CN109240085A - Non-Gaussian filtering dynamic data rectification and system control performance optimization method - Google Patents

Non-Gaussian filtering dynamic data rectification and system control performance optimization method Download PDF

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CN109240085A
CN109240085A CN201811199510.0A CN201811199510A CN109240085A CN 109240085 A CN109240085 A CN 109240085A CN 201811199510 A CN201811199510 A CN 201811199510A CN 109240085 A CN109240085 A CN 109240085A
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CN109240085B (en
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任密蜂
张雯
陈荣辉
张旭霞
梁艳
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Taiyuan University of Technology
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    • 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

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Abstract

The present invention relates to system control performance optimization methods, specially non-Gaussian filtering dynamic data rectification and system control performance optimization method, wind-power electricity generation process is solved by nongausian process noise and non-gaussian measurement influence of noise, not enough close to true value after DATA REASONING amendment, the unconspicuous problem of control strategy optimization effect, step: one, non-gaussian disturbs lower system model description；Two, the derivation of iterative formula in the problem description is carried out using EM algorithm；Three, it is exported after solving correction using iterative formulay r ；Four, the performance indicator based on statistical information is chosen, and obtains optimal control law.Advantage: 1, consider influence of the non-gaussian random noise to system；2, the dynamic characteristic for considering process, preferably expresses real process；3, there is higher computational efficiency, meet the requirement of actual industrial process；4, the stochastic behaviour that non-gaussian random quantity is sufficiently portrayed using entropy statistical information establishes tracing control index.

