CN110045606A - A kind of increment space-time learning method for distributed parameter system line modeling - Google Patents
A kind of increment space-time learning method for distributed parameter system line modeling Download PDFInfo
- Publication number
- CN110045606A CN110045606A CN201910228353.XA CN201910228353A CN110045606A CN 110045606 A CN110045606 A CN 110045606A CN 201910228353 A CN201910228353 A CN 201910228353A CN 110045606 A CN110045606 A CN 110045606A
- Authority
- CN
- China
- Prior art keywords
- space
- time
- increment
- data
- basic function
- Prior art date
- Legal status (The legal status is an assumption and is not a legal conclusion. Google has not performed a legal analysis and makes no representation as to the accuracy of the status listed.)
- Granted
Links
- 238000000034 method Methods 0.000 title claims abstract description 71
- 230000006870 function Effects 0.000 claims abstract description 59
- 230000015572 biosynthetic process Effects 0.000 claims abstract description 22
- 238000003786 synthesis reaction Methods 0.000 claims abstract description 22
- 230000002123 temporal effect Effects 0.000 claims abstract description 17
- 238000012549 training Methods 0.000 claims description 15
- 238000000926 separation method Methods 0.000 claims description 13
- 238000004364 calculation method Methods 0.000 claims description 6
- 238000004422 calculation algorithm Methods 0.000 claims description 5
- 238000004458 analytical method Methods 0.000 abstract description 4
- 230000000694 effects Effects 0.000 abstract description 4
- 239000012141 concentrate Substances 0.000 abstract description 2
- 230000007812 deficiency Effects 0.000 abstract description 2
- 239000011159 matrix material Substances 0.000 description 19
- 238000000354 decomposition reaction Methods 0.000 description 11
- 230000008569 process Effects 0.000 description 11
- 238000010586 diagram Methods 0.000 description 6
- 238000012360 testing method Methods 0.000 description 6
- 241001269238 Data Species 0.000 description 5
- 238000006243 chemical reaction Methods 0.000 description 5
- 238000005259 measurement Methods 0.000 description 5
- 238000010606 normalization Methods 0.000 description 5
- 238000013528 artificial neural network Methods 0.000 description 4
- 238000006555 catalytic reaction Methods 0.000 description 4
- 238000012545 processing Methods 0.000 description 4
- 101150041759 boss gene Proteins 0.000 description 3
- 230000008859 change Effects 0.000 description 3
- 238000009826 distribution Methods 0.000 description 3
- 238000004519 manufacturing process Methods 0.000 description 3
- 238000007796 conventional method Methods 0.000 description 2
- 238000005314 correlation function Methods 0.000 description 2
- 239000000203 mixture Substances 0.000 description 2
- 238000005457 optimization Methods 0.000 description 2
- 238000005070 sampling Methods 0.000 description 2
- 238000003860 storage Methods 0.000 description 2
- 239000000126 substance Substances 0.000 description 2
- 230000004913 activation Effects 0.000 description 1
- 230000003190 augmentative effect Effects 0.000 description 1
- 230000009286 beneficial effect Effects 0.000 description 1
- 230000008901 benefit Effects 0.000 description 1
- 230000005540 biological transmission Effects 0.000 description 1
- 238000003889 chemical engineering Methods 0.000 description 1
- 230000000295 complement effect Effects 0.000 description 1
- 238000010276 construction Methods 0.000 description 1
- 239000002826 coolant Substances 0.000 description 1
- 238000001816 cooling Methods 0.000 description 1
- 230000008878 coupling Effects 0.000 description 1
- 238000010168 coupling process Methods 0.000 description 1
- 238000005859 coupling reaction Methods 0.000 description 1
- 230000007423 decrease Effects 0.000 description 1
- 230000003247 decreasing effect Effects 0.000 description 1
- 238000011161 development Methods 0.000 description 1
- 238000011156 evaluation Methods 0.000 description 1
- 230000005284 excitation Effects 0.000 description 1
- 238000002474 experimental method Methods 0.000 description 1
- 239000004744 fabric Substances 0.000 description 1
- 238000012905 input function Methods 0.000 description 1
- 239000000463 material Substances 0.000 description 1
- 238000013178 mathematical model Methods 0.000 description 1
- 238000003062 neural network model Methods 0.000 description 1
- 210000002569 neuron Anatomy 0.000 description 1
- 230000002085 persistent effect Effects 0.000 description 1
- 238000003672 processing method Methods 0.000 description 1
- 239000000376 reactant Substances 0.000 description 1
- 230000000306 recurrent effect Effects 0.000 description 1
- 230000009467 reduction Effects 0.000 description 1
- 239000004065 semiconductor Substances 0.000 description 1
- 238000004088 simulation Methods 0.000 description 1
- 238000001228 spectrum Methods 0.000 description 1
- 238000012546 transfer Methods 0.000 description 1
Classifications
-
- G—PHYSICS
- G05—CONTROLLING; REGULATING
- G05B—CONTROL OR REGULATING SYSTEMS IN GENERAL; FUNCTIONAL ELEMENTS OF SUCH SYSTEMS; MONITORING OR TESTING ARRANGEMENTS FOR SUCH SYSTEMS OR ELEMENTS
- G05B13/00—Adaptive control systems, i.e. systems automatically adjusting themselves to have a performance which is optimum according to some preassigned criterion
- G05B13/02—Adaptive control systems, i.e. systems automatically adjusting themselves to have a performance which is optimum according to some preassigned criterion electric
- G05B13/04—Adaptive control systems, i.e. systems automatically adjusting themselves to have a performance which is optimum according to some preassigned criterion electric involving the use of models or simulators
