Summary of the invention
The problem existing for prior art, the invention provides a kind of penicillin fermentation process method for diagnosing faults based on the reconstruct of core offset minimum binary.
Technical scheme of the present invention is achieved in that
Based on the penicillin fermentation process method for diagnosing faults of core offset minimum binary reconstruct, comprise the following steps:
Step 1: gather the historical normal data of off-line of penicillin fermentation process, comprise the historical normal data set of penicillin fermentation process performance variable off-line and the historical normal data set of penicillin fermentation process state variable off-line;
Penicillin fermentation process performance variable comprises the temperature of temperature, pH value and the fermentation reactor of flow velocity, the substrate feeding of ventilation rate, agitator power, substrate feeding;
Penicillin fermentation process state variable comprises the concentration of penicillin, the heat that penicillin reaction produces, concentration, the volume of nutrient culture media and the concentration of thalline of carbon dioxide;
Step 2: respectively the historical normal data set of penicillin fermentation process performance variable off-line and the historical normal data set of penicillin fermentation process state variable off-line are carried out to specification and standardization;
Step 3: utilize improved core offset minimum binary method to set up the malfunction monitoring model of penicillin fermentation process, this model be input as the historical normal data set of penicillin fermentation process performance variable off-line, this model is output as the historical normal data set of penicillin fermentation process state variable off-line;
Step 3.1: data core mapping: historical penicillin fermentation process performance variable off-line normal data set is mapped to high-dimensional feature space by kernel function from original data space;
Step 3.2: utilize kernel partial least squares that historical penicillin fermentation process performance variable off-line normal data set and the historical normal data set of penicillin fermentation process state variable off-line are divided into respectively to principal component space and residual error space;
Step 3.3: utilize principal component space that kernel principal component analysis is residual error space by the residual error spatial division of historical penicillin fermentation process performance variable off-line normal data set and the residual error space in residual error space, and then obtain the malfunction monitoring model of penicillin fermentation process:
Historical penicillin fermentation process performance variable off-line normal data set is expressed as to data set, the data set of principal component space in residual error space and the data set sum in the residual error space in residual error space of its principal component space, historical penicillin fermentation process state variable off-line normal data set is expressed as to the data set of its principal component space and the data set sum in residual error space;
Step 4: utilize the malfunction monitoring model of penicillin fermentation process, the fault of on-line monitoring penicillin fermentation process;
Step 4.1: obtain online penicillin fermentation process performance variable data and penicillin fermentation process state variable data;
Step 4.2: the penicillin fermentation process performance variable data of obtaining online and penicillin fermentation process state variable data are carried out to specification and standardization;
Step 4.3: data core mapping: the penicillin fermentation process performance variable data of obtaining are online mapped to high-dimensional feature space by kernel function from original data space;
Step 4.4: calculate Hotelling statistic in the principal component space of the historical normal data set of penicillin fermentation process performance variable off-line of the penicillin fermentation process performance variable data obtained online, online Hotelling statistic in the residual error space of the historical normal data set of penicillin fermentation process performance variable off-line of the penicillin fermentation process performance variable data obtained and the penicillin fermentation process performance variable data obtained the online SPE statistic in the residual error space of the historical normal data set of penicillin fermentation process performance variable off-line;
Step 4.5: the Hotelling statistic of the penicillin fermentation process performance variable data of obtaining online that judgement calculates in the principal component space of the historical normal data set of penicillin fermentation process performance variable off-line, in the Hotelling statistic of the penicillin fermentation process performance variable data of obtaining online in the residual error space of the historical normal data set of penicillin fermentation process performance variable off-line and the penicillin fermentation process performance variable data obtained the online SPE statistic in the residual error space of penicillin fermentation process performance variable off-line history normal data set, whether there is at least one statistic higher than its corresponding confidence limit: be, current penicillin fermentation process breaks down, execution step 5, otherwise return to step 4.1,
Step 5: set up the relevant direction model of penicillin fermentation process fault based on the reconstruct of improved core offset minimum binary;
Step 5.1: gather the off-line historical failure data of penicillin fermentation process, comprise penicillin fermentation process performance variable off-line historical failure data set and penicillin fermentation process state variable off-line historical failure data set;
Step 5.2: penicillin fermentation process performance variable off-line historical failure data set and penicillin fermentation process state variable off-line historical failure data set are carried out to specification and standardization;
Step 5.3: penicillin fermentation process performance variable off-line historical failure data set is mapped to high-dimensional feature space by kernel function from original data space;
