Intelligent identification method of sludge bulking based on type-2 fuzzy neural network

Abstract

An intelligent identification method of sludge bulking based on type-2 fuzzy-neural-network belongs to the field of intelligent detection technology. The sludge volume index (SVI) in wastewater treatment plant is an important index to measure the sludge bulking of activated sludge process. However, poor production conditions and serious random interference in sewage treatment process are characterized by strong coupling, large time-varying and serious hysteresis, which makes the detection of SVI concentration of sludge volume index extremely difficult. At the same time, there are many types of sludge bulking faults, which are difficult to identify effectively. Due to the sludge volume index (SVI) is unable to online monitoring and the fault type of sludge bulking is difficult to determined, the invention develop soft-computing model based on type-2 fuzzy-neural-network to complete the real-time detection of sludge volume index (SVI). Combined with the target-related identification algorithm, the fault type of sludge bulking is determined. Results show that the intelligent identification method can quickly obtain the sludge volume index (SVI), accurate identification fault type of sludge bulking, improve the quality and ensure the safety operation of the wastewater treatment process.

Claims

1. An intelligent identification method for sludge bulking based on a type-2 fuzzy-neural-network, comprising the following steps: (1) determine input and output variables of sludge volume index (SVI): in an activated sludge wastewater treatment process, the input variables of SVI soft-computing model include: dissolved oxygen (DO) concentration, total nitrogen (TN) concentration, organic load rate (F/M), pH, T, output values of the soft-computing model are SVI values, the sludge bulking contains the following fault types: low DO concentration, nutrient deficit, low sludge loading, low pH, and low temperature; (2) SVI soft-computing model: establish the SVI soft-computing model based on type-2 fuzzy-neural-network, a structure of type-2 fuzzy-neural-network contains five layers: input layer, membership function layer, firing layer, consequent layer and output layer, the network is 5-M-L-2-1, including 5 neurons in the input layer, M neurons in the membership function layer, L neurons in the firing layer, 2 neurons in the consequent layer and 1 neurons in the output layer, M and L are integers larger than 2; connecting weights between the input layer and the membership function layer are assigned 1; the number of training samples is N, the input of type-2 fuzzy-neural-network is x(t)=[x.sub.1(t), x.sub.2(t), x.sub.3(t), x.sub.4(t), x.sub.5(t)] at time t, x.sub.1(t) represents DO concentration at time t; x.sub.2(t) represents TN concentration at time t, x.sub.3(t) represents an organic load rate (F/M) value at time t, x.sub.4(t) represents pH value at time t, and x.sub.5(t) represents T value at time t, the output of type-2 fuzzy-neural-network is y.sub.d(t) and an actual output is y(t); type-2 fuzzy-neural-network includes: an input layer: there are 5 neurons in this layer, the output is:
o.sub.i(t)=x.sub.i(t)(1) where o.sub.i(t) is the ith output value at time t, i=1, 2, . . . , 5, a membership function layer: there are M neurons in the membership function layer, the output is: $\begin{array}{cc}{}_m^i\left(t\right)=N\left(c_m^i\left(t\right),{}_m^i\left(t\right);o_i\left(t\right)\right)=\exp \left\{-\frac{1}{2}{\left(\frac{o_i\left(t\right)-c_m^i\left(t\right)}{{}_m^i\left(t\right)}\right)}^2\right\},i=1,2,\mathrm{.Math.},5;m=1,2,\mathrm{.Math.},M,& \left(2\right)\\ c_m^i\left(t\right)\left[{\underset{\_}{c}}_m^i\left(t\right),{\stackrel{}{c}}_m^i\left(t\right)\right],& \left(3\right)\end{array}$ where .sup.i.sub.m(t) is the mth membership function with the ith input at time t, N represents the membership function, c.sup.i.sub.m(t) is the uncertain center of the mth membership function neuron with the ith input at time t, c.sup.i.sub.m(t) is the lower center value of the mth membership function neuron with the ith input at time t, c.sup.i.sub.m(t) is the upper center value of the mth membership function neuron with the ith input at time t (where the initial lower center value and initial upper center value of the mth membership function neuron with the ith input, i.e., c.sup.i.sub.m(0) and c.sup.i.sub.m(t) is obtained by that random initial center of the mth membership function neuron with the ith input c.sup.i.sub.m(0) add and subtract a constant), .sup.i.sub.m(t) is the standard deviation of the mth membership function neuron with the ith input at time t, the bounded internal of .sup.i.sub.m(t) is [.sup.i.sub.m(t), .sup.i.sub.m(t)] $\begin{array}{cc}{\underset{\_}{}}_m^i\left(o_i\left(t\right)\right)=\{\begin{array}{c}N\left({\stackrel{}{c}}_m^i\left(t\right),{}_m^i\left(t\right);o_i\left(t\right)\right),o_i\left(t\right)\left({\underset{\_}{c}}_m^i\left(t\right)+{\stackrel{}{c}}_m^i\left(t\right)\right)/2\\ N\left({\underset{\_}{c}}_m^i\left(t\right),{}_m^i\left(t\right);o_i\left(t\right)\right),o_i\left(t\right)>\left({\underset{\_}{c}}_m^i\left(t\right)+{\stackrel{}{c}}_m^i\left(t\right)\right)/2\end{array},& \left(4\right)\\ {\stackrel{}{}}_m^i\left(o,\left(t\right)\right)=\{\begin{array}{c}N\left({\underset{\_}{c}}_m^i\left(t\right),{}_m^i\left(t\right);o_i\left(t\right)\right),o_i\left(t\right){\underset{}{c}}_m^i\left(t\right)\\ \begin{array}{cc}1,& {\underset{}{c}}_m^i\left(t\right)<o_i\left(t\right)<{\stackrel{}{c}}_m^i\left(t\right)\end{array}\\ N\left({\stackrel{}{c}}_m^i\left(t\right),{}_m^i\left(t\right);o_i\left(t\right)\right),o_i\left(t\right)>{\stackrel{}{c}}_m^i\left(t\right)\end{array},& \left(5\right)\end{array}$ where .sup.i.sub.m(t) and .sup.i.sub.m(t) are the lower value and upper value of the mth membership function neuron with the ith input at time t, respectively, 0<.sup.i.sub.m(t).sup.i.sub.m(t)1, a firing layer: there are L neurons in this layer, and the output values are: $\begin{array}{cc}{F}_l\left(t\right)=\left[{\underset{}{f}}_l\left(t\right),{\stackrel{}{f}}_l\left(t\right)\right],{\underset{}{f}}_l\left(t\right)=\underset{i=1}{\overset{5}{.Math.}}{\underset{}{}}_m^i\left(t\right),{\stackrel{}{f}}_l\left(t\right)=\underset{i=1}{\overset{5}{.Math.}}{\stackrel{}{}}_m^i\left(t\right),l=1,2,\mathrm{.Math.},L,& \left(6\right)\end{array}$ where F.sub.l(t) is the firing strength of the lth firing neuron, f.sub.l(t) and f.sub.l(t) are the lower firing strength and upper firing strength of the lth firing neuron, respectively, 0<f.sub.lt)f.sub.l(t)1, a consequent layer: this layer contains two consequent neurons, the output values are $\begin{array}{cc}\underset{}{y}\left(t\right)=\frac{\underset{l=1}{\overset{L}{.Math.}}{\underset{}{f}}_l\left(t\right)a_l\left(t\right)}{\underset{l=1}{\overset{L}{.Math.}}{\underset{}{f}}_l\left(t\right)},\stackrel{}{y}\left(t\right)=\frac{\underset{l=1}{\overset{L}{.Math.}}{\underset{}{f}}_l\left(t\right)a_l\left(t\right)}{\underset{l=1}{\overset{L}{.Math.}}{\underset{}{f}}_l\left(t\right)},a_l\left(t\right)=\underset{i=1}{\overset{5}{.Math.}}{}_l^i\left(t\right)x_i\left(t\right),& \left(7\right)\end{array}$ where y(t) and y(t) are the low and up output values of the consequent neurons, a.sub.l(t) is weight of the lth firing neuron, .sup.i.sub.l(t) is the weight coefficient of the lth firing neuron with the ith input at time t, an output layer: the output value is:
y(t)=(t)y(t)+(1(t))y(t)(8) where (t) and y(t) are the proportion of the low output and the output value of type-2 fuzzy-neural-network, the error of type-2 fuzzy-neural-network is: $\begin{array}{cc}E\left(t\right)=\frac{1}{N}\underset{t=1}{\overset{N}{.Math.}}{\left(y_d\left(t\right)-y\left(t\right)\right)}^2& \left(9\right)\end{array}$ where y.sub.d(t) is the output of type-2 fuzzy-neural-network and the actual output is expressed as y(t); (3) train type-2 fuzzy-neural-network (a) give the type-2 fuzzy-neural-network, the initial number of firing layer neurons is M, M>2 is a positive integer; the input of type-2 fuzzy-neural-network is x(1), x(2), . . . , x(t), . . . , x(N), correspondingly, the output is y.sub.d(1), y.sub.d(2), . . . , y.sub.d(t), . . . , y.sub.d(N), expected error value is set to E.sub.d, E.sub.d(0, 0.01), (b) set the learning step s=1; (c) t=s; according to Eqs. (1)-(7), calculate the output of type-2 fuzzy-neural-network, exploiting adaptive second-order algorithm:
(t+1)=(t)+(H(t)+(t)I).sup.1v(t)(10) where (t)=[c.sup.i.sub.m(t), c.sup.i.sub.m(t), .sup.i.sub.m(t), (t), w.sup.i.sub.m(t)] is the parameter matrix of type-2 fuzzy-neural-network at time t, c.sup.i.sub.m(t) is the lower center value of the mth membership function neuron with the ith input at time t, c.sup.i.sub.m(t) is the upper center value of the membership function neuron with the ith input at time t, .sup.i.sub.m(t) is the standard deviation of the mth membership function neuron with the ith input at time t, (t) is the proportion of the lower output, .sup.i.sub.l(t) is the weight coefficient of the lth firing neuron with the ith input at time t, H(t) is the quasi Hessian matrix, v(t) is gradient vector, I is the identity matrix and (t) is the adaptive learning rate defined as:
(t)=|E(t)|+(1)v(t)(11) where (0, 1), the expression of H(t) and v(t) are defined as:
H(t)=J.sup.T(t)J(t)(12)
v(t)=J.sup.T(t)E(t)(13) where the Jacobian vector J(t) is calculated as: $\begin{array}{cc}J\left(t\right)=\left[\frac{e\left(t\right)}{{\underset{}{c}}_m^i\left(t\right)},\frac{e\left(t\right)}{{\stackrel{\_}{c}}_m^i\left(t\right)},\frac{e\left(t\right)}{{}_m^i\left(t\right)},\frac{e\left(t\right)}{\left(t\right)},\frac{e\left(t\right)}{{}_m^i\left(t\right)}\right]& \left(14\right)\end{array}$ (d) according to Eq. (9), calculate the performance of type-2 fuzzy-neural-network, if E(t)E.sub.d, go to step (c); if E(t)<E.sub.d, stop the training process; (4) the target-related identification algorithm is used to determine the fault type of sludge bulking, which