US 11,144,816 B2 · Fault identifying method for sludge bulking based on a recurrent RBF neural network

Abstract

The wastewater treatment process by using activated sludge process often appear the sludge bulking fault phenomenon. Due to production conditions of wastewater treatment process, the correlation and restriction between variables, the characteristics of nonlinear and time-varying, which lead to hard identification of sludge bulking; Sludge bulking is not easy to detect and the reasons resulting in the sludge bulking are difficult to identify, are current RBF neural network is designed for detecting and identifying the causes of sludge volume index (SVI) in this patent. The method builds soft-computing model of SVI based on recurrent RBF neural network, it has been completed to the real-time prediction of SVI concentration and better accuracy were obtained. Once the fault of sludge bulking is detected, the identifying cause variables (CVI) algorithm can find the cause variables of sludge bulking. The method can effectively identify the fault of sludge bulking and ensure the safety operation of the wastewater treatment process.

A fault identification method for sludge bulking based on a recurrent radial basis function neural network (RRBFNN) comprising the following steps:

(1) determine input and output variables of sludge volume index (SVI):
for sewage treatment process of an activated sludge system, by analyzing detailed mechanism of the sludge bulking, analyzing five process variables and selecting the input variables of SVI soft-computing model:
dissolved oxygen concentration-DO, mixed liquor suspended solids concentration-MLSS, temperature-T, chemical oxygen demand-COD and total nitrogen-TN, wherein an output value of the SVI soft-computing model is SVI value;
(2) initial RRBFNN:
a structure of RRBFNN comprises three layers:
an input layer, a hidden layer and an output layer, the RRBFNN adopts 5-J−1 connection, the number of neurons of the input layer is 5, the number of neurons of the hidden layer is J, where J is an integer larger than 2, and the number of neurons of the output layer is 1;
connection weight between the input layer and the hidden layer is assigned 1, connection weight between the hidden layer and the output layer is randomly assigned a value in the range of [−1, 1];
the number of training samples is N and an input of the RRBFNN is x(t)=[x1(t), x2(t), x3(t), x4(t), x5(t)] at time t;
an expectation output of the RRBFNN is expressed as yd(t) and an actual output of the RRBFNN is expressed as y(t);
a soft-computing method of SVI is as follows:
{circle around (1)} input layer:
there are 5 neurons which represent the input variables in this layer, the output values of each neuron are as follows:
ui(t)=xi(t) (1)
wherein ui(t) is ith output value at time t, i=1, 2, . . . , 5;
and an input vector is x(t)=[x1(t), x2(t), . . . , xn(t)];
{circle around (2)} hidden layer:
there are J neurons of the hidden layer, outputs of hidden neurons are:
θ
j
⁡
(
t
)
=
e
-

h
j
⁡
(
t
)
-
c
j
⁡
(
t
)

