US2017061305A1PendingUtilityA1
Fuzzy curve analysis based soft sensor modeling method using time difference Gaussian process regression
Est. expiryAug 28, 2035(~9.1 yrs left)· nominal 20-yr term from priority
G06N 5/048G06N 5/022F23N 2223/52
38
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Claims
Abstract
The invention provides a fuzzy curve analysis based soft sensor modeling method using time difference Gaussian process regression, it is suitable for application in chemical process with time delay characteristics. This method can extract stable delay information from the historical database of process and introduce more relevant modeling data sequence to the dominant variable sequence. First of all, the method of fuzzy curve analysis (FCA) can intuitively judge the importance of the input sequence to the output sequence, estimate the time-delay parameters of process, and such offline time-delay parameter set can be utilized to restructure the modeling data. For the new input data, based on the historical variable value before a certain time, the current dominant value can be predicted by time difference Gaussian Process Regression (TDGPR) model. This method does not encounter the problem of model updating and can effectively track the drift between input and output data. Compared with steady-state modeling methods, this invention can achieve more accurate predictions of the key variable, thus improving product quality and reducing production costs.
Claims
exact text as granted — not AI-modifiedWhat is claimed is:
1 . A soft sensor modeling method of fuzzy curve analysis based time difference Gaussian process regression, wherein the method comprises the following steps:
step 1: collecting input and output variables of a process, constructing a historical training database and obtaining N samples: {X(t), y(t)}, t=1, 2, . . . , N; and then preprocessing the data; according to a process mechanism and experience, determining a maximum time delay T max existing in auxiliary variables; step2: for each original auxiliary variable x i , i∈{1, 2, . . . , m}, extending it to input variable set with time delay {x i (t−λ), λ=0, 1, . . . , T max }, wherein an extension mode is:
Φ
it
(
x
i
)
=
exp
[
-
(
x
i
(
t
)
-
x
i
b
)
2
]
(
2
)
step 3: determining importance of each variable in time delay input variable set by fuzzy curve analysis and obtaining an optimal time delay variable x i (t−d i ); wherein determining the importance comprises:
wherein the input variable set is {x i , i=1, 2, . . . , m} and output variable is y, for input an variable x i , whose sample value collected at time t is denoted as x i (t), for (x i (t),y(t)), a fuzzy membership function of variable x i is defined as:
Φ
it
(
x
i
)
=
exp
[
-
(
x
i
(
t
)
-
x
i
b
)
2
]
,
(
2
)
wherein for each x i , {Φ it , y(t)} provides a fuzzy rule which is described as {if x i is Φ it (x i ), then y is y(t)}, and Φ it is a fuzzy membership function of input variable x i at the t-th data point;
wherein in formula (2), a Gaussian fuzzy membership function is selected; wherein b is determined as 20% the range of variable x i ; wherein as a result, for N training samples, each sample corresponding to each variable has N fuzzy rules; in the fuzzy membership function, Φ it =1 holds true at each point {x i (t),y(t)};
wherein for time delay process, by introducing time delay information, the original variable x i becomes (T max +1)-dimensional, which can be expressed as x i (t−λ), λ=0, 1, . . . , T max , λ is a variable delay value introduced; fuzzy curve C i,λ with the condition that λ is the i-th variable delay value can be obtained by making centroid defuzzification of each new expanded variable with formula (3);
wherein as shown in the formula (4), d i is the λ which can make the maximum coverage of fuzzy curve C i,λ ;
wherein C i,λ (λ) max is the maximum value of the fuzzy curve point range, while C i,λ (λ) min is the minimum value of the fuzzy curve point range;
