pair
The complexity of elephant so that RBF neural usually requires the None-linear approximation precision that higher order increasingly improves to meet will
Ask.RBF-ARX models combine State-Dependent ARX model to the descriptive power of non-linear dynamic characteristic and RBF neural
Function approximation capabilities can effectively reduce the order of RBF neural, be transported extensively to the learning ability of process localized variation
For fields such as time series forecasting, nonlinear system modelings.
In general, RBF class models comprise at least 3 class parameters：RBF network centers, width and linear weight, wherein RBF
Network center and width are nonlinear parameter, and linear weight is linear dimensions.Typical parameter optimisation procedure is using non-linear
The center for the network for optimizing to select RBF and width；Linear weight is determined using linear center least square.Research shows,
The optimization method of this parametric classification will cause RBF class models to have higher non-thread relative to simple nonlinear optimization method
Property approximation accuracy and faster learning ability.Principle based on the optimization method, the nonlinear parameter of RBF class models and linear ginseng
Number is alternately to update, that is to say, that in the optimization process of parameter, the renewal of linear dimensions is by based on different non-linear ginsengs
Number, this is easy to cause to meet with the problem of matrix is ill when solving linear dimensions using least square method.In this case, solve
Linear dimensions and based on the linear dimensions update nonlinear parameter will likely be diverging；On the other hand, the RBF god of high-order
Generally there is more parameter through network or RBF-ARX models, model structure is relative complex.Based on statistical error offset-
Variation decomposition is theoretical, and more complicated model structure is more easy to cause institute's established model to have less modeling error biasing and larger
Modeling error variance, and larger modeling error variance is poor by the robustness for causing model.Therefore, we have proposed a kind of base
Come into operation in the nonlinear system modeling method of RBF-ARX model stability parameter Estimations, to solve the above problems.
The content of the invention
It is an object of the invention to provide a kind of nonlinear system modeling side based on RBF-ARX model stability parameter Estimations
Method, to solve the problems mentioned in the above background technology.
To achieve the above object, the present invention provides following technical scheme：One kind is based on RBF-ARX model stability parameter Estimations
Nonlinear system modeling method, should nonlinear system modeling method based on RBF-ARX model stability parameter Estimations it is specific
Step is as follows：
S1：The structure of RBF neural is represented in the form of Gaussian function, its specific form of expression isX is input vector, c in formulaiFor the center of the function, have with x identical
The vector of dimension, σiFor the scaling factor, number, x-c centered on miFor vectorial two normal form of the equation；
S2：Build ARX model structure A (z-1) Y (k)=z-dB(z-1) U (k)+e (k), wherein U ∈ RnU and Y ∈ RnY is is
System input and output amount, e ∈ RnY is white noise, z-1For backward shift operator, d is the pure delay of system, wherein
S3：Using gaussian network come the model coefficient in approximation step S1 and step S2, RBF-ARX is obtained
Model structure
X (t) is state variable, n in formulay、nu、nv, m and nw=dim { X (t-1) } is model order,For the center of RBF networks,For pantograph ratio
Example coefficient,WithFor weight coefficient,
||·||2The normal form of representative vector two；
S4：The performance indications of model coefficient in step S3 are calculated using quadratic form adjuster,Time started t in formula0With terminal time tfAll it is solid
Fixed, F is the weighting matrix that n × n ties up the symmetrical constant of positive semidefinite, xT(tf)Fx(tf) it is referred to as terminal cost, represent in tfMoment be
Final state of uniting is close to the degree of predetermined final state, and Q (t) is the weighting matrix that n × n ties up the symmetrical time-varying of positive semidefinite, integral term xT(t)Q(t)
X (t) represents the error between given state and given state, and R (t) is the weighting matrix of the symmetrical time-varying of dimension of m m positive semidefinite, uT
(t) R (t) u (t) represent constraint of the dynamic process to control, by realizing Q (t) and R (t) to systematic function control and control
The limitation of energy；
S5：Utilize formulaTo output error and
The optimal solution of controlling increment weighting is exported, and E is mathematic expectaion, N in formula2For maximum predicted time domain length, B typically should be greater than
(z-1) order, N1For minimum prediction time domain length, usual N1=1 or equal to Time Delay of Systems d, NuFor control time domain length, lead to
Often take Nu＜ N2, qjFor output predicated error weight coefficient, λjFor controlling increment weight coefficient, yr(k+j) it is reference locus, is thing
The curve that one first set is intended to following setting value.
It is preferred that, in the step S1, RBF neural includes input layer, hidden layer and output layer, wherein input layer
Interstitial content is equal to the dimension of input signal, and the nodes of hidden layer are selected by designer according to the complexity of system, defeated
Go out layer to respond the state of input layer, be the linear combination of hidden layer output valve.