Step 5.4: according to the historical normal data set of penicillin fermentation process performance variable off-line and penicillin fermentation process performance variable off-line historical failure data set, the fault related direction of the principal component space of reconstruct penicillin fermentation process performance variable off-line historical failure data set;
Step 5.4.1: utilize core offset minimum binary method that penicillin fermentation process performance variable off-line historical failure data set and the historical normal data set of penicillin fermentation process performance variable off-line are divided respectively to principal component space and residual error space, obtain respectively the core partial least square model of penicillin fermentation process performance variable off-line historical failure data set and the core partial least square model of the historical normal data set of penicillin fermentation process performance variable off-line;
Step 5.4.2: the data set of the principal component space of historical penicillin fermentation process performance variable off-line normal data set respectively orthogonal mapping to the load matrix in the load matrix of the principal component space of penicillin operational process performance variable off-line historical failure data set and the residual error space of penicillin operational process performance variable off-line historical failure data set, obtain the data set in the residual error space of the principal component space of the penicillin fermentation process performance variable off-line history normal data set after data set and the orthogonal mapping of principal component space of the principal component space of the historical normal data set of penicillin fermentation process performance variable off-line after orthogonal mapping;
Step 5.4.3: utilize kernel principal component analysis to determine the pivot of the data set in the residual error space of the principal component space of the historical normal data set of penicillin fermentation process performance variable off-line after pivot and the orthogonal mapping of data set of the principal component space of the principal component space of the historical normal data set of penicillin fermentation process performance variable off-line after orthogonal mapping;
Step 5.4.4: the pivot in the load matrix direction in the residual error space of the principal component space of the historical normal data set of penicillin fermentation process performance variable off-line of the data set in the pivot in the load matrix direction of the principal component space of the principal component space of the historical normal data set of penicillin fermentation process performance variable off-line of the data set of principal component space of asking respectively penicillin fermentation process performance variable off-line historical failure data set after orthogonal mapping and the residual error space of penicillin fermentation process performance variable off-line historical failure data set after orthogonal mapping, obtains respectively the fault pivot of principal component space of penicillin fermentation process performance variable off-line historical failure data set and the fault pivot in the residual error space of penicillin fermentation process performance variable off-line historical failure data set;
Step 5.4.5: proportion in the pivot of the principal component space of the principal component space of the historical normal data set of penicillin fermentation process performance variable off-line of the fault pivot of the principal component space of calculating penicillin fermentation process performance variable off-line historical failure data set after orthogonal mapping, proportion in the pivot in the residual error space of the principal component space of the historical normal data set of penicillin fermentation process performance variable off-line of the fault pivot in the residual error space of calculating penicillin fermentation process performance variable off-line historical failure data set after orthogonal mapping;
Step 5.4.6: the fault pivot that is greater than the residual error space of the historical normal data set of penicillin fermentation process performance variable off-line after fault pivot and the orthogonal mapping of principal component space of the corresponding penicillin fermentation process performance variable of the each ratio value off-line historical failure data set of the ratio lower limit of setting in two class ratio values forms respectively the pivot direction of principal component space of new penicillin fermentation process performance variable off-line historical failure data set and the pivot direction in the residual error space of new penicillin fermentation process performance variable off-line historical failure data set;
Step 5.4.7: load matrix corresponding to pivot direction of utilizing the residual error space of load matrix corresponding to the pivot direction of principal component space of new penicillin fermentation process performance variable off-line historical failure data set and new penicillin fermentation process performance variable off-line historical failure data set, the load matrix in the residual error space of the principal component space of the load matrix of the principal component space of the principal component space of the historical normal data set of reconstruct penicillin fermentation process performance variable off-line and the historical normal data set of penicillin fermentation process performance variable off-line, it is the fault related direction of the principal component space of penicillin fermentation process performance variable off-line historical failure data set,
Step 5.5: according to the fault related direction of the principal component space in the residual error space of the historical normal data set of penicillin fermentation process performance variable off-line and penicillin fermentation process performance variable off-line historical failure Data set reconstruction penicillin fermentation process performance variable off-line historical failure data set;
