CN103606006A - Sludge volume index (SVI) soft measuring method based on self-organized T-S fuzzy nerve network - Google Patents

Abstract

The invention discloses a sludge volume index (SVI) soft measuring method based on a self-organized T-S fuzzy nerve network and belongs to both the field of control and the field of sewage treatment. The accurate prediction of an SVI is the guarantee for normal operation of a sewage treatment process. The method comprises: first of all, taking the output quantity of a rule layer, i.e., the space activation intensity of the rule layer as a basis for determining whether a fuzzy rule is increased; secondly, on the basis of generating a new fuzzy rule, taking the output quantity of a membership function layer as a basis for determining whether a fuzzy set is increased; and finally obtaining a self-organized T-S fuzzy recursion nerve network by using a gradient decrease algorithm to adjust the weight value parameter of a model and the center value and width of a Gauss function, and establishing an SVI on-line soft measuring model based on an SOTSFEN such that real-time detection of the SVI is realized, and an effective method is provided for preventing sludge expansion.

Description

Sludge volume index flexible measurement method based on self-organization T-S fuzzy neural network

Technical field

The present invention utilizes the fuzzy Recursive Networks of self-organization T-S to set up the soft-sensing model of sludge volume index (SVI) SVI, realizes the real-time estimate to sludge settling index S VI.The Accurate Prediction of sludge volume index SVI is the assurance of the normal operation of sewage disposal process, and the present invention had both belonged to control field, belonged to again sewage treatment area.

Background technology

Wastewater treatment is the important component part of Important Action ，Ye Shi China strategy of sustainable development of Chinese government's water resources comprehensive utilization.At present, each city, the whole nation, county have set up urban wastewater treatment firm substantially, and the national developed countries such as sewage treatment capacity and the U.S. are suitable.But wastewater treatment operation conditions allows of no optimist, wherein sludge bulking problem is seriously restricting the development of wastewater treatment.Once sludge bulking occurs, der Pilz amount reproduction, sludge settling property variation, Separation of Solid and Liquid difficulty, causes effluent quality to exceed standard, and mud overflows loss, even may draw barmy generation, causes sewage disposal system collapse.Therefore the soft measurement research that, the present invention is based on the SVI of the fuzzy recurrent neural network SOTSRFNN of self-organization T-S is with a wide range of applications.

Sludge volume index (SVI) SVI is one of important evaluation index of sludge settling property.At present, for the detection method of SVI, mainly contain two classes: 1. manual detection method, utilize graduated cylinder timing sampling to detect, calculate SVI value, but the method is consuming time and error is large, be difficult to meet the wastewater treatment actual requirement of complexity day by day; 2. automatic detection method, but there is the shortcomings such as equipment manufacturing cost is high, and the life-span is short, poor stability in the method, and be subject to site environment and manually-operated impact, accuracy of detection to can not get ensureing.Soft-measuring technique utilizes the relation between system change and parameter, sets up the model between input and output, by easy survey water quality variable, estimates SVI value.Have small investment, time short, be swift in response, be easy to the advantages such as maintenance and maintenance.Therefore, the flexible measurement method of research SOTSRFNN has important practical significance to solving SVI measurement problem in real time.

The present invention proposes the online soft sensor method of SVI a kind of: first, with the space intensity of activation of rules layer, i.e. the output of rules layer is as the foundation of judging whether fuzzy rule increases; Secondly, generating on the basis of new fuzzy rule, usining subordinate function layer output quantity as the foundation of judging whether fuzzy set increases; Finally, utilize the weighting parameter of gradient descent algorithm adjustment model and the central value of Gaussian function and width, obtain the fuzzy recurrent neural network of a kind of self-organization T-S, and based on SOTSRFNN, set up the online soft sensor model of SVI, realized the real-time detection of SVI, for prevention sludge bulking provides a kind of effective ways.

Summary of the invention

The present invention is directed to the problem of SVI on-line measurement difficulty, analyze the formation reason of sludge bulking, sum up and the closely-related easy survey water quality parameter of SVI, utilize principle component analysis PCA to determine the input quantity of model; And a kind of improved fuzzy recurrent neural network has been proposed, and based on structural self-organizing algorithm, designed SOTSRFNN, set up the online soft sensor model of SVI; Finally, utilize the model of setting up to carry out the soft measurement of SVI, realize the on-line measurement of SVI;

The present invention has adopted following technical scheme and performing step:

1 one kinds of SVI flexible measurement methods, is characterized in that, comprise the following steps:

(1) data pre-service and auxiliary variable are selected;

Sample set data are normalized with zero-mean standardized method, by pivot analysis PCA, carry out the selected of auxiliary variable, finally determine mixed liquor concentration of suspension MLSS, acidity-basicity ph, aeration tank water temperature T, aeration tank ammonia NH ₄input variable as model.

(2) set up the Recurrent Fuzzy Neural Network model of the soft measurement of SVI, input quantity is MLSS, pH, T, NH ₄, the output quantity of model is SVI.Recurrent Fuzzy Neural Network topological structure: input layer is that ground floor, subordinate function layer are that the 3rd layer of the second layer, rules layer, the 4th layer, parameter layer, output layer are layer 5, feedback layer.

Neural network structure: input layer has 4 input nodes, each input layer connects m subordinate function node layer, rules layer has m node, m represents number of fuzzy rules, the number of fuzzy rules generating in network structure training process is determined the value of m, parameter node layer number, feedback layer nodes equate with the nodes of rules layer, and output layer has 1 node.X=[x ₁, x ₂, x ₃, x ₄] represent the input of neural network, y _dthe desired output that represents neural network.If k group sample data is x (k)=[x ₁(k), x ₂(k), x ₃(k), x ₄(k)].During the input of k group sample data:

The output of i node of input layer is expressed as:

$o_i^{\left(1\right)}\left(k\right)=x_i\left(k\right),i=\mathrm{1,2,3,4}---\left(1\right)$

Wherein, the output of i node of expression input layer when input k group sample;

The node of subordinate function layer adds up to: 4m, and the node of each input layer all connects the node of m subordinate function layer, and subordinate function layer is output as:

$o_{\mathrm{ij}}^{\left(2\right)}\left(k\right)=\exp (-\frac{{(o_i^{\left(1\right)}\left(k\right)-c_{\mathrm{ij}}\left(k\right))}^2}{{\left({\mathrm{\σ}}_{\mathrm{ij}}\left(k\right)\right)}^2}),j=\mathrm{1,2}...m---\left(2\right)$

Wherein, subordinate function adopts Gaussian function, c _ijand σ _ijrepresent respectively central value and the width of the Gaussian function of j the node of subordinate function layer that i node of input layer is corresponding, each Gaussian function is a fuzzy set, in the structural adjustment stage to Gaussian function initialize.

the output of j the node that represents the subordinate function layer that i node of input layer is corresponding when inputting k and organize sample;

The nodes of rules layer is m, and j node of the subordinate function layer that each node of input layer is corresponding is all connected to j node of rules layer.In rules layer, introduce feedback link, at feedback layer, add built-in variable.The node that feedback layer node comprises two types: accept node, the output quantity of rules layer and weights are weighted to summation operation, calculate built-in variable; Feedback node, adopts sigmoid function as subordinate function, calculates the output quantity of feedback layer.Each node of rules layer all connects all feedback layers and accepts node.Feedback layer to accept node corresponding one by one with feedback node, nodes equates, feedback node is corresponding one by one with rules layer node, nodes is equal, and changes along with the variation of number of fuzzy rules, equals all the time number of fuzzy rules.J node of rules layer is output as:

$h_q=\underset{j=1}{\overset{m}{\mathrm{\Σ}}}{o}_j^{\left(3\right)}(k-1){\mathrm{\ω}}_{\mathrm{jq}},j=\mathrm{1,2},...,m;q=\mathrm{1,2},...,m---\left(3\right)$

$f_q=\frac{1}{1+\exp \left({-h}_q\right)}---\left(4\right)$

$o_j^{\left(3\right)}\left(k\right)=f_q\underset{i=1}{\overset{4}{\mathrm{\Π}}}{o}_{\mathrm{ij}}^{\left(2\right)}\left(k\right)$

(5)

Wherein, ω _jqbe j node of rules layer and the q of feedback layer the weights that are connected of accepting node, initial assignment is the random number of 0 to 1. represent that j node of rules layer is in the output quantity of k-1 group sample,

h _qrepresent that feedback layer q accepts the built-in variable of node.F _qthe output quantity that represents q feedback node of feedback layer.The output of rules layer

be the intensity of activation of fuzzy rule, wherein representation space intensity of activation, f _qexpression time intensity of activation.

The node of the node of rules layer and parameter layer is one to one, and parameter layer has m node, and the output of this layer is expressed as:

$W_j\left(k\right)=\underset{i=1}{\overset{4}{\mathrm{\Σ}}}{a}_{\mathrm{ij}}{x}_i\left(k\right)---\left(6\right)$

$o_j^{\left(4\right)}\left(k\right)=o_j^{\left(3\right)}\left(k\right)W_j\left(k\right)$

(7)

Wherein, a _ijrepresent linear dimensions, initial value assignment is 0 to 1 random number, a _j=[a _1j, a _2j, a _3j, a _4j].W _j(k) represent the value of the linear dimensions weighted sum of j node of parameter layer when input k group sample,

represent that j node of parameter layer is in the output of k group sample.

Network model is the single outputs of many inputs, and output layer has 1 node, and all parameter node layers are connected to output node.Network output is expressed as:

$y\left(k\right)=\frac{\underset{j=1}{\overset{m}{\mathrm{\Σ}}}{o}_j^{\left(4\right)}\left(k\right)}{\underset{j=1}{\overset{m}{\mathrm{\Σ}}}{o}_j^{\left(3\right)}\left(k\right)}---\left(8\right)$

Wherein, y (k) represents the network output of k sample.

(3) first fuzzy neural network determines network structure by structural self-organizing adjustment.The structural self-organizing adjustment of network: x (k)=[x ₁(k), x ₂(k), x ₃(k), x ₄(k)] represent the current input of model k group sample, since first group of sample data input, to total data, inputted, one group of sample data of every input all adopts following steps to judge whether to increase new fuzzy rule, on the basis that increases fuzzy rule, judges whether to increase new fuzzy set.

1. in network model initial configuration, number of fuzzy rules is 0, the first group of data input, and number of fuzzy rules becomes 1, and increases new fuzzy set.The initialization of fuzzy set, the initial table of Gaussian function central value and width value is shown:

c(1)=x(1)=[x ₁(1),x ₂(1),x ₃(1),x ₄(1),] (9)

σ (1)=[σ ₁₁, σ ₂₁, σ ₃₁, σ ₄₁]=[0.5,0.5,0.5,0.5] (10) wherein c (1) represent the central value of first group of fuzzy set generating, the i.e. central value of subordinate function.σ (1) represents the width value of first fuzzy set of generation, the i.e. width value of subordinate function.

2. input data and input successively, one group of data of every input, all judging whether increases new fuzzy rule, and judgment formula is expressed as:

Wherein

the space intensity of activation that represents j node of rules layer.J represents to work as

the value of j while getting maximal value.N represents present Fuzzy rule number.

for predefined threshold value, value is 0.24.

If meet formula (13), increase a new fuzzy rule, 3. N'=N+1, carry out.

If do not meet formula (13), repeat 2., input next group data;

3. increasing on the basis of a new fuzzy rule, judging whether increases new fuzzy set, and judgment formula is expressed as:

$I=\mathrm{<figure-callout\; id="1"\; label="arg\; max"\; filenames="HDA0000412124180000012.png,HDA0000412124180000022.png"\; state="\{\{state\}\}">arg</figure-callout>}\underset{}{\max }\underset{1<=j<=h}{}\left(o_{\mathrm{ij}}^{\left(2\right)}\left(k\right)\right)---\left(14\right)$

$o_{\mathrm{iI}}^{\left(2\right)}\left(k\right)\text{>}{I}_{\mathrm{th}}$

(15)

Wherein I represents to work as

the value of j while getting maximal value, h represents the fuzzy set number of "current" model, h=N.I _thfor predefined threshold value, value is 0.92.

If meet formula (15), increase a new fuzzy set, h'=h+1, h'=N'.To i.e. newly-increased Gaussian function central value and the width value initialize to subordinate function layer of newly-increased fuzzy set initialize.Initial table is shown:

c _N+1=x(k) (16)

$c^{+}=\mathrm{<figure-callout\; id="1"\; label="arg\; min"\; filenames="HDA0000412124180000012.png,HDA0000412124180000022.png"\; state="\{\{state\}\}">arg</figure-callout>}\underset{}{\min }\underset{1<=p<=N}{}\left|\right|x\left(k\right)-c_p\left|\right|---\left(17\right)$

${\mathrm{\&sigma;}}_{i,N+1}=r|x_i\left(k\right)-c_i^{+}|,i=\mathrm{1,2,3,4}---\left(18\right)$

Wherein, N represents the existing number of fuzzy rules of "current" model, p=1, and 2 ..., N, c _n+1the initial value that represents the central value of newly-increased subordinate function, r represents overlap coefficient, value is 0.6.C _pbe expressed as the central value of p Gaussian function in "current" model.C ⁺represent as x (k) and c _pspace length is hour c _pvalue.σ _{i, N+1}the width initial value that represents newly-increased subordinate function, input quantity x (k) and c ⁺the absolute value of difference and the product of overlap coefficient.Increase new fuzzy set, at subordinate function layer corresponding to each input layer, increase a new node, rules layer, feedback layer, parameter layer respectively increase corresponding node accordingly.

If do not met (15), do not increase new fuzzy set h'=h, and N''=N'-1, the fuzzy rule that is about to newly increase is deleted.

4. continue to adjust the structure of neural network, input data are inputted successively, repeat 2. 3., and after all input data have been inputted, neural network structure adjustment has been trained.

(4) determined the structure of network model, then network parameter is just adjusted, by the data after proofreading and correct, carry out neural network training, totally 150 groups of sample datas wherein, 90 groups of training sample data, 60 groups of test sample book data, train epochs is 1000 steps, in the training process of each step, 90 groups of training sample data are all inputted, every group of training sample data input all adopts gradient descent algorithm to adjust network parameter, the parameter of wherein adjusting comprises: the linear dimensions a of parameter layer, rules layer is to the connection weights ω of feedback layer, the central value c of subordinate function layer Gaussian function and width value σ.

The objective function of definition training is that systematic error is defined as:

$E\left(k\right)=\frac{1}{2}{(y\left(k\right)-y_d\left(k\right))}^2---\left(19\right)$

The actual output quantity that wherein y (k) is network, y _d(k) be the desired output amount of network, E (k) represents systematic error.

Gradient descent algorithm: adopt objective function to ask partial derivative to the output quantity of every one deck, calculate the error propagation item of every layer of output.By function of functions, ask partial derivative, the partial derivative of calculating target function to parameter value, partial derivative is the adjustment amount of each parameter.

The error propagation item δ of parameter layer ⁽⁴⁾, the partial derivative that objective function is exported parameter layer:

${\mathrm{\&delta;}}_j^{\left(4\right)}\left(k\right)=-\frac{\&PartialD;E\left(k\right)}{\&PartialD;y\left(k\right)}\frac{\&PartialD;y\left(k\right)}{\&PartialD;o_j^{\left(4\right)}\left(k\right)}---\left(20\right)$

To linear dimensions a _jadjustment amount be:

$\frac{\&PartialD;E\left(k\right)}{{\&PartialD;a}_j\left(k\right)}=\frac{\&PartialD;E\left(k\right)}{\&PartialD;o_j^{\left(4\right)}\left(k\right)}\frac{{\&PartialD;o}_j^{\left(4\right)}\left(k\right)}{\&PartialD;a_j\left(k\right)}=-{\mathrm{\&delta;}}_j^{\left(4\right)}\left(k\right)\frac{o_j^{\left(3\right)}\left(k\right)}{\underset{j=1}{\overset{m}{\mathrm{\&Sigma;}}}{o}_j^{\left(3\right)}\left(k\right)}---\left(21\right)$

$a_j(k+1){=a}_j\left(k\right)-\mathrm{\&eta;}\frac{\&PartialD;E\left(k\right)}{{\&PartialD;a}_j\left(k\right)}---\left(22\right)$

Rules layer error propagation item

as follows:

${\mathrm{\&delta;}}_j^{\left(3\right)}\left(k\right)=-\frac{\&PartialD;E\left(k\right)}{{\&PartialD;o}_j^{\left(3\right)}\left(k\right)}={\mathrm{\&delta;}}^{\left(4\right)}\left(k\right)\frac{{\&PartialD;o}^{\left(4\right)}\left(k\right)}{{\&PartialD;o}_j^{\left(3\right)}\left(k\right)}---\left(23\right)$

Recurrence layer connects weights ω to rules layer _jqregulation rule as follows:

$\frac{\&PartialD;E\left(k\right)}{{\&PartialD;\mathrm{\&omega;}}_{\mathrm{jq}}\left(k\right)}=\frac{\&PartialD;E\left(k\right)}{{\&PartialD;o}_j^{\left(3\right)}\left(k\right)}\frac{{\&PartialD;o}_j^{\left(3\right)}\left(k\right)}{{\&PartialD;\mathrm{\&omega;}}_{\mathrm{jq}}\left(k\right)}=-{\mathrm{\&delta;}}_j^{\left(3\right)}\left(k\right)\frac{{\&PartialD;o}_j^{\left(3\right)}\left(k\right)}{{\&PartialD;\mathrm{\&omega;}}_{\mathrm{jq}}\left(k\right)}---\left(24\right)$

${\mathrm{\&omega;}}_{\mathrm{jq}}(k+1)={\mathrm{\&omega;}}_{\mathrm{jq}}\left(k\right)-\mathrm{\&eta;}\frac{\&PartialD;E}{{\&PartialD;\mathrm{\&omega;}}_{\mathrm{jq}}}\left(k\right)---\left(25\right)$

The error propagation item of subordinate function layer

as follows:

${\mathrm{\&delta;}}_{\mathrm{ij}}^{\left(2\right)}\left(k\right)=-\frac{\&PartialD;E\left(k\right)}{{\&PartialD;o}_{\mathrm{ij}}^{\left(2\right)}\left(k\right)}={\mathrm{\&delta;}}_j^{\left(3\right)}\left(k\right)\frac{{\&PartialD;o}_j^{\left(3\right)}\left(k\right)}{{\&PartialD;o}_{\mathrm{ij}}^{\left(2\right)}\left(k\right)}---\left(26\right)$

The central value c of subordinate function layer Gaussian function _ijregulation rule as follows:

$\frac{\&PartialD;E\left(k\right)}{{\&PartialD;c}_{\mathrm{ij}}\left(k\right)}=\frac{\&PartialD;E\left(k\right)}{{\&PartialD;o}_j^{\left(2\right)}\left(k\right)}\frac{{\&PartialD;o}_j^{\left(2\right)}\left(k\right)}{{\&PartialD;c}_{\mathrm{ij}}\left(k\right)}\left(k\right)=-{\mathrm{\&delta;}}_j^{\left(2\right)}\left(k\right)\frac{{\&PartialD;o}_j^{\left(2\right)}\left(k\right)}{{\&PartialD;c}_{\mathrm{ij}}\left(k\right)}---\left(27\right)$

$c_{\mathrm{ij}}(k+1)=c_{\mathrm{ij}}\left(k\right)-\mathrm{\&eta;}\frac{\&PartialD;E\left(k\right)}{{\&PartialD;c}_{\mathrm{ij}}\left(k\right)}---\left(28\right)$

The width cs of subordinate function layer Gaussian function _ijregulation rule as follows:

$\frac{\&PartialD;E\left(k\right)}{{\&PartialD;\mathrm{\&sigma;}}_{\mathrm{ij}}\left(k\right)}=\frac{\&PartialD;E\left(k\right)}{{\&PartialD;o}_j^{\left(3\right)}\left(k\right)}\frac{{\&PartialD;o}_j^{\left(3\right)}\left(k\right)}{{\&PartialD;\mathrm{\&sigma;}}_{\mathrm{ij}}\left(k\right)}=-{\mathrm{\&delta;}}_j^{\left(3\right)}\left(k\right)\frac{{\&PartialD;o}_j^{\left(3\right)}\left(k\right)}{{\&PartialD;\mathrm{\&sigma;}}_{\mathrm{ij}}\left(k\right)}---\left(29\right)$

${\mathrm{\&sigma;}}_{\mathrm{ij}}(k+1)={\mathrm{\&sigma;}}_{\mathrm{ij}}\left(k\right)-\mathrm{\&eta;}\frac{\&PartialD;E\left(k\right)}{{\&PartialD;\mathrm{\&sigma;}}_{\mathrm{ij}}\left(k\right)}---\left(30\right)$

The learning rate that wherein η is parameter, value is 0.15.

(5) test sample book is predicted, the input using test sample book data as the neural network training, the output of neural network is predicting the outcome of SVI.

Creativeness of the present invention is mainly reflected in:

(1). the present invention is directed to current sludge volume index (SVI) SVI and be difficult to the online problem detecting, proposed the flexible measurement method based on the fuzzy Recursive Networks of a kind of self-organization T-S, realized mapping relations between auxiliary variable and SVI and the online detection of SVI; This model has that precision is high, good stability, the feature such as real-time, for prevention sludge bulking provides a kind of effective detection method, has promoted the raising of wastewater treatment automatization level;

(2). the present invention is directed to the characteristic of sludge bulking, the feedback layer of fuzzy recurrent neural network is improved.Rule-based generation criterion, generates fuzzy rule automatically, by effective fuzzy set generating algorithm, dynamically adjusts network structure.Solve network structure and be difficult to definite problem, when guaranteeing model accuracy, effectively simplified network structure.Adopt Gradient Descent Parameter Learning Algorithm, improved the learning ability of network.

Accompanying drawing explanation

Fig. 1. the topology diagram of the fuzzy recurrent neural network of self-organization T-S;

Fig. 2. online fuzzy rule of the present invention generates figure;

Fig. 3. network training fitting result figure of the present invention;

Fig. 4. the soft measurement result figure of the present invention;

Embodiment

Experimental data derives from the actual daily sheet of Beijing small sewage treatment plant.Fig. 1 has provided the neural network prediction model of SVI, and its input is respectively mixed liquor concentration of suspension MLSS, acidity-basicity ph, aeration tank water temperature T, aeration tank ammonia NH ₄, model is output as sludge volume index (SVI) SVI.Wherein MLSS refers to the weight of the contained dewatered sludge of unit volume biochemistry pool mixed liquor; The soda acid degree of pH reaction influent quality; T is the current sewage temperature in aeration tank; NH ₄represent the ammonia content of aeration tank water inlet, SVI represents that aeration tank mixed liquor is after 30 minutes precipitations, corresponding 1 gram of volume that dewatered sludge is shared.In input quantity, except pH and T, other unit is mg/litre.Output quantity unit ml/g.Totally 150 groups of data, wherein 90 groups of data are for training network, another 60 groups as test sample book, adopt structural self-organizing algorithm to carry out dynamic change to neural network.

Utilize the fuzzy recurrent neural network of self-organization T-S to set up the soft-sensing model of SVI, SVI is detected in real time; Concrete steps are as follows:

(1) initialization neural network, input node is 4, and output node is 1, and number of fuzzy rules is 0, the weights initialize to neural network, it is 0 to 1 random number that the initial weight of this experiment is.

(2) sample data is proofreaied and correct, then do normalized.

(3) structure of neural network is carried out to self-organization adjustment, formula (13)

formula (15) I _th=0.92, the input data that input has been proofreaied and correct:

1. input first group of data x (1)=[4.72 23.1 43.6 250.4], normalized x (1)=[0.1092 0.8867 0.7572 0.3915].Number of fuzzy rules becomes 1, according to formula (9) (10) to first group of fuzzy set Gaussian function central value and width value initialization: central value c ₁(1)=[0.1092 0.8867 0.7572 0.3915], width value σ ₁(1)=[0.5 0.5 0.5 0.5];

2. input second group of data x (2)=[5.63 23.4 37.2 250.1], the output of subordinate function layer is calculated in normalized x (2)=[0.3707 0.9434 0.5527 0.33907] according to formula (1) (2)

formula (11) computer memory intensity of activation

value,

because only have a fuzzy rule,

for maximal value,

do not meet formula (13), do not increase new fuzzy rule;

3. input successively data, until input the 23rd group of data, normalized x (23)=[0.1954 0.1886 0.5495 0.3968].According to formula (1) (2), calculate the output of subordinate function layer

formula (11) computer memory intensity of activation value because only have a fuzzy rule,

for maximal value, meet formula (13):

increase a new fuzzy rule;

Calculate the output of subordinate function node layer $o_1^{\left(2\right)}\left(23\right)=\left[\begin{array}{cccc}0.9881& 0.4555& 0.5636& 0.8579\end{array}\right],o_{11}^{\left(2\right)}\left(23\right)=0.9881$ For maximal value, meet formula (15)

the fuzzy rule newly increasing is generated to corresponding fuzzy set, according to formula (16)～(18) parameter initialization to newly-increased fuzzy set: central value initial value value c ₂=x (23), r value is 0.6, width initial value σ _i2=r*|x _i(23)-c _i1|, i=1,2,3,4, σ _i2=[0.0517 0.0.4189 0.1246 0.0032].

4. when input k group data, according to (1) (2), calculate the node of subordinate function layer and export

the space intensity of activation of computation rule node layer

value, according to formula (12), find out maximal value; Whether the value that judges space intensity of activation is less than predetermined threshold if meet formula (13), increase a new fuzzy rule, carry out the 5. step; If do not meet formula (13), input k+1 group data, carry out the 6. step.

5. according to the output of formula (15) judgement subordinate function node

maximal value whether be greater than predetermined threshold I _th, meet formula (15), for the fuzzy rule newly increasing, generate corresponding fuzzy set, according to formula (16)～(18) parameter initialization to fuzzy set; If do not meet formula (15), do not generate new fuzzy set, and delete the fuzzy rule newly increasing;

6. whether judgement input data all inputs, complete and enter (4) step, otherwise forward the to, 4. walk, and total data has trained symbiosis to become 4 fuzzy rules.The initial value of Gaussian function is:

The central value initial value of Gaussian function is $c\left(1\right)=\left[\begin{array}{cccc}0.1092& 0.8867& 0.7572& 0.3915\\ 0.1954& 0.1886& 0.5495& 0.3968\\ 0.7052& 0.5495& 0.7124& 0.6166\\ 0.2328& 0.3968& 0.3723& 0.5638\end{array}\right]$

The width value initial value of Gaussian function is $\mathrm{\&sigma;}\left(1\right)=\left[\begin{array}{cccc}0.5& 0.5& 0.5& 0.5\\ 0.0517& 0.4189& 0.1246& 0.0032\\ 0.4394& 0.1456& 0.0127& 0.2776\\ 0.3704& 0.2701& 0.0046& 0.4414\end{array}\right]$

Rules layer to the initial weight of feedback layer is $\mathrm{\&omega;}\left(1\right)=\left[\begin{array}{cccc}0.6229& 0.7149& 0.6219& 0.8923\\ 0.8571& 0.0309& 0.3152& 0.8153\\ 0.3965& 0.9725& 0.8241& 0.6114\\ 0.7359& 0.4310& 0.8726& 0.2938\end{array}\right]$

The initial value of linear dimensions is $a\left(1\right)=\left[\begin{array}{cccc}0.5& 0.5& 0.5& 0.5\\ 0.5& 0.5& 0.5& 0.5\\ 0.5& 0.5& 0.5& 0.5\\ 0.5& 0.5& 0.5& 0.5\end{array}\right],$

$W\left(1\right)=\underset{i=1}{\overset{4}{\mathrm{\&Sigma;}}}{a}_{\mathrm{ij}}{x}_i\left(1\right)=\left[\begin{array}{cccc}1.0723& 1.0723& 1.0723& 1.0723\end{array}\right]$

(4) with the training sample data neural network training after proofreading and correct, train epochs s=1000, if train epochs choosing is too small, the quantity of information gathering is inadequate; If train epochs choosing is excessive, there will be over-fitting phenomenon.

(5) parameter adjustment to neural network, train epochs s=1, input data are inputted from first group of data, calculate the network input and output amount of every one deck, according to formula (19) calculating target function value, adopt gradient descent method to 4 parameter adjustments: the linear dimensions a of parameter layer, rules layer is to the connection weights ω of feedback layer, the central value c of subordinate function layer Gaussian function and width value σ.

1. input first group of data x (1)=[0.1092 0.8867 0.7572 0.3915]

The output of input layer: o ⁽¹⁾(1)=x (1)=[0.1092 0.8867 0.7572 0.3915]

The output of subordinate function layer: $o^{\left(2\right)}\left(1\right)=\exp (-\frac{{(o^{\left(1\right)}\left(1\right)-c\left(1\right))}^2}{{\left(\mathrm{\&sigma;}\left(1\right)\right)}^2})=\left[\begin{array}{cccc}1& 1& 1& 1\\ 0.0620& 0.0622& 0.0621& 0.0646\\ 0.1588& 0.0047& 0& 0.5181\\ 0.8946& 0.0373& 0& 0.8412\end{array}\right]$

Feedback layer and rules layer output:

o ⁽³⁾(0)=[0 00 0], so h=[0 00 0]

$f=\frac{1}{1+\exp (-h)}=\left[\begin{array}{cccc}0.5& 0.5& 0.5& 0.5\end{array}\right]$

so o ⁽³⁾(1)=[0.0044 00 0.0281]

The output of parameter layer: o ⁽⁴⁾(1)=o ⁽³⁾(1) W (1)=[0.0047 00 0.0301]

The output of model: $y\left(1\right)=\frac{\underset{j=1}{\overset{4}{\mathrm{\&Sigma;}}}{o}_j^{\left(4\right)}\left(1\right)}{\underset{j=1}{\overset{4}{\mathrm{\&Sigma;}}}{o}_j^{\left(3\right)}\left(1\right)}=1.0723$

2. y _d(1)=0.5960, computing system error $E\left(1\right)=\frac{1}{2}{(y\left(1\right)-y_d\left(1\right))}^2=0.1134$

3. adopt gradient descent method to parameter adjustment: according to formula (20)～(22), calculating parameter layer linear dimensions a adjustment amount, obtains the parameter value after adjusting; According to formula (23)～(25), computation rule layer, to the connection weights ω adjustment amount of feedback layer, obtains the parameter value after adjusting; According to formula (26)～(30), calculate central value c and the width value σ adjustment amount of Gaussian function, obtain the parameter value after adjusting.

4. input next group data, the output quantity of the every one deck of computation model, adopts gradient descent algorithm to adjust each parameter value, until all training datas have all been inputted.Train epochs adds 1.

(6) continue neural network training, repeat (5) step, until train epochs reaches 1000 steps, complete network training.

(7) test sample book is predicted: the input using test sample book data as the neural network training, neural network is output as sludge volume index (SVI) SVI.

Claims (1)

1. a SVI flexible measurement method, is characterized in that, comprises the following steps:

(1) data pre-service and auxiliary variable are selected;

Sample set data are normalized with zero-mean standardized method, by pivot analysis PCA, carry out the selected of auxiliary variable, finally determine mixed liquor concentration of suspension MLSS, acidity-basicity ph, aeration tank water temperature T, aeration tank ammonia NH ₄input variable as model;

(2) set up the Recurrent Fuzzy Neural Network model of the soft measurement of SVI, input quantity is MLSS, pH, T, NH ₄, the output quantity of model is SVI; Recurrent Fuzzy Neural Network topological structure: input layer is that ground floor, subordinate function layer are that the 3rd layer of the second layer, rules layer, the 4th layer, parameter layer, output layer are layer 5, feedback layer;

Neural network structure: input layer has 4 input nodes, each input layer connects m subordinate function node layer, rules layer has m node, m represents number of fuzzy rules, the number of fuzzy rules generating in network structure training process is determined the value of m, parameter node layer number, feedback layer nodes equate with the nodes of rules layer, and output layer has 1 node; X=[x ₁, x ₂, x ₃, x ₄] represent the input of neural network, y _dthe desired output that represents neural network; If k group sample data is x (k)=[x ₁(k), x ₂(k), x ₃(k), x ₄(k)]; During the input of k group sample data:

The output of i node of input layer is expressed as:

$o_i^{\left(1\right)}\left(k\right)=x_i\left(k\right),i=\mathrm{1,2,3,4}$

(1)

Wherein,

the output of i node of expression input layer when input k group sample;

The node of subordinate function layer adds up to: 4m, and the node of each input layer all connects the node of m subordinate function layer, and subordinate function layer is output as:

$o_{\mathrm{ij}}^{\left(2\right)}\left(k\right)=\exp (-\frac{{(o_i^{\left(1\right)}\left(k\right)-c_{\mathrm{ij}}\left(k\right))}^2}{{\left({\mathrm{\&sigma;}}_{\mathrm{ij}}\left(k\right)\right)}^2}),j=\mathrm{1,2}...m$

(2)

Wherein, subordinate function adopts Gaussian function, c _ijand σ _ijrepresent respectively central value and the width of the Gaussian function of j the node of subordinate function layer that i node of input layer is corresponding, each Gaussian function is a fuzzy set, in the structural adjustment stage to Gaussian function initialize;

the output of j the node that represents the subordinate function layer that i node of input layer is corresponding when inputting k and organize sample;

The nodes of rules layer is m, and j node of the subordinate function layer that each node of input layer is corresponding is all connected to j node of rules layer; In rules layer, introduce feedback link, at feedback layer, add built-in variable; The node that feedback layer node comprises two types: accept node, the output quantity of rules layer and weights are weighted to summation operation, calculate built-in variable; Feedback node, adopts sigmoid function as subordinate function, calculates the output quantity of feedback layer; Each node of rules layer all connects all feedback layers and accepts node; Feedback layer to accept node corresponding one by one with feedback node, nodes equates, feedback node is corresponding one by one with rules layer node, nodes is equal, and changes along with the variation of number of fuzzy rules, equals all the time number of fuzzy rules; J node of rules layer is output as:

$h_q=\underset{j=1}{\overset{m}{\mathrm{\&Sigma;}}}{o}_j^{\left(3\right)}(k-1){\mathrm{\&omega;}}_{\mathrm{jq}},j=\mathrm{1,2},...,m;q=\mathrm{1,2},...,m$

(3)

$f_q=\frac{1}{1+\exp \left({-h}_q\right)}$

(4)

$o_j^{\left(3\right)}\left(k\right)=f_q\underset{i=1}{\overset{4}{\mathrm{\&Pi;}}}{o}_{\mathrm{ij}}^{\left(2\right)}\left(k\right)$

(5)

Wherein, ω _jqbe j node of rules layer and the q of feedback layer the weights that are connected of accepting node, initial assignment is the random number of 0 to 1;

represent that j node of rules layer is in the output quantity of k-1 group sample,

h _qrepresent that feedback layer q accepts the built-in variable of node; f _qthe output quantity that represents q feedback node of feedback layer; The output of rules layer

be the intensity of activation of fuzzy rule, wherein

representation space intensity of activation, f _qexpression time intensity of activation;

The node of the node of rules layer and parameter layer is one to one, and parameter layer has m node, and the output of this layer is expressed as:

$W_j\left(k\right)=\underset{i=1}{\overset{4}{\mathrm{\&Sigma;}}}{a}_{\mathrm{ij}}{x}_i\left(k\right)$

(6)

$o_j^{\left(4\right)}\left(k\right)=o_j^{\left(3\right)}\left(k\right)W_j\left(k\right)$

(7)

Wherein, a _ijrepresent linear dimensions, initial value assignment is 0 to 1 random number, a _j=[a _1j, a _2j, a _3j, a _4j]; W _j(k) represent the value of the linear dimensions weighted sum of j node of parameter layer when input k group sample,

represent that j node of parameter layer is in the output of k group sample;

Network model is the single outputs of many inputs, and output layer has 1 node, and all parameter node layers are connected to output node; Network output is expressed as:

$y\left(k\right)=\frac{\underset{j=1}{\overset{m}{\mathrm{\&Sigma;}}}{o}_j^{\left(4\right)}\left(k\right)}{\underset{j=1}{\overset{m}{\mathrm{\&Sigma;}}}{o}_j^{\left(3\right)}\left(k\right)}$

(8)

Wherein, y (k) represents the network output of k sample;

(3) first fuzzy neural network determines network structure by structural self-organizing adjustment; The structural self-organizing adjustment of network: x (k)=[x ₁(k), x ₂(k), x ₃(k), x ₄(k)] represent the current input of model k group sample, since first group of sample data input, to total data, inputted, one group of sample data of every input all adopts following steps to judge whether to increase new fuzzy rule, on the basis that increases fuzzy rule, judges whether to increase new fuzzy set;

1. in network model initial configuration, number of fuzzy rules is 0, the first group of data input, and number of fuzzy rules becomes 1, and increases new fuzzy set; The initialization of fuzzy set, the initial table of Gaussian function central value and width value is shown:

c(1)=x(1)=[x ₁(1),x ₂(1),x ₃(1),x ₄(1),] (9)

σ(1)=[σ ₁₁,σ ₂₁,σ ₃₁,σ ₄₁]=[0.5,0.5,0.5,0.5] (10)

Wherein c (1) represents the central value of first group of fuzzy set of generation, the i.e. central value of subordinate function; σ (1) represents the width value of first fuzzy set of generation, the i.e. width value of subordinate function;

2. input data and input successively, one group of data of every input, all judging whether increases new fuzzy rule, and judgment formula is expressed as:

(11)

(12)

(13)

Wherein

the space intensity of activation that represents j node of rules layer; J represents to work as the value of j while getting maximal value; N represents present Fuzzy rule number;

for predefined threshold value, value is 0.24;

If meet formula (13), increase a new fuzzy rule, 3. N'=N+1, carry out;

If do not meet formula (13), repeat 2., input next group data;

3. increasing on the basis of a new fuzzy rule, judging whether increases new fuzzy set, and judgment formula is expressed as:

$I=\arg \underset{1<=j<=h}{\max }\left(o_{\mathrm{ij}}^{\left(2\right)}\left(k\right)\right)---\left(14\right)$

$o_{\mathrm{iI}}^{\left(2\right)}\left(k\right)>I_{\mathrm{th}}$

(15)

Wherein I represents to work as

the value of j while getting maximal value, h represents the fuzzy set number of "current" model, h=N; I _thfor predefined threshold value, value is 0.92;

If meet formula (15), increase a new fuzzy set, h'=h+1, h'=N'; To i.e. newly-increased Gaussian function central value and the width value initialize to subordinate function layer of newly-increased fuzzy set initialize; Initial table is shown:

c _N+1=x(k)

(16)

$c^{+}\arg \underset{1<=p<=N}{\min }\left|\right|x\left(k\right)-c_p\left|\right|---\left(17\right)$

${\mathrm{\&sigma;}}_{i,N+1}=r|x_i\left(k\right)-c_i^{+}|,i=\mathrm{1,2,3,4}---\left(18\right)$

Wherein, N represents the existing number of fuzzy rules of "current" model, p=1, and 2 ..., N, c _n+1the initial value that represents the central value of newly-increased subordinate function, r represents overlap coefficient, value is 0.6; c _pbe expressed as the central value of p Gaussian function in "current" model; c ⁺represent as x (k) and c _pspace length is hour c _pvalue; σ _{i, N+1}the width initial value that represents newly-increased subordinate function, input quantity x (k) and c ⁺the absolute value of difference and the product of overlap coefficient; Increase new fuzzy set, at subordinate function layer corresponding to each input layer, increase a new node, rules layer, feedback layer, parameter layer respectively increase corresponding node accordingly;

If do not met (15), do not increase new fuzzy set h'=h, and N''=N'-1, the fuzzy rule that is about to newly increase is deleted;

4. continue to adjust the structure of neural network, input data are inputted successively, repeat 2. 3., and after all input data have been inputted, neural network structure adjustment has been trained;

(4) determined the structure of network model, then network parameter is just adjusted, by the data after proofreading and correct, carry out neural network training, totally 150 groups of sample datas wherein, 90 groups of training sample data, 60 groups of test sample book data, train epochs is 1000 steps, in the training process of each step, 90 groups of training sample data are all inputted, every group of training sample data input all adopts gradient descent algorithm to adjust network parameter, the parameter of wherein adjusting comprises: the linear dimensions a of parameter layer, rules layer is to the connection weights ω of feedback layer, the central value c of subordinate function layer Gaussian function and width value σ,

The objective function of definition training is that systematic error is defined as:

$E\left(k\right)=\frac{1}{2}{(y\left(k\right)-y_d\left(k\right))}^2$

(19)

The actual output quantity that wherein y (k) is network, y _d(k) be the desired output amount of network, E (k) represents systematic error;

Gradient descent algorithm: adopt objective function to ask partial derivative to the output quantity of every one deck, calculate the error propagation item of every layer of output; By function of functions, ask partial derivative, the partial derivative of calculating target function to parameter value, partial derivative is the adjustment amount of each parameter;

The error propagation item δ of parameter layer ⁽⁴⁾, the partial derivative that objective function is exported parameter layer:

${\mathrm{\&delta;}}_j^{\left(4\right)}\left(k\right)=-\frac{\&PartialD;E\left(k\right)}{\&PartialD;y\left(k\right)}\frac{\&PartialD;y\left(k\right)}{\&PartialD;o_j^{\left(4\right)}\left(k\right)}---\left(20\right)$

To linear dimensions a _jadjustment amount be:

$\frac{\&PartialD;E\left(k\right)}{{\&PartialD;a}_j\left(k\right)}=\frac{\&PartialD;E\left(k\right)}{\&PartialD;o_j^{\left(4\right)}\left(k\right)}\frac{{\&PartialD;o}_j^{\left(4\right)}\left(k\right)}{\&PartialD;a_j\left(k\right)}=-{\mathrm{\&delta;}}_j^{\left(4\right)}\left(k\right)\frac{o_j^{\left(3\right)}\left(k\right)}{\underset{j=1}{\overset{m}{\mathrm{\&Sigma;}}}{o}_j^{\left(3\right)}\left(k\right)}$

$\left(21\right)$ $a_j(k+1)=a_j\left(k\right)-\mathrm{\&eta;}\frac{\&PartialD;E\left(k\right)}{{\&PartialD;a}_j\left(k\right)}---\left(22\right)$

Rules layer error propagation item

as follows:

${\mathrm{\&delta;}}_j^{\left(3\right)}\left(k\right)=-\frac{\&PartialD;E\left(k\right)}{{\&PartialD;o}_j^{\left(3\right)}\left(k\right)}={\mathrm{\&delta;}}^{\left(4\right)}\left(k\right)\frac{{\&PartialD;o}^{\left(4\right)}\left(k\right)}{{\&PartialD;o}_j^{\left(3\right)}\left(k\right)}---\left(23\right)$

Recurrence layer connects weights ω to rules layer _jqregulation rule as follows:

$\frac{\&PartialD;E\left(k\right)}{{\&PartialD;\mathrm{\&omega;}}_{\mathrm{jq}}\left(k\right)}=\frac{\&PartialD;E\left(k\right)}{{\&PartialD;o}_j^{\left(3\right)}\left(k\right)}\frac{{\&PartialD;o}_j^{\left(3\right)}\left(k\right)}{{\&PartialD;\mathrm{\&omega;}}_{\mathrm{jq}}\left(k\right)}=-{\mathrm{\&delta;}}_j^{\left(3\right)}\left(k\right)\frac{{\&PartialD;o}_j^{\left(3\right)}\left(k\right)}{{\&PartialD;\mathrm{\&omega;}}_{\mathrm{jq}}\left(k\right)}---\left(24\right)$

${\mathrm{\&omega;}}_{\mathrm{jq}}(k+1)={\mathrm{\&omega;}}_{\mathrm{jq}}\left(k\right)-\mathrm{\&eta;}\frac{\&PartialD;E}{{\&PartialD;\mathrm{\&omega;}}_{\mathrm{jq}}}\left(k\right)---\left(25\right)$

The error propagation item of subordinate function layer as follows:

${\mathrm{\&delta;}}_{\mathrm{ij}}^{\left(2\right)}\left(k\right)=-\frac{\&PartialD;E\left(k\right)}{{\&PartialD;o}_{\mathrm{ij}}^{\left(2\right)}\left(k\right)}={\mathrm{\&delta;}}_j^{\left(3\right)}\left(k\right)\frac{{\&PartialD;o}_j^{\left(3\right)}\left(k\right)}{{\&PartialD;o}_{\mathrm{ij}}^{\left(2\right)}\left(k\right)}---\left(26\right)$

The central value c of subordinate function layer Gaussian function _ijregulation rule as follows:

$\frac{\&PartialD;E\left(k\right)}{{\&PartialD;c}_{\mathrm{ij}}\left(k\right)}=\frac{\&PartialD;E\left(k\right)}{{\&PartialD;o}_j^{\left(2\right)}\left(k\right)}\frac{{\&PartialD;o}_j^{\left(2\right)}\left(k\right)}{{\&PartialD;c}_{\mathrm{ij}}\left(k\right)}\left(k\right)=-{\mathrm{\&delta;}}_j^{\left(2\right)}\left(k\right)\frac{{\&PartialD;o}_j^{\left(2\right)}\left(k\right)}{{\&PartialD;c}_{\mathrm{ij}}\left(k\right)}---\left(27\right)$

$c_{\mathrm{ij}}(k+1)=c_{\mathrm{ij}}\left(k\right)-\mathrm{\&eta;}\frac{\&PartialD;E\left(k\right)}{{\&PartialD;c}_{\mathrm{ij}}\left(k\right)}$

(28)

The width cs of subordinate function layer Gaussian function _ijregulation rule as follows:

$\frac{\&PartialD;E\left(k\right)}{{\&PartialD;\mathrm{\&sigma;}}_{\mathrm{ij}}\left(k\right)}=\frac{\&PartialD;E\left(k\right)}{{\&PartialD;o}_j^{\left(3\right)}\left(k\right)}\frac{{\&PartialD;o}_j^{\left(3\right)}\left(k\right)}{{\&PartialD;\mathrm{\&sigma;}}_{\mathrm{ij}}\left(k\right)}=-{\mathrm{\&delta;}}_j^{\left(3\right)}\left(k\right)\frac{{\&PartialD;o}_j^{\left(3\right)}\left(k\right)}{{\&PartialD;\mathrm{\&sigma;}}_{\mathrm{ij}}\left(k\right)}---\left(29\right)$

${\mathrm{\&sigma;}}_{\mathrm{ij}}(k+1)={\mathrm{\&sigma;}}_{\mathrm{ij}}\left(k\right)-\mathrm{\&eta;}\frac{\&PartialD;E\left(k\right)}{{\&PartialD;\mathrm{\&sigma;}}_{\mathrm{ij}}\left(k\right)}$

(30)

The learning rate that wherein η is parameter, value is 0.15;

(5) test sample book is predicted, the input using test sample book data as the neural network training, the output of neural network is predicting the outcome of SVI.

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