is specifically as follows: (a) the test samples are used as the input of the type-2 fuzzy-neural-network, and the sludge volume index (SVI) is calculated; (b) if SVI150, it is determined that there is no sludge bulking during the wastewater treatment process; (c) if SVI>150, sludge bulking at the wastewater treatment operation is determined and regression coefficients of all variables are calculated: $\begin{array}{cc}{b}_i\left(t\right)=\frac{{u_i\left(t\right)}^T{t}_i\left(t\right)}{{t_i\left(t\right)}^T{t}_i\left(t\right)},& \left(15\right)\end{array}$ where b.sub.i(t) is the regression coefficient of ith input at time t, b(t)=[b.sub.1(t), . . . , b.sub.i(t), . . . , b.sub.5(t)] is the regression coefficient vector, u.sub.i(t) is the ith score vector of the output vector at time t, U(t)=[u.sub.1(t), . . . , u.sub.i(t), . . . , u.sub.5(t)] is score matrix of the output vector at time t, t.sub.i(t) is the ith score vector of the input matrix at time t, T(t)=[t.sub.1(t), . . . , t.sub.i(t), . . . , t.sub.5(t)] is score matrix of the input matrix at time t, u.sub.i(t) and t.sub.i(t) are given as: $\begin{array}{cc}{u}_i\left(t\right)=\frac{y\left(t\right)q_i\left(t\right)}{{q_i\left(t\right)}^T{q}_i\left(t\right)},& \left(16\right)\\ t_i\left(t\right)=\frac{X\left(t\right)w_i\left(t\right)}{{w_i\left(t\right)}^T{w}_i\left(t\right)},& \left(17\right)\end{array}$ where q.sub.i(t) is the ith loading value of output vector at time t, q(t)R.sup.15 is the loading vector of output vector at time t, y(t)=[y(tK+1), y(tK+2), . . . , y(t)].sup.T, y(t) is the SVI value at time t, X(t)=[x.sub.1(t), . . . , x.sub.i(t), . . . , x.sub.5(t)] is the input matrix of type-2 fuzzy-neural-network, x.sub.i(t)=[x.sub.i(tK+1), x.sub.i(tK+2), . . . , x.sub.i(t)].sup.T, x.sub.i(t) is the ith input variable at time t, w.sub.i(t) is the ith feature vector at time t, W(t)=[w.sub.1(t), . . . , w.sub.i(t), . . . , w.sub.5(t)] is the feature matrix of X(t).sup.Ty(t), the expressions of q.sub.i(t) and W(t) are $\begin{array}{cc}{q_i\left(t\right)}^T=\frac{{t_i\left(t\right)}^{T}y\left(t\right)}{{t_i\left(t\right)}^T{t}_i\left(t\right)},& \left(18\right)\\ {W\left(t\right)}^T\left(t\right)W\left(t\right)=E\left\{{X\left(t\right)}^{T}y\left(t\right){y\left(t\right)}^{T}X\left(t\right)\right\},& \left(19\right)\end{array}$ where (t) is the eigenvalue matrices of X(t).sup.Ty(t), the function E represents the eigenvector and eigenvalue of the matrix, the inner relative model of y(t) and X(t) can be expressed as: $\begin{array}{cc}\{\begin{array}{c}X\left(t\right)=T\left(t\right){P\left(t\right)}^T+\left(t\right)=\underset{i=1}{\stackrel{5}{.Math.}}{t}_i\left(t\right){p_i\left(t\right)}^T+\left(t\right)\\ y\left(t\right)=U\left(t\right){q\left(t\right)}^T+G\left(t\right)=\stackrel{5}{\underset{i=1}{.Math.}}{u}_i\left(t\right){q_i\left(t\right)}^T+G\left(t\right)\end{array},& \left(20\right)\end{array}$ where (t)R.sup.K5 is the residual matrix of X(t), (t)=[.sub.1(t), . . . , .sub.i(t), . . . , .sub.5(t)], where .sub.i(t) present the residual vector of ith input, G(t)R.sup.K1 is the residual vector of y(t); (d) when the regression coefficient of the input variable satisfies:
b.sub.max(t)=max b(t),(21) where b.sub.max(t) is the maximum regression coefficient of the input variables, and the corresponding fault type is the source of sludge bulking.

Description

DESCRIPTION OF DRAWINGS

(1) FIG. 1 is the initial structural topology diagram of the type-2 fuzzy neural network.

(2) FIG. 2 is the SVI test result diagram of the sludge volume index, where the blue line is the desired output value of sludge volume index SVI, and the black line is the predicted value of type-2 fuzzy neural network.

(3) FIG. 3 is the SVI prediction error diagram of the sludge volume index.

(4) FIG. 4 is the fault category identification diagram of the sludge bulking.

DETAILED DESCRIPTION OF THE INVENTION

(5) The invention select the characteristic variables to measure sludge volume index SVI as dissolved oxygen concentration DO, total nitrogen TN, load activated sludge F/M, power of hydrogen pH and temperature T, where pH no unit. The unit of temperature is Celsius. Others units are mg/l.

(6) The experimental data come from the 2017 water quality data analysis report of a wastewater treatment plant. Where the actual testing data about dissolved oxygen concentration DO, total nitrogen TN, load activated sludge F/M, power of hydrogen pH and temperature T is selected for the experimental sample data. There are 1000 groups data are available after eliminate the abnormal, where 500 group used as training samples and the rest of 500 as test sample. The technical scheme and implementation steps as following.

(7) An intelligent identification method for sludge bulking based on a type-2 fuzzy-neural-network comprise the following steps:

(8) (1) Determine the input and output variables of sludge volume index (SVI): in the activated sludge wastewater treatment process, the input variables of SVI soft-computing model include: dissolved oxygen (DO) concentration, total nitrogen (TN) concentration, organic load rate (F/M), pH, T. The output value of soft-computing model is the SVI values. The sludge bulking contains the following fault types: low DO concentration, nutrient deficit, low sludge loading, low pH, and low temperature;

(9) (2) SVI soft-computing model: establish SVI soft-computing model based on type-2 fuzzy-neural-network, the structure of type-2 fuzzy-neural-network contains five layers: input layer, membership function layer, firing layer, consequent layer and output layer, the network is 5-15-3-2-1, including 5 neurons in input layer, 15 neurons in membership function layer, 3 neurons in firing layer, 2 neurons in consequent layer and 1 neurons in output layer; connecting weights between input layer and membership function layer are assigned 1; the number of the training sample is N, the input of type-2 fuzzy-neural-network is x(t)=[x.sub.1(t), x.sub.2(t), x.sub.3(t), x.sub.4(t), x.sub.5(t)] at time t, x.sub.1(t) represents the DO concentration at time t; x.sub.2(t) represents the TN concentration at time t, x.sub.3(t) represents the organic load rate (F/M) value at time t, x.sub.4(t) represents the pH value at time t, and x.sub.5(t) represents the T value at time t, the output of type-2 fuzzy-neural-network is y.sub.d(t) and the actual output is y(t); type-2 fuzzy-neural-network includes:

(10) {circle around (1)} input layer: there are 5 neurons in this layer, the output is:
o.sub.i(t)=x.sub.i(t)(1)
where o.sub.i(t) is the ith output value at time t, i=1, 2, . . . , 5,

(11) {circle around (2)} membership function layer: there are M neurons in membership function layer, the output is:

(12) $\begin{array}{cc}{}_m^i\left(t\right)=N\left(c_m^i\left(t\right),{}_m^i\left(t\right);o_i\left(t\right)\right)=\exp \left\{-\frac{1}{2}{\left(\frac{o_i\left(t\right)-c_m^i\left(t\right)}{{}_m^i\left(t\right)}\right)}^2\right\},i=1,2,\mathrm{.Math.},5;m=1,2,\mathrm{.Math.},M,& \left(2\right)\\ c_m^i\left(t\right)\left[{\underset{\_}{c}}_m^i\left(t\right),{\stackrel{\_}{c}}_m^i\left(t\right)\right],& \left(3\right)\end{array}$
where .sup.i.sub.m(t) is the mth membership function with the ith input at time t, N represents the membership function, c.sup.i.sub.m(t) is the uncertain center of the mth membership function neuron with the ith input at time t, c.sup.i.sub.m(t) is the lower center value of the mth membership function neuron with the ith input at time t, c.sup.i.sub.m(t) is the upper center value of the mth membership function neuron with the ith input at time t (where the initial lower center value and initial upper center value of the mth membership function neuron with the ith input i.e., c.sup.i.sub.m(0) and c.sup.i.sub.m(t) is obtained by that random initial center of the mth membership function neuron with the ith input c.sup.i.sub.m(0) add and subtract a constant), .sup.i.sub.m(t) is the standard deviation of the mth membership function neuron with the ith input at time t, the bounded internal of .sup.i.sub.m(t) is [.sup.i.sub.m(t), .sup.i.sub.m(t)]

(13) $\begin{array}{cc}{\underset{\_}{}}_m^i\left(o_i\left(t\right)\right)=\{\begin{array}{cc}N\left({\stackrel{\_}{c}}_m^i\left(t\right),{}_m^i\left(t\right);o_i\left(t\right)\right),& o_i\left(t\right)\left({\underset{\_}{c}}_m^i\left(t\right)+{\stackrel{\_}{c}}_m^i\left(t\right)\right)/2\\ N\left({\underset{\_}{c}}_m^i\left(t\right),{}_m^i\left(t\right);o_i\left(t\right)\right),& o_i\left(t\right)>\left({\underset{\_}{c}}_m^i\left(t\right)+{\stackrel{\_}{c}}_m^i\left(t\right)\right)/2\end{array},& \left(4\right)\\ {\stackrel{\_}{}}_m^i\left(o_i\left(t\right)\right)=\{\begin{array}{cc}N\left({\underset{\_}{c}}_m^i\left(t\right),{}_m^i\left(t\right);o_i\left(t\right)\right),& o_i\left(t\right){\underset{\_}{c}}_m^i\left(t\right)\\ 1,& {\underset{\_}{c}}_m^i\left(t\right)<o_i\left(t\right)<{\stackrel{\_}{c}}_m^i\left(t\right)\\ N\left({\stackrel{\_}{c}}_m^i\left(t\right),{}_m^i\left(t\right);o_i\left(t\right)\right),& o_i\left(t\right)>{\stackrel{\_}{c}}_m^i\left(t\right)\end{array},& \left(5\right)\end{array}$
where .sup.i.sub.m(t) and .sup.i.sub.m(t) are the lower value and upper value of the mth membership function neuron with the ith input at time t, respectively, 0<.sup.i.sub.m(t).sup.i.sub.m(t)1,

(14) {circle around (3)} firing layer: there are L neurons in this layer, and the output values are:

(15) $\begin{array}{cc}{F}_l\left(t\right)=\left[{\underset{\_}{f}}_l\left(t\right),{\stackrel{\_}{f}}_l\left(t\right)\right],{\underset{\_}{f}}_l\left(t\right)=\underset{i=1}{\overset{5}{.Math.}}{\underset{\_}{}}_m^i\left(t\right),{\stackrel{\_}{f}}_l\left(t\right)=\underset{i=1}{\overset{5}{.Math.}}{\stackrel{\_}{}}_m^i\left(t\right),l=1,2,\mathrm{.Math.},L,& \left(6\right)\end{array}$
where F.sub.l(t) is the firing strength of the lth firing neuron, f.sub.l(t) and f.sub.l(t) are the lower firing strength and upper firing strength of the lth firing neuron, respectively, 0<f.sub.lt)f.sub.l(t)1,

(16) {circle around (4)} consequent layer: this layer contains two consequent neurons, the output values are

(17) $\begin{array}{cc}\underset{\_}{y}\left(t\right)=\frac{\underset{l=1}{\overset{L}{.Math.}}{\underset{\_}{f}}_l\left(t\right)a_l\left(t\right)}{\underset{l=1}{\overset{L}{.Math.}}{\underset{\_}{f}}_l\left(t\right)},\stackrel{\_}{y}\left(t\right)=\frac{\underset{l=1}{\overset{L}{.Math.}}{\underset{\_}{f}}_l\left(t\right)a_l\left(t\right)}{\underset{l=1}{\overset{L}{.Math.}}{\underset{\_}{f}}_l\left(t\right)},& \left(7\right)\\ a_l\left(t\right)=\underset{l=1}{\overset{5}{.Math.}}{}_l^i\left(t\right)x_i\left(t\right),& \end{array}$
where y(t) and y(t) are the low and up output values of the consequent neurons, a.sub.i(t) is weight of the lth firing neuron, .sup.i.sub.l(t) is the weight coefficient of the lth firing neuron with the ith input at time t,

(18) {circle around (5)} output layer: the output value is:
y(t)=(t)y(t)+(1(t))y(t)(8)
where (t) and y(t) are the proportion of the low output and the output value of type-2 fuzzy-neural-network, the error of type-2 fuzzy-neural-network is:

(19) $\begin{array}{cc}E\left(t\right)=\frac{1}{N}\underset{i=1}{\overset{N}{.Math.}}{\left(y_d\left(t\right)-y\left(t\right)\right)}^2& \left(9\right)\end{array}$
where y.sub.d(t) is the output of type-2 fuzzy-neural-network and the actual output is expressed as y(t);

(20) (3) train type-2 fuzzy-neural-network

(21) {circle around (1)} give the type-2 fuzzy-neural-network, the initial number of firing layer neurons is M, M>2 is a positive integer; the input of type-2 fuzzy-neural-network is x(1), x(2), . . . , x(t), . . . , x(N), correspondingly, the output is y.sub.d(1), y.sub.d(2), . . . , y.sub.d(t), . . . , y.sub.d(N), expected error value is set to E.sub.d, E.sub.d(0, 0.01),

(22) {circle around (2)} set the learning step s=1;

(23) {circle around (3)} t=s; according to Eqs. (1)-(7), calculate the output of type-2 fuzzy-neural-network, exploiting adaptive second-order algorithm:
(t+1)=(t)+(H(t)+(t)I).sup.1v(t)(10)
where (t)=[c.sup.i.sub.m(t), c.sup.i.sub.m(t), .sup.i.sub.m(t), (t), w.sup.i.sub.m(t)] is the parameter matrix of type-2 fuzzy-neural-network at time t, c.sup.i.sub.m(t) is the lower center value of the mth membership function neuron with the ith input at time t, c.sup.i.sub.m(t) is the upper center value of the membership function neuron with the ith input at time t, .sup.i.sub.m(t) is the standard deviation of the mth membership function neuron with the ith input at time t, (t) is the proportion of the lower output, .sup.i.sub.l(t) is the weight coefficient of the lth firing neuron with the ith input at time t, H(t) is the quasi Hessian matrix, v(t) is gradient vector, I is the identity matrix and (t) is the adaptive learning rate defined as:
(t)=|E(t)|+(1)v(t)(11)
where (0, 1), the expression of H(t) and v(t) are defined as:
H(t)=J.sup.T(t)J(t)(12)
v(t)=J.sup.T(t)E(t)(13)
where the Jacobian vector J(t) is calculated as:

(24) $\begin{array}{cc}J\left(t\right)=\left[\frac{e\left(t\right)}{{\underset{\_}{c}}_m^i\left(t\right)},\frac{e\left(t\right)}{{\stackrel{\_}{c}}_m^i\left(t\right)},\frac{e\left(t\right)}{{}_m^i\left(t\right)},\frac{e\left(t\right)}{\left(t\right)},\frac{e\left(t\right)}{{}_m^i\left(t\right)}\right]& \left(14\right)\end{array}$

(25) {circle around (4)} according to Eq. (9), calculate the performance of type-2 fuzzy-neural-network, if E(t)E.sub.d, go to step {circle around (3)}; if E(t)<E.sub.d, stop the training process;

(26) The predicted results of sludge volume index SVI is shown in FIG. 2, the X axis: sample, the unit is a; Y axis: the test output of sludge volume index SVI, the unit is ml/g; the blue line is the predict output value of sludge volume index SVI; the black line is actual output values of sludge volume index SVI; The error between the predicted output and the actual output of sludge volume index (SVI) is shown in FIG. 3. The X axis: sample, the unit is a; Y axis: the test output of sludge volume index SVI, the unit is ml/g;

(27) (4) The target-related identification algorithm is used to determine the fault type of sludge bulking, which is specifically as follows:

(28) {circle around (1)} the test samples is used as the input of the type-2 fuzzy-neural-network, and the sludge volume index (SVI) is calculated;

(29) {circle around (2)} if SVI150, it is determined that there is no sludge bulking during the wastewater treatment process;

(30) {circle around (3)} if SVI>150, sludge bulking at the wastewater treatment operation was determined and regression coefficients of all variables were calculated:

(31) $\begin{array}{cc}{b}_i\left(t\right)=\frac{{u_i\left(t\right)}^T{t}_i\left(t\right)}{{t_i\left(t\right)}^T{t}_i\left(t\right)},& \left(15\right)\end{array}$
where b.sub.i(t) is the regression coefficient of ith input at time t, b(t)=[b.sub.1(t), . . . , b.sub.i(t), . . . , b.sub.5(t)] is the regression coefficient vector, u.sub.i(t) is the ith score vector of the output vector at time t, U(t)=[u.sub.1(t), . . . . , u.sub.i(t), . . . , u.sub.5(t)] is score matrix of the output vector at time t, t.sub.i(t) is the ith score vector of the input matrix at time t, T(t)=[t.sub.i(t), . . . , t.sub.i(t), . . . , t.sub.5(t)] is score matrix of the input matrix at time t, u.sub.i(t) and t.sub.i(t) are given as

(32) $\begin{array}{cc}{u}_i\left(t\right)=\frac{y\left(t\right)q_i\left(t\right)}{{q_i\left(t\right)}^T{q}_i\left(t\right)},& \left(16\right)\\ t_i\left(t\right)=\frac{X\left(t\right)w_i\left(t\right)}{{w_i\left(t\right)}^T{w}_i\left(t\right)},& \left(17\right)\end{array}$
where q.sub.i(t) is the ith loading value of output vector at time t, q(t)R.sup.15 is the loading vector of output vector at time t, y(t)=[y(tK+1), y(tK+2), . . . , y(t)].sup.T, y(t) is the SVI value at time t, X(t)=[x.sub.1(t), . . . , x.sub.i(t), . . . , x.sub.5(t)] is the input matrix of type-2 fuzzy-neural-network, x.sub.i(t)=[x.sub.i(tK+1), x.sub.i(tK+2), . . . , x.sub.i(t)].sup.T, x.sub.i(t) is the ith input variable at time t, w.sub.i(t) is the ith feature vector at time t, W(t)=[w.sub.1(t), . . . , w.sub.i(t), . . . , w.sub.5(t)] is the feature matrix of X(t).sup.Ty(t), the expressions of q.sub.i(t) and W(t) are

(33) $\begin{array}{cc}{q_i\left(t\right)}^T=\frac{{t_i\left(t\right)}^{T}y\left(t\right)}{{t_i\left(t\right)}^T{t}_i\left(t\right)},& \left(18\right)\\ {W\left(t\right)}^T\left(t\right)W\left(t\right)=E\left\{{X\left(t\right)}^{T}y\left(t\right){y\left(t\right)}^{T}X\left(t\right)\right\},& \left(19\right)\end{array}$
where (t) is the eigenvalue matrices of X(t).sup.Ty(t). The function E represents the eigenvector and eigenvalue of the matrix, the inner relative model of y(t) and X(t) can be expressed as:

(34) 0$\begin{array}{cc}\{\begin{array}{c}X\left(t\right)=T\left(t\right){P\left(t\right)}^T+\left(t\right)=\underset{i=1}{\overset{5}{.Math.}}{t}_i\left(t\right){p_i\left(t\right)}^T+\left(t\right)\\ y\left(t\right)=U\left(t\right){q\left(t\right)}^T+G\left(t\right)=\underset{i=1}{\overset{5}{.Math.}}{u}_i\left(t\right){q_i\left(t\right)}^T+G\left(t\right)\end{array},& \left(20\right)\end{array}$
where (t)R.sup.K5 is the residual matrix of X(t), (t)=[.sub.1(t), . . . , .sub.i(t), . . . , .sub.5(t)], where .sub.i(t) present the residual vector of ith input. G(t)R.sup.K1 is the residual vector of y(t);

(35) {circle around (4)} when the regression coefficient of the input variable satisfies:
b.sub.max(t)=max b(t),(21)
where b.sub.max(t) is the maximum regression coefficient of the input variables, and the corresponding fault type is the source of sludge bulking.

(36) FIG. 4 shows the fault classification of sludge bulking. X-axis: input variable, no unit, Y-axis: contribution, no unit.