- G05B13/042—Adaptive control systems, i.e. systems automatically adjusting themselves to have a performance which is optimum according to some preassigned criterion electric involving the use of models or simulators in which a parameter or coefficient is automatically adjusted to optimise the performance
Abstract
Present example provides a kind of increment space-time learning method for distributed parameter system line modeling, after this method first concentrates the newly-increased data of addition to data increment, incremental update is carried out to space basic function, renewal time coefficient, recognize new temporal model, historical data is rebuild with updated space basic function and the temporal model of identification by old space-time synthesis collection again, predicts the following output.The method of the embodiment of the present invention compensates for the deficiency of existing method, it reduces operation time and equipment uses amount of ram, it is simple and easy, there is universality in industry modeling, theory analysis and experimental result all prove that increment space-time learning method can be realized good on-line performance, significant effect is calculated simultaneously, is had a extensive future.
Description
Technical field
The invention belongs to industrial stokehold technical fields, and in particular to one kind is used for distributed parameter system line modeling
Increment space-time learning method.
Background technique
Distributed parameter system (distributed parameter system, DPS) is widely present in industrial process neck
In domain, such as the fields such as semiconductors manufacture, nanotechnology, bioengineering and chemical engineering, usually use partial differential equation
(partial differential equation, PDE) is indicated.Due to the state change in location with space at any time of DPS
And consecutive variations, it needs to be described with infinite dimensional state space, and PDE is finite dimension, therefore model successively decreases in practice
It is difficult to avoid that, the appropriate modeling of DPS complication system is most important for Industrial Simulation, control and optimization.
Space-time separation method is a kind of method that can effectively simplify unknown DPS model modeling.It is separated in existing space-time
In method, KL decomposes (Karhunen-Loeve Decomposition, KLD) and is primarily used for space-time separation, and wherein space-time is defeated
It is broken down into one group of space basic function (BF) with corresponding time coefficient out.Secondly, being picked out from the low-dimensional data of decomposition
Depression of order temporal model.Time structure can be by various modelling techniques come approximate, such as containing externally input nonlinear auto-companding
(NARX) model, Hammerstein model, neural network model (NNs) etc..Finally, the space-time to be successively decreased by model is with logarithm
According to reconstruction, can rebuild and predict space-time dynamic system on entire time-space domain.
Space-time separation method has been found to be a kind of method for effectively simplifying unknown DPS model modeling.At these
In the method for sky modeling, KL decomposes (Karhunen-Loeve Decomposition, KLD) and is primarily used for space-time separation.It passes
In the space-time modeling of system, KLD and time structure recognize the method for taking batch processing, and this method is based on all output datas and is building
Mold process can be used when starting it is assumed that being therefore only applicable to off-line procedure.Existing method can to the DSP of slow dynamics
Row, however be difficult to it is generally applicable, be not particularly suitable for for space-time synthesize collection Model Construction.In traditional batch processing method
In, if it is desired to additional new output data is merged into existing space-time synthesis and is concentrated, when needing to restart from the beginning
Empty separation process, and the process includes all new and old training datas.Since the quantity of training data is continuously increased, batch
The method of processing needs re -training entire space-time synthesis collection, one with data continuous inflow, the quantity of training set is increasingly
Greatly, aspect can take considerable time, on the other hand can cause to bear to storage.The prior art is due to that can not collect space-time separation
All training datas are not available all data yet and recognize space-time synthesis collection from the beginning, therefore there are space-time synthesis collection is online
Update difficult problem.
Summary of the invention
To solve problems of the prior art, the purpose of the present invention is to provide one kind to be used for distributed parameter system
The increment space-time learning method of line modeling.
To achieve the above object, the invention adopts the following technical scheme:
A kind of increment space-time learning method for distributed parameter system line modeling, comprising:
(1) after concentrating addition data to data increment, incremental update is carried out to space basic function；
(2) renewal time coefficient recognizes temporal model；
(3) timing by being recognized in old space-time synthesis collection and step (1) updated space basic function and step (2)
Model Reconstruction historical data predicts the following output；
(4) step (1)~(3) are repeated, the online updating of space-time synthesis collection is completed.
Preferably, the data increment collection is to collect the obtained continuous data stream with specific time step-length.
Preferably, the space basic function is the basic function of n-dimensional space.