It is preferred that, in the step S5, to prevent controlled quentity controlled variable acute variation from causing system phenomenon out of control to occur, generally join
Examine geometric locus0 ＜ α ＜ 1 in formula, w are input set-point,
The smaller reference locus of wherein α just can be faster keep up with the set-point of system, but be likely to result in system overshoot, α is bigger, then is
Robustness of uniting is stronger, but response speed is slack-off.
Compared with prior art, the beneficial effects of the invention are as follows：The present invention has the ability of adaptive and self study, can
The long-term forecast precision and robustness of RBF-ARX models are increased substantially, with higher practical value and market prospects.
Brief description of the drawings
Fig. 1 is workflow diagram of the present invention.
Embodiment
Below in conjunction with the accompanying drawing in the embodiment of the present invention, the technical scheme in the embodiment of the present invention is carried out clear, complete
Site preparation is described, it is clear that described embodiment is only a part of embodiment of the invention, rather than whole embodiments.It is based on
Embodiment in the present invention, it is every other that those of ordinary skill in the art are obtained under the premise of creative work is not made
Embodiment, belongs to the scope of protection of the invention.
Referring to Fig. 1, the present invention provides a kind of technical scheme：It is a kind of based on the non-of RBF-ARX model stability parameter Estimations
Linear system modeling method, is somebody's turn to do the specific steps of the nonlinear system modeling method based on RBF-ARX model stability parameter Estimations
It is as follows：
S1：The structure of RBF neural is represented in the form of Gaussian function, its specific form of expression isX is input vector, c in formulaiFor the center of the function, have with x identical
The vector of dimension, σiFor the scaling factor, number, x-c centered on miFor vectorial two normal form of the equation, RBF neural bag
Input layer, hidden layer and output layer are included, the wherein interstitial content of input layer is equal to the dimension of input signal, the nodes of hidden layer
By designer selects according to the complexity of system, output layer is responded to the state of input layer, is hidden layer output valve
Linear combination；
S2：Build ARX model structure A (z-1) Y (k)=z-dB(z-1) U (k)+e (k), wherein U ∈ RnU and Y ∈ RnY is is
System input and output amount, e ∈ RnY is white noise, z-1For backward shift operator, d is the pure delay of system, wherein
S3：Using gaussian network come the model coefficient in approximation step S1 and step S2, RBF-ARX model structures are obtained
X (t) is state variable, n in formulay、nu、nv, m and nw=dim { X (t-1) } is model order,For the center of RBF networks,For pantograph ratio
Example coefficient,WithFor weight coefficient,
||·||2The normal form of representative vector two；
S4：The performance indications of model coefficient in step S3 are calculated using quadratic form adjuster,Time started t in formula0With terminal time tfAll it is solid
Fixed, F is the weighting matrix that n × n ties up the symmetrical constant of positive semidefinite, xT(tf)Fx(tf) it is referred to as terminal cost, represent in tfMoment be
Final state of uniting is close to the degree of predetermined final state, and Q (t) is the weighting matrix that n × n ties up the symmetrical time-varying of positive semidefinite, integral term xT(t)Q(t)
X (t) represents the error between given state and given state, and R (t) is the weighting matrix of the symmetrical time-varying of dimension of m m positive semidefinite, uT
(t) R (t) u (t) represent constraint of the dynamic process to control, by realizing Q (t) and R (t) to systematic function control and control
The limitation of energy；
S5：Utilize formulaTo output error and
The optimal solution of controlling increment weighting is exported, and E is mathematic expectaion, N in formula2For maximum predicted time domain length, B typically should be greater than
(z-1) order, N1For minimum prediction time domain length, usual N1=1 or equal to Time Delay of Systems d, NuFor control time domain length, lead to
Often take Nu＜ N2, qjFor output predicated error weight coefficient, λjFor controlling increment weight coefficient, yr(k+j) it is reference locus, is thing
The curve that one first set is intended to following setting value, to prevent controlled quentity controlled variable acute variation from causing system phenomenon hair out of control
It is raw, it is typically referenced to geometric locus0 ＜ α ＜ 1 in formula, w are defeated
Enter set-point, what the smaller reference locus of wherein α just can be faster keeps up with the set-point of system, but is likely to result in system overshoot, α
Bigger, then system robustness is stronger, but response speed is slack-off.
Although an embodiment of the present invention has been shown and described, for the ordinary skill in the art, can be with
A variety of changes, modification can be carried out to these embodiments, replace without departing from the principles and spirit of the present invention by understanding
And modification, the scope of the present invention is defined by the appended.
