CN103530818B - A kind of water supply network modeling method based on BRB system - Google Patents

Abstract

The present invention discloses a kind of water supply network modeling method based on BRB system. The historical data of the present invention's first collection tube network operation, next determines input variable and the output variable of water supply network model, then sets up the water supply network model based on BRB, finally sets up the water supply network MIMO model based on BRB. The present invention can well describe water supply pipe net system operating mode, for water supply network real-time optimization dispatch time, can compare favourably with the neural network model of water supply network. And, by analyzing the rule base trained by pipe network history run data and obtain, it is possible to excavate the unknown characteristics of water supply network further.

Description

A kind of water supply network modeling method based on BRB system

Technical field

The invention belongs to Urban water supply field, specifically a kind of water supply network modeling method based on BRB (Belief-Rule-Base) system.

Background technology

Urban water supply pipe network system is a topological framework complexity, in large scale, water use variation randomness is strong, quantity of parameters is uncertain, run the network structure of control multiple goal. Setting up the condition model matched with pipe network system feature is the prerequisite realizing water supply network optimizing operation, the prerequisite that foundation can process pipeline parameter uncertainty simultaneously, water supply network model that is quantitative and qualitative information is assessment and analysis network security and reliability. Chinese scholars has carried out big quantity research in water supply network modeling, and the most representative pipe net leakage rate is realistic model and neural network model. These models adopt the method determined to describe the behavior of pipe network system, helpless for unascertained information input. So, it is badly in need of foundation and can describe water supply pipe net system operating mode, the water supply network model of pipe network system unascertained information can be processed again.

Based on the modeling of BRB system, theoretical with Dempster-Shafer evidence, decision-making is theoretical and based on Fuzzy Set Theory, can process quantitative information and qualitative information, it is determined that property information and unascertained information simultaneously. Based on the water supply network model of BRB system, it is possible to well describe water supply pipe net system operating mode, can be used for the scheduling of the real-time optimization of water supply network and predictive control. And this model allows the input of uncertain information, such as uncertain parameter, external disturbance etc., and model exports the interval for quantizing, and can be used for assessing and analyzing the safety and reliability of water supply pipe net system.

Summary of the invention

The present invention is directed to the deficiencies in the prior art, it provides a kind of water supply network modeling method based on BRB (Belief-Rule-Base) system.

The inventive method is specific as follows:

1. the historical data of collection tube network operation

The historical data of pipe network operation is obtained from the SCADA system of water supply network and Database Systems. The historical data that water supply network runs generally comprises: water factory dispatches from the factory pressure, water factory's service discharge, pressurized pump station pressure and flow in pipe network, the opening degree of controllable valve on pipeline, the pressure of pressure monitoring point, the flow of flow monitoring point, water reservoir water level, user's water consumption etc.

2. determine input variable and the output variable of water supply network model

(1) from the historical data of the actual pipe network operation obtained, water supply network mode input output variable is chosen.

Input variable generally comprises: water factory dispatches from the factory pressure, water factory's service discharge, pressurized pump station pressure and flow in pipe network, the opening degree etc. of controllable valve on pipeline. In addition, can by measurable disturbance (user's water consumption) and not measurable disturbance (system input noise), also as the input variable of system.

Output variable comprises: the pressure of pressure monitoring point, the flow of flow monitoring point, water reservoir water level.

(2) according to the input and output variable chosen, the historical data of pipe network operation is screened, obtain only containing the historical data of input and output variable, as sampled data. Meanwhile, sampled data being divided into two portions, front portion is as training dataset, and rear portion is as check data collection.

3. set up the water supply network model based on BRB

Model based on BRB (Belief-Rule-Base) system is MISO model, and water supply network is MIMO model. Therefore, based on the water supply network MIMO model of BRB it is the synthesis of multiple water supply network MISO model based on BRB. Establishment step based on the water supply network MISO model of BRB is as follows:

(1) determine rule base inputs vector sum output vector:

Inputting the vector that vector is in (2) input variable selected and forms in rule base, in rule base, output vector is a certain of the output variable selected in (2). If input vector U=(U_i, i=1 ..., T), wherein T is the component number of input vector, i.e. the number of input variable; If output variable is O (U), it is the function of input vector U.

(2) initial rules storehouse is set up:

In BRB system, the rule in rule base is:

$R_k:IF\left(U_{1}is{A}_1^k\right)\mathrm{\Λ}\left(U_{2}is{A}_2^k\right)\mathrm{\Λ}...\mathrm{\Λ}\left(U_{T}is{A}_T^k\right);$

$THEN\{(D_1,{\mathrm{\β}}_{1k}),(D_2,{\mathrm{\β}}_{2k}),...,(D_N,{\mathrm{\β}}_{Nk})\},(\underset{n=1}{\overset{N}{\Σ}}{\mathrm{\β}}_{nk}\≤1),k=1,...L;$

The weight of rule: ��_k(k=1 ..., L), input variable weight: ��_1,k,��_2,k,...,��_T,k;

Wherein, L is the sum of rule,For the i-th input variable in kth rule reference value (reference value be training data concentrate input variable some exemplary value, as reference value be 3 time, optional maximum value, mean value, minimum value), D=(D₁,D₂,...,D_N) it is reasoning output vector, ��_nk(n=1 ..., N) it is reasoning output D_nDegree of belief. IfThen kth rule is claimed to be complete, ifThen kth rule is almost completely neglected. ��_k(k=1 ..., L) it is the regular relative weighting in rule base of kth, ��_i,k(i=1 ..., T, k=1 ..., L) it is the i-th input variable weight in kth rule.

In rule base, varying parameter is P=(��_nk,��_k,��_i,k; N=1 ..., N; K=1 ..., L; I=1 ..., T). For setting up initialize rule base, random initial ��_nk, and ��_k, ��_i,kIt is initially set 1.

(3) rule base is trained:

Initial rules storehouse, by the mapping relation of the input data set of learning training data centralization and output data set, adjusts varying parameter P=(�� automatically_nk,��_k,��_i,k; N=1 ..., N; K=1 ..., L; I=1 ..., T), final acquisition describes input vector U=(U_i, i=1 ..., T) and the rule base of output variable O (U) relation.

Reasoning process in rule base is as follows:

Step1: vector U=(U will be inputted_i, i=1 ..., T) convert to and trust distribution:

S(U_i)={ (A_i,j,��_i,j), j=1 ..., J_i;

Wherein J_iFor the number of reference value, ��_i,jFor input U_iWith reference value A_i,jSimilarity. ��_i,jIt is calculated as follows:

If A_i,j��U_i��A_i,j+1, then��_i,j+1=1-��_i,j, and for j '=1 ..., J_i, j ' �� j, j+1, has ��_i,j��=0;

Step2: calculate the weight w that kth rule is activated_k:

$w_k=\frac{{\mathrm{\θ}}_k\×\underset{i=1}{\overset{T}{\Π}}{\left({\mathrm{\α}}_{i,j}^k\right)}^{{\stackrel{\‾}{\mathrm{\δ}}}_{i,k}}}{\underset{k=1}{\overset{L}{\Σ}}\[{\mathrm{\θ}}_k\×\underset{i=1}{\overset{T}{\Π}}{\left({\mathrm{\α}}_{i,j}^k\right)}^{{\stackrel{\‾}{\mathrm{\δ}}}_{i,k}}\]},{\stackrel{\‾}{\mathrm{\δ}}}_{i,k}=\frac{{\mathrm{\δ}}_{i,k}}{\underset{i=1,\mathrm{...},T}{\max }\left\{{\mathrm{\δ}}_{i,k}\right\}}$

Step3: calculate output variable O (U):

First calculate trust distribution O (the U)={ (D of output variable_n,��_n(U)), n=1 ..., N}, wherein

$\left\{D_n\right\}:{\mathrm{\β}}_n\left(U\right)=\mathrm{\μ}\×\[\underset{k=1}{\overset{L}{\Π}}(w_k{\mathrm{\β}}_{n,k}+1-w_k\underset{n=1}{\overset{N}{\Σ}}{\mathrm{\β}}_{n,k})-\underset{k=1}{\overset{L}{\Π}}(1-w_k\underset{n=1}{\overset{N}{\Σ}}{\mathrm{\β}}_{n,k})\]$

$\left\{D\right\}:{\mathrm{\β}}_D\left(U\right)=\mathrm{\μ}\×\[\underset{k=1}{\overset{L}{\Π}}(1-w_k\underset{n=1}{\overset{N}{\Σ}}{\mathrm{\β}}_{n,k})-\underset{k=1}{\overset{L}{\Π}}(1-w_k)\]$

$\mathrm{\μ}={\[\underset{n=1}{\overset{N}{\Σ}}\underset{k=1}{\overset{L}{\Π}}(w_k{\mathrm{\β}}_{nk}+1-w_k\underset{n=1}{\overset{N}{\Σ}}{\mathrm{\β}}_{nk})-(N-1)\underset{k=1}{\overset{L}{\Π}}(1-w_k\underset{n=1}{\overset{N}{\Σ}}{\mathrm{\β}}_{nk})-\underset{k=1}{\overset{L}{\Π}}(1-w_k)\]}^{-1};$

��_D(U) represent the degree of belief of unknown the reasoning results D, and meet

If it is complete for trusting rule, namely have��_D(U)=0, then what final output was L rule is comprehensive, and table is O (U)={ (D_n,��_n(U)), n=1 ..., N}, numerical value exports and is $O\left(U\right)=\underset{n=1}{\overset{N}{\Σ}}{D}_n{\mathrm{\β}}_n\left(U\right).$

If it is imperfect to trust rule, namely there is ��_D(U) > 0, then final numerical value exports has bound O (U) �� [O_min(U),O_max], (U) wherein

$O_{min}\left(U\right)=\underset{n=1}{\overset{N-1}{\Σ}}{D}_n{\mathrm{\β}}_n\left(U\right)+D_N\[{\mathrm{\β}}_N\left(U\right)+{\mathrm{\β}}_D\left(U\right)\]$

$O_{max}\left(U\right)=D_1\[{\mathrm{\β}}_1\left(U\right)+{\mathrm{\β}}_D\left(U\right)\]+\underset{n=2}{\overset{N}{\Σ}}{D}_n{\mathrm{\β}}_n\left(U\right);$

So far, a given input U=(U_i, i=1 ..., T) just there is one to export O (U) to rule base. For trust rule be complete picture, the training of rule base is exactly solve following optimization problem, and wherein H is learning sample number,For the actual output of learning sample

$\left\{\begin{array}{c}0\≤{\mathrm{\β}}_{nk},{\mathrm{\θ}}_k,{\mathrm{\δ}}_{i,k}\≤1\\ \underset{n=1}{\overset{N}{\Σ}}{\mathrm{\β}}_{nk}=1\end{array}\right.;$

For the regular imperfect situation of trust, the training of rule base is exactly solve following optimization problem

(4) inspection rule storehouse:

Check data is utilized to be checked by the rule base that (1) (2) (3) are set up, with the precision of evaluation model. The standard of precision is usedWeigh. If �� (P) does not meet modeling accuracy requirement, repeat (1) (2) (3) modeling again.

So far, water supply network MISO model based on BRB is set up.

4. set up the water supply network MIMO model based on BRB

Based on the synthesis that the water supply network MIMO model of BRB is multiple water supply network MISO model based on BRB. So, according to the number of output variable, for each output variable repeats the modeling process of MISO model.

The useful effect of the present invention: based on the water supply network model of BRB system, it is possible to well describe water supply pipe net system operating mode, when dispatching for the real-time optimization of water supply network, can compare favourably with the neural network model of water supply network. And, by analyzing the rule base trained by pipe network history run data and obtain, it is possible to excavating the unknown characteristics of water supply network further, this is the feature that neural network model does not possess. In addition, allowing the input of uncertain information based on the water supply network model of BRB system, such as uncertain parameter, external disturbance etc., now model exports the interval for quantizing. This is conducive to assessing and analyzing the safety and reliability of water supply pipe net system. As when user's water requirement random fluctuation, model can measure the pressure variation range of monitoring point in advance, and now staff or intelligent optimization dispatching system can take reasonably to dispatch measure accordingly.

Accompanying drawing explanation

Fig. 1 rule base training process schematic diagram;

Fig. 2 embodiment water supply network topology schematic diagram.

Embodiment

For making technique means that the present invention realizes and creation characteristic be easy to clear, below in conjunction with drawings and Examples, embodiments of the present invention are described in further detail.

The present embodiment considers that a single watersupply pipe network is such as Fig. 2, sets up the water factory based on BRB and dispatches from the factory pressure, the relational model of dispatch from the factory flow and pressure monitoring point 55,90,170 pressure.

1. the historical data of collection tube network operation

The historical data of pipe network operation is obtained from the SCADA system of water supply network and Database Systems. The historical data that water supply network runs comprises: water factory dispatches from the factory pressure, water factory's service discharge, the pressure of pressure monitoring point 55,90,170, monitoring point 55,90,170 user's water consumption. Meanwhile, historical data being divided into two portions, front portion is as training dataset, and rear portion is as check data collection.

2. determine water supply network mode input variable and output variable

Because being the synthesis of multiple water supply network MISO model based on BRB based on the water supply network MIMO model of BRB. So, here, first set up water factory and dispatch from the factory pressure, the relational model of dispatch from the factory flow and monitoring point 55 pressure. Meanwhile, using monitoring point 55 user's water consumption as measuring disturbance input variable. So input and output are as follows respectively:

Input variable: U=(U_i, i=1,2,3), wherein U₁, U₂, U₃It is respectively water factory to dispatch from the factory pressure, dispatch from the factory flow and monitoring point 55 user's water consumption. Output variable: P₅₅, it is monitoring point 55 pressure.

3. set up the water supply network model based on BRB

(1) determine rule base inputs vector sum output variable

Inputting vector in rule base is U=(U_i, i=1,2,3), output variable is P₅₅. The input and output of the present embodiment all adopt 3 reference values, get the minimum value of each variable respectively, mean value and maximum value, and these reference values are calculated by the historical data of pipe network operation. Therefore have

Dispatch from the factory pressure U₁: $A_1^k=\{sp,mp,lp\};$

Dispatch from the factory flow U₂: $A_2^k=\{sf,mf,lf\};$

Monitoring point 55 user water consumption U₃:

Monitoring point 55 pressure P₅₅: D={sp₅₅,mp₅₅,lp₅₅;

And meetA_i={ A_i,j; J=1 ..., 3}, D={D₁,D₂,D₃. Wherein, sp, mp, lp are respectively the pressure minimum that dispatches from the factory, mean value and maximum value, and sf, mf, lf are respectively flow minimum value of dispatching from the factory, mean value and maximum value, and sd, md, ld are respectively monitoring point 55 user's water consumption minimum value, mean value and maximum value, sp₅₅,mp₅₅,lp₅₅It is respectively monitoring point 55 pressure minimum, mean value and maximum value.

(2) initial rules storehouse is set up

The selection of the reference point of input vector sum output variable is to set up rule base, and input reference point has 27 combinations, therefore rule base has 27 rules.

Wherein kth rule form is as follows:

$R_k:IF{U}_{1}is{A}_1^{k}AND{U}_{2}is{A}_2^{k}AND{U}_{3}is{A}_3^k$

$THEN{P}_{55}is\{({\mathrm{sp}}_{55},{\mathrm{\β}}_{1k}),({\mathrm{mp}}_{55},{\mathrm{\β}}_{2k}),({\mathrm{lp}}_{55},{\mathrm{\β}}_{3k})\},(\underset{n=1}{\overset{N}{\Σ}}{\mathrm{\β}}_{nk}\≤1),k\∈\{1,...,27\}$

In rule base, varying parameter is P=(��_nk,��_k,��_i,k; N=1 ..., N; K=1 ..., L; I=1 ..., T), wherein N=3, L=27, T=3. For setting up initialize rule base, random initial ��_nk, and ��_k, ��_ikIt is initially set 1.

(3) rule base is trained

Initial rules storehouse maps relation by the input data set of learning training data centralization and output data set, adjustment varying parameter P=(��_nk,��_k,��_i,k; N=1,2,3; K=1 ..., 27; I=1,2,3), final acquisition describes input vector U=(U_i, i=1,2,3) and output variable p₅₅The rule base of relation, see Fig. 1. Concrete steps are as follows:

Step1: input vector is converted to and trusts distribution:

Based on input vector reference point A_i={ A_i,j; J=1 ..., 3}, will input vector U={U_i, i=1,2,3}, converts the trust distribution of following input vector to

S(U_i)={ (A_i,j,��_i,j), j=1,2,3};

Wherein ��_i,jFor input U_iWith reference value A_i,jSimilarity. ��_i,jIt is calculated as follows:

Work as A_i,j��U_i��A_i,j+1, then ${\mathrm{\α}}_{i,j}=\frac{A_{i,j+1}-U_i}{A_{i,j+1}-A_{i,j}},{\mathrm{\α}}_{i,j+1}=1-{\mathrm{\α}}_{i,j}$

Work as j '=1 ..., J_i, j ' �� j, j+1, has ��_i,j��=0;

Step2: calculate the weight w that kth rule is activated_k:

$w_k=\frac{{\mathrm{\θ}}_k\×\underset{i=1}{\overset{T}{\Π}}{\left({\mathrm{\α}}_{i,j}^k\right)}^{{\stackrel{\‾}{\mathrm{\δ}}}_{i,k}}}{\underset{k=1}{\overset{L}{\Σ}}\[{\mathrm{\θ}}_k\×\underset{i=1}{\overset{T}{\Π}}{\left({\mathrm{\α}}_{i,j}^k\right)}^{{\stackrel{\‾}{\mathrm{\δ}}}_{i,k}}\]},{\stackrel{\‾}{\mathrm{\δ}}}_{i,k}=\frac{{\mathrm{\δ}}_{i,k}}{\underset{i=1,\mathrm{...},T}{\max }\left\{{\mathrm{\δ}}_{i,k}\right\}};$

Step3: comprehensive K rule, reasoning obtains the trust distribution of monitoring point 55 pressure:

The present embodiment adopts IDSMulticriteriaAssessor (many attributes decision analysis software) to calculate the trust distribution of output variable. Can obtain:

p₅₅(U)={ (D_n,��_n), (U) n=1,2,3}

Step4: the pressure p obtaining detection by monitoring point 55 calculation of pressure distribution₅₅:

p₅₅=U₁��₁+U₂��₂+U₃��₃

Step5: adopting MATLAB to solve following optimization problem, wherein H is learning sample number,For monitoring point in learning sample 55 pressure:

$\left\{\begin{array}{c}0\≤{\mathrm{\β}}_{nk},{\mathrm{\θ}}_k,{\mathrm{\δ}}_{i,k}\≤1\\ \underset{n=1}{\overset{N}{\Σ}}{\mathrm{\β}}_{nk}=1\end{array}\right.$

Wherein P=(��_nk,��_k,��_i,k; N=1,2,3; K=1 ..., 27; I=1,2,3).

Step6: inspection rule storehouse

Check data is utilized to be checked by the rule base set up, with the precision of evaluation model. The standard of precision is usedWeigh.

4. set up and dispatch from the factory pressure based on the water factory of BRB, the relational model of dispatch from the factory flow and pressure monitoring point 55,90,170 pressure

Dispatching from the factory pressure based on the water factory of BRB according to setting up, the relational model method steps of dispatch from the factory flow and pressure monitoring point 55 pressure, sets up water factory respectively and dispatches from the factory pressure, the relational model of dispatch from the factory flow and pressure monitoring point 90 and 170 pressure. Then 3 model combinations are become 1 model.

The principle of the just the present invention described in above-described embodiment and specification sheets, protection scope of the present invention is not restricted to the described embodiments, and also has various changes and modifications not departing from the present invention under spirit and scope of the invention prerequisite. Such as: those skilled in the art can adopt EPANET to build water supply network microvisual model, produce the data for training rule base by this modeling, and for system modeling; And for example: different learning algorithms can be adopted to train rule base, can on-line study also can off-line learning etc. These changes and improvements all fall in the scope of protection of present invention.

Claims (2)

1. the water supply network modeling method based on BRB system, it is characterised in that the method comprises the following steps:

The historical data of step 1. collection tube network operation, specifically:

The historical data of pipe network operation is obtained from the SCADA system of water supply network and Database Systems, described historical data comprises water factory and dispatches from the factory in pressure, water factory's service discharge, pipe network pressurized pump station flow in pressurized pump station pressure, pipe network, the flow of the pressure of the opening degree of controllable valve, pressure monitoring point, flow monitoring point, water reservoir water level and user's water consumption on pipeline;

Step 2. determines input variable and the output variable of water supply network model, specifically:

(2-1) from the historical data of the actual pipe network operation obtained, choose water supply network mode input output variable, input variable comprises: water factory dispatches from the factory in pressure, water factory's service discharge, pipe network pressurized pump station flow in pressurized pump station pressure, pipe network, the opening degree of controllable valve on pipeline; Output variable comprises: the pressure of pressure monitoring point, the flow of flow monitoring point and water reservoir water level;