Preferably, the basic function of the n-dimensional space is by space-time separation method, is L with time step, by training data
Middle school's acquistion is arrived.
Preferably, the incremental update refers to incremental mode through SVD more new algorithm, calculates new space basic function.
It is further preferred that the calculation method of new space basic function are as follows:
Preferably, the method for step (2) the renewal time coefficient are as follows:
Preferably, the method for the new temporal model of step (3) identification are as follows:
The particular technique details of above-mentioned increment space-time learning method are as follows:
Firstly, common one kind DPS can be indicated with following nonlinear PDE:
Constraint of the system by boundary condition of mixed type:
Primary condition are as follows:
Y (x, 0)=y0(x) (3)。
Wherein t ∈ [0, ∞) be time variable,It is space coordinate,
It is the output of space-time,It is the input of time,It is that a complicated phasor function includes a Nonlinear Space
Between order of a differential operator n0,It is the matrix function of an appropriate dimension, it describes how time input divides in spatial domain
Cloth, q are a Nonlinear Vector function, y0(x) the initial output of a smooth vector function is referred to.
Common method to unknown nonlinear DPS modeling is space-time separation frame, and wherein space-time output y (x, t) can divide
Xie Chengyi group orthogonal intersection space basic functionWith the inner product of corresponding time coefficient a (t):
In practice, a limited n Wiki functionIt is decomposed by KL for obtaining relevant parameter.Then, from
The low-dimensional coefficient of decompositionMiddle identification low order temporal modelIt is denoted as:
Wherein duAnd daMaximum Input Hysteresis and maximum output lag are respectively indicated, e (t) indicates residual error.
Space-time modeling is specific as follows:
1, space-time separates
Assuming for simplicity that system exportsThe uniform sampling in time and space coordinate, wherein L be
Time span.
Define inner product, norm, average value are as follows:
||f1(x) | |=(f1(x),f1(x))1/2、
Temporal-Spatial Variables y (x, t) can extend to infinite dimensional orthogonal intersection spaceBasic function and time constantRelationship on, indicate are as follows:
Because time constant is orthogonal, it may be assumed that
Time constant can be from following acquisition:
In practice, it can be truncated as the scene of a limited dimension
Wherein, yn(x, t) is expressed as the approximation of n dimension.
The purpose of space-time separation is to decompose to export in space-time using KLMiddle calculating highest dimension space base letter
Number
By minimizing objective function, can find typical
Restrictive condition isThe orthogonality constraint being appliedIt is unique
's.Lagrangian is used for the constrained optimization of this problem are as follows:
The necessary condition of this problem are as follows:
Wherein R (x, ξ)=<y (x, t) y (ξ, t)>is expressed as the correlation function of space two o'clock.
Characteristic function (space basic function)The linear combination that can be converted to, as follows:
After formula (28) alternate form (27), necessary condition calculating becomes:
Then this feature value problem can simplify as L × L matrix- eigenvector-decomposition problem:
Cγi=λiγi (30)。
Wherein, γi=[γi1,…,γiL]TIt is i-th of feature vector, and
It is defined as two point correlation function in time domain.The solution of formula (30) is feature vector γi1,…,γiL, and characteristic function
It can be used for the characteristic function of structural formula (28) againSince Matrix C is symmetrical positive semi-definite, calculated feature
Function is orthogonal.
If K≤min (N, L) is maximum one in nonzero eigenvalue.If eigenvalue λ1>λ2>…>λkAnd corresponding special
Levy functionIt is arranged according to size descending.Characteristic function corresponding with first characteristic value should be
Most " vibrant ".Total " energy " of PDE system is considered as the summation of characteristic value.Each characteristic function relevant to characteristic value
Energy ratio be defined as following formula:
N value in formula (24) can be greater than 99% by the accounting in all characteristic values of preceding n maximum eigenvalue sum and obtain
Arrive, rule of thumb, only fraction principal space basic function extension could some space-time systems of approximate evaluation most of power
Learn model.For arbitrary spaceObtain following result:
The result shows that it is optimal for taking mean value situation KL decomposition using linear combination this kind as representative.This is why
KL decomposition can provide minimum dimension n value.
2, temporal model is recognized
Understand and passes through the isolated optimal spatial of space-timeLater, the temporal model a of low orderiIt (t) can be from decomposition
It is picked out in low-dimensional data afterwards.Space-time exports y (x, t) corresponding time coefficient ai(t) it can be calculated by formula (21):
Time series data a (t) is usually obtained with certainty NARX model approximation:
Wherein duAnd daMaximum input delay and maximum output delay are respectively indicated, e (t) indicates residual error.Unknown function
It can be defeated to inputting by using the various approximate functions such as radial basis function neural network, polynomial function, small echo and kernel function
Data estimation out.If providing primary condition, after identification, model (35) can provide predicted value at any timeThe dimensionality reduction
The Time-Space Kinetics state in entire time domain can be rebuild and predicted after models coupling formula (24).
Herein, temporal model is considered as a simplified form, because are as follows:
Wherein matrixWithIt is linear, transmission functionIt is non-linear partial.
