CN110703599A - Organic Rankine cycle system control performance optimization method based on dynamic data correction - Google Patents

Organic Rankine cycle system control performance optimization method based on dynamic data correction Download PDF

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CN110703599A
CN110703599A CN201910877359.XA CN201910877359A CN110703599A CN 110703599 A CN110703599 A CN 110703599A CN 201910877359 A CN201910877359 A CN 201910877359A CN 110703599 A CN110703599 A CN 110703599A
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任密蜂
张雯
程兰
张建华
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Taiyuan University of Technology
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Abstract

The invention discloses an organic Rankine cycle system control performance optimization method based on dynamic data correction, which comprises the following steps of: the first stage, dynamic data correction: describing a system model under non-Gaussian disturbance; solving a likelihood function of the correction data according to a maximum posterior distribution principle; supplementing complete data by utilizing a maximum expectation algorithm idea to obtain a likelihood function of the complete data, and taking a logarithm of the likelihood function; finding a tight lower bound of the logarithm of the likelihood function to obtain an optimal estimation of the unknown parameter; and a second stage, optimizing the performance based on the minimum entropy control of dynamic data correction: selecting performance indexes based on statistical information; solving for control input; and constructing a performance evaluation standard. The invention considers the defect that the Renyi entropy does not meet the consistency, provides the minimum rational entropy control performance optimization method based on dynamic data correction, and can obviously improve the control performance of the organic Rankine cycle system containing non-Gaussian noise.

Description

Organic Rankine cycle system control performance optimization method based on dynamic data correction
Technical Field
The invention discloses an organic Rankine cycle system control performance optimization method based on dynamic data correction, and belongs to the technical field of organic Rankine cycle systems.
Background
An Organic Rankine Cycle (ORC) waste heat utilization process is a thermodynamic Cycle process that converts waste heat into electrical energy. The waste heat utilization has important significance for improving the energy utilization efficiency, reducing the industrial operation cost and reducing the pollution emission. The superheated steam temperature is one of the most important parameters in an organic rankine cycle process throughout the thermodynamic description of the organic rankine cycle. In order to improve the energy conversion efficiency of the organic rankine cycle process, the temperature of the organic working medium at the outlet of the evaporator cannot be too high from the aspects of safety and economy, and the temperature cannot be too low in order to avoid some critical conditions, namely, the temperature at the outlet of the evaporator should be controlled within a reasonable range. The temperature sensor is used for accurately measuring the outlet temperature of the evaporator and effectively controlling the outlet temperature, so that the organic Rankine cycle energy conversion efficiency is improved. If a bad control loop is not discovered in time, the energy conversion efficiency and the service life of the equipment are affected. Therefore, Control Performance Assessment (CPA) is very important in the industry.
Because factors such as aging and unstable voltage inevitably exist in the use process of the sensor, the measured data of the sensor are inaccurate, and the control effect is poor. The influence brought by measurement noise is not considered in the conventional control strategy and control performance evaluation method applied to the organic Rankine cycle waste heat utilization process. Dynamic data correction (DDR) can improve the quality of measurement data in a transient state, so that the measurement data including measurement noise is dynamically corrected to operate in an optimal state, which is significant for improving the economy and stability of the organic rankine cycle system.
At present, the dynamic data correction method mainly comprises a Kalman filtering method, an extended Kalman filtering method and an unscented Kalman filtering method, the methods are derived under the assumption of Gauss, and when the measurement noise distribution does not meet the assumption of Gauss, the data correction method cannot obtain a satisfactory result. The patent of non-gaussian system dynamic data correction and system control performance optimization (patent application number: 201811199510.0) is published, and combines a dynamic data correction method with a minimum Renyi entropy control strategy to provide a control performance optimization method, but does not consider the importance of control system performance evaluation, and the Renyi entropy in the patent does not meet the requirement of consistency, so that a new non-gaussian system control performance optimization and evaluation method is needed.