(2-2) according to the input variable chosen and output variable, the historical data of pipe network operation is screened, obtain only containing the historical data of input variable and output variable, as sampled data; Meanwhile, sampled data being divided into two portions, front portion is as training dataset, and rear portion is as check data collection;

Step 3. sets up the water supply network model based on BRB, specifically:

Model based on BRB system is MISO model, and water supply network is MIMO model; Therefore, based on the water supply network MIMO model of BRB it is the synthesis of multiple water supply network MISO model based on BRB; Establishment step based on the water supply network MISO model of BRB is as follows:

(3-1) determine rule base inputs vector sum output vector;

The vector that the input variable that in rule base, input vector is in step 2 to select is formed, in rule base, output vector is a certain of the output variable selected in step 2; If input vector U=(U_i, i=1 ..., T), wherein T is the component number of input vector, i.e. the number of input variable; If output variable is O (U), it is the function of input vector U;

(3-2) initial rules storehouse is set up;

In BRB system, the rule in rule base is:

R_k: $IF\left(U_1{\mathrm{isA}}_1^k\right)\mathrm{\Λ}\left(U_2{\mathrm{isA}}_2^k\right)\mathrm{\Λ}...\mathrm{\Λ}\left(U_T{\mathrm{isA}}_T^k\right);$

$THEN\{(D_1,{\mathrm{\β}}_{1k}),(D_2,{\mathrm{\β}}_{2k}),...,(D_N,{\mathrm{\β}}_{Nk})\},(\underset{n=1}{\overset{N}{\Σ}}{\mathrm{\β}}_{nk}\≤1),k=1,...L;$

The weight of rule: ��_k(k=1 ..., L), input variable weight: ��_1,k,��_2,k,...,��_T,k;

Wherein, L is the sum of rule,For the reference value of the i-th input variable in kth rule, D=(D₁,D₂,...,D_N) it is reasoning output vector, ��_nk(n=1 ..., N) it is reasoning output D_nDegree of belief; IfThen kth rule is claimed to be complete; IfThen kth rule is almost completely neglected; ��_k(k=1 ..., L) it is the regular relative weighting in rule base of kth, ��_i,k(i=1 ..., T, k=1 ..., L) it is the i-th input variable weight in kth rule;

In rule base, varying parameter is P=(��_nk,��_k,��_i,k; N=1 ..., N; K=1 ..., L; I=1 ..., T); For setting up initialize rule base, random initial ��_nk, and ��_k, ��_i,kIt is initially set 1;

(3-3) rule base is trained;

Initial rules storehouse, by the mapping relation of the input data set of learning training data centralization and output data set, adjusts varying parameter P=(�� automatically_nk,��_k,��_i,k; N=1 ..., N; K=1 ..., L; I=1 ..., T), final acquisition describes input vector U=(U_i, i=1 ..., T) and the rule base of output variable O (U) relation;

Reasoning process in rule base is as follows:

Step1: vector U=(U will be inputted_i, i=1 ..., T) convert to and trust distribution:

S(U_i)={ (A_i,j,��_i,j), j=1 ..., J_i;

Wherein J_iFor the number of reference value, ��_i,jFor input U_iWith reference value A_i,jSimilarity; ��_i,jIt is calculated as follows:

If A_i,j��U_i��A_i,j+1, then��_i,j+1=1-��_i,jAnd for j '=1 ..., J_i, j ' �� j, j+1, has ��_i,j��=0;

Step2: calculate the weight w that kth rule is activated_k:

$w_k=\frac{{\mathrm{\θ}}_k\×\underset{i=1}{\overset{T}{\Π}}{\left({\mathrm{\α}}_{i,j}^k\right)}^{{\stackrel{\‾}{\mathrm{\δ}}}_{i,k}}}{\underset{k=1}{\overset{L}{\Σ}}\[{\mathrm{\θ}}_k\×\underset{i=1}{\overset{T}{\Π}}{\left({\mathrm{\α}}_{i,j}^k\right)}^{{\stackrel{\‾}{\mathrm{\δ}}}_{i,k}}\]},{\stackrel{\‾}{\mathrm{\δ}}}_{i,k}=\frac{{\mathrm{\δ}}_{i,k}}{\underset{i=1,...,T}{\max }\left\{{\mathrm{\δ}}_{i,k}\right\}};$

Step3: calculate output variable O (U):

First calculate trust distribution O (the U)={ (D of output variable_n,��_n(U)), n=1 ..., N}, wherein

$\left\{D_n\right\}:{\mathrm{\β}}_n\left(U\right)=\mathrm{\μ}\×\[\underset{k=1}{\overset{L}{\Π}}(w_k{\mathrm{\β}}_{n,k}+1-w_k\underset{n=1}{\overset{N}{\Σ}}{\mathrm{\β}}_{n,k})-\underset{k=1}{\overset{L}{\Π}}(1-w_k\underset{n=1}{\overset{N}{\Σ}}{\mathrm{\β}}_{n,k})\]$

$\left\{D\right\}:{\mathrm{\β}}_D\left(U\right)=\mathrm{\μ}\×\[\underset{k=1}{\overset{L}{\Π}}(1-w_k\underset{n=1}{\overset{N}{\Σ}}{\mathrm{\β}}_{n,k})-\underset{k=1}{\overset{L}{\Π}}(1-w_k)\]$

$\mathrm{\μ}={\[\underset{n=1}{\overset{N}{\Σ}}\underset{k=1}{\overset{L}{\Π}}(w_k{\mathrm{\β}}_{nk}+1-w_k\underset{n=1}{\overset{N}{\Σ}}{\mathrm{\β}}_{nk})-(N-1)\underset{k=1}{\overset{L}{\Π}}(1-w_k\underset{n=1}{\overset{N}{\Σ}}{\mathrm{\β}}_{nk})-\underset{k=1}{\overset{L}{\Π}}(1-w_k)\]}^{-1};$

��_D(U) represent the degree of belief of unknown the reasoning results D, and meet

If it is complete for trusting rule, namely have��_D(U)=0, then what final output was L rule is comprehensive, and table is O (U)={ (D_n,��_n(U)), n=1 ..., N}, numerical value exports and is $O\left(U\right)=\underset{n=1}{\overset{N}{\Σ}}{D}_n{\mathrm{\β}}_n\left(U\right);$

If it is imperfect to trust rule, namely there is ��_D(U) > 0, then final numerical value exports has bound O (U) �� [O_min(U),O_max], (U) wherein

$O_{min}\left(U\right)=\underset{n=1}{\overset{N-1}{\Σ}}{D}_n{\mathrm{\β}}_n\left(U\right)+D_N\[{\mathrm{\β}}_N\left(U\right)+{\mathrm{\β}}_D\left(U\right)\]$

$O_{max}\left(U\right)=D_1\[{\mathrm{\β}}_1\left(U\right)+{\mathrm{\β}}_D\left(U\right)\]+\underset{n=2}{\overset{N}{\Σ}}{D}_n{\mathrm{\β}}_n\left(U\right);$

So far, a given input U=(U_i, i=1 ..., T) just there is one to export O (U) to rule base; For trust rule be complete picture, the training of rule base is exactly solve following optimization problem, and wherein H is learning sample number,For the actual output of learning sample;

$\left\{\begin{array}{c}0\≤{\mathrm{\β}}_{nk},{\mathrm{\θ}}_k,{\mathrm{\δ}}_{i,k}\≤1\\ \underset{n=1}{\overset{N}{\Σ}}{\mathrm{\β}}_{nk}=1\end{array}\right.;$

For the regular imperfect situation of trust, the training of rule base is exactly solve following optimization problem:

(3-4) inspection rule storehouse;

Check data is utilized to be checked by the rule base that (3-1) (3-2) (3-3) sets up, with the precision of evaluation model; The standard of precision is usedWeigh; If �� (P) does not meet modeling accuracy requirement, repeat (3-1) (3-2) (3-3) modeling again;

So far, water supply network MISO model based on BRB is set up;

Step 4. sets up the water supply network MIMO model based on BRB

Based on the synthesis that the water supply network MIMO model of BRB is multiple water supply network MISO model based on BRB; So, according to the number of output variable, for each output variable repeats the modeling process of MISO model.

2. a kind of water supply network modeling method based on BRB system according to claim 1, it is characterised in that: described water supply network mode input also comprises user's water consumption and system input noise.