Step 5.5.1: utilize core pivot element analysis method, be the principal component space in residual error space and the residual error space in residual error space by the residual error spatial division of the residual error space of penicillin fermentation process performance variable off-line historical failure data set and the historical normal data set of penicillin fermentation process performance variable off-line respectively, obtain respectively the kernel pivot model in residual error space of penicillin fermentation process performance variable off-line historical failure data set and the kernel pivot model in the residual error space of the historical normal data set of penicillin fermentation process performance variable off-line;
Step 5.5.2: the data set of the principal component space in the residual error space of historical penicillin fermentation process performance variable off-line normal data set respectively orthogonal mapping to the load matrix in the residual error space in the load matrix of the principal component space in the residual error space of penicillin fermentation process performance variable off-line historical failure data set and the residual error space of penicillin fermentation process performance variable off-line historical failure data set, obtain the data set in the residual error space in the residual error space of the penicillin fermentation process performance variable off-line history normal data set after data set and the orthogonal mapping of principal component space in the residual error space of the historical normal data set of penicillin fermentation process performance variable off-line after orthogonal mapping;
Step 5.5.3: utilize kernel principal component analysis to determine the pivot of the data set in the residual error space in the residual error space of the penicillin fermentation process performance variable off-line historical failure data set after pivot and the orthogonal mapping of data set of the principal component space in the residual error space of the historical normal data set of penicillin fermentation process performance variable off-line after orthogonal mapping;
Step 5.5.4: the pivot in the load matrix direction of the principal component space in the residual error space of the historical normal data set of penicillin fermentation process performance variable off-line of the data set of principal component space of asking the residual error space of the historical normal data set of penicillin fermentation process performance variable off-line after orthogonal mapping, pivot in the load matrix direction in the residual error space in the residual error space of the penicillin fermentation process performance variable off-line historical failure data set of the data set in residual error space of asking the residual error space of the historical normal data set of penicillin fermentation process performance variable off-line after orthogonal mapping, it is the fault pivot in the fault pivot of principal component space in the residual error space of the historical normal data set of penicillin fermentation process performance variable off-line and the residual error space in the residual error space of the historical normal data set of penicillin fermentation process performance variable off-line,
Step 5.5.5: proportion in the pivot of the principal component space in the residual error space of the historical normal data set of penicillin fermentation process performance variable off-line of the fault pivot of the principal component space in the residual error space of the historical normal data set of calculating penicillin fermentation process performance variable off-line after orthogonal mapping, proportion in the pivot of fault pivot principal component space in the residual error space of penicillin fermentation process performance variable off-line historical failure data set after orthogonal mapping in the residual error space in the residual error space of the historical normal data set of calculating penicillin fermentation process performance variable off-line;
Step 5.5.6: the fault pivot that is greater than the residual error space in the fault pivot of principal component space in the residual error space of the corresponding penicillin fermentation process performance variable of the each ratio value off-line historical failure data set of the ratio lower limit of setting and the residual error space of the historical normal data set of penicillin fermentation process performance variable off-line in two class ratio values forms respectively the pivot direction in the pivot direction of principal component space in the residual error space of new penicillin fermentation process performance variable off-line historical failure data set and the residual error space in the residual error space of new penicillin fermentation process performance variable off-line historical failure data set;
Step 5.5.7: load matrix corresponding to pivot direction of utilizing the residual error space in the residual error space of load matrix corresponding to the pivot direction of principal component space in the residual error space of new penicillin fermentation process performance variable off-line historical failure data set and new penicillin fermentation process performance variable off-line historical failure data set, the load matrix in the residual error space in the load matrix of the principal component space in the residual error space of reconstruct penicillin fermentation process performance variable off-line historical failure data set and the residual error space of penicillin fermentation process performance variable off-line historical failure data set, it is the fault related direction of the principal component space in the residual error space of penicillin fermentation process performance variable off-line historical failure data set,
Step 5.6: according to the fault related direction in the residual error space in the residual error space of the historical normal data set of penicillin fermentation process performance variable off-line and penicillin fermentation process performance variable off-line historical failure Data set reconstruction penicillin fermentation process performance variable off-line historical failure data set;