Disclosure of Invention
In order to overcome the defects of the prior art, the invention provides the organic Rankine cycle system control performance optimization method based on dynamic data correction, and the method can obviously improve the control performance of the organic Rankine cycle system containing non-Gaussian noise.
The invention is realized by the following technical scheme:
the organic Rankine cycle system control performance optimization method based on dynamic data correction comprises the following steps:
the first stage, dynamic data correction:
step 1.1, describing a system model under non-Gaussian disturbance;
step 1.2, solving correction data y according to the maximum posterior distribution principler(t) a likelihood function;
step 1.3, supplementing complete data by utilizing the thought of a maximum expectation algorithm to obtain a likelihood function of the complete data, and taking a logarithm of the likelihood function;
step 1.4. find the logarithm of the likelihood function
Figure BDA0002204781990000022
Obtaining the optimal estimation of the unknown parameter theta by the tight lower bound of the parameter theta;
and a second stage, optimizing the performance based on the minimum entropy control of dynamic data correction:
2.1, selecting performance indexes based on statistical information;
step 2.1, solving a control input u (t);
and 2.3, constructing a performance evaluation standard.
Preferably, step 1.1 is obtained by:
in a non-linear system, the output at time t is decomposed into two parts: prediction outputAnd an unpredictable output δ (t), the process output y (t) being expressed as:
Figure BDA0002204781990000021
wherein u (t) is a control input, d (t) is random process interference, and f (-) and g (-) are arbitrary nonlinear relations which do not affect each other; true measurement output y due to the presence of measurement noise ε (t)m(t) is:
ym(t)＝y(t)+ε(t) (2)
probability density functions of non-gaussian features have arbitrary shapes that are difficult to directly represent and process. As is well known, any probability density function can be approximated by a mixture of a finite number of gaussian probability density functions, and therefore, using a gaussian mixture model to derive a general dynamic data correction method, the probability density functions for the measured noise, epsilon (t) and delta (t), are as follows:
Figure BDA0002204781990000032
wherein K and N are the number of Gaussian mixture models, lambdakAnd munRespectively the mean value of each gaussian model,
Figure BDA0002204781990000033
and
Figure BDA0002204781990000034
variance, a, of each Gaussian mixture modelkAnd bnAre weighted and satisfy
Figure BDA0002204781990000036
φ1kProbability density function, phi, representing the kth Gaussian fraction model of epsilon (t)2nA probability density function representing the nth gaussian component model of delta (t),
Figure BDA0002204781990000037
θ1and theta2All unknown parameters in the probability density function representing ε (t) and δ (t), respectively, i.e. θ1＝(a1，a2，…，aK；θ11，θ12，…，θ1K)，θ2＝(b1，b2，…，bN；θ21，θ22，…，θ2N)。
Preferably, step 1.2 is obtained by:
measurement output ym(t) likelihood function L [ y [)m(t)|yr(t)，θ2]And predicted output
Figure BDA0002204781990000038
Likelihood function ofIs represented as follows:
Figure BDA00022047819900000310
Figure BDA00022047819900000311
wherein, yr(t) denotes the correction output, and all unknown parameters are denoted as θ ═ yr，θ1，θ2) Output y from the measurement according to Bayesian criterionm(t) and prediction output
Figure BDA00022047819900000312
Given of yrThe posterior probability of (t) is proportional to the product of the likelihood functions of the measured output and the predicted output, i.e.
