CN103530818A - Water supply pipe network modeling method based on BRB (belief-rule-base) system - Google Patents

Abstract

The invention discloses a water supply pipe network modeling method based on a BRB (belief-rule-base) system. According to the method, firstly, historical data of pipe network operation is collected, secondly, the input variable and the output variable of a water supply pipe network model are determined, then, a water supply pipe network model based on BRB is built, and finally, a water supply pipe network MIMO (multiple input multiple output) model based on BRB is built. The water supply pipe network modeling method has the advantages that the working condition of the water supply pipe network system can be perfectly described, the water supply pipe network model can compare with a neural network model of a water supply pipe network when being used for the real-time optimal scheduling of the water supply pipe network, and in addition, the unknown features of the water supply pipe network can be further excavated through analyzing a rule base obtained through the historical operation data training of the pipe network.

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 based on BRB(Belief-Rule-Base) the water supply network modeling method of system.

Background technology

Public supply mains system is a topological structure complexity, in large scale, water variation randomness is strong, quantity of parameters is uncertain, multiobject network structure is controlled in operation.Setting up the condition model matching with pipe network system feature is the condition precedent that realizes water supply network optimization operation, and foundation can be processed pipeline parameter uncertainty simultaneously, water supply network model quantitative and qualitative information is the prerequisite of assessment and analysis network security and reliability.Chinese scholars has been carried out large quantity research aspect water supply network modeling, and the most representative pipe network model is realistic model and neural network model.These models adopt definite method to describe the behavior of pipe network system, helpless for uncertain input information.So, be badly in need of setting up and can describe water supply pipe net system operating mode, can process again the water supply network model of the uncertain information of pipe network system.

Modeling based on BRB system, with Dempster-Shafer evidence theory, decision theory and Fuzzy Set Theory are basis, can process quantitative information and qualitative information, certainty information and uncertain information simultaneously.Water supply network model based on BRB system, can well describe water supply pipe net system operating mode, can be used for Real time optimal dispatch and the PREDICTIVE CONTROL of water supply network.And this model allows the input of uncertain information, as uncertain parameter, external disturbance etc., and model is output as the interval of quantification, can be used for the safety and reliability of assessment and analysis water supply pipe net system.

Summary of the invention

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

The inventive method is specific as follows:

1. the historical data of collection tube network operation

From the SCADA system of water supply network and Database Systems, obtain the historical data of pipe network operation.The historical data of water supply network operation generally comprises: water factory's pressure that dispatches from the factory, Water Works amount, 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, cistern water level, user's water consumption etc.

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

(1) historical data of the pipe network operation obtaining from reality, chooses water supply network mode input output variable.

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

Output variable generally comprises: the pressure of pressure monitoring point, the flow of flow detection point, cistern water level etc.

(2) according to the input/output variable of choosing, the historical data of pipe network operation is screened, obtain only containing the historical data of input/output variable, as sample data.Meanwhile, sample data is divided into two parts, 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

Based on BRB(Belief-Rule-Base) model of system is MISO model, water supply network is MIMO model.Therefore, the water supply network MIMO model based on BRB is the synthetic of a plurality of water supply network MISO models based on BRB.The establishment step of the water supply network MISO model based on BRB is as follows:

(1) determine input vector and output vector in rule base

In rule base, input vector is the vector of the input variable formation of selecting in (2), and in rule base, output vector is the some of (2) middle output variable of selecting.And establish input vector U=(U _i, i=1 ..., T), output variable is O.

(2) set up initial rules storehouse

Rule in BRB system in rule base is:

$R_k:\mathrm{IF}\left(\begin{array}{ccc}{\mathrm{<figure-callout\; id="1"\; label="U"\; filenames="HDA0000394859710000012.png"\; state="\{\{state\}\}">U</figure-callout>}}_1& \mathrm{is}& A_1^k\end{array}\right)\mathrm{\&Lambda;}\left(\begin{array}{ccc}{U}_2& \mathrm{is}& A_2^k\end{array}\right)\mathrm{\&Lambda;}...\mathrm{\&Lambda;}\left(\begin{array}{ccc}{U}_{T_k}& \mathrm{is}& A_{T_k}^k\end{array}\right)$

$\mathrm{THEN}\{({\mathrm{<figure-callout\; id="1"\; label="D"\; filenames="HDA0000394859710000012.png"\; state="\{\{state\}\}">D</figure-callout>}}_1,{\mathrm{\&beta;}}_{1k}),(D_2,{\mathrm{\&beta;}}_{2k}),\&CenterDot;\&CenterDot;\&CenterDot;,(D_N,{\mathrm{\&beta;}}_{\mathrm{Nk}})\},(\underset{i=1}{\overset{N}{\mathrm{\&Sigma;}}}{\mathrm{\&beta;}}_{\mathrm{ik}}\&le;1),k=1,...L$

The weight of rule: θ _k(k=1 ..., L), input variable weight: δ ₁, δ ₂...,

Wherein, L is regular sum,

for input vector,

be the reference value (reference value is some exemplary value that training data is concentrated input variable, while being 3 as reference value, optional maximal value, mean value, minimum value) of i input variable in k rule, D=(D ₁, D ₂..., D _n) be reasoning output vector, β _ik(i=1 ..., T _k) be the degree of belief of reasoning output Di.If

claim that k rule is complete, if

k rule is ignored completely.θ _k(k=1 ..., L) be the relative weighting of k rule in rule base, δ ₁, δ ₂...,

it is the relative weighting of each input variable in k rule.

In rule base, variable element is P=(β _ik, θ _k, δ _j; I=1 ..., N; K=1 ..., L; J=1 ..., T).For setting up initialization rule base, random initial β _ik, and θ _k, δ _jbe initially set 1.

(3) training rules storehouse

Variable element P=(β, by the input data set of learning training data centralization and the mapping relations of output data set, is adjusted automatically in initial rules storehouse _ik, θ _k, δ _j; I=1 ..., N; K=1 ..., L; J=1 ..., T), final acquisition described input vector U=(U _i, i=1 ..., T) and the rule base of output variable O relation.

Reasoning process in rule base is as follows:

Step1: by input vector U=(U _i, i=1 ..., T) convert to and trust distribution:

S(U _i)＝{(A _i,j,α _i,j),j＝1,...,J _i}

J wherein _ifor the number of reference value, α _i,jfor input U _iwith reference value A _i,jsimilarity.α _i,jbe calculated as follows:

If A _i,j≤ U _i≤ A _{i, j+1},

α _{i, j+1}=1-α _i,j, and for j '=1 ..., J _i, j ' ≠ j, j+1, has α _{i, j '}=0

Step2: calculate the weight w that k rule is activated _k:

$w_k=\frac{{\mathrm{\&theta;}}_k\&times;\underset{i=1}{\overset{T_k}{\mathrm{\&Pi;}}}{\left({\mathrm{\&alpha;}}_{i,j}^k\right)}^{\stackrel{\&OverBar;}{{\mathrm{\&delta;}}_i}}}{\underset{j=1}{\overset{L}{\mathrm{\&Sigma;}}}[{\mathrm{\&theta;}}_j\&times;\underset{l=1}{\overset{T_k}{\mathrm{\&Pi;}}}{\left({\mathrm{\&alpha;}}_{i,j}^l\right)}^{\stackrel{\&OverBar;}{{\mathrm{\&delta;}}_l}}]},\stackrel{\&OverBar;}{{\mathrm{\&delta;}}_i}=\frac{{\mathrm{\&delta;}}_i}{\underset{i=1,...,T_k}{\max }\left\{{\mathrm{\&delta;}}_i\right\}}$

Step3: calculate output variable O:

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

${\left\{D_n\right\}:\mathrm{\&beta;}}_n\left(U\right)=\mathrm{\&mu;}\&times;[\underset{k=1}{\overset{K}{\mathrm{\&Pi;}}}(w_k\left(U\right){\mathrm{\&beta;}}_{n,k}+1-w_k\left(U\right)\underset{i=1}{\overset{N}{\mathrm{\&Sigma;}}}{\mathrm{\&beta;}}_{i,k})-\underset{k=1}{\overset{K}{\mathrm{\&Pi;}}}(1-w_k\left(U\right)\underset{i=1}{\overset{N}{\mathrm{\&Sigma;}}}{\mathrm{\&beta;}}_{i,k})]$

$\left\{D\right\}:{\mathrm{\&beta;}}_D\left(U\right)=\mathrm{\&mu;}\&times;[\underset{k=1}{\overset{K}{\mathrm{\&Pi;}}}(1-w_k\left(U\right)\underset{i=1}{\overset{N}{\mathrm{\&Sigma;}}}{\mathrm{\&beta;}}_{i,k})-\underset{k=1}{\overset{K}{\mathrm{\&Pi;}}}(1-w_k\left(U\right))]$

$\mathrm{\&mu;}=\underset{j=1}{\overset{N}{\mathrm{\&Sigma;}}}\underset{k=1}{\overset{L}{\mathrm{\&Pi;}}}(w_k{\mathrm{\&beta;}}_{\mathrm{jk}}+1-w_k\underset{j=1}{\overset{N}{\mathrm{\&Sigma;}}}{\mathrm{\&beta;}}_{\mathrm{jk}})-(N-1)\underset{k=1}{\overset{L}{\mathrm{\&Pi;}}}(1-w_k\underset{j=1}{\overset{N}{\mathrm{\&Sigma;}}}{\mathrm{\&beta;}}_{\mathrm{jk}})-\underset{k=1}{\overset{K}{\mathrm{\&Pi;}}}(1-w_k\left(U\right))$

β _drepresent unknown the reasoning results D _ndegree of belief, and meet

If it is complete trusting rule, have

β _d(U)=0, is finally output as the comprehensive of K rule, shows as O (U)={ (D _n, β _n(U)), n=1 ..., N}, numerical value is output as $O\left(U\right)=\underset{n=1}{\overset{N}{\mathrm{\&Sigma;}}}{D}_n{\mathrm{\&beta;}}_n\left(U\right).$

If it is imperfect to trust rule, there is β _d(U) > 0, and final numerical value output has bound O (U) ∈ [O _min(U), O _max(U)], wherein

$O_{\min }\left(U\right)=\underset{n=1}{\overset{N-1}{\mathrm{\&Sigma;}}}u\left(D_n\right){\mathrm{\&beta;}}_n\left(U\right)+u\left(D_N\right)({\mathrm{\&beta;}}_N\left(U\right)+{\mathrm{\&beta;}}_D\left(U\right))$

$O_{\max }\left(U\right)=u\left(D_1\right)({\mathrm{\&beta;}}_1\left(U\right)+{\mathrm{\&beta;}}_D\left(U\right))+\underset{n=2}{\overset{N}{\mathrm{\&Sigma;}}}u\left(D_n\right){\mathrm{\&beta;}}_n\left(U\right)$

So far, a given input U=(U _i, i=1 ..., T) to rule base, just there is an output O.For trusting rule, be complete situation, the training of rule base is exactly to solve following optimization problem, and wherein H is training sample number,

for the actual output of training sample

$\left\{\begin{array}{c}0\&le;{\mathrm{\&beta;}}_{\mathrm{ik}},{\mathrm{\&theta;}}_k,{\mathrm{\&delta;}}_j\&le;1\\ \underset{i=1}{\overset{N}{\mathrm{\&Sigma;}}}{\mathrm{\&beta;}}_{\mathrm{ik}}=1\end{array}\right.$

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

(4) inspection rule storehouse

The rule base that utilizes check data to set up (1) (2) (3) is tested, with the precision of evaluation model.The standard of precision is used

weigh.If ε (P) does not meet modeling accuracy requirement, repeat (1) (2) (3) modeling again.

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

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

Water supply network MIMO model based on BRB is the synthetic of a plurality of water supply network MISO models based on BRB.So, according to the number of output variable, be the modeling process of each output variable repetition MISO model.

Beneficial effect of the present invention: the water supply network model based on BRB system, water supply pipe net system operating mode can well be described, during for the Real time optimal dispatch of water supply network, can compare favourably with the neural network model of water supply network.And, by analyzing the rule base being obtained by the training of pipe network history data, can further excavate the unknown characteristics of water supply network, this is the feature that neural network model does not possess.In addition, the water supply network model based on BRB system allows the input of uncertain information, as uncertain parameter, and external disturbance etc., now model is output as the interval of quantification.The safety and reliability that this is conducive to assessment and analyzes water supply pipe net system.As when the random fluctuation of user's water requirement, model can dope the pressure range of monitoring point, and now staff or intelligent optimization dispatching system can be taked rational Operation Measures accordingly.

Accompanying drawing explanation

Fig. 1 rule base training process schematic diagram;

Fig. 2 embodiment water supply network topology schematic diagram.

Embodiment

For making technological means and creation characteristic that the present invention realizes be easy to understand, 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 as Fig. 2, sets up water factory based on the BRB pressure that dispatches from the factory, 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

From the SCADA system of water supply network and Database Systems, obtain the historical data of pipe network operation.The historical data of water supply network operation comprises: water factory's pressure that dispatches from the factory, Water Works amount, pressure monitoring point 55,90,170 pressure, monitoring point 55,90,170 user's water consumptions.Meanwhile, historical data is divided into two parts, 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 the water supply network MIMO model based on BRB is the synthetic of a plurality of water supply network MISO models based on BRB.So,, first set up water factory's pressure that dispatches from the factory, the relational model of dispatch from the factory flow and monitoring point 55 pressure here.Meanwhile, using monitoring point 55 user's water consumptions as measuring disturbance input variable.So input and output are as follows respectively:

Input variable: U=(U _i, i=1,2,3), U wherein ₁, U ₂, U ₃be respectively water factory's pressure that dispatches from the factory, dispatch from the factory flow and monitoring point 55 user's water consumptions.Output variable: P ₅₅, be monitoring point 55 pressure.

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

(1) determine input vector and output variable in rule base

In rule base, input vector is U=(U _i, i=1,2,3), output variable is P ₅₅.The input and output of the present embodiment all adopt 3 reference values, the minimum value of getting respectively each variable, and mean value and maximal value, these reference values are calculated by the historical data of pipe network operation.Therefore have

Pressure U dispatches from the factory ₁: $A_1^k=\{\mathrm{sp},\mathrm{mp},\mathrm{lp}\};$

Flow U dispatches from the factory ₂: $A_2^k=\{\mathrm{sf},\mathrm{mf},\mathrm{lf}\};$

Monitoring point 55 user's water consumption U ₃:

Monitoring point 55 pressure P ₅₅: D={sp ₅₅, mp ₅₅, lp ₅₅;

And meet

a _i={ A _i,j; J=1 ..., 3}, D={D ₁, D ₂, D ₃.Wherein, sp, mp, lp is respectively the pressure minimum value of dispatching from the factory, mean value and maximal value, sf, mf, lf is respectively the flow minimum value of dispatching from the factory, mean value and maximal value, sd, md, ld is respectively monitoring point 55 user's water consumption minimum value, mean value and maximal value, sp ₅₅, mp ₅₅, lp ₅₅be respectively monitoring point 55 pressure minimum value, mean value and maximal values.

(2) set up initial rules storehouse

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

Wherein k rule format is as follows:

$R_k:\mathrm{IF}{\mathrm{<figure-callout\; id="1"\; label="U"\; filenames="HDA0000394859710000012.png"\; state="\{\{state\}\}">U</figure-callout>}}_1\mathrm{is}{A}_1^k{\mathrm{ANDU}}_2\mathrm{is}{A}_2^k{U}_3\mathrm{is}{A}_3^k$

$\mathrm{THEN}{\mathrm{<figure-callout\; id="55"\; label="P"\; filenames="HDA0000394859710000012.png"\; state="\{\{state\}\}">P</figure-callout>}}_{55}\mathrm{is}\{({\mathrm{<figure-callout\; id="55"\; label="sp"\; filenames="HDA0000394859710000012.png"\; state="\{\{state\}\}">sp</figure-callout>}}_{55},{\mathrm{\&beta;}}_{1k}),({\mathrm{<figure-callout\; id="55"\; label="mp"\; filenames="HDA0000394859710000012.png"\; state="\{\{state\}\}">mp</figure-callout>}}_{55},{\mathrm{\&beta;}}_{2k}),({\mathrm{<figure-callout\; id="55"\; label="lp"\; filenames="HDA0000394859710000012.png"\; state="\{\{state\}\}">lp</figure-callout>}}_{55},{\mathrm{\&beta;}}_{3k})\},(\underset{i=1}{\overset{N}{\mathrm{\&Sigma;}}}{\mathrm{\&beta;}}_{\mathrm{ik}}\&le;1),k\&Element;\{1,...,27\}$

In rule base, variable element is P=(β _ik, θ _k, δ _j; I=1 ..., N; K=1 ..., L; J=1 ..., T), N=3 wherein, L=27, T=3.For setting up initialization rule base, random initial β _ik, and θ _k, δ _jbe initially set 1.

(3) training rules storehouse

Variable element P=(β, by input data set and the output data set mapping relations of learning training data centralization, is adjusted in initial rules storehouse _ik, θ _k, δ _j; I=1,2,3; K=1 ..., 27; J=1,2,3), final acquisition described input vector U=(U _i, i=1,2,3) and output variable p ₅₅the rule base of relation, referring to 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}, by input vector U={U _i, i=1,2,3}, the trust that converts following input vector to distributes

S(U _i)＝{(A _i,j,α _i,j),j＝1,2,3}

α wherein _i,jfor input U _iwith reference value A _i,jsimilarity.α _i,jbe calculated as follows:

Work as A _i,j≤ U _i≤ A _{i, j+1},

α _{i, j+1}=1-α _i,j

Work as j '=1 ..., J _i, j ' ≠ j, j+1, has α _{i, j '}=0

Step2: calculate the weight w that k rule is activated _k:

$w_k=\frac{{\mathrm{\&theta;}}_k\&times;\underset{i=1}{\overset{T_k}{\mathrm{\&Pi;}}}{\left({\mathrm{\&alpha;}}_{i,j}^k\right)}^{\stackrel{\&OverBar;}{{\mathrm{\&delta;}}_i}}}{\underset{j=1}{\overset{L}{\mathrm{\&Sigma;}}}[{\mathrm{\&theta;}}_j\&times;\underset{l=1}{\overset{T_k}{\mathrm{\&Pi;}}}{\left({\mathrm{\&alpha;}}_{i,j}^l\right)}^{\stackrel{\&OverBar;}{{\mathrm{\&delta;}}_l}}]},\stackrel{\&OverBar;}{{\mathrm{\&delta;}}_i}=\frac{{\mathrm{\&delta;}}_i}{\underset{i=1,...,T_k}{\max }\left\{{\mathrm{\&delta;}}_i\right\}}$

Step3: comprehensive K rule, the trust that reasoning obtains monitoring point 55 pressure distributes:

The trust distribution of the present embodiment employing IDS Multicriteria Assessor(multi-attribute Decision-making Analysis software) calculating output variable.Can obtain:

p ₅₅(U)＝{(D _n,β _n(U)),n＝1,2,3}

Step4: the pressure p that is obtained detection by monitoring point 55 calculation of pressure distribution ₅₅:

p ₅₅＝U ₁β ₁+U ₂β ₂+U ₃β ₃

Step5: adopt MATLAB to solve following optimization problem, wherein H is training sample number,

for 55 pressure of monitoring point in training sample:

$\left\{\begin{array}{c}0\&le;{\mathrm{\&beta;}}_{\mathrm{ik}},{\mathrm{\&theta;}}_k,{\mathrm{\&delta;}}_j\&le;1\\ \underset{i=1}{\overset{N}{\mathrm{\&Sigma;}}}{\mathrm{\&beta;}}_{\mathrm{ik}}=1\end{array}\right.$

P=(β wherein _ik, θ _k, δ _j; I=1,2,3; K=1 ..., 27; J=1,2,3).

Step6: inspection rule storehouse

Utilize check data to test to the rule base of setting up, with the precision of evaluation model.The standard of precision is used

weigh.

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

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

What in above-described embodiment and instructions, describe is principle of the present invention, and 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, by this modeling, produce the data for training rules storehouse, and for system modelling; And for example: can adopt different learning algorithms to come training rules storehouse, 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, is characterized in that the method comprises the following steps:

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

From the SCADA system of water supply network and Database Systems, obtain the historical data of pipe network operation, described historical data comprises water factory's pressurized pump station flow in pressurized pump station pressure in pressure, Water Works amount, pipe network, pipe network that dispatches from the factory, and the opening degree of controllable valve on pipeline is, the flow of the pressure of pressure monitoring point, flow monitoring point, cistern water level and user's water consumption;

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

(2-1) historical data of the pipe network operation obtaining from reality, choose water supply network mode input output variable, input variable comprises: water factory's pressurized pump station flow in pressurized pump station pressure in pressure, Water Works amount, pipe network, pipe network that dispatches from the factory, the opening degree of controllable valve on pipeline; Output variable comprises: the pressure of pressure monitoring point, the flow of flow detection point and cistern water level;

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

Step 3. is set 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, the water supply network MIMO model based on BRB is the synthetic of a plurality of water supply network MISO models based on BRB; The establishment step of the water supply network MISO model based on BRB is as follows:

(3-1) determine input vector and output vector in rule base

In rule base, input vector is in step 2 vector that the input variable selected forms, and in rule base, output vector is the some of the output variable selected in step 2; And establish input vector U=(U _i, i=1 ..., T), output variable is O;

(3-2) set up initial rules storehouse

Rule in BRB system in rule base is:

$R_k:\mathrm{IF}\left(\begin{array}{ccc}{U}_1& \mathrm{is}& A_1^k\end{array}\right)\mathrm{\&Lambda;}\left(\begin{array}{ccc}{U}_2& \mathrm{is}& A_2^k\end{array}\right)\mathrm{\&Lambda;}...\mathrm{\&Lambda;}\left(\begin{array}{ccc}{U}_{T_k}& \mathrm{is}& A_{T_k}^k\end{array}\right)$

$\mathrm{THEN}\{(D_1,{\mathrm{\&beta;}}_{1k}),(D_2,{\mathrm{\&beta;}}_{2k}),\&CenterDot;\&CenterDot;\&CenterDot;,(D_N,{\mathrm{\&beta;}}_{\mathrm{Nk}})\},(\underset{i=1}{\overset{N}{\mathrm{\&Sigma;}}}{\mathrm{\&beta;}}_{\mathrm{ik}}\&le;1),k=1,...L$

The weight of rule: θ _k(k=1 ..., L), input variable weight: δ ₁, δ ₂...,

Wherein, L is regular sum,

for input vector, be the reference value of i input variable in k rule, D=(D ₁, D ₂..., D _n) be reasoning output vector, β _ik(i=1 ..., T _k) be reasoning output D _idegree of belief; If

claim that k rule is complete, if k rule is ignored completely; θ _k(k=1 ..., L) be the relative weighting of k rule in rule base, δ ₁, δ ₂...,

it is the relative weighting of each input variable in k rule;

In rule base, variable element is P=(β _ik, θ _k, δ _j; I=1 ..., N; K=1 ..., L; J=1 ..., T); For setting up initialization rule base, random initial β _ik, and θ _k, δ _jbe initially set 1;

(3-3) training rules storehouse

Variable element P=(β, by the input data set of learning training data centralization and the mapping relations of output data set, is adjusted automatically in initial rules storehouse _ik, θ _k, δ _j; I=1 ..., N; K=1 ..., L; J=1 ..., T), final acquisition described input vector U=(U _i, i=1 ..., T) and the rule base of output variable O relation;

Reasoning process in rule base is as follows:

Step1: by input vector U=(U _i, i=1 ..., T) convert to and trust distribution:

S(U _i)＝{(A _i,j,α _i,j),j＝1,...,J _i}

J wherein _ifor the number of reference value, α _i,jfor input U _iwith reference value A _i,jsimilarity; α _i,jbe calculated as follows:

If A _i,j≤ U _i≤ A _{i, j+1}, α _{i, j+1}=1-α _i,jand for j '=1 ..., J _i, j ' ≠ j, j+1, has α _{i, j '}=0

Step2: calculate the weight w that k rule is activated _k:

$w_k=\frac{{\mathrm{\&theta;}}_k\&times;\underset{i=1}{\overset{T_k}{\mathrm{\&Pi;}}}{\left({\mathrm{\&alpha;}}_{i,j}^k\right)}^{\stackrel{\&OverBar;}{{\mathrm{\&delta;}}_i}}}{\underset{j=1}{\overset{L}{\mathrm{\&Sigma;}}}[{\mathrm{\&theta;}}_j\&times;\underset{l=1}{\overset{T_k}{\mathrm{\&Pi;}}}{\left({\mathrm{\&alpha;}}_{i,j}^l\right)}^{\stackrel{\&OverBar;}{{\mathrm{\&delta;}}_l}}]},\stackrel{\&OverBar;}{{\mathrm{\&delta;}}_i}=\frac{{\mathrm{\&delta;}}_i}{\underset{i=1,...,T_k}{\max }\left\{{\mathrm{\&delta;}}_i\right\}}$

Step3: calculate output variable O:

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

${\left\{D_n\right\}:\mathrm{\&beta;}}_n\left(U\right)=\mathrm{\&mu;}\&times;[\underset{k=1}{\overset{K}{\mathrm{\&Pi;}}}(w_k\left(U\right){\mathrm{\&beta;}}_{n,k}+1-w_k\left(U\right)\underset{i=1}{\overset{N}{\mathrm{\&Sigma;}}}{\mathrm{\&beta;}}_{i,k})-\underset{k=1}{\overset{K}{\mathrm{\&Pi;}}}(1-w_k\left(U\right)\underset{i=1}{\overset{N}{\mathrm{\&Sigma;}}}{\mathrm{\&beta;}}_{i,k})]$

$\left\{D\right\}:{\mathrm{\&beta;}}_D\left(U\right)=\mathrm{\&mu;}\&times;[\underset{k=1}{\overset{K}{\mathrm{\&Pi;}}}(1-w_k\left(U\right)\underset{i=1}{\overset{N}{\mathrm{\&Sigma;}}}{\mathrm{\&beta;}}_{i,k})-\underset{k=1}{\overset{K}{\mathrm{\&Pi;}}}(1-w_k\left(U\right))]$

$\mathrm{\&mu;}=\underset{j=1}{\overset{N}{\mathrm{\&Sigma;}}}\underset{k=1}{\overset{L}{\mathrm{\&Pi;}}}(w_k{\mathrm{\&beta;}}_{\mathrm{jk}}+1-w_k\underset{j=1}{\overset{N}{\mathrm{\&Sigma;}}}{\mathrm{\&beta;}}_{\mathrm{jk}})-(N-1)\underset{k=1}{\overset{L}{\mathrm{\&Pi;}}}(1-w_k\underset{j=1}{\overset{N}{\mathrm{\&Sigma;}}}{\mathrm{\&beta;}}_{\mathrm{jk}})-\underset{k=1}{\overset{K}{\mathrm{\&Pi;}}}(1-w_k\left(U\right))$

β _drepresent unknown the reasoning results D _ndegree of belief, and meet

If it is complete trusting rule, have

β _d(U)=0, is finally output as the comprehensive of K rule, shows as O (U)={ (D _n, β _n(U)), n=1 ..., N}, numerical value is output as $O\left(U\right)=\underset{n=1}{\overset{N}{\mathrm{\&Sigma;}}}{D}_n{\mathrm{\&beta;}}_n\left(U\right);$

If it is imperfect to trust rule, there is β _d(U) > 0, and final numerical value output has bound O (U) ∈ [O _min(U), O _max(U)], wherein

$O_{\min }\left(U\right)=\underset{n=1}{\overset{N-1}{\mathrm{\&Sigma;}}}u\left(D_n\right){\mathrm{\&beta;}}_n\left(U\right)+u\left(D_N\right)({\mathrm{\&beta;}}_N\left(U\right)+{\mathrm{\&beta;}}_D\left(U\right))$

$O_{\max }\left(U\right)=u\left(D_1\right)({\mathrm{\&beta;}}_1\left(U\right)+{\mathrm{\&beta;}}_D\left(U\right))+\underset{n=2}{\overset{N}{\mathrm{\&Sigma;}}}u\left(D_n\right){\mathrm{\&beta;}}_n\left(U\right)$

So far, a given input U=(U _i, i=1 ..., T) to rule base, just there is an output O; For trusting rule, be complete situation, the training of rule base is exactly to solve following optimization problem, and wherein H is training sample number,

for the actual output of training sample;

$\left\{\begin{array}{c}0\&le;{\mathrm{\&beta;}}_{\mathrm{ik}},{\mathrm{\&theta;}}_k,{\mathrm{\&delta;}}_j\&le;1\\ \underset{i=1}{\overset{N}{\mathrm{\&Sigma;}}}{\mathrm{\&beta;}}_{\mathrm{ik}}=1\end{array}\right.$

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

(3-4) inspection rule storehouse

Utilize check data to (3-1) (3-2) rule base that (3-3) sets up test, with the precision of evaluation model; The standard of precision is used

weigh; If ε (P) does not meet modeling accuracy requirement, repeat (3-1) (3-2) (3-3) modeling again;

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

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

Water supply network MIMO model based on BRB is the synthetic of a plurality of water supply network MISO models based on BRB; So, according to the number of output variable, be the modeling process of each output variable repetition MISO model.

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

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