Claims (3)
1. a kind of nonlinear system modeling method based on RBF-ARX model stability parameter Estimations, it is characterised in that：This is based on
The nonlinear system modeling methods of RBF-ARX model stability parameter Estimations is comprised the following steps that：
S1：The structure of RBF neural is represented in the form of Gaussian function, its specific form of expression isX is input vector, c in i=1,2 ..., m, formulaiFor the center of the function, there is identical dimension with x
Several vectors, σiFor the scaling factor, number centered on m, | | x-ci| | it is vectorial two normal form of the equation；
S2：Build ARX model structure A (z-1) Y (k)=z-dB(z-1) U (k)+e (k), wherein U ∈ RnU and Y ∈ RnY is that system is defeated
Enter output quantity, e ∈ RnY is white noise, z-1For backward shift operator, d is the pure delay of system, wherein
S3：Using gaussian network come the model coefficient in approximation step S1 and step S2, RBF-ARX model structures are obtained
X (t) is state variable, n in formulay、nu、nv, m and nw=dim { X (t-1) } is model order,For the center of RBF networks,For pantograph ratio
Example coefficient,WithFor weight coefficient,
||·||2The normal form of representative vector two；
S4：The performance indications of model coefficient in step S3 are calculated using quadratic form adjuster,Time started t in formula0With terminal time tfAll it is solid
Fixed, F is the weighting matrix that n × n ties up the symmetrical constant of positive semidefinite, xT(tf)Fx(tf) it is referred to as terminal cost, represent in tfMoment be
Final state of uniting is close to the degree of predetermined final state, and Q (t) is the weighting matrix that n × n ties up the symmetrical time-varying of positive semidefinite, integral term xT(t)Q(t)
X (t) represents the error between given state and given state, and R (t) is the weighting matrix of the symmetrical time-varying of dimension of m m positive semidefinite, uT
(t) R (t) u (t) represent constraint of the dynamic process to control, by realizing Q (t) and R (t) to systematic function control and control
The limitation of energy；
S5：Utilize formulaTo output error and control
The optimal solution of increment weighting is exported, and E is mathematic expectaion, N in formula2For maximum predicted time domain length, B (z are typically should be greater than-1)
Order, N1For minimum prediction time domain length, usual N1=1 or equal to Time Delay of Systems d, NuFor control time domain length, generally take
Nu＜ N2, qjFor output predicated error weight coefficient, λjFor controlling increment weight coefficient, yr(k+j) it is reference locus, is to set in advance
The curve that fixed one is intended to following setting value.
2. a kind of nonlinear system modeling method based on RBF-ARX model stability parameter Estimations according to claim 1,
It is characterized in that：In the step S1, RBF neural includes the node of input layer, hidden layer and output layer, wherein input layer
Number is equal to the dimension of input signal, and the nodes of hidden layer are selected by designer according to the complexity of system, output layer
State to input layer is responded, and is the linear combination of hidden layer output valve.
3. a kind of nonlinear system modeling method based on RBF-ARX model stability parameter Estimations according to claim 1,
It is characterized in that：In the step S5, to prevent controlled quentity controlled variable acute variation from causing system phenomenon out of control to occur, rail is typically referenced to
Trace curve0 ＜ α ＜ 1 in formula, w are input set-point, wherein α
Smaller reference locus just can be faster keep up with the set-point of system, but be likely to result in system overshoot, α is bigger, then system Shandong
Rod is stronger, but response speed is slack-off.
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Cited By (3)
| Publication number | Priority date | Publication date | Assignee | Title |
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| CN109669355A (en) * | 2018-12-13 | 2019-04-23 | 东南大学 | Miniature gas turbine combined cooling and power control system and control method based on generalized predictive control |
| CN112883326A (en) * | 2021-03-19 | 2021-06-01 | 吉林大学 | Self-adaptive time-frequency transformation method based on stream algorithm |
| CN117407675A (en) * | 2023-10-26 | 2024-01-16 | 国网青海省电力公司海北供电公司 | Lightning arrester leakage current prediction method based on multi-variable reconstruction combined dynamic weight |
-
2017
- 2017-05-18 CN CN201710351377.5A patent/CN106970533A/en active Pending
Cited By (5)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| CN109669355A (en) * | 2018-12-13 | 2019-04-23 | 东南大学 | Miniature gas turbine combined cooling and power control system and control method based on generalized predictive control |
| CN109669355B (en) * | 2018-12-13 | 2021-10-19 | 东南大学 | Micro gas turbine combined cooling and power supply control system and control method based on generalized predictive control |
| CN112883326A (en) * | 2021-03-19 | 2021-06-01 | 吉林大学 | Self-adaptive time-frequency transformation method based on stream algorithm |
| CN112883326B (en) * | 2021-03-19 | 2022-07-08 | 吉林大学 | Self-adaptive time-frequency transformation method based on stream algorithm |
| CN117407675A (en) * | 2023-10-26 | 2024-01-16 | 国网青海省电力公司海北供电公司 | Lightning arrester leakage current prediction method based on multi-variable reconstruction combined dynamic weight |
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