Figure BDA00022047819900000313
According to the maximum a posteriori distribution principle, yr(t) is obtained by the following formula:
Figure BDA0002204781990000041
preferably, step 1.3 is obtained by:
to obtain the unknown parameter θ, a set of dataObviously, the method of Monte Carlo is adopted to generate J group dataThe estimation of the optimal parameters is obtained by:
Figure BDA0002204781990000044
let observation data ym(ym1，ym2，Λ，ymJ) Is generated as follows:
first according to the probability akSelecting the kth Gaussian distribution partial model g (y)m|θk) (ii) a Then according to the probability distribution g (y) of the k-th partial modelm|θk) Generating data ym(ii) a At this time, observation data ymjJ ═ 1,2, Λ, J, known; observation data of reaction ymjData from the K-th partial model is unknown, K1, 2jkRepresenting observation data ymjData from the kth partial model, defined as follows:
Figure BDA0002204781990000045
data are obtained by the same methodCorresponding hidden variable
Figure BDA0002204781990000047
n＝1，2，...，N，
Figure BDA0002204781990000048
Representing observed data of reaction
Figure BDA0002204781990000049
Data from the nth partial model is defined as follows:
Figure BDA00022047819900000410
then, the full data is:
Figure BDA00022047819900000411
from this, the likelihood function of the full data is written:
to pairTaking the logarithm to obtain:
then it is determined that,
Figure BDA0002204781990000054
the process of solving for θ directly by equation (14) is still complicated if found
Figure BDA0002204781990000055
And then continually optimize this tight lower bound, an optimal estimate of the unknown parameter theta will be obtained.
Said step 1.4 finding
Figure BDA0002204781990000056
The optimal estimate of the unknown parameter θ is obtained by the tight lower bound of:
according to the Jensen inequality,
Figure BDA0002204781990000057
an equal sign holds if and only if x is a constant;
will be provided with
Figure BDA0002204781990000058
Constructed in the form of the Jensen inequality:
Figure BDA0002204781990000059
wherein, Q (gamma)jk) Andare respectively gammajkAnd
Figure BDA00022047819900000511
the distribution of (a);
order to
Figure BDA00022047819900000512
Then the process of the first step is carried out,
Figure BDA00022047819900000513
according to formula (15), obtaining
Figure BDA0002204781990000061
Order toThen
Figure BDA0002204781990000063
In conclusion, the method has the advantages that,
Figure BDA0002204781990000064
satisfies the following conditions:
Figure BDA0002204781990000065
namely find out
Figure BDA0002204781990000066
The equal sign of the formula (20) is ensured to be established, and the lower bound is further ensured to be tight, then
Figure BDA0002204781990000067
Wherein, C1And C2Is a constant; due to Q (gamma)jk) And
Figure BDA0002204781990000068
are respectively gammajkAnd
Figure BDA0002204781990000069
is a distribution function of
Figure BDA00022047819900000610
Q(γjk) And
Figure BDA00022047819900000611
obtained by the following formula:
Figure BDA0002204781990000071
Q(γjk) And
Figure BDA0002204781990000072
has obtained, Q (gamma)jk) Represents gammajkThe probability of 1 is given as the probability of,
Figure BDA0002204781990000073
represents
Figure BDA0002204781990000074
The probability of (d); define Q (γ) respectivelyjk) And
Figure BDA0002204781990000075
is estimated as
Figure BDA0002204781990000076
And
Figure BDA0002204781990000078
find out
Figure BDA0002204781990000079
Tight lower bound of
Figure BDA00022047819900000710
Figure BDA00022047819900000711
So far, a function which is easy to solve for the unknown parameter theta is found, and the maximization is realized
Figure BDA00022047819900000712
The iteration is carried out until the required precision is reached,
Figure BDA00022047819900000713
θ(i)representing the value of theta at the i-th iteration, theta(i)The unknown parameters contained in the data are passed through the pairsAnd respectively calculating partial derivatives, and respectively setting the partial derivatives to be 0 to obtain:
Figure BDA0002204781990000082
Figure BDA0002204781990000083
Figure BDA0002204781990000084
Figure BDA0002204781990000088
repeating the iterative equations (27) - (33) until convergence to obtain the corrected output yr。
Preferably, in the second stage, the minimum entropy control performance optimization method based on dynamic data correction is as follows:
step 2.1. Performance index selection based on statistical information
Defining the tracking error e (t) as: e (t) ═ r (t) -yr(t) since the process is affected by non-gaussian random disturbances, more general statistical information besides mean, variance is usedA measure of row randomness, i.e., entropy, replaces the variance in a gaussian system; considering that the Renyi entropy does not meet the requirement of consistency, the rational entropy has the advantages of the Renyi entropy and meets the requirement of consistency, and therefore the entropy measure selected by the method is the rational entropy.