Step 5.6.1: by the data set in the residual error space in the residual error space of historical penicillin fermentation process performance variable off-line normal data set respectively orthogonal mapping to the load matrix in the residual error space in the load matrix of the principal component space in the residual error space of penicillin fermentation process performance variable off-line historical failure data set and the residual error space of penicillin fermentation process performance variable off-line historical failure data set, obtain the residual error space in the residual error space in the residual error space of the penicillin fermentation process performance variable off-line history normal data set after principal component space and the orthogonal mapping in residual error space in the residual error space of the historical normal data set of penicillin fermentation process performance variable off-line after orthogonal mapping;
Step 5.6.2: utilize kernel principal component analysis to determine the pivot of the data set in the residual error space in the residual error space in the residual error space of the historical normal data set of penicillin fermentation process performance variable off-line after pivot and the orthogonal mapping of data set of the principal component space in the residual error space in the residual error space of the historical normal data set of penicillin fermentation process performance variable off-line after orthogonal mapping;
Step 5.6.3: the load matrix that the data set of the principal component space in the residual error space of the historical normal data set of penicillin fermentation process performance variable off-line is mapped to the principal component space in the residual error space in the residual error space of the historical normal data set of penicillin fermentation process performance variable off-line after orthogonal mapping, the data set in the residual error space in the residual error space of the historical normal data set of penicillin fermentation process performance variable off-line is mapped to the load matrix in the residual error space in the residual error space in the residual error space of the historical normal data set of penicillin fermentation process performance variable off-line after orthogonal mapping, obtain the data set of the mapping space in the residual error space in the data set of mapping space of the principal component space in the residual error space in the residual error space of the historical normal data set of penicillin fermentation process performance variable off-line and the residual error space in the residual error space of the historical normal data set of penicillin fermentation process performance variable off-line,
Step 5.6.4: the data set of the principal component space in the residual error space of calculating penicillin fermentation process performance variable off-line historical failure data set is to the distance of the load matrix of the data set of the mapping space of the principal component space in the residual error space in the residual error space of the historical normal data set of penicillin fermentation process performance variable off-line, the data set in the residual error space in the residual error space of the historical normal data set of calculating penicillin fermentation process performance variable off-line is to the distance of the load matrix of the data set of the mapping space in the residual error space in the residual error space in the residual error space of the historical normal data set of penicillin fermentation process performance variable off-line, and calculate the ratio of two distances,
Step 5.6.5: the data set in the residual error space in the residual error space of calculating penicillin fermentation process performance variable off-line historical failure data set is to the distance of the load matrix of the data set of the mapping space of the principal component space in the residual error space in the residual error space of the historical normal data set of penicillin fermentation process performance variable off-line, the data set in the residual error space in the residual error space of the historical normal data set of calculating penicillin fermentation process performance variable off-line is to the distance of the load matrix of the data set of the mapping space in the residual error space in the residual error space in the residual error space of the historical normal data set of penicillin fermentation process performance variable off-line, and calculate the ratio of two distances,
Step 5.6.6: the ratio of this two classes distance is greater than the pivot direction that the principal component space in residual error space of penicillin fermentation process performance variable off-line historical failure data set that the ratio of its all distances of setting ratio lower limit is corresponding and the residual error space in the residual error space of penicillin fermentation process performance variable off-line historical failure data set form respectively the residual error space in the pivot direction of principal component space in the residual error space in the residual error space of new penicillin fermentation process performance variable off-line historical failure data set and the residual error space in the residual error space of new penicillin fermentation process performance variable off-line historical failure data set;
Step 5.6.7: utilize the pivot direction in the residual error space in the pivot direction of principal component space in the residual error space in the residual error space of new penicillin fermentation process performance variable off-line historical failure data set and the residual error space in the residual error space of new penicillin fermentation process performance variable off-line historical failure data set, the fault related direction in the residual error space in the residual error space of the historical normal data set of reconstruct penicillin fermentation process performance variable off-line;
Step 5.7: for all faults of penicillin fermentation process, applying step 5.1-5.6 reconstructs respectively the fault related direction of the principal component space of penicillin fermentation process performance variable off-line historical failure data set, the fault related direction of the principal component space in the residual error space of penicillin fermentation process performance variable off-line historical failure data set, the fault related direction in the residual error space in the residual error space of the historical normal data set of penicillin fermentation process performance variable off-line forms the penicillin fermentation process fault related direction based on the reconstruