CN107194026A - Absorption tower sweetening process modeling method based on Bayesian network - Google Patents
Absorption tower sweetening process modeling method based on Bayesian network Download PDFInfo
- Publication number
- CN107194026A CN107194026A CN201710249056.4A CN201710249056A CN107194026A CN 107194026 A CN107194026 A CN 107194026A CN 201710249056 A CN201710249056 A CN 201710249056A CN 107194026 A CN107194026 A CN 107194026A
- Authority
- CN
- China
- Prior art keywords
- mrow
- absorption tower
- sweetening process
- variable
- bayesian network
- 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
Classifications
-
- G—PHYSICS
- G06—COMPUTING; CALCULATING OR COUNTING
- G06F—ELECTRIC DIGITAL DATA PROCESSING
- G06F30/00—Computer-aided design [CAD]
- G06F30/20—Design optimisation, verification or simulation
Abstract
The invention belongs to thermoelectricity technical field, more particularly to a kind of absorption tower sweetening process modeling method based on Bayesian network, including：Absorption tower sweetening process model structure is determined based on Bayesian network, including by load, entrance SO2Concentration, inlet temperature, entrance O2Concentration, pH value, using absorption tower lime stone slurry quantity delivered and pump operating cycle combination as controllable input variable, will export SO as non-dimmable control input variable2Concentration is used as output variable；Absorption tower sweetening process model structure based on determination determines sweetening process model parameter, including the desulfurization history data and correlation test data according to absorption tower, prior information is combined with sample knowledge by the strong and weak probability point of dependence between each desulfurization operation variable, it is automatic to carry out off-line learning model parameter；Set up absorption tower sweetening process model.The sweetening process on absorption tower not only may be better understood in the present invention, and when external disturbance is more, can make accurate prediction.
Description
Technical field
The invention belongs to thermoelectricity technical field, more particularly to a kind of absorption tower sweetening process modeling based on Bayesian network
Method.
Background technology
Because the sweetening process in absorption tower is complicated physics, chemical reaction process, effective mechanism mould is lacked at present
The Parameters variation that type can accurately reflect in sweetening process.In the prior art, to many users of modeling of absorption tower sweetening process
Artificial neural networks scheduling algorithm, these algorithms can reflect the non-linear relation of each physical quantity in combustion process within the specific limits,
But the precision to model and the requirement of generalization ability can not be met simultaneously in actual use, need further to be changed
Enter.
The content of the invention
In order to solve the above technical problems, it is an object of the invention to provide a kind of absorption tower desulfurization based on Bayesian network
Journey modeling method, is learned the operation history data and correlation test data of desulfuration absorbing tower offline using Bayesian network
Practise, the Multiple input-output sweetening process model on absorption tower is set up offline, reflect outlet SO2 concentration how with difference with this
Absorption tower lime stone slurry quantity delivered, pump operating cycle combination and the cause and effect characteristic changed.
The invention provides a kind of absorption tower sweetening process modeling method based on Bayesian network, including：
Absorption tower sweetening process model structure is determined based on Bayesian network, including by load, entrance SO2Concentration, entrance
Temperature, entrance O2Concentration, pH value are as non-dimmable control input variable, by absorption tower lime stone slurry quantity delivered and pump operating cycle
Combination will export SO as controllable input variable2Concentration is used as output variable；
Absorption tower sweetening process model structure based on determination determines sweetening process model parameter, including according to absorption tower
Desulfurization history data and correlation test data, will by the strong and weak probability point of dependence between each desulfurization operation variable
Prior information is combined with sample knowledge, automatic to carry out off-line learning model parameter；
According to the absorption tower sweetening process model structure and parameter of determination, the absorption tower desulfurization based on Bayesian network is set up
Process model.
Further, the absorption tower sweetening process model structure based on determination determines that sweetening process model parameter is specifically wrapped
Include：The whole sample space of the desulfurization operation historical data on absorption tower is learnt, trained, conditional probability table is obtained；Wherein,
In conditional probability table, each probable value is expressed as P (Xi|parents(Xi)), then the joint probability allocation table of Bayesian network
It is shown as：
Wherein, XjIt is relative to X to eachiDependent variable, n, i, j be positive integer.
Further, when the observation of desulfurization history data is complete, desulfurization is determined by maximum likelihood estimate
Journey model parameter, maximum likelihood estimator is tried to achieve by following formula：
In formula, N (Y=y1, W=w1) represents that in training sample data variable Y takes y1 values and its direct precursor variable
W takes the number of times of w1 values, and N (Y=y1, W=w2) represents that variable Y takes y1 values and its direct precursor variable W takes the number of times of w2 values.
Further, when the observation of desulfurization history data is imperfect, sweetening process model is determined by EM algorithms
The region of parameter is optimal general like estimate.
Further, the step of EM algorithms are as follows：
(1) one initial value of parameter to be estimated is given, using this initial value and other observations, other is obtained and does not see
Survey the conditional expectation of node；
(2) estimated value is considered as observation, the maximum likelihood for bringing this complete observation sample into model is estimated
In meter formula；Wherein, the maximum likelihood estimator of a conditional probability of variable Y is tried to achieve by following formula：
Wherein, E [N (x)] is represented under current estimation parameter, and variable X=x conditional probability desired value is：
Wherein, I (x | D (k)) is counting function, when event x occurs in k-th of training sample, remembers 1, otherwise remembers 0；N
(Y=y1, W=w1) represents that in training sample data variable Y takes y1 values and its direct precursor variable W takes the number of times of w1 values,
N (Y=y1, W=w2) represents that variable Y takes y1 values and its direct precursor variable W takes the number of times of w2 values；
(3) the maximum likelihood estimator formula in maximization steps (2), obtains the maximum likelihood value of this parameter, so weight
Multiple step (1) and (2), untill parameter restrains, that is, obtain optimal estimates of parameters.