Any continuous function can be approximately arbitrary accuracy by neural network, and be widely studied applied to various industrial process.?
Time recognizes the stage, willIt is estimated as radial basis function neural network, then model (36) will be rewritten as:
A (t)=Ba (t-1)+WK (a (t-1))+Du (t-1)+e (t) (37).
WhereinIndicate weight,Indicate radial basis function, l
Indicate the quantity of neuron.Radial basis function is normally selected as Gaussian kernel
With center vector appropriateWith norm matrixIt uses KL to decompose as preprocessor, can greatly reduce
The size of temporal model.The unknown parameter A, B, W of hybrid radial basis function neural network can be estimated with recurrent least square method.
Finally, space-time synthesis collection can be used to rebuild Time-Space Kinetics system, the following output of forecasting system.
The technical detail of increment space-time modeling method is as follows:
General frame as shown in Fig. 2, continuous data stream be collected into specific time step-length (..., ti-1,ti,ti+1...)
Data increment collection (..., ID(i-1),ID(i),ID(i+1)...) in.Firstly, we have proposed a kind of efficient method, when one group it is new
When the data of increasing reach, incremental update is carried out to space basic function.Next, when being recognized again using updated time coefficient
Sequence model.Finally, we by old space-time synthesis collection (..., T/S(i-1), T/S(i), T/S(i+1)...) with update space base letter
It counts with temporal model and rebuilds historical dataThe following output of prediction
Then, when reaching next group of newly-increased data, we are repeated the above process.In a manner of this increment, by new increment
Data are added continuously to existing space-time synthesis and concentrate.Over time, the structure and parameter of model will by inherit and
Recurrence updates.
Online updating:
Assuming that moment tjThe output data of (j=1 ..., L) be measure in N number of spatial position N-dimensional vector y (x,
tj)=[y (x1,tj),…,y(xN,tj)]T.Remember yj=y (x, tj).The basic function of n-dimensional space is typically expressed asIt
It is L with time step, from one group of training data Y usually by space-time separation method1=[y1,…,yL] middle school's acquistion arrives.
Even if space-time synthesis collection learns to tLAfter step, output data can also be continuously generated.Assuming that space-time synthesis collection
It should be in new time step tL+MWhen handle, and Y2=[yL+1,…,yL+M] it is newly-increased data set with step-length for M.For criticizing
The method of amount mode, to Augmented Data matrix Y=[Y1 Y2] carry out KL decomposition re-start from the beginning space-time separation.Due to
Line process generates more and more historical datas, therefore computationally cost is very big for this method.In contrast to this, we derive
Gone out this method how to pass through incremental learning method effectively inherit and update space-time synthesis collection detailed process.
According to (31), initial time incidence matrix C be can be written as:
Pass through singular value decomposition (SVD), matrix Y1 TIt can be broken down into:
Y1 T=U ∑ VT (7)。
Following C can be expressed as:
Herein, Λ=(1/L) ∑ ∑TOne be a L × L diagonal matrix.It is decomposed by KL, we are according to formula
(32) n value of 99% features above of embodiment system is selected.The best fit approximation value of so C is
Wherein UnIt is made of the preceding n column of U, ΛnIt is n-th order sequence boss's battle array.According to formula (28), we can construct base letter
Number scale is made
Picking out space basic functionLater, it is corresponding that formula (23) acquisition space-time output y (x, t) can be used
Time coefficientAssuming that the time coefficient matrix obtained is An×L=[a (1) ..., a (L)], wherein a (t)=[a1
(t),…,an(t)]T, t=1 ... L, we can verify output data Y1It is resorted toUse space basic function φ and
Corresponding time coefficient A can be indicated are as follows:
As one group of new data Y2When addition, Y=[Y1,Y2], new time constant matrix becomesIt indicates are as follows:
Assuming that data Y before1It is inaccessible, newIt cannot directly calculate.Opposite, we can more new data
The feature vector of matrix Y calculates new basic function by SVD more new algorithm with incremental mode.
It is known thatHere UnAnd VnIt is the preceding n column of U and V, particularly, ∑nIt is
The preceding n rank sequence boss battle array of ∑.Next, we wish to carry out bigger matrixSVD, wherein Y2 TIt is by M
M × N matrix of additional row composition.
We rememberQR decompose are as follows:
Wherein Q is orthogonal, and R is the upper triangular matrix of m × M, and m (m≤min (N, M)) isOrder.This
It walks newlineProject to the orthocomplement, orthogonal complement of old weight characteristic vector space, i.e. span { Vn}.It can be certified as:
It may be noted that [VnQ] be orthogonal, (n+M) × (n+m) matrix after SVD can be obtained:
Here
Then, new Time correlation matrixIt can be rewritten as:
The diagonal matrix of updateThe feature vector of updatePass through KL
It decomposes, we embody n' feature of 99% features above of system according to formula (32).The best fit approximation value of so C is:
HereIt isPreceding n' column,It isThe n-th ' rank sequence boss battle array.