Description

Non-Gaussian filtering dynamic data rectification and system control performance optimization method
Technical field
The present invention relates to system control performance optimization method, specially non-Gaussian filtering dynamic data rectification and system is controlled Performance optimization method.
Background technique
In systems in practice, random disturbances are widely present, and wind speed becomes especially in industrial process, such as in wind power system The enchancement factor of change, the enchancement factor of the measurement error of sensor measurement data.
At present for the correction of control system measurement noise, it is all based on to be Gaussian it is assumed that by control correction The mean value of data, variance afterwards, to optimize.And actual industrial process measurement error is often non-gaussian, if with tradition Gauss assume under method be corrected, optimal control effect is not obvious.
One control strategy is able to the control effect obtained, it is important that premise be obtained in control process it is accurate Measurement data, for the system containing measurement noise, even if the existing optimal performance indicator of building, control effect is also not worth It must trust.In industrial processes, measurement data unavoidably contains error (including random error and gross error), and surveys Measuring noise is often non-gaussian.Gross error may be quite big, and for needing the system of accurate estimated state and measurement, this two Kind error has detrimental effect to process control.Therefore, in order to guarantee that system keeps preferable control effect, it should provide compared with Accurate measurement data should carry out Data correction to raw measurement data, make it as close possible to truthful data.At present for Control system measures the correction of noise, is all based on it to be Gaussian it is assumed that by the mean value of data, side after control correction Difference, to optimize.Such optimisation strategy has the following deficiencies: 1, for stochastic control system control theory without clearly Consider to measure noise present in real sensor equipment, even if it is considered that and doing based on it for the hypothesis of Gaussian Profile It discusses；2, in traditional data correcting method, the dynamic characteristic of process is not accounted for, therefore cannot be guaranteed the reachable of setting value Property；3, in terms of non-gaussian STOCHASTIC CONTROL, in existing scientific achievement, setting value, which usually takes, does constant value or preset ginseng Examine track, but in fact, setting value/reference locus needs to be set according to the actual situation, such as the randomness of wind speed, be with When a motion profile changing, thus this processing scheme needs further to be considered.
Since the prior art is there are drawbacks described above and insoluble problem, design a kind of non-Gaussian filtering dynamic Data correction and system control performance optimization method be very it is necessary to.
Summary of the invention
Technical problem solved by the present invention is for wind-power electricity generation process by nongausian process noise (random wind speed) In the case where measuring influence of noise with non-gaussian, not enough close to true value after DATA REASONING amendment, control strategy optimization effect is not Obvious problem provides a kind of non-Gaussian filtering dynamic data rectification and system control performance optimization method.
The present invention is realized by following operating procedure: non-Gaussian filtering dynamic data rectification and system control performance are excellent Change method, including following operating procedure:
Step 1: non-gaussian disturbs lower system model description:
In a single-variable system, the output of t moment can be broken down into two parts: predictable partWith Uncertain part (δ (t)):
Wherein, ω (t) be process noise, set δ (t) and measure noise ε (t) as gauss hybrid models, probability density letter Number is as follows:
In formula, g [] is Gaussian distribution density, ckAnd fnFor mean value,WithFor variance；
Measurement output ymWith the relational expression of true output y are as follows:
ym(t)=y (t)+ε (t),
Y is exported after correctionr(t) Posterior distrbutionp exports y by measurementm(t) and predictable partIt provides；According to pattra leaves This criterion, yr(t) Posterior distrbutionp and ym(t) likelihood function andLikelihood function product it is directly proportional, it may be assumed that
With L [ym(t)|yr(t)] calculation formula is as follows:
Wherein, the mean value of each Gaussian component meets such as relational expression:
p(yrIt (t)) is yr(t) prior probability, it is a constant, then:
Based on maximum a posteriori Distribution Principle, yr(t) estimated value can be obtained by following formula:
MaximizeWith L [ym(t)|yr(t)] product obtains optimal correction signal yr(t).For Measurement data y containing non-Gaussian noisem(t), optimal correction signal y directly is sought with the method for maximal possibility estimationr (t), it is evident that the excessively huge problem of calculation amount will be faced, therefore first define the hidden variable that can not be observed, foundation depends on The probabilistic model of hidden variable finds parameter maximal possibility estimation in probabilistic model, i.e., completes correction signal y using EM algorithmr (t) solution；
Step 2: carrying out the derivation of iterative formula in the problem description using EM algorithm:
(1) clear hidden variable writes out the log-likelihood function of complete data:
Imagine observation data ym(ym1,ym2,…,ymJ) generation are as follows: first according to probability akK-th of Gaussian Profile is selected to divide mould Type g (ym|θk)；Then according to the probability distribution g (y of k-th of sub-modelm|θk) generate data ym；At this moment data y is observedmj, j=1, 2 ..., J, it is known that；Reaction observation data ymjData from k-th of sub-model are unknown, k=1,2 ..., K, with hidden variable γjk It indicates, is defined as follows:
Data must similarly be observedCorresponding hidden variableN=1,2 ..., N it is defined as follows:
Complete data is:The likelihood function of complete data is write out accordingly:
Wherein,
So, the log-likelihood function of complete data are as follows:
(2) the E step of EM algorithm: Q function is determined；
Expectation is asked to the log-likelihood function of complete data to get Q function is arrived:
Calculate E (γjk),It is denoted as respectively
Similarly:
It is the observation data y under "current" model parametermjProbability from k-th of sub-model becomes sub-model k to sight Measured data ymjResponsiveness；
It is to observe data under "current" model parameterProbability from n-th of sub-model becomes sub-model n to observation DataResponsiveness；
According to above-mentioned calculating to get
(3) the M step of EM algorithm: Q function is maximized, iterative formula is obtained；
The M step of iteration is to ask Q function to the maximum of parameter, that is, seeks the model parameter of new round iteration:
WithIndicate θ(i+1)Parameters；It asksIt only need to be right respectively by Q function λk,ηk,μn,ρnSeeking local derviation and enabling it is 0, be can be obtained；It asksIt is in ∑ ak=1, ∑ bnPartial derivative is sought under the conditions of=1 simultaneously It is enabled to obtain for 0, as a result as follows:
Obtain solving the iterative formula of each parameter；The above calculating is repeated, until there is no obvious for log-likelihood function value Until variation；
Step 3: exporting y after solving correction using above-mentioned iterative formular:
There are following relationships for each Gaussian component:
Equation group is solved, exports y after optimal correction can be obtainedr；
Step 4: the performance indicator based on statistical information is chosen, it is specific as follows:
Since process is influenced by non-gaussian random disturbances, using the more generally statistics in addition to mean value, variance Information carries out randomness metrics；In order to portray tracking performance and AF panel performance, the average value of square tracking error and tracking The entropy of error all minimizes；In addition, control energy also minimizes；Therefore, control is obtained by minimizing following performance indicator Device:
Here generally estimated using probabilistic, i.e. entropy, instead of the variance in Gaussian system；In view of computational efficiency, The entropy measure of selection is secondary any entropyKnown by the definition of information potential (IP), Secondary any entropy is the monotonic function of secondary information gesture, and therefore, the maximization of secondary any entropy is equivalent to the minimum of information potential, Using Stochastic gradient method, i.e. realization method for optimally controlling.
The present invention compared with prior art, has the advantage that
(1) since actual industrial process is unavoidably influenced by random noise, and generally non-gaussian random noise, this hair It is bright determine measurement noise and process noise be distributed when consider its bring influence, than ignore in existing method influence of noise or Assuming that noise Gaussian distributed is with more general and practical significance；
(2) present invention has fully considered the dynamic characteristic of process, preferably expresses real process；
(3) under the premise of initial parameter chooses reasonable, the present invention has higher computational efficiency, meets actual industrial mistake The requirement of journey；
(4) present invention sufficiently portrays the stochastic behaviour of non-gaussian random quantity using entropy statistical information, establishes tracing control and refers to Mark.
Detailed description of the invention
Fig. 1 is single step algorithm flow chart of the present invention.
Fig. 2 is the method for the present invention and existing method correction output comparison diagram.Horizontal axis is the time, and the longitudinal axis is non-Gaussian filtering Output response, three tracks respectively represent the output after setting value, the correction of existing Gauss method, non-gaussian method school in the present invention Output after just.Illustrated by figure, existing side is substantially better than in accuracy, rapidity using the system output after this method Method.
Specific embodiment
The method of the present invention is described below in conjunction with specific example: for typical wind-energy changing system, permanent-magnet synchronous The equivalent load of generator is by constant inductance LsWith variable resistance RsParallel connection is constituted.Under this application example, non-Gaussian filtering dynamic Data correction and system control performance optimization method, including following operating procedure:
Step 1: magneto alternator model can be described as:
Wherein, R is stator resistance, udAnd uqIt is the d component of stator and the voltage of q component, L respectivelydAnd LqIt is stator respectively D component and q component inductance, idAnd iqIt is the d component of stator and the electric current of q component, φ respectivelymIt is that (it is one normal to magnetic flux Number), p is the quantity of pole pair, ΩGIt is the revolving speed of generator, JhIt is total inertia of turbine, referred to as high speed shaft, RtIt is turbine half Diameter, i are transmission ratio, u=RsIt is control input, y=ΩGIt is system output；
The state-space model of magneto alternator based on wind generator system is established as follows:
Wherein:
In order to realize real-time control, to its state-space model discretization:
Wherein, xk∈R3×1It is state vector, all variables are all continuous, bounded in F () and G () and single order can be micro- , ωkIt is the non-gaussian disturbance of random wind speed；
Step 2: obtaining measurement after being measured influence of noise in control process exports ym, the step of being corrected to it, is such as Under:
For the measurement data y containing non-Gaussian noisem, its correction directly, which is sought, with the method for maximal possibility estimation believes Number yr, it is evident that the excessively huge problem of calculation amount will be faced, therefore first defines the hidden variable that can not be observed, foundation depends on The probabilistic model of hidden variable finds parameter maximal possibility estimation in probabilistic model, i.e., completes y using EM algorithmmCorrection signal Solution.
(1) initiation parameter λk,ηk,μn,ρn,ak,bn,ymj,
(2) E is walked: according to "current" model parameter, calculating responsiveness；
(3) M is walked: following iterative formula is utilized, the model parameter of new round iteration is calculated:
(4) (2) step and (3) step are repeated, until convergence；
(5) final argument a is obtainedk,bn,λk,μnEstimated valueBy
System of linear equations can be obtained:
Above-mentioned equation group is solved, exports y after being correctedr, for follow-up system dynamic optimization and control provide it is closer The measurement data of true value；
Step 3: the performance indicator based on statistical information is chosen, it is specific as follows:
Since process is influenced by non-gaussian random disturbances, using the more generally statistics in addition to mean value, variance Information carries out randomness metrics；In order to portray tracking performance and AF panel performance, the average value of square tracking error and tracking The entropy of error all minimizes；In addition, control energy also minimizes；Therefore, control is obtained by minimizing following performance indicator Device:
Here generally estimated using probabilistic, i.e. entropy, instead of the variance in Gaussian system；In view of computational efficiency, The entropy measure of selection is secondary any entropyKnown by the definition of information potential (IP), Secondary any entropy is the monotonic function of secondary information gesture, and therefore, the maximization of secondary any entropy is equivalent to the minimum of information potential, Using Stochastic gradient method, i.e. realization method for optimally controlling.