Further, this method also includes absorption tower sweetening process model as the object function in optimal control, leads to
Cross Bayesian inference and corresponding absorption tower running status is derived by every group of candidate's desulphurization control amount, it is optimal to select economy
Desulphurization control amount.
Further, Bayesian inference uses variable elimination method, and being added removing irrelevant variable by joint probability distribution obtains
To the conditional probability of any variable.
Further, the desulphurization control amount prediction that Bayesian inference is included from exports SO obtained from being affected by it2
Concentration.
Further, Bayesian inference also includes the outlet SO from2Concentration is inferred to the desulfurization control for causing it to occur
Amount change processed.
Further, this method also includes selecting optimal absorption tower sweetening process model by calculating root-mean-square error rate
Structure describes the sweetening process on absorption tower.
, not only can be more preferable by the absorption tower sweetening process modeling method based on Bayesian network by such scheme
The sweetening process on geography solution absorption tower, and when external disturbance is more, accurate prediction can be made.
Described above is only the general introduction of technical solution of the present invention, in order to better understand the technological means of the present invention,
And can be practiced according to the content of specification, below with presently preferred embodiments of the present invention and coordinate accompanying drawing describe in detail as after.
Brief description of the drawings
Fig. 1 is the flow chart of the Desulphurization for Coal-fired Power Plant optimal control method of the invention based on artificial intelligence；
Fig. 2 is the schematic diagram of a Bayesian network；
Fig. 3 is the bayesian network structure I of present invention reflection absorption tower sweetening process；
Fig. 4 is the schematic diagram of the bayesian network structure of a variety of reflection absorption towers sweetening process of the invention；Wherein, 4a is suction
It is absorption tower sweetening process model structure III to receive tower sweetening process model structure II, 4b, and 4c is absorption tower sweetening process model knot
Structure IV, 4d are absorption tower sweetening process model structure V；
Fig. 5 is actual outlet SO of the invention2Concentration is compared figure with model predication value.
Embodiment
With reference to the accompanying drawings and examples, the embodiment to the present invention is described in further detail.Implement below
Example is used to illustrate the present invention, but is not limited to the scope of the present invention.
Join shown in Fig. 1, present embodiments provide a kind of Desulphurization for Coal-fired Power Plant optimal control method based on artificial intelligence, wrap
Include：
Step S1, absorption tower sweetening process model structure is determined based on Bayesian network, including by load, entrance SO2It is dense
Degree, inlet temperature, entrance O2Concentration, pH value by absorption tower lime stone slurry quantity delivered and are followed as non-dimmable control input variable
Ring pump operation is combined as controllable input variable, will export SO2Concentration is used as output variable.
Step S2, the absorption tower sweetening process model structure based on determination determines sweetening process model parameter, including basis
The desulfurization history data and correlation test data on absorption tower, by between each desulfurization operation variable dependence it is strong and weak
Prior information is combined by probability point with sample knowledge, automatic to carry out off-line learning model parameter.
Step S3, according to the absorption tower sweetening process model structure and parameter of determination, sets up the suction based on Bayesian network
Receive tower sweetening process model.
The system uses operation history data and phase of the Bayesian network (Bayesian Network) to desulfuration absorbing tower
Close test data and carry out off-line learning, the Multiple input-output sweetening process model on absorption tower is set up offline, outlet is reflected with this
SO2The cause and effect how concentration changes with different absorption tower lime stone slurry quantity delivereds, pump operating cycle combination is special
Property.Because the sweetening process on absorption tower has substantial amounts of uncertain information, and artificial neural network scheduling algorithm is realized to uncertain
The processing of information is typically relatively difficult, and Bayesian network is the ideal model that data mining and uncertain knowledge are represented, Ke Yizhun
Really uncertain information is expressed and reasoning.Specific technical scheme includes：
1st, on BN modeling algorithm.
Bayesian network is the Cognitive Thinking reasoning pattern for simulating people, with directed acyclic graph and one group of conditional probability function
To probabilistic causal reasoning relationship modeling, therefore it has very high practical value.One Bayesian network definition includes
One directed acyclic graph (DAG) and a conditional probability table set.The node of each in DAG represents a stochastic variable, can be with
Be can directly observational variable or hidden variable, and directed edge represents that the condition between stochastic variable is relied on；It is every in conditional probability table
Unique node in one element correspondence DAG, stores combination condition probability of this node for its all direct precursor node.Shellfish
One particularly important property of this network of leaf is that each node is after the value of its direct precursor node is determined, this node
Conditional sampling is in its all indirect forerunner's ANCESTORS.The significance of this characteristic is to specify that Bayesian network can be with
Easily calculate joint probability distribution.Generally, the dependent combination condition probability distribution of multivariable is asked by equation below
：
P(x1, x2..., xn)=P (x1)P(x2|x1)P(x3|x1, x2)...P(xn|x1, x2..., xn-1) (1)
And in Bayesian network, due to there are aforesaid properties, the combination condition probability distribution of any stochastic variable combination
Can be simplified as：
Wherein, Parents (xi) represent variable xiDirect precursor node joint, probable value can be from by historical data
Train and found in obtained corresponding conditionses probability tables.As can be seen here, to greatly reduce both combination condition general for Bayesian network
The amount of calculation of rate, therefore the calculating speed of real-time optimal control computing can be ensured.
As shown in Fig. 2 Fig. 2 is a Bayesian network example, the Bayesian network describes 5 stochastic variables W, X, Y,
Causality between V, Z.Wherein, each one discrete random variable of node on behalf, every single arrow line represents two changes
Condition between amount is relied on, for example, W → Y represents that W is " because of (parents) " variable, Y is " fruit (descendants or
Children) " variable.In addition, except directed acyclic graph represents the structure of Bayesian network, each node has a condition
Probability tables (CPT), is represented under conditions of each possible combinations of states of all " because " variables of the node, this node
Every kind of state occur conditional probability value.For example, node W has two states W1 and W1, then, his " fruit " node Y tools
Probable value of having ready conditions includes：
P (y1 | w1), P (y2 | w1), P (y1 | w2) and P (y2 | w2).
From the structure of Bayesian network, variable X is not " fruit " node of variable Y, and variable Y only one of which is straight
Meet predecessor node W, according to equine husband it is assumed that P (Y | W, X)=P (Y | W), substituting into formula (2) can obtain：
P (W, X, Y, V, Z)=P (W) P (X) P (Y | W) P (V | Y) P (Z | X, Y) (3)
Fig. 2 shows bayesian network structure and parameter, each one stochastic variable of node on behalf, respectively W, X, Y, V,
Z.Its structure is represented that the parameter of each node is represented by a conditional probability table (CPT) by directed acyclic graph (DAG).
For application method, Bayesian network is mainly used in probability inference and decision-making, specifically, be exactly in information not
The stochastic variable of not observable is inferred in the case of complete by the way that stochastic variable can be observed, and observable random variable can not
With more than with one, general initial stage can not observation variable be set to random value, then carry out probability inference.
2nd, the determination of the absorption tower sweetening process model structure based on Bayesian network.
As shown in figure 3, each node in Bayesian network represents a random change related to absorption tower sweetening process
Amount, including desulfurization adjustment controlled quentity controlled variable and absorption tower running state parameter.The arrow of two nodes of connection represents this two random changes
Amount is with causality or unconditional independence；And if being connected with each other situation together just without arrow between variable in node
Its stochastic variable is called conditional sampling to each other.If being linked together between two nodes with a single arrow, one of them is represented
Node is " because of (parents) " that another is " fruit (descendants or children) ", and two nodes will produce one
Conditional probability value.For example, according to load, entrance SO2The real-time working conditions such as concentration, adjustment lime stone slurry quantity delivered and circulation pump group
The desulphurization control such as conjunction mode amount can directly affect the SO that outlet is surveyed2Concentration, therefore these duty parameters and desulphurization control amount are all
It is outlet SO2" because " node of concentration, as foregoing direct precursor node.Thus it can derive, each desulphurization control amount and go out
Mouth SO2Concentration be with causality or unconditional independence, therefore represent desulphurization control amount and outlet SO2Two of concentration
Connected between node with a directed edge with single arrow.
In the Multiple input-output sweetening process model on absorption tower, the change of desulphurization control amount directly results in absorption
The change of tower internal operation state, therefore in Bayesian network, desulphurization control amount is used as " because " node, the operation shape on absorption tower
State parameter is as " fruit " node, and the directed edge between node then represents each running state parameter on absorption tower by which
The influence of desulphurization control amount.Table 1 elaborates input and the output variable of absorption tower sweetening process model, and wherein input variable is divided again
For controllable variable and non-dimmable control variable.
The input of the absorption tower sweetening process model of table 1 and output variable
3rd, the determination of the sweetening process model parameter based on Bayesian network.
Secondly, according to the desulfurization operation historical data and correlation test data on absorption tower, Bayesian network can enter automatically
Row off-line learning model parameter, that is, represent the strong and weak probability point of dependence between each desulfurization operation variable by prior information with
Sample knowledge combines.
The determination of absorption tower sweetening process model parameter based on Bayesian network, be Bayesian network structure it is fixed
On the basis of, after being learnt, trained by the whole sample space of the desulfurization operation historical data to absorption tower, obtain one
Conditional probability table (Condition Probability Table, CPT).In conditional probability table, each probable value can be with table
It is shown as P (Xi|parents(Xi)), then the joint probability distribution of Bayesian network can be expressed as：
Wherein, XjIt is relative to X to eachi" because " variable.
When the structure of Bayesian network, it is known that the determination of parameter is divided to has two kinds of situations：A kind of situation is the sample of training data
This spatial integrity, another situation is that sample space has missing.Because there is Bayes net algorithm very strong uncertainty to ask
Disposal ability is inscribed, the algorithm possesses to be modeled under conditions of data sample space missing, therefore, based on Bayesian network
Desulfurization object model in absorption tower can more objectively reflect the real conditions of absorption tower sweetening process.
(1) bayesian network structure is, it is known that the observation of history data is complete.
Now we ask pattra leaves using maximum likelihood estimate (Maximum Likelihood Estimation, MLE)
The parameter of this network.Known training sample data are D={ x1..., xm, wherein xl=(xl1..., xln)T, it is assumed that parameter set
It is combined into Θ=(θ1..., θn), wherein θiRepresent variable XiConditional probability vector.The training sample data can then be reflected
The Log Likelihood Function (Log-likelihood) of parameter is：
Wherein, pa (Xi) represent Xi" because " variable, i.e. its direct precursor variable, DiThe desulfurization operation for representing absorption tower is gone through
One sample of history data, N represents the total sample number of operation history data, generally, in order that training sample data is general like value
Maximize, typically calculated by the occurrence frequency of each event.For example, in the example shown in Fig. 2, estimating Bayesian network
The conditional probability table of middle variable Y.