According to formula (28), we can be by n Wiki vector beforeIt is updated to new n' dimensionWherein:
Since on-line storage cannot be accessed about primary data Y1Complete information, therefore we are according to formula (11) Lai Chongjian
Initial data, new basic function calculation method are as follows:
WhereinByPreceding n' arrange composition.With this incremental mode, as one group of new data Y2When arrival, old base letter
Number φ is converted into the basic function of updateWithout storing previous data Y1.This function use recursive calculation, this
It is particularly significant in line modeling.
After updating space basic function, corresponding time coefficient can be updated according to formula (34), then pass through formula (35)
In the progress of low-dimensional temporal model confirm again.At this point, entire space-time synthesis collection has been completed online succession and updates.Pass through
Incremental learning, modeling structure are continued to develop with the typing of the new space measurement generated in the whole life cycle of DPS.
Therefore, the structure of this continuous development can track and adapt to online the dynamic of system.
Effect analysis:
The first step of increment modeling is formula (13)QR decompose, need O (NM2) secondary floating-point operation.
It is to minor matrix in next stepSVD calculating is carried out, O ((n+m) (n+M) is needed2) secondary floating-point operation.Very
In more situations, the quantity n of basic function is much smaller than other parameters, i.e. n < < { m, N, M }, m < < { N, M }.Ignore initialization step
Influence, the total time complexity of incremental learning process is in O (NM2) level, this depends on the length M of newly-increased data.So
And in batch mode method, it needs about O ((L+M)3) secondary floating-point operation goes to new incidence matrixCarry out KL decomposition.
Therefore, the complexity of the calculation method of increment modeling will be far below batch mode method, because in on-line mode
Length of history data L constantly increase, this leads to { N, M } < < L in many actual conditions.
The beneficial effect of the embodiment of the present invention
The embodiment of the present invention is used for the increment space-time learning method of distributed parameter system line modeling, with process after
Continuous, space-time synthesis collection is also evolved accordingly, as long as there is new data study, model structure is inherited and updated, new number
It is added in existing model structure in a manner of increment according to the information of carrying, compensates for the deficiency of existing method, greatly reduce
It calculates the time of operation and uses memory, it is simple and easy, there is universality in industry modeling, theory analysis and experimental result are all
It proves that increment space-time learning method can be realized good on-line performance, while calculating significant effect, have a extensive future.
Detailed description of the invention
Fig. 1 is conventional batch mode and increment type runing time comparison diagram.
Fig. 2 is the increment space-time modeling online updating schematic diagram of DPS.
Fig. 3 is catalysis reaction stick lab diagram.
Fig. 4 is 100s measurement data distribution map.
Fig. 5 is prediction data distribution map after 100s.
Fig. 6 is conventional method training data space-time Error Graph.
Fig. 7 is present invention method training data space-time Error Graph.
Fig. 8 is the spatial normalization Error Graph of two methods.
Fig. 9 is prediction data figure after measurement data training.
Figure 10 is prediction data figure after new data training.
Figure 11 is the space-time error comparison diagram of conventional method test data under new data.
Figure 12 is the space-time error comparison diagram of present invention method test data under new data.
Figure 13 is the normalization Error Graph of two methods under new data.
Specific embodiment
The following is specific embodiments of the present invention, and further retouches to technical solution of the present invention work in conjunction with the embodiments
It states, however, the present invention is not limited to these examples.
Embodiment 1
This example provides a kind of increment space-time learning methods for distributed parameter system line modeling, comprising:
(1) it is concentrated to data increment after adding newly-increased data, incremental update is carried out to space basic function；
(2) renewal time coefficient recognizes new temporal model；
(3) timing by being recognized in old space-time synthesis collection and step (1) updated space basic function and step (2)
Model Reconstruction historical data predicts the following output；
(4) step (1)~(3) are repeated, the online updating of space-time synthesis collection is completed.
Wherein, data increment collection is to collect the obtained continuous data stream with specific time step-length, and space basic function is n
The basic function of dimension space, the basic function of n-dimensional space are by space-time separation method, are L with time step, by training data middle school
Acquistion is arrived., incremental update refers to incremental mode through SVD more new algorithm, calculates new space basic function.
The calculation method of new space basic function are as follows:
The method of renewal time coefficient are as follows:
The method for recognizing new temporal model are as follows:
Embodiment 2
In order to prove embodiment 1 the increment space-time learning method for distributed parameter system line modeling performance,
Embodiment 1 is compared, to illustrate to increase by we by taking catalysis reaction stick experiment as an example with the method for traditional batch processing mode
Measure the feasibility and advantage of study.
It test condition and is described as follows:
All algorithms realize that the computer uses Intel kernel, CPU type in the MATLAB R2013a of Windows 7
Number be i5-4590, dominant frequency is that 3.30GHz running memory is 4GB RAM.All experimental results referred to herein are 100 times
The average value of operation.
If y (x, t) and yn(x, t) respectively indicates the output of measurement and the output of prediction.Assess three fingers of modeling accuracy
Mark is defined as follows.