Claims (1)

1. a kind of non-Gaussian filtering dynamic data rectification and system control performance optimization method, it is characterised in that: including following behaviour Make step:
Step 1: non-gaussian disturbs lower system model description:
In a single-variable system, the output of t moment can be broken down into two parts: predictable partWith can not be pre- The part (δ (t)) of survey:
Wherein, ω (t) is process noise, sets δ (t) and measurement noise ε (t) as gauss hybrid models, probability density function is such as Shown in lower:
In formula, g [] is Gaussian distribution density, ckAnd fnFor mean value,WithFor variance；
Measurement output ymWith the relational expression of true output y are as follows:
ym(t)=y (t)+ε (t),
Y is exported after correctionr(t) Posterior distrbutionp exports y by measurementm(t) and predictable partIt provides；According to Bayes's standard Then, yr(t) Posterior distrbutionp and ym(t) likelihood function andLikelihood function product it is directly proportional, it may be assumed that
With L [ym(t)|yr(t)] calculation formula is as follows:
Wherein, the mean value of each Gaussian component meets such as relational expression:
p(yrIt (t)) is yr(t) prior probability, it is a constant, then:
Based on maximum a posteriori Distribution Principle, yr(t) estimated value can be obtained by following formula:
MaximizeWith L [ym(t)|yr(t)] product obtains optimal correction signal yr(t)；For containing The measurement data y of non-Gaussian noisem(t), the hidden variable that can not be observed first is defined, the probability mould for depending on hidden variable is established Type finds parameter maximal possibility estimation in probabilistic model, i.e., completes correction signal y using EM algorithmr(t) solution；
Step 2: carrying out the derivation of iterative formula in the problem description using EM algorithm:
(1) clear hidden variable writes out the log-likelihood function of complete data:
Imagine observation data ym(ym1,ym2,…,ymJ) generation are as follows: first according to probability akSelect k-th of Gaussian Profile sub-model g (ym|θk)；Then according to the probability distribution g (y of k-th of sub-modelm|θk) generate data ym；At this moment data y is observedmj, j=1, 2 ..., J, it is known that；Reaction observation data ymjData from k-th of sub-model are unknown, k=1,2 ..., K, with hidden variable γjk It indicates, is defined as follows:
Data must similarly be observedCorresponding hidden variableIt is defined as follows:
Complete data is:The likelihood function of complete data is write out accordingly:
Wherein,
So, the log-likelihood function of complete data are as follows:
(2) the E step of EM algorithm: Q function is determined；
Expectation is asked to the log-likelihood function of complete data to get Q function is arrived:
Calculate E (γjk),It is denoted as respectively
Similarly:
It is the observation data y under "current" model parametermjProbability from k-th of sub-model becomes sub-model k to observation data ymjResponsiveness；
It is to observe data under "current" model parameterProbability from n-th of sub-model becomes sub-model n to observation dataResponsiveness；
According to above-mentioned calculating to get
(3) the M step of EM algorithm: Q function is maximized, iterative formula is obtained；
The M step of iteration is to ask Q function to the maximum of parameter, that is, seeks the model parameter of new round iteration:
WithIndicate θ(i+1)Parameters；It asksIt only need to be by Q function respectively to λk,ηk, μn,ρnSeeking local derviation and enabling it is 0, be can be obtained；It asksIt is in ∑ ak=1, ∑ bnSeeking partial derivative under the conditions of=1 and enabling it is 0 It obtains, as a result as follows:
Obtain solving the iterative formula of each parameter；The above calculating is repeated, until there is no significant changes for log-likelihood function value Until；
Step 3: exporting y after solving correction using above-mentioned iterative formular:
There are following relationships for each Gaussian component:
Equation group is solved, exports y after optimal correction can be obtainedr；
Step 4: the performance indicator based on statistical information is chosen, it is specific as follows:
Since process is influenced by non-gaussian random disturbances, using the more generally statistical information in addition to mean value, variance Carry out randomness metrics；In order to portray tracking performance and AF panel performance, the average value and tracking error of square tracking error Entropy all minimize；In addition, control energy also minimizes；Therefore, controller is obtained by minimizing following performance indicator:
Here generally estimated using probabilistic, i.e. entropy, instead of the variance in Gaussian system；In view of computational efficiency, choose Entropy measure be secondary any entropyKnown by the definition of information potential (IP),It is secondary Any entropy is the monotonic function of secondary information gesture, and therefore, the maximization of secondary any entropy is equivalent to the minimum of information potential, is used Stochastic gradient method, i.e. realization method for optimally controlling.
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