C
i
,
λ
(
λ
)
=
∑
i
=
1
N
Φ
it
[
x
i
(
t
-
λ
)
]
·
y
(
t
)
∑
i
=
1
N
Φ
it
[
x
i
(
t
-
λ
)
]
(
3
)
d
i
=
argmax
λ
[
C
i
,
λ
(
λ
)
max
-
C
i
,
λ
(
λ
)
min
]
(
4
)
wherein, if the scope of the C i,λ (λ) range is closer to that of y, then the input variable x i (t−λ) is more important;
wherein the important degree of each variable is determined by sorting the coverage of C i,λ (λ);
wherein the optimal time delay variable x i (t−d i ) is obtained;
step 4: using obtained x i (t−d i ) in step 3 to form a delay input set X d (t)=[x 1 (t−d 1 ), x 2 (t−d 2 ), . . . , x m (t−d m )] T , and reconstructing soft sensor training sample set {X d (t),y(t)};
wherein if there is a new input sample X(t+1) available, then the delay input set could be restructured based on historical database samples with the same parameters, then go to step 5, otherwise, wait for the arrival of new data;
step 5: processing the training set and the new data by j order time difference treatment, wherein the value of j is determinable according to a sampling period and property of dominant variable;
wherein a formula for time difference step is:
Δ X d,j ( t )= X d ( t )− X d ( t−j )
Δ y j ( t )= y ( t )− y ( t−j ) (5)
establishing a Gaussian process model between differential input samples and output samples;
wherein a Gaussian process regression algorithm is presented as follows:
wherein given training sample sets X∈R m×N and y∈R N , m is the dimension of input data points, N is the number of samples, and the relationship between input sample x i ∈′″ and output sample y i ∈R satisfies:
y i =f ( x i )+ε
ε˜ N (0,σ n 2 ) (6)
wherein in formula (6), f is an unknown function, ε is Gaussian noise with zero mean and σ n 2 variance; for a new input sample, its corresponding probability prediction output also follows Gaussian distribution and the joint Gaussian distribution N( f gp , cov(f gp )) is described as below:
f gp |X,y,x * ˜N ( f gp ,cov( f gp ))
s.i. f gp = k ( x * ,X )[ K ( X,X )+σ n 2 I n ] −1 y
cov( f gp )= k ( x * ,x * )− k ( X,x * ) T [K ( X,X )+σ n 2 I n ] −1 ·k ( X,x * ) (7)
wherein K(X, X) is a n-dimensional covariance matrix of training samples;
wherein k(x * ,X) is a covariance vector between test sample and training samples;
wherein k(x * ,x * ) is the autocovariance of test sample;
wherein a Gaussian covariance function is:
k
(
x
p
,
x
q
)
=
v
exp
[
-
1
2
∑
d
=
1
m
π
d
(
x
p
d
-
x
q
d
)
2
]
(
8
)
wherein, in GPR algorithm, hyper-parameter Θ gp =(v, π 1 , . . . , π D , σ n 2 ) is obtained via maximum likelihood estimation approach;
wherein the likelihood function is derived as:
L
(
Θ
gp
)
=
-
1
2
y
T
[
K
(
X
,
X
)
+
σ
n
2
I
]
-
1
y
-
1
2
log
det
[
K
(
X
,
X
)
+
σ
n
2
I
]
-
n
2
log
2
π
(
9
)
wherein the hyper-parameter Θ gp is set to be a random value within a reasonable range in the first place;
wherein the conjugate gradient algorithm is utilized to obtain the optimized parameter set;
wherein after obtaining the optimal hyper-parameter, for the test sample x * , formula (7) is used to estimate the output value of GPR model;
step 6: after all samples are restructured with delays, when a new input data arrives at time t+1, based on y j (t+1−j), calculating a predictive value y j,pred (t+1) by TDGPR algorithm, wherein the formula is presented as below:
Δ X d,j ( t+ 1)= X d ( t+ 1)− X d ( t+ 1− j )
Δ y j,pred ( t+ 1)= f GPR (Δ X d,j ( t+ 1))
y j,pred ( t+ 1)= y j ( t+ 1− j )+Δ y j,pred ( t+ 1) (10)
wherein y j,pred (t+1) in formula (10) is the final dominant variable prediction value of the present invention.
2 . A soft sensor modeling method of fuzzy curve analysis based time difference Gaussian process regression according to claim 1 , characterized in that this method extracts information of variable delay from process historical database, reconstructing soft sensor modeling data and correcting causal relationship between input and output data.Join the waitlist — get patent alerts
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