And (3) carrying out randomness measurement by adopting rational entropy:
Figure BDA0002204781990000091
wherein γ (e) is the probability density function of e (t);
in order to characterize tracking performance and interference rejection performance, the average value and entropy of the tracking error are minimized; furthermore, the control energy is also minimized; thus, the controller is obtained by minimizing the following performance indicators:
Figure BDA0002204781990000092
wherein R is1Weights, R, representing rational entropy2Weight representing mean value of error, R3A weight representing the input square;
step 2.1. solving for control input u (t):
obtaining an optimal control input u (t) by adopting a random gradient method:
Figure BDA0002204781990000093
wherein λ is the learning rate, and the iteration is stopped when the required precision is reached;
the method for constructing the performance evaluation criterion in the step 2.3 comprises the following steps:
the control performance evaluation criterion is defined as the ratio of the optimal control performance index to the current control performance index:
Figure BDA0002204781990000094
wherein the content of the first and second substances,is the entropy value of the system output in the minimum rational entropy control strategy,
Figure BDA0002204781990000096
is the actual entropy value of the current controller, and the control performance evaluation reference etaMRECA scalar value, eta, is given for evaluating the performance of the currently used controllerMRECHas a value between 0 and 1, when ηMRECWhen the value of (A) is close to 0, the current control state of the system is poor; when etaMRECWhen the value of (b) is close to 1, it indicates that the current process has a good control effect.
Compared with the prior art, the invention has the following beneficial effects:
because the actual industrial process is inevitably influenced by random noise and is generally non-Gaussian random noise, the influence caused by the random noise and the non-Gaussian random noise is considered when the distribution of the measurement noise and the process noise is determined, and compared with the existing method in which the influence of the noise is ignored or the noise is assumed to obey Gaussian distribution, the method has more generality and practical significance. In addition, the invention considers the defect that the Renyi entropy does not meet the consistency, provides the minimum rational entropy control performance optimization method based on dynamic data correction, is suitable for all non-Gaussian nonlinear processes, has a larger application value in practice, and has a larger significance for improving the safety and the stability of a control system.
Drawings
FIG. 1 is a structural diagram of temperature control of an organic Rankine cycle system according to the present invention.
FIG. 2 is a schematic diagram of a conventional organic Rankine cycle system.
FIG. 3 is a graph of the process noise and measurement noise distribution of the present invention.
FIG. 4 is a graph comparing control results according to the present invention.
Detailed Description
The present invention will be described in further detail with reference to specific examples, but the scope of the present invention is not limited to these examples, and all changes or equivalent substitutions that do not depart from the spirit of the present invention are intended to be included within the scope of the present invention.
Taking an input and output model of a superheated steam temperature system in an organic Rankine cycle process as an example, the ORC system mainly comprises the following components: working medium pump, evaporator, expander, condenser. As shown in the attached drawing 2, in the thermodynamic cycle process, a low-temperature low-pressure liquid organic working medium R245fa is pressurized by a working medium pump and enters an evaporator, in the evaporator, the working medium exchanges heat with a low-temperature waste heat source for evaporation, the working medium is heated by the heat source into superheated steam with higher temperature and high pressure, and then the steam enters an expander and expands in the expander to work to drive a generator to generate power. The low-temperature low-pressure organic working medium (namely exhaust gas) after acting enters a condenser, the organic working medium is condensed into a liquid state by releasing heat to a low-temperature heat source, and finally, the working medium pump conveys the liquid working medium back to the evaporator again to complete the whole cycle.
The rotating speed of a working medium pump in the model is used as control input, namely u (t), the temperature of the superheated steam in the ORC process is used as control output, namely y (t), and d (t) represents non-Gaussian random disturbance in the control process, namely non-Gaussian random disturbance of inlet temperature and smoke mass flow.
The organic Rankine cycle system temperature control method based on dynamic data correction comprises two stages of performance optimization of dynamic data correction and minimum entropy control performance evaluation based on the dynamic data correction, wherein the dynamic data correction performance optimization stage comprises the following steps:
the method comprises the following steps: and (4) describing a system model under non-Gaussian disturbance.
In an organic rankine cycle process superheated steam temperature system, the output at time t can be broken down into two parts: predictable portion
Figure BDA0002204781990000111
And an unpredictable portion δ (t), the true measurement output, i.e. the measurement y of the superheated steam temperaturem(t) is:
ym(t)＝y(t)+ε(t) (37)
ε (t) is the temperature sensor measurement noise. The Probability Density Function (PDF) of the measurement noise ∈ (t) and δ (t) is as follows:
Figure BDA0002204781990000112
Figure BDA0002204781990000113
the distribution diagram is shown in fig. 3, wherein K-N-3,
Figure BDA0002204781990000114
θ1and theta2All unknown parameters in the probability density function representing ε (t) and δ (t), respectively, i.e. θ1＝(a1，a2，…，aK；θ11，θ12，…，θ1K)，θ2＝(b1，b2，…，bN；θ21，θ22，…，θ2N)。
Step two: obtaining solving correction data y according to maximum posterior distribution principlerLikelihood function of (t)
Likelihood function
Figure BDA0002204781990000115
And L [ y ]m(t)|yr(t)，θ2]As follows:
Figure BDA0002204781990000116
Figure BDA0002204781990000117
all unknown parameters are noted as θ ═ yr，θ1，θ2). According to Bayes' rule, by ym(t) and
Figure BDA0002204781990000118
given of yrThe posterior probability of (t) is proportional to the product of the likelihood functions of the measured output and the predicted output, i.e.
Figure BDA00022047819900001111
According to the maximum a posteriori distribution principle, yr(t) can be obtained by the following formula:
obviously, the calculation amount of the above formula is too large for directly solving the unknown parameter θ ═ yr，θ1，θ2)。
Step three: full data is supplemented using the most desirable algorithm concept.
Generating J-group data by adopting Monte Carlo method
Figure BDA0002204781990000121
In this example J is 200. The estimate of the optimal parameters can be obtained by:
Figure BDA0002204781990000122
imagine observation data ym(ym1，ym2，Λ，ymJ) Is generated as follows: first according to the probability akSelecting the kth Gaussian distribution partial model g (y)m|θk) (ii) a Then according to the probability distribution g (y) of the k-th partial modelm|θk) Generating data ym(ii) a At this time, observation data ymjJ ═ 1,2, Λ, J, known; observation data of reaction ymjData from the K-th partial model is unknown, K1, 2jkWhich is defined as follows:
Figure BDA0002204781990000123
data are obtained by the same methodRelative to each otherImplicit variable of response
Figure BDA0002204781990000125
N ═ 1,2,., N is defined as follows:
Figure BDA0002204781990000126
then, the full data is:
Figure BDA0002204781990000127
from this, the likelihood function of the full data is written:
Figure BDA0002204781990000128
to pair
Figure BDA0002204781990000129
Taking the logarithm to obtain:
then it is determined that,
Figure BDA0002204781990000132
the process of solving for theta directly by the above equation is still complex if found
Figure BDA0002204781990000133
And then continually optimize this tight lower bound, an optimal estimate of the unknown parameter theta will be obtained.
Step four: finding
Figure BDA0002204781990000134
The optimal estimate of the unknown parameter theta is obtained.