2
2
⁢
⁢
σ
j
2
⁡
(
t
)
,
⁢
j
=
1
,
2
,
K
,
J
(
2
)
where θj(t) is an output value of jth hidden neuron at time t, e is an exponential function, cj(t)=[cj1(t), . . . , cj5(t)]T is a center vector of the jth hidden neuron at time t, ∥hj(t)−cj(t)∥ is Euclidean distance between hj(t) and cj(t), σj(t) is a width of the jth hidden neuron at time t, hj(t) is input vector of the jth hidden neuron at time t described as
hj(1)=[u1(t),u2(t), . . . u5(t),vj(t)×y(t−1)]T (3)
where u1(t) is dissolved oxygen concentration at time t, u2(t) is mixed liquor suspended solids concentration at time t, u3(t) is temperature at time t, u4(t) is chemical oxygen demand at time t, u5(t) is total nitrogen at time t, y(t−1) is an output value of an output neuron at time t−1, vj(t) denotes the connection weight from th output layer to the jth hidden neuron at time t, and v(t)=[v1(t), v2(t), . . . , vJ(t)]T is a vector of connection weight from the output laver to the hidden layer at time t, T represents transpose;
{circle around (3)} output layer:
there is only one node in this layer, the output is:
y
⁡
(
t
)
=
f
⁡
(
w
⁡
(
t
)
,
θ
⁡
(
t
)
)
=
∑
j
=
1
J
⁢
w
j
⁡
(
t
)
×
θ
j
⁡
(
t
)
,
⁢
j
=
1
,
L
,
J
(
4
)
where w(t)=[w1(t), w2(t), . . . , wJ(t)]T is a vector of connection weight from the hidden layer to the output layer at time t, wj(t) is connection weight from the jth hidden neuron to the output layer at time t, θ(t)=[θ1(t), θ2(t), . . . , θJ(t)]T is an output vector of the hidden layer, y(t) represents the output of RRBFNN at time t;
the error of RRBFNN is:
E
⁡
(
t
)
=
1
N
⁢
∑
t
=
1
N
⁢
(
y
d
⁡
(
t
)
-
y
⁡
(
t
)
)
2
(
5
)
yd(t) is an expectation output of the RRBFNN and an actual output is expressed as y(t);
(3) train RRBFNN:
{circle around (1)} given the RRBFNN, the input of RRBFNN is x(1), x(2), . . . , x(t), . . . , x(N), correspondingly, the expectation output is yd(1), yd(2), . . . , yd(t), . . . , yd(N), expected error value is set to Ed, Ed∈(0, 0.01);
initial centre value cj(1)∈(−2, 2), width value σj(1)∈(0, 1), initial feedback weight vj(1)∈(0, 1), j=1, 2, . . . , J;
initial weight w(1)∈(0, 1);
{circle around (2)} set the learning step s=1;
{circle around (3)} t=s;
according to Eqs. (1)-(4), calculate the output of RRBFNN, exploiting fast gradient descent algorithm:
⁢
c
j
⁡
(
t
+
1
)
=
c
j
⁡
(
t
)
-
η
c
⁢
1
σ
j
2
⁢
(
y
d
⁡
(
t
)
-
y
⁡
(
t
)
)
⁢
w
j
⁡
(
t
)
×
θ
⁡
(
t
)
⁡
[
h
j
⁡
(
t
)
-
c
j
⁡
(
t
)
]
(
6
)
σ
j
⁡
(
t
+
1
)
=
σ
j
⁡
(
t
)
-
η
σ
⁢
1
σ
j
3
⁢
(
y
d
⁡
(
t
)
=
y
⁡
(
t
)
)
⁢
w
j
⁡
(
t
)
×
θ
⁡
(
t
)
⁢

h
j
⁡
(
t
)
-
c
j
⁡
(
t
)

2
(
7
)
⁢
v
j
⁡
(
t
+
1
)
=
v
j
⁡
(
t
)
-
η
v
⁡
(
y
d
⁡
(
t
)
-
y
⁡
(
t
)
)
⁢
w
j
⁡
(
t
)
⁢
θ
⁡
(
t
)
⁢
y
⁡
(
t
-
1
)
(
8
)
⁢
w
j
⁡
(
t
+
1
)
=
w
j
⁡
(
t
)
-
η
w
⁡
(
y
d
⁡
(
t
)
-
y
⁡
(
t
)
)
⁢
θ
j
⁡
(
t
)
(
9
)
ηc, ησ, ηv, ηw are the learning rate of centre, width, feedback connection weight from output layer to hidden layer and the connection weight between hidden layer and output layer, respectively;
in addition, ηc∈(0, 0.01], ησ∈(0, 0.01], ηvE (0, 0.02], ηw∈(0, 0.01];
cj(t+1)=[c1j(t+1), c2j(t+1), . . . , c5j(t+1)] denotes the center vector of the jth hidden neuron at time t+1, σj(t+1) is the radius or width of the jth hidden neuron at time t+1, vj(t+1) denotes the connection weight from output layer to the jth hidden neuron at time t+1, wj(t+1) is the connection weights between the hidden neurons and output neuron at time t+1;
{circle around (4)} increase 1 learning step s, if s<N, then turn to step {circle around (3)};
if s=N, turn to step {circle around (5)};
{circle around (5)} according to Eq. (5), calculate the performance of RRBFNN, if E(t)≥Ed, then turn to step {circle around (3)};
if E(t)<Ed, stop the training process;
(4) SVI concentration prediction:
testing samples used as the input of RRBFNN, the output of neural network is the soft-computing values of SVI;
(5) cause variable identification (CVI) algorithm for sludge bulking:
{circle around (1)} fault condition setting:
calculate a residual of the expectation output and the output of RRBFNN at time t, if
{
y
⁡
(
t
)
-
y
d
⁡
(
t
)
≥
5
y
⁡
(
t
)
≥
150
(
10
)
then turn to step {circle around (2)}, otherwise, stop the process of fault identification for sludge bulking;
{circle around (2)} fault point finding:
define two formula:
{
IC
1
⁡
(
t
)
=
δ
T
⁡
(
t
)
⁢
Λ
M
-
1
⁡
(
t
)
⁢
δ
⁡
(
t
)
IC
2
⁡
(
t
)
=

θ
M
⁡
(
t
)