(1) space-time error e (x, t)=y (x, t)-yn(x, t),
(2) spatial normalization absolute error
(3) root-mean-square error
Detailed process is as follows:
The benchmark PDE system of catalysis stick is made of the stock in reactor, as shown in Figure 3.It is classical in chemical industry
And the reactant transport process being widely studied.Zero level heat-producing chemical reaction is generated with the process of A → B in inside, and wherein A is charging
Pure material into reactor.For cooling down exothermic process, it is contacted cooling medium with catalysis reaction stick.
Assuming that substance A in furnace is excessive, and the following parameter for being catalyzed stick is constant: density, thermal capacity, conductivity and
The temperature of two sides.The mathematical model of following second order PDE can be used for describing the change in time and space of stock temperature:
It is influenced by the boundary Dirichlet and primary condition:
Y (0, t)=0, y (π, t)=0, y (x, 0)=y0(x)。
Wherein y (x, t) is the temperature of stock, and u (t) is time input function, and b (x) is the spatial distribution for inputting actuator.
βTIt is reaction heat, βuIt is heat transfer coefficient, γ indicates activation energy.These parameters are usually arranged as:
βT=50, βu=2, γ=4.
There are four input actuator u (t)=[u1(t),…,u4(t)]T, spatially distributed functions b (t)=[b1(t),…,b4
(t)]T, bi(t)=H (π/4 x- (i-1))-H (π/4 x-i), (i=1 ..., 4).Meanwhile H () is standard Heaviside letter
Number.In order to collect useful data, simultaneously dynamically whole frequency spectrums, input signal are had Persistent Excitation nonlinear system using a series of
The SIN function of different frequency motivates, such as ui(t)=1.1+5sin (t/2+i/10), (i=1 ..., 4).For modeling
The quantity of required sensor depends on the precision of inherent physical system and practical external model.In this case, system is defeated
Y (x outi, t), (i=1 ..., N) is collected from 18 identical sensors, these sensors are evenly distributed on spatial domain
(N=18) in.
What noise free data was continuously generated according to formula (20), with interval of delta t=0.01 sampling.Primary condition y0(x) it is arranged
U is inputted for stable statei(t)=1.1, (i=1 ..., 4).It is 0 that average value is added in noise free data stream, standard deviation sigma (xi)=Ad
(xi)ndWhite Gaussian noise (additional nd=2% condition) derive noise output, wherein Ad(xi)=(max (y (xi,t))-
min(y(xi, t)))/3, (i=1 ..., N).Output stream is acquired, renewal time interval delta is used forcThe space-time of t=10 synthesizes
Collection.That is, when collecting first group of 1000 output data in time t=10, meter calculate initial space basic function and when
Sequence model.Then, 1000 data are collected at the correspondence moment that space-time synthesis is concentrated when in t=20,30 ....Then, it receives every time
When collecting next 1000 data newly, space-time synthesis collection can be all inherited and updated by way of incremental learning.At these
It carves, newest space-time synthesis collection is used to reconstructing system from original state output till now as a result, it can also be verified simultaneously
The performance of line modeling.It is for predicting future time intervals Δc1000 output datas in t.By this method, we
Real-time on-line training and test are carried out to increment space-time model, and it can adapt to the dynamic change of system.
Interpretation of result:
The training data on t ∈ (0,100) gives prediction output ynThe comparison diagram of (x, t) and actual value y (x, t), when
Empty error e (x, t) and spatial normalization absolute error SNAE (t), as shown in Fig. 4~8.Equally, in order to further examine mould
The performance of type test also tests one group of 2000 new data, and in Fig. 9~13, new measurement output y is set forth
(x, t), prediction output yn(x, t), space-time error e (x, t) and spatial normalization absolute error SNAE (t).Obviously, proposed
Increment modeling has same performance with traditional batch processing mode method, can also provide extremely close with primal system
Approximation.
Theory analysis and experimental result all prove that the method for the embodiment of the present invention can be realized good on-line performance, simultaneously
Calculate significant effect.
Claims (8)
1. a kind of increment space-time learning method for distributed parameter system line modeling characterized by comprising
(1) after concentrating addition data to data increment, incremental update is carried out to space basic function；
(2) renewal time coefficient recognizes temporal model；
(3) temporal model by being recognized in old space-time synthesis collection and step (1) updated space basic function and step (2)
Historical data is rebuild, predicts the following output；
(4) step (1)~(3) are repeated, the online updating of space-time synthesis collection is completed.
2. increment space-time learning method according to claim 1, which is characterized in that the data increment collection is to collect to obtain
The continuous data stream with specific time step-length.
3. increment space-time learning method according to claim 1, which is characterized in that the space basic function is n-dimensional space
Basic function.
4. increment space-time learning method according to claim 3, which is characterized in that the basic function of the n-dimensional space is logical
It is out-of-date sky separation method, be L with time step, by the acquistion of training data middle school to.