According to the Jensen inequality
Figure BDA0002204781990000135
Is found, defined as
Figure BDA0002204781990000136
So far, a function which is easy to solve for the unknown parameter theta is found, and the maximization is realized
Figure BDA0002204781990000138
The iteration is carried out until the required precision is reached,
Figure BDA0002204781990000139
θ(i)representing the value of theta at the ith iteration. Theta(i)The unknown parameters contained in the data can be processed by the pair
Figure BDA00022047819900001310
The partial derivatives were calculated and made to be 0, respectively. The results were:
Figure BDA00022047819900001311
Figure BDA0002204781990000143
Figure BDA0002204781990000144
Figure BDA0002204781990000145
repeating the iterative equations (50) - (56) until convergence to obtain the corrected output yr。
The minimum entropy control performance optimization stage based on dynamic data correction comprises the following steps:
the method comprises the following steps: selecting performance indexes based on statistical information, which is specifically as follows:
defining a tracking error as e (t) ═ r (t) -yr(t), the entropy measure selected by the invention is rational entropy
Figure BDA0002204781990000147
Wherein γ (e) is the probability density function of e (t); in order to characterize tracking performance and interference rejection performance, the average value and entropy of the tracking error are minimized; furthermore, the control energy is also minimized; thus, the controller is obtained by minimizing the following performance indicators:
Figure BDA0002204781990000148
wherein R is1，R2And R3Are weighted and are respectively set as R1＝0.06，R20.02 and R3＝0.001。
Step two: solving for the control input u (t).
If a target set point for the superheated steam temperature is given, then minimizing the objective function allows control and regulation of the pump speed u (t). Obtaining an optimal control input u (t) by adopting a random gradient method:
Figure BDA0002204781990000151
where λ is the learning rate, and empirically, λ is 0.001 and the accuracy is set to 0.001.
Step three: and constructing a performance evaluation standard.
The control performance evaluation criterion is defined as the ratio of the optimal control performance index to the current control performance index, and is a convenient method for measuring relative performance, and is as follows:
Figure BDA0002204781990000152
whereinIs the entropy value of the system output in the minimum rational entropy control strategy,
Figure BDA0002204781990000154
is the actual entropy value, η, of the current controllerMRECScalar values for evaluating the performance of the currently used controller are given. Obviously, etaMRECIs between 0 and 1. When approaching 0, it is indicated that the current control state of the system is very poor. If the value is close to 1, the control effect of the current process is good.
Table 1 and FIG. 4 show the performance optimization results of the minimum entropy control based on the dynamic data correction in this embodiment, and table 1 shows the entropy values of the tracking errors
Output of Noiseless output Measuring output Corrected output of the invention
Entropy of the entropy 0.004 0.018 0.006
From table 1, it can be found that the present invention can significantly improve the control performance of the organic rankine cycle system containing non-gaussian noise, and the stabilized correction output is close to the case without measurement noise, with a good effect. Based on the proposed performance evaluation criterion etaMRECThe control performance of the PID controller in the organic rankine cycle system was evaluated. When the system control performance is good, the parameters of the PID controller are respectively kp＝0.035、ki0.15 and k d0. When the system control performance is poor, the parameters of the PID controller are respectively kp＝0.11、ki0.09 and kd＝0。
TABLE 2 control Performance evaluation criteria based on dynamic data correction
Figure BDA0002204781990000161
Table 2 shows the minimum entropy control performance evaluation result based on dynamic data correction in this embodiment, and it can be found that the present invention can accurately evaluate the actual control effect of the organic rankine cycle system.
The present invention is not intended to be limited to the embodiments shown herein but is to be accorded the widest scope consistent with the principles and novel features disclosed herein.

Claims (6)

1. The method for optimizing the control performance of the organic Rankine cycle system based on dynamic data correction is characterized by comprising the following steps of:
the first stage, dynamic data correction:
step 1.1, describing a system model under non-Gaussian disturbance;
step 1.2, solving correction data y according to the maximum posterior distribution principler(t) a likelihood function;
step 1.3, supplementing complete data by utilizing the thought of a maximum expectation algorithm to obtain a likelihood function of the complete data, and taking a logarithm of the likelihood function;
step 1.4. find the logarithm of the likelihood function
Figure FDA0002204781980000012
Obtaining the optimal estimation of the unknown parameter theta by the tight lower bound of the parameter theta;
and a second stage, optimizing the performance based on the minimum entropy control of dynamic data correction:
2.1, selecting performance indexes based on statistical information;
step 2.1, solving a control input u (t);
and 2.3, constructing a performance evaluation standard.
2. The dynamic data correction based organic rankine cycle system control performance optimization method according to claim 1, characterized in that the step 1.1 is obtained by the following method:
in a non-linear system, the output at time t is decomposed into two parts: prediction output
Figure FDA0002204781980000013
And an unpredictable output δ (t), the process output y (t) being expressed as:
Figure FDA0002204781980000011
wherein u (t) is a control input, d (t) is random process interference, and f (-) and g (-) are arbitrary nonlinear relations which do not affect each other; true measurement output y due to the presence of measurement noise ε (t)m(t) is:
ym(t)＝y(t)+ε(t) (2)
the probability density functions of the measured noise epsilon (t) and delta (t) are as follows:
Figure FDA0002204781980000021
Figure FDA0002204781980000022
wherein K and N are the number of Gaussian mixture models, lambdakAnd munRespectively the mean value of each gaussian model,
Figure FDA0002204781980000023
and
Figure FDA0002204781980000024
variance, a, of each Gaussian mixture modelkAnd bnAre weighted and satisfy
Figure FDA0002204781980000025
φ1kProbability density function, phi, representing the kth Gaussian fraction model of epsilon (t)2nA probability density function representing the nth gaussian component model of delta (t),θ1and theta2All unknown parameters in the probability density function representing ε (t) and δ (t), respectively, i.e. θ1＝(a1,a2,…,aK；θ11,θ12,…,θ1K)，θ2＝(b1,b2,…,bN；θ21,θ22,…,θ2N)。
3. The dynamic data correction based organic rankine cycle system control performance optimization method according to claim 1, characterized in that the step 1.2 is obtained by the following method:
measurement output ym(t) likelihood function L [ y [)m(t)|yr(t),θ2]And predicted output
Figure FDA0002204781980000028
Likelihood function of
Figure FDA0002204781980000029
Is represented as follows:
Figure FDA00022047819800000211
wherein, yr(t) denotes the correction output, and all unknown parameters are denoted as θ ═ yr,θ1,θ2) Output y from the measurement according to Bayesian criterionm(t) and prediction outputGiven of yrThe posterior probability of (t) is proportional to the product of the likelihood functions of the measured output and the predicted output, i.e.
Figure FDA00022047819800000213
According to the maximum posterior distribution principle, y is obtainedr(t) is:
Figure FDA0002204781980000031
4. the dynamic data correction based organic rankine cycle system control performance optimization method according to claim 1, characterized in that the step 1.3 is obtained by the following method:
generating J-group data by adopting Monte Carlo method
Figure FDA0002204781980000032
The estimation of the optimal parameters is obtained by:
Figure FDA0002204781980000033
let observation data ym(ym1,ym2,Λ,ymJ) Is generated as follows:
first according to the probability akSelecting the kth Gaussian distribution partial model g (y)m|θk) (ii) a Then according to the probability distribution g (y) of the k-th partial modelm|θk) Generating data ym(ii) a At this time, observation data ymjJ ═ 1,2, Λ, J, known; observation data of reaction ymjData from the K-th partial model is unknown, K1, 2jkRepresenting observation data ymjData from the kth partial model, defined as follows:
Figure FDA0002204781980000034
data are obtained by the same method
Figure FDA0002204781980000035
Corresponding hidden variable
Figure FDA0002204781980000036
Figure FDA0002204781980000037
Representing observed data of reactionData from the nth partial model is defined as follows:
Figure FDA0002204781980000039
then, the full data is:
Figure FDA00022047819800000310
from this, the likelihood function of the full data is written:
Figure FDA0002204781980000041
to pairTaking the logarithm to obtain:
Figure FDA0002204781980000043
then it is determined that,
Figure FDA0002204781980000044
5. the dynamic data correction based organic rankine cycle system control performance optimization method according to claim 1, characterized in that the step 1.4 is obtained by the following method:
according to the Jensen inequality,
Figure FDA0002204781980000045
an equal sign holds if and only if x is a constant;
will be provided with
Figure FDA0002204781980000046
Constructed in the form of the Jensen inequality:
Figure FDA0002204781980000047
wherein, Q (gamma)jk) And
Figure FDA0002204781980000048
are respectively gammajkAndthe distribution of (a);
order to
Then the process of the first step is carried out,
Figure FDA00022047819800000411
according to formula (15), obtaining
Figure FDA0002204781980000051
Order to
Figure FDA0002204781980000052
Then
Figure FDA0002204781980000053
In conclusion, the method has the advantages that,
Figure FDA0002204781980000054
satisfies the following conditions:
Figure FDA0002204781980000055
namely find outThe equal sign of the formula (20) is ensured to be established, and the lower bound is further ensured to be tight, then
Figure FDA0002204781980000057
Wherein, C1And C2Is a constant; due to Q (gamma)jk) And
Figure FDA0002204781980000058
are respectively gammajkAnd
Figure FDA0002204781980000059
is a distribution function of
Figure FDA00022047819800000510
Q(γjk) And
Figure FDA00022047819800000511
obtained by the following formula:
Figure FDA0002204781980000061
Q(γjk) And
Figure FDA0002204781980000062
has been obtained to represent respectively gammajk1 and
Figure FDA0002204781980000063
the probability of (d); define Q (γ) respectivelyjk) And
Figure FDA0002204781980000064
is estimated as
Figure FDA0002204781980000065
And
Figure FDA0002204781980000066
Figure FDA0002204781980000067
find out
Figure FDA0002204781980000068
Tight lower bound of
Figure FDA0002204781980000069
So far, a function which is easy to solve for the unknown parameter theta is found, and the maximization is realized
Figure FDA00022047819800000611
The iteration is carried out until the required precision is reached,
Figure FDA00022047819800000612
θ(i)representing the value of theta at the i-th iteration, theta(i)The unknown parameters contained in the data are passed through the pairsAnd respectively calculating partial derivatives, and respectively setting the partial derivatives to be 0 to obtain:
Figure FDA0002204781980000072
Figure FDA0002204781980000073
Figure FDA0002204781980000074
Figure FDA0002204781980000075
Figure FDA0002204781980000078
repeating the iterative equations (27) - (33) until convergence to obtain the corrected output yr。
6. The dynamic data correction-based organic Rankine cycle system control performance optimization method according to claim 1, wherein the second stage, minimum entropy control performance optimization based on dynamic data correction is obtained by:
step 2.1. Performance index selection based on statistical information
Defining the tracking error e (t) as: e (t) ═ r (t) -yr(t)，
And (3) carrying out randomness measurement by adopting rational entropy:
Figure FDA0002204781980000081
wherein γ (e) is the probability density function of e (t);
the controller is obtained by minimizing the following performance indicators:
Figure FDA0002204781980000082
wherein R is1Weights, R, representing rational entropy2Weight representing mean value of error, R3A weight representing the input square;
step 2.1. solving for control input u (t):
obtaining an optimal control input u (t) by adopting a random gradient method:
wherein λ is the learning rate, and the iteration is stopped when the required precision is reached;
the method for constructing the performance evaluation criterion in the step 2.3 comprises the following steps:
the control performance evaluation criterion is defined as the ratio of the optimal control performance index to the current control performance index:
Figure FDA0002204781980000084
wherein the content of the first and second substances,
Figure FDA0002204781980000085
is the entropy value of the system output in the minimum rational entropy control strategy,is the actual entropy value of the current controller, and the control performance evaluation reference etaMRECA scalar value, eta, is given for evaluating the performance of the currently used controllerMRECHas a value between 0 and 1, when ηMRECWhen the value of (A) is close to 0, the current control state of the system is poor; when etaMRECWhen the value of (b) is close to 1, it indicates that the current process has a good control effect.
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