N (Y=y1, W=w1) represents that in the training sample data variable Y takes y1 values and its direct precursor variable W takes
The number of times of w1 values.Similarly, N (Y=y1, W=w2) represents that variable Y takes y1 values and its direct precursor variable W takes time of w2 values
Number.So, the maximum likelihood estimator (Maximum Likelihood Estimation) of a conditional probability of variable Y can
To be tried to achieve by following formula：
(2) bayesian network structure, it is known that the observation of history data imperfect (record at some time points has something lost
Leak data).
If some sweetening process variables are not observed, EM algorithms (Expectation- can be used
Maximization Algorithm) determine that the region of parameter is optimal general like estimate.The step of EM algorithms, is as follows：
(1) one initial value of parameter to be estimated is given, then using this initial value and other observations, other are obtained
The conditional expectation of non-observer nodes；
(2) estimated value is considered as observation, the maximum likelihood for bringing this complete observation sample into model is estimated
In meter formula.For example, the maximum likelihood estimator of a conditional probability of variable Y can be tried to achieve by following formula in Fig. 2：
Wherein, E [N (x)] is represented under current estimation parameter, and variable X=x conditional probability desired value is：
Wherein, I (x | D (k)) is counting function, when event x occurs in k-th of training sample, remembers 1, otherwise remembers 0.
(3) maximize this maximal possibility estimation formula, obtain the maximum likelihood value of this parameter, such repeat step (1) and
(2), untill parameter restrains, you can obtain optimal estimates of parameters.
System pass through a certain absorption tower of off-line learning desulfurization historical data, can obtain the absorption tower based on Bayesian network
The sweetening process model of network.When some or some desulfurization parameters change, this model can push over out other and can adjust
The most probable value of variable, and export SO under the operating mode2The probability distribution of concentration.
4th, sweetening process model is applied to the Bayesian inference in optimal control.
After the structure and parameter of model is determined, the absorption tower sweetening process model based on Bayesian network using as
Object function (Fitness Function) in optimal control, for judging the quality of every group of candidate's desulphurization control amount.Pass through
Bayesian inference, can derive corresponding absorption tower running status by every group of candidate's desulphurization control amount, economy is selected with this
Optimal desulphurization control amount, while outlet SO can be met2The emission request of concentration.The Bayesian inference of this programme uses variable
Null method (Variable Elimination), i.e., be added by joint probability distribution and remove irrelevant variable, it is hereby achieved that
The conditional probability of any variable.Including two kinds of reasoning situations, a kind of is that the desulphurization control amount prediction from is affected by it
Obtained from export SO2Concentration (prediction support, predict support), another is the outlet SO from2Concentration can be with
The desulphurization control amount change (diagnosis support, diagnostic support) for causing it to occur is inferred to for example, shown in Fig. 2
Example in, when given variable Z observed value, the conditional probability of its direct priori variable Y can be obtained by Bayesian inference,
Outlet SO as from2Concentration can be inferred that the desulphurization control amount change for causing it to occur.Its Bayesian inference formula
For,
Wherein,
Moreover,
5th, optimal sweetening process model is selected according to model accuracy rate.
For the Multiple input-output sweetening process model on absorption tower, the structure of its Bayesian network can be by inhaling
The expertise and experience of tower desulfurization are received to determine, and it is not unique.Fig. 4 illustrates a variety of reflection absorption towers sweetening process
Bayesian network structure.
This project selects optimal shellfish by calculating root-mean-square error rate (Root Mean Squared Error, RMSE)
Leaf this network structure describes the sweetening process on absorption tower.
Table 2 elaborates the prediction root mean square of 5 kinds of absorption tower sweetening process models that Fig. 3, Fig. 4 included to test data set
Error.As can be seen here, absorption tower sweetening process model structure I predicted root mean square error rate is minimum, therefore we select this
Model structure describes the sweetening process on absorption tower.
The predicted root mean square error of 25 kinds of absorption tower sweetening process models of table
| Sweetening process model | I | II | III | IV | V |
| RMSE | 2.6716 | 3.2489 | 2.794 | 4.8191 | 5.3241 |
6th, actual test result.
Now by taking the desulfurizing tower of Yangcheng Power Plant #3 units as an example, 1 day 00 December in 2016 is used:00:In December, 00~2016
16 days 05:26:30 historical data is as the training dataset of model, and sample frequency is 30 seconds.And use December 16 in 2016
Day 05:27:00~2016 on December 16,14:00:00 historical data examines absorption tower desulfurization as test data set with this
The accuracy of process model.As shown in Figure 5.
Multi input of the present embodiment based on Bayesian network-absorption tower sweetening process model is counted more, compared to data mining
Other algorithms, have the advantages that：
1st, the multi input based on Bayesian network-count more absorption tower sweetening process model can reflect outlet SO2Concentration
How with different absorption tower lime stone slurry quantity delivereds, pump operating cycle combination the cause and effect characteristic changed.Not only
The sweetening process on absorption tower may be better understood, and when external disturbance is more, accurate prediction can be made.
2nd, Bayesian network can easily handle fragmentary data.For example, artificial neural network is handling some variables
When having missing value, very big deviation will occur in the pre- geodesic structure of its model, and there is Bayesian network very strong uncertainty to ask
Disposal ability is inscribed, the algorithm can be modeled under conditions of data sample space missing, and be provided more intuitively general
Rate association relation model.Therefore, the absorption tower desulfurization object model based on Bayesian network can more objectively reflect absorption
The real conditions of tower sweetening process.
3rd, Bayesian network is a kind of intelligent algorithm of data-driven, and its structure and parameter is entirely by absorbing
History data study, the training of tower desulfurization are obtained.Therefore, the multi input based on Bayesian network-count more absorption tower takes off
The modeling algorithm of sulphur process model has very strong adaptivity, and this modeling algorithm is adapted to all producers, the absorption of model
Tower, after change research object, it is not necessary to redesign the theme algorithm built with compiling model.
4th, Bayesian inference can be rapidly according to unit load and entrance SO2The known absorbing tower desulfurization parameter such as concentration,
It is inferred to the most probable value of the adjustable variables such as absorption tower lime stone slurry quantity delivered, pump operating cycle combination, and
SO is exported under the operating mode2The probability distribution of concentration.
5th, the multi input based on Bayesian network-count absorption tower sweetening process model more can be required according to user, be appointed
Meaning increases or decreases input, output parameter, and the number to input, output parameter is not limited, and changes the number of parameter simultaneously
Bayesian inference is not influenceed in the calculating speed of real-time optimal control computing.
6th, Bayesian network is combined with genetic algorithm, can be effectively prevented from the undue fitting problems of data and training
Local extremum problem.
7th, different from artificial neural network, the generalization ability and model accuracy of Bayesian network are simultaneously increased.Pattra leaves
This network can be updated to network parameter at any time according to new training sample, and increasing with training sample, pattra leaves
The causality that this network can more accurately reflect between variable.
Described above is only the preferred embodiment of the present invention, is not intended to limit the invention, it is noted that for this skill
For the those of ordinary skill in art field, without departing from the technical principles of the invention, can also make it is some improvement and
Modification, these improvement and modification also should be regarded as protection scope of the present invention.
Claims (10)
1. a kind of absorption tower sweetening process modeling method based on Bayesian network, it is characterised in that including：
Absorption tower sweetening process model structure is determined based on Bayesian network, including by load, entrance SO2Concentration, inlet temperature,
Entrance O2Concentration, pH value combine absorption tower lime stone slurry quantity delivered and pump operating cycle as non-dimmable control input variable
As controllable input variable, SO will be exported2Concentration is used as output variable；
Absorption tower sweetening process model structure based on determination determines sweetening process model parameter, including according to the desulfurization on absorption tower
History data and correlation test data, are divided priori by the strong and weak probability of dependence between each desulfurization operation variable
Information is combined with sample knowledge, automatic to carry out off-line learning model parameter；
According to the absorption tower sweetening process model structure and parameter of determination, the absorption tower sweetening process based on Bayesian network is set up
Model.
2. the absorption tower sweetening process modeling method according to claim 1 based on Bayesian network, it is characterised in that base
In it is determined that absorption tower sweetening process model structure determine that sweetening process model parameter is specifically included：To the desulfurization operation on absorption tower
The whole sample space of historical data is learnt, trained, and obtains conditional probability table；Wherein, in conditional probability table, each is general
Rate value is expressed as P (Xi|parents(Xi)), then the joint probability distribution of Bayesian network is expressed as：
<mrow>
<mi>P</mi>
<mrow>
<mo>(</mo>
<msub>
<mi>X</mi>
<mn>1</mn>
</msub>
<mo>=</mo>
<msub>
<mi>x</mi>
<mn>1</mn>
</msub>
<mo>,</mo>
<mo>...</mo>
<mo>,</mo>
<msub>
<mi>X</mi>
<mi>n</mi>
</msub>
<mo>=</mo>
<msub>
<mi>x</mi>
<mi>n</mi>
</msub>
<mo>)</mo>
</mrow>
<mo>=</mo>
<munderover>
<mo>&Pi;</mo>
<mrow>
<mi>i</mi>
<mo>=</mo>
<mn>1</mn>
</mrow>
<mi>n</mi>
</munderover>
<mi>P</mi>
<mrow>
<mo>(</mo>
<msub>
<mi>X</mi>
<mi>i</mi>
</msub>
<mo>=</mo>
<msub>
<mi>x</mi>
<mi>i</mi>
</msub>
<mo>|</mo>
<msub>
<mi>X</mi>
<mi>j</mi>
</msub>
<mo>=</mo>
<msub>
<mi>x</mi>
<mi>j</mi>
</msub>
<mo>)</mo>
</mrow>
<mo>;</mo>
</mrow>
Wherein, XjIt is relative to X to eachiDependent variable, n, i, j be positive integer.
3. the absorption tower sweetening process modeling method according to claim 2 based on Bayesian network, it is characterised in that when
The observation of the desulfurization history data is complete, and sweetening process model parameter is determined by maximum likelihood estimate, maximum
Likelihood estimator is tried to achieve by following formula：
<mrow>
<mi>P</mi>
<mrow>
<mo>(</mo>
<mi>Y</mi>
<mo>=</mo>
<mi>y</mi>
<mn>1</mn>
<mo>|</mo>
<mi>W</mi>
<mo>=</mo>
<mi>w</mi>
<mn>1</mn>
<mo>)</mo>
</mrow>
<mo>=</mo>
<mfrac>
<mrow>
<mi>N</mi>
<mrow>
<mo>(</mo>
<mi>Y</mi>
<mo>=</mo>
<mi>y</mi>
<mn>1</mn>
<mo>,</mo>
<mi>W</mi>
<mo>=</mo>
<mi>w</mi>
<mn>1</mn>
<mo>)</mo>
</mrow>
</mrow>
<mrow>
<mi>N</mi>
<mrow>
<mo>(</mo>
<mi>Y</mi>
<mo>=</mo>
<mi>y</mi>
<mn>1</mn>
<mo>,</mo>
<mi>W</mi>
<mo>=</mo>
<mi>w</mi>
<mn>1</mn>
<mo>)</mo>
</mrow>
<mo>+</mo>
<mi>N</mi>
<mrow>
<mo>(</mo>
<mi>Y</mi>
<mo>=</mo>
<mi>y</mi>
<mn>1</mn>
<mo>,</mo>
<mi>W</mi>
<mo>=</mo>
<mi>w</mi>
<mn>2</mn>
<mo>)</mo>
</mrow>
</mrow>
</mfrac>
<mo>;</mo>
</mrow>
In formula, N (Y=y1, W=w1) represents that in training sample data variable Y takes y1 values and its direct precursor variable W takes
The number of times of w1 values, N (Y=y1, W=w2) represents that variable Y takes y1 values and its direct precursor variable W takes the number of times of w2 values.
4. the absorption tower sweetening process modeling method according to claim 3 based on Bayesian network, it is characterised in that when
The observation of the desulfurization history data is imperfect, determines that the region of sweetening process model parameter is most preferably general by EM algorithms
Like estimate.
5. the absorption tower sweetening process modeling method according to claim 4 based on Bayesian network, it is characterised in that institute
The step of stating EM algorithms is as follows：
(1) one initial value of parameter to be estimated is given, using this initial value and other observations, other is obtained and does not observe section
The conditional expectation of point；
(2) estimated value is considered as observation, this complete observation sample is brought into the maximal possibility estimation formula of model
In；Wherein, the maximum likelihood estimator of a conditional probability of variable Y is tried to achieve by following formula：
<mrow>
<mi>P</mi>
<mrow>
<mo>(</mo>
<mi>Y</mi>
<mo>=</mo>
<mi>y</mi>
<mn>1</mn>
<mo>|</mo>
<mi>W</mi>
<mo>=</mo>
<mi>w</mi>
<mn>1</mn>
<mo>)</mo>
</mrow>
<mo>=</mo>
<mfrac>
<mrow>
<mi>E</mi>
<mo>&lsqb;</mo>
<mi>N</mi>
<mrow>
<mo>(</mo>
<mi>Y</mi>
<mo>=</mo>
<mi>y</mi>
<mn>1</mn>
<mo>,</mo>
<mi>W</mi>
<mo>=</mo>
<mi>w</mi>
<mn>1</mn>
<mo>)</mo>
</mrow>
<mo>&rsqb;</mo>
</mrow>
<mrow>
<mi>E</mi>
<mo>&lsqb;</mo>
<mi>N</mi>
<mrow>
<mo>(</mo>
<mi>Y</mi>
<mo>=</mo>
<mi>y</mi>
<mn>1</mn>
<mo>,</mo>
<mi>W</mi>
<mo>=</mo>
<mi>w</mi>
<mn>1</mn>
<mo>)</mo>
</mrow>
<mo>&rsqb;</mo>
<mo>+</mo>
<mi>E</mi>
<mo>&lsqb;</mo>
<mi>N</mi>
<mrow>
<mo>(</mo>
<mi>Y</mi>
<mo>=</mo>
<mi>y</mi>
<mn>1</mn>
<mo>,</mo>
<mi>W</mi>
<mo>=</mo>
<mi>w</mi>
<mn>2</mn>
<mo>)</mo>
</mrow>
<mo>&rsqb;</mo>
</mrow>
</mfrac>
<mo>;</mo>
</mrow>
Wherein, E [N (x)] is represented under current estimation parameter, and variable X=x conditional probability desired value is：
<mrow>
<mi>E</mi>
<mo>&lsqb;</mo>
<mi>N</mi>
<mrow>
<mo>(</mo>
<mi>x</mi>
<mo>)</mo>
</mrow>
<mo>&rsqb;</mo>
<mo>=</mo>
<munder>
<mo>&Sigma;</mo>
<mi>k</mi>
</munder>
<mi>I</mi>
<mrow>
<mo>(</mo>
<mi>x</mi>
<mo>|</mo>
<mi>D</mi>
<mo>(</mo>
<mi>k</mi>
<mo>)</mo>
<mo>)</mo>
</mrow>
<mo>=</mo>
<munder>
<mo>&Sigma;</mo>
<mi>k</mi>
</munder>
<mi>P</mi>
<mrow>
<mo>(</mo>
<mi>x</mi>
<mo>|</mo>
<mi>D</mi>
<mo>(</mo>
<mi>k</mi>
<mo>)</mo>
<mo>)</mo>
</mrow>
<mo>;</mo>
</mrow>
Wherein, I (x | D (k)) is counting function, when event x occurs in k-th of training sample, remembers 1, otherwise remembers 0；N (Y=
Y1, W=w1) represent in training sample data, variable Y takes y1 values and its direct precursor variable W takes the number of times of w1 values, N (Y
=y1, W=w2) represent that variable Y takes y1 values and its direct precursor variable W takes the number of times of w2 values；
(3) the maximum likelihood estimator formula in maximization steps (2), obtains the maximum likelihood value of this parameter, so repeats to walk
Suddenly (1) and (2), untill parameter restrains, that is, optimal estimates of parameters is obtained.
6. the absorption tower sweetening process modeling method according to claim 1 based on Bayesian network, it is characterised in that also
Including using absorption tower sweetening process model as the object function in optimal control, by Bayesian inference by every group of candidate's desulfurization
Controlled quentity controlled variable derives corresponding absorption tower running status, the desulphurization control amount optimal to select economy.
7. the absorption tower sweetening process modeling method according to claim 6 based on Bayesian network, it is characterised in that institute
State Bayesian inference and use variable elimination method, the condition that irrelevant variable obtains any variable that removes is added by joint probability distribution
Probability.
8. the absorption tower sweetening process modeling method according to claim 7 based on Bayesian network, it is characterised in that institute
The desulphurization control amount prediction that stating Bayesian inference is included from exports SO obtained from being affected by it2Concentration.
9. the absorption tower sweetening process modeling method according to claim 8 based on Bayesian network, it is characterised in that institute
Stating Bayesian inference also includes the outlet SO from2Concentration is inferred to the desulphurization control amount change for causing it to occur.
10. the absorption tower sweetening process modeling method according to claim 1 based on Bayesian network, it is characterised in that
Also include selecting optimal absorption tower sweetening process model structure to describe the desulfurization on absorption tower by calculating root-mean-square error rate
Process.
Priority Applications (1)
| Application Number | Priority Date | Filing Date | Title |
|---|---|---|---|
| CN201710249056.4A CN107194026B (en) | 2017-04-17 | 2017-04-17 | Bayesian network-based absorption tower desulfurization process modeling method |
Applications Claiming Priority (1)
| Application Number | Priority Date | Filing Date | Title |
|---|---|---|---|
| CN201710249056.4A CN107194026B (en) | 2017-04-17 | 2017-04-17 | Bayesian network-based absorption tower desulfurization process modeling method |
Publications (2)
| Publication Number | Publication Date |
|---|---|
| CN107194026A true CN107194026A (en) | 2017-09-22 |
| CN107194026B CN107194026B (en) | 2021-03-23 |
Family
ID=59871002
Family Applications (1)
| Application Number | Title | Priority Date | Filing Date |
|---|---|---|---|
| CN201710249056.4A Active CN107194026B (en) | 2017-04-17 | 2017-04-17 | Bayesian network-based absorption tower desulfurization process modeling method |
Country Status (1)
| Country | Link |
|---|---|
| CN (1) | CN107194026B (en) |
Cited By (8)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| CN109173631A (en) * | 2018-09-19 | 2019-01-11 | 华能辛店发电有限公司 | A kind of energy conservation optimizing method for double tower flue gas desulphurization system of connecting |
| CN109523027A (en) * | 2018-10-22 | 2019-03-26 | 新智数字科技有限公司 | A kind of boiler operatiopn data monitoring method and device based on Bayesian network |
| CN109657909A (en) * | 2018-11-13 | 2019-04-19 | 北京国电龙源环保工程有限公司 | A kind of desulfurization based on big data grinds system ratio of water to material method of adjustment and system |
| CN109932909A (en) * | 2019-03-27 | 2019-06-25 | 江苏方天电力技术有限公司 | The big system of fired power generating unit desulphurization system couples Multi-variables optimum design match control method |
| CN110334855A (en) * | 2019-06-17 | 2019-10-15 | 浙江大学 | Intelligence determines the prediction and optimization system and method for waste water water-coal-slurry preparation program |
| CN111013370A (en) * | 2019-11-08 | 2020-04-17 | 中国大唐集团科学技术研究院有限公司火力发电技术研究院 | Wet desulphurization slurry supply amount prediction method based on deep neural network |
| CN111240282A (en) * | 2019-12-31 | 2020-06-05 | 联想(北京)有限公司 | Process optimization method, device, equipment and computer readable storage medium |
| CN111340199A (en) * | 2020-03-26 | 2020-06-26 | 中煤能源研究院有限责任公司 | Desulfurization system energy-saving method based on material balance and deep learning |
Citations (4)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| US20090125155A1 (en) * | 2007-11-08 | 2009-05-14 | Thomas Hill | Method and System for Optimizing Industrial Furnaces (Boilers) through the Application of Recursive Partitioning (Decision Tree) and Similar Algorithms Applied to Historical Operational and Performance Data |
| CN104238545A (en) * | 2014-07-10 | 2014-12-24 | 中国石油大学(北京) | Fault diagnosis and pre-warning system in oil refining production process and establishment method thereof |
| CN105718717A (en) * | 2016-01-12 | 2016-06-29 | 叶翔 | Method and device for establishing boiler combustion process model by utilizing Bayesian network algorithm |
| CN106485022A (en) * | 2016-11-01 | 2017-03-08 | 河北华电石家庄热电有限公司 | A kind of modeling method of circulating fluid bed boiler desulfurization denitration running optimizatin control |
-
2017
- 2017-04-17 CN CN201710249056.4A patent/CN107194026B/en active Active
Patent Citations (4)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| US20090125155A1 (en) * | 2007-11-08 | 2009-05-14 | Thomas Hill | Method and System for Optimizing Industrial Furnaces (Boilers) through the Application of Recursive Partitioning (Decision Tree) and Similar Algorithms Applied to Historical Operational and Performance Data |
| CN104238545A (en) * | 2014-07-10 | 2014-12-24 | 中国石油大学(北京) | Fault diagnosis and pre-warning system in oil refining production process and establishment method thereof |
| CN105718717A (en) * | 2016-01-12 | 2016-06-29 | 叶翔 | Method and device for establishing boiler combustion process model by utilizing Bayesian network algorithm |
| CN106485022A (en) * | 2016-11-01 | 2017-03-08 | 河北华电石家庄热电有限公司 | A kind of modeling method of circulating fluid bed boiler desulfurization denitration running optimizatin control |
Non-Patent Citations (5)
| Title |
|---|
| MONTSERRAT FUENTES 等: "Model Evaluation and Spatial Interpolation by Bayesian Combination of Observations with Outputs from Numerical Models", 《BIOMETRICS》 * |
| 但斌斌 等: "基于神经网络的KR脱硫控制工艺模型的研究", 《制造业自动化》 * |
| 冯金煌 等: "脱硫喷淋塔除尘的影响因素及效果分析", 《环境工程》 * |
| 张旭 等: "一种具备规则趋势的模糊神经网络脱硫预报模型", 《江苏冶金》 * |
| 谭清磊 等: "基于因果图和贝叶斯网络的高含硫井口分离器风险分析", 《安全与环境学报》 * |
Cited By (12)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| CN109173631A (en) * | 2018-09-19 | 2019-01-11 | 华能辛店发电有限公司 | A kind of energy conservation optimizing method for double tower flue gas desulphurization system of connecting |
| CN109523027A (en) * | 2018-10-22 | 2019-03-26 | 新智数字科技有限公司 | A kind of boiler operatiopn data monitoring method and device based on Bayesian network |
| CN109523027B (en) * | 2018-10-22 | 2021-01-05 | 新智数字科技有限公司 | Boiler operation data monitoring method and device based on Bayesian network |
| CN109657909A (en) * | 2018-11-13 | 2019-04-19 | 北京国电龙源环保工程有限公司 | A kind of desulfurization based on big data grinds system ratio of water to material method of adjustment and system |
| CN109657909B (en) * | 2018-11-13 | 2022-07-29 | 国能龙源环保有限公司 | Big data-based water-material ratio adjusting method and system for desulfurization grinding system |
| CN109932909A (en) * | 2019-03-27 | 2019-06-25 | 江苏方天电力技术有限公司 | The big system of fired power generating unit desulphurization system couples Multi-variables optimum design match control method |
| CN110334855A (en) * | 2019-06-17 | 2019-10-15 | 浙江大学 | Intelligence determines the prediction and optimization system and method for waste water water-coal-slurry preparation program |
| CN111013370A (en) * | 2019-11-08 | 2020-04-17 | 中国大唐集团科学技术研究院有限公司火力发电技术研究院 | Wet desulphurization slurry supply amount prediction method based on deep neural network |
| CN111240282A (en) * | 2019-12-31 | 2020-06-05 | 联想(北京)有限公司 | Process optimization method, device, equipment and computer readable storage medium |
| CN111240282B (en) * | 2019-12-31 | 2021-12-24 | 联想(北京)有限公司 | Process optimization method, device, equipment and computer readable storage medium |
| CN111340199A (en) * | 2020-03-26 | 2020-06-26 | 中煤能源研究院有限责任公司 | Desulfurization system energy-saving method based on material balance and deep learning |
| CN111340199B (en) * | 2020-03-26 | 2023-05-12 | 中煤能源研究院有限责任公司 | Material balance and deep learning-based energy-saving method for desulfurization system |
Also Published As
| Publication number | Publication date |
|---|---|
| CN107194026B (en) | 2021-03-23 |
Similar Documents
| Publication | Publication Date | Title |
|---|---|---|
| CN107194026A (en) | Absorption tower sweetening process modeling method based on Bayesian network | |
| Lyu et al. | SDRL: interpretable and data-efficient deep reinforcement learning leveraging symbolic planning | |
| Kisi et al. | Forecasting daily lake levels using artificial intelligence approaches | |
| Wang et al. | A hybrid forecasting model based on outlier detection and fuzzy time series–A case study on Hainan wind farm of China | |
| CN111311577A (en) | Intelligent water seepage detection method based on generation of confrontation network and reinforcement learning | |
| Attarzadeh et al. | Software development effort estimation based on a new fuzzy logic model | |
| Beruvides et al. | Fault pattern identification in multi-stage assembly processes with non-ideal sheet-metal parts based on reinforcement learning architecture | |
| CN105718717A (en) | Method and device for establishing boiler combustion process model by utilizing Bayesian network algorithm | |
| Wieland et al. | From neural networks to qualitative models in environmental engineering | |
| Petchinathan et al. | Local linear model tree and Neuro-Fuzzy system for modelling and control of an experimental pH neutralization process | |
| Stathopoulos et al. | Fuzzy rule-based system approach to combining traffic count forecasts | |
| Chen | Analyzing and forecasting the global CO2 concentration-a collaborative fuzzy-neural agent network approach | |
| Zhang et al. | A role-based POMDPs approach for decentralized implicit cooperation of multiple agents | |
| Kumar et al. | Transfer Learning based GDP Prediction from Uncertain Carbon Emission Data | |
| Behera et al. | A state-of-the-art neuro-swarm approach for prediction of software reliability | |
| Mohammed et al. | Deep learning and neural network-based wind speed prediction model | |
| Schwung et al. | Actor-critic reinforcement learning for energy optimization in hybrid production environments | |
| CN114130034A (en) | Multi-agent game AI (Artificial Intelligence) design method based on attention mechanism and reinforcement learning | |
| Khan et al. | A highly optimized multi-stage teacher-learner inspired particle swarm optimizer system | |
| Zhu et al. | Decomposing Synthesized Strategies for Reactive Multi-agent Reinforcement Learning | |
| Logan et al. | Comparing Approaches to Distributed Control of Fluid Systems based on Multi-Agent Systems | |
| Wu et al. | Model-based Bayesian Reinforcement Learning in Factored Markov Decision Process. | |
| Roman Cardell | Python-based Deep-Learning methods for energy consumption forecasting | |
| Daoui et al. | Control design for untimed Petri nets using Markov decision processes | |
| Chen et al. | Training fuzzy logic controller software components by combining adaptation algorithms |
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 |