5. increment space-time learning method according to claim 1, which is characterized in that the incremental update refers to incremental mode
By SVD more new algorithm, new space basic function is calculated.
6. increment space-time learning method according to claim 5, which is characterized in that the calculation method of new space basic function
Are as follows:
7. increment space-time learning method according to claim 1, which is characterized in that step (2) the renewal time coefficient
Method are as follows:
8. increment space-time learning method according to claim 1, which is characterized in that step (3) the identification temporal model
Method are as follows:
Priority Applications (1)
| Application Number | Priority Date | Filing Date | Title |
|---|---|---|---|
| CN201910228353.XA CN110045606B (en) | 2019-03-25 | 2019-03-25 | Increment space-time learning method for online modeling of distributed parameter system |
Applications Claiming Priority (1)
| Application Number | Priority Date | Filing Date | Title |
|---|---|---|---|
| CN201910228353.XA CN110045606B (en) | 2019-03-25 | 2019-03-25 | Increment space-time learning method for online modeling of distributed parameter system |
Publications (2)
| Publication Number | Publication Date |
|---|---|
| CN110045606A true CN110045606A (en) | 2019-07-23 |
| CN110045606B CN110045606B (en) | 2021-07-27 |
Family
ID=67275103
Family Applications (1)
| Application Number | Title | Priority Date | Filing Date |
|---|---|---|---|
| CN201910228353.XA Expired - Fee Related CN110045606B (en) | 2019-03-25 | 2019-03-25 | Increment space-time learning method for online modeling of distributed parameter system |
Country Status (1)
| Country | Link |
|---|---|
| CN (1) | CN110045606B (en) |
Cited By (5)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| CN112241836A (en) * | 2020-10-10 | 2021-01-19 | 天津大学 | Virtual load dominant parameter identification method based on incremental learning |
| CN113552802A (en) * | 2021-07-22 | 2021-10-26 | 泰铂（上海）环保科技股份有限公司 | Heavy-truck intelligent air conditioner control method and system |
| CN113568309A (en) * | 2021-07-27 | 2021-10-29 | 中南大学 | Online space-time control method for temperature field |
| CN113848723A (en) * | 2021-10-11 | 2021-12-28 | 浙江大学 | Fast dynamic matrix control method based on ORC waste heat recovery system |
| CN116504341A (en) * | 2022-05-20 | 2023-07-28 | 大连理工大学 | Sequential singular value filtering method for data-driven identification partial differential equation |
Citations (7)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| CN1234947A (en) * | 1996-10-23 | 1999-11-10 | 埃瑞康姆公司 | Spectrally efficient high capacity wireless communication system with spatio-temporal processing |
| US20130227238A1 (en) * | 2012-02-28 | 2013-08-29 | Thomas VIJVERBERG | Device and method for a time and space partitioned based operating system on a multi-core processor |
| CN108710767A (en) * | 2018-05-29 | 2018-10-26 | 广东工业大学 | A kind of lithium battery thermal process space-time modeling method based on ISOMAP |
| CN108717505A (en) * | 2018-05-29 | 2018-10-30 | 广东工业大学 | A kind of solidification thermal process space-time modeling method based on K-RVFL |
| CN108763759A (en) * | 2018-05-29 | 2018-11-06 | 广东工业大学 | A kind of solidification thermal process space-time modeling method based on ISOMAP |
| CN109145346A (en) * | 2018-05-29 | 2019-01-04 | 广东工业大学 | Solidification thermal process space-time modeling method based on dual least square method supporting vector machine |
| CN109145421A (en) * | 2018-08-08 | 2019-01-04 | 中南大学 | A kind of space-time fuzzy Modeling Method applied to distributed parameter system |
-
2019
- 2019-03-25 CN CN201910228353.XA patent/CN110045606B/en not_active Expired - Fee Related
Patent Citations (7)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| CN1234947A (en) * | 1996-10-23 | 1999-11-10 | 埃瑞康姆公司 | Spectrally efficient high capacity wireless communication system with spatio-temporal processing |
| US20130227238A1 (en) * | 2012-02-28 | 2013-08-29 | Thomas VIJVERBERG | Device and method for a time and space partitioned based operating system on a multi-core processor |
| CN108710767A (en) * | 2018-05-29 | 2018-10-26 | 广东工业大学 | A kind of lithium battery thermal process space-time modeling method based on ISOMAP |
| CN108717505A (en) * | 2018-05-29 | 2018-10-30 | 广东工业大学 | A kind of solidification thermal process space-time modeling method based on K-RVFL |
| CN108763759A (en) * | 2018-05-29 | 2018-11-06 | 广东工业大学 | A kind of solidification thermal process space-time modeling method based on ISOMAP |
| CN109145346A (en) * | 2018-05-29 | 2019-01-04 | 广东工业大学 | Solidification thermal process space-time modeling method based on dual least square method supporting vector machine |
| CN109145421A (en) * | 2018-08-08 | 2019-01-04 | 中南大学 | A kind of space-time fuzzy Modeling Method applied to distributed parameter system |
Non-Patent Citations (2)
| Title |
|---|
| ZHANG HAITAO等: "Greatly enhancing the modeling accuracy for distributed parameter systems by nonlinear time/space separation", 《PHYSICA A: STATISTICAL MECHANICS AND ITS APPLICATIONS》 * |
| 郑迪: ""分布参数系统的非线性时空分离建模和预测控制策略研究"", 《中国优秀硕士学位论文全文数据库 信息科技辑》 * |
Cited By (8)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| CN112241836A (en) * | 2020-10-10 | 2021-01-19 | 天津大学 | Virtual load dominant parameter identification method based on incremental learning |
| CN112241836B (en) * | 2020-10-10 | 2022-05-20 | 天津大学 | Virtual load leading parameter identification method based on incremental learning |
| CN113552802A (en) * | 2021-07-22 | 2021-10-26 | 泰铂（上海）环保科技股份有限公司 | Heavy-truck intelligent air conditioner control method and system |
| CN113552802B (en) * | 2021-07-22 | 2022-05-24 | 泰铂（上海）环保科技股份有限公司 | Heavy-truck intelligent air conditioner control method and system |
| CN113568309A (en) * | 2021-07-27 | 2021-10-29 | 中南大学 | Online space-time control method for temperature field |
| CN113848723A (en) * | 2021-10-11 | 2021-12-28 | 浙江大学 | Fast dynamic matrix control method based on ORC waste heat recovery system |
| CN116504341A (en) * | 2022-05-20 | 2023-07-28 | 大连理工大学 | Sequential singular value filtering method for data-driven identification partial differential equation |
| CN116504341B (en) * | 2022-05-20 | 2023-11-07 | 大连理工大学 | Sequential singular value filtering method for data-driven identification partial differential equation |
Also Published As
| Publication number | Publication date |
|---|---|
| CN110045606B (en) | 2021-07-27 |
Similar Documents
| Publication | Publication Date | Title |
|---|---|---|
| CN110045606A (en) | A kind of increment space-time learning method for distributed parameter system line modeling | |
| CN109060001B (en) | Multi-working-condition process soft measurement modeling method based on feature transfer learning | |
| Rezaee et al. | Data-driven fuzzy modeling for Takagi–Sugeno–Kang fuzzy system | |
| CN110414788B (en) | Electric energy quality prediction method based on similar days and improved LSTM | |
| Wu | Product demand forecasts using wavelet kernel support vector machine and particle swarm optimization in manufacture system | |
| CN113722877A (en) | Method for online prediction of temperature field distribution change during lithium battery discharge | |
| CN109242223B (en) | Quantum support vector machine evaluation and prediction method for urban public building fire risk | |
| Yao et al. | Cooperative deep dynamic feature extraction and variable time-delay estimation for industrial quality prediction | |
| Zhao et al. | Soft sensor modeling of chemical process based on self-organizing recurrent interval type-2 fuzzy neural network | |
| CN109523155B (en) | Power grid risk assessment method of Monte Carlo and least square support vector machine | |
| Eftekhari et al. | Extracting compact fuzzy rules for nonlinear system modeling using subtractive clustering, GA and unscented filter | |
| CN113641722A (en) | Long-term time series data prediction method based on variant LSTM | |
| CN112800675A (en) | KPCA and ELM-based time-space separation distribution parameter system modeling method | |
| Feng et al. | A multimode mechanism-guided product quality estimation approach for multi-rate industrial processes | |
| CN114565021A (en) | Financial asset pricing method, system and storage medium based on quantum circulation neural network | |
| Zheng et al. | Improved mahalanobis distance based JITL-LSTM soft sensor for multiphase batch processes | |
| CN110245398B (en) | Soft measurement deep learning method for thermal deformation of air preheater rotor | |
| CN108762072A (en) | Forecast Control Algorithm based on nuclear norm subspace method and augmentation vector method | |
| Liu et al. | Soil water content forecasting by ANN and SVM hybrid architecture | |
| CN112381279B (en) | Wind power prediction method based on VMD and BLS combined model | |
| CN115952685B (en) | Sewage treatment process soft measurement modeling method based on integrated deep learning | |
| Dai et al. | Online sequential model for multivariate time series prediction with adaptive forgetting factor | |
| Springer et al. | Robust parameter estimation of chaotic systems | |
| CN114871000B (en) | Flotation dosing self-adaptive regulation and control method | |
| Tian et al. | A new incremental learning modeling method based on multiple models for temperature prediction of molten steel in LF |
Legal Events
| Date | Code | Title | Description |
|---|---|---|---|
| PB01 | Publication | ||
| PB01 | Publication | ||
| SE01 | Entry into force of request for substantive examination | ||
| SE01 | Entry into force of request for substantive examination | ||
| GR01 | Patent grant | ||
| GR01 | Patent grant | ||
| CF01 | Termination of patent right due to non-payment of annual fee | ||
| CF01 | Termination of patent right due to non-payment of annual fee |
Granted publication date: 20210727 |