2
-
δ
T
⁡
(
t
)
⁢
δ
⁡
(
t
)
(
11
)
wherein IC1(t) is a Mahalanobis distance of input variables at time t and IC2(t) is a squared prediction error at time t, M is numbers of principal component of input data;
K is a number of front samples, δ(t)=[δ1(t), . . . , δi(t), . . . , δ5(t)]T is a projection of the training data, and δm(t) is
δ
m
⁡
(
t
)
=
∑
k
=
1
K
⁢
a
k
⁡
(
t
)
⁢
(
θ
_
m
⁡
(
t
)
·
θ
_
new
⁡
(
t
)
)
,
k
=
1
,
L
,
K
;
m
=
1
,
L
,
M
(
12
)
wherein θnew(t) is a mean-centered output vector of the hidden layer for M principal components training data at time t, θm(t) is the output vector of the hidden layer for the mth principal component training data at time t, ak(t) is a constant, and ak(t)∈(0, 0.01];
a diagonal matrix of eigenvalues associated with M principal components is defined as
where λ1(t), λ2(t), λ3(t), λ4(t) and λ5(t) are eigenvalues of training data matrix:
Λ(t) satisfies
Λ
M
⁡
(
t
)
=
[
λ
1
λ
2
O
λ
M
]
⁢
(
λ
1
≥
λ
2
≥
L
≥
λ
M
≥
0
)
(
13
)
where λ1, λ2, . . . and λM are the eigenvalues of training data matrix, ΛM(t) is the diagonal matrix of eigenvalues at time t and satisfies
wherein l′(t) is a constant value, I(t) is a unit matrix, {tilde over (C)}(t) is a regularized covariance matrix of C(t) at time, C(t) is a mean square of hidden output vector:
Ω
⁡
(
t
)
=
θ
⁡
(
t
)
T
⁢
⁢
C
%
-
1
⁡
(
t
)
⁢
θ
⁡
(
t
)
⁢
(
15
)
Ω
⁡
(
t
)
=
IC
1
⁡
(
t
)
+
l
′
-
1
⁡
(
t
)
⁢
IC
2
⁡
(
t
)
(
16
)
C
⁡
(
t
)
=
1
K
⁢
∑
k
=
1
K
⁢
θ
k
⁡
(
t
)
⁢
θ
k
⁡
(
t
)
T
(
17
)
where Ω(t) is an energy of each variable, θk(t) is the hidden output vector of the kth principal component at time t;
the constant vector a(t)=[a1(t), . . . aj(t), . . . aK(t)]T is given as
λ
⁡
(
t
)
⁢
a
⁡
(
t
)
=
1
K
⁢
G
⁡
(
t
)
⁢
a
⁡
(
t
)
(
18
)
G(t) is a Gaussian matrix and λ(t) denotes an eigenvalue
G(t)={θi(t)·θj(t)}K×K (19)
λ(t)p(t)=C(t)p(t) (20)
p(t) denotes an eigenvector of a covariance matrix C(t) at time t;
{circle around (3)} cause variable identification:
for the ith input variable, a contribution degree index satisfies:
G
i
⁡
(
t
)
=
κ
i
⁡
(
t
)
∑
i
=
1
n
⁢
κ
i
⁡
(
t
)
(
21
)
where Gi(t) is the contribution degree index of ith variable at time t, κi(t) is the contribution degree which is calculated by mutual information between this testing samples and difference sets for testing samples xi(t) of ith variable at time t, which can be expressed as
κi(t)=I(xi(t),VΔ(t)) (22)
I(xi(t), VΔ(t)) is the mutual information of xi(t) and VΔ(t) at time t, VΔ(t) is difference matrix sets of data of training set and testing set at time t, which is expressed as
VΔ(t)=Vtr(t)−Vte(t) (23)
where Vtr(t) and Vte(t) is independent data sets of training set and testing set at time t, respectively:
Vtr(t)=D−1(t)G(t) (24)
Vte(t)=Dte−1(t)Gte(t) (25)
D(t) is a covariance matrix of Φ(t) at time t, Φ(t) is output matrix of hidden layer at time t,
D(t)=E{Φ(t)ΦT(t)} (26)
Φ(t)=[θ(t−K+1), . . . ,θ(t−1),θ(t)]T (27)
where E(Φ(t)) is the expectation of Φ(t), Φ(t) is output matrix of hidden layer at time t, θ(t−K+1) is the hidden output vector at time t−K+1;
{circle around (4)} for the ith input variable, if the Gi(t) at time t satisfies:
G1(t)+ . . . Gi(t)≥0.8 (28)
where variables 1, . . . , i are cause variables resulted in sludge bulking.

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Fault identifying method for sludge bulking based on a recurrent RBF neural network

Life of this patent

Fault identifying method for sludge bulking based on a recurrent RBF neural network

Life of this patent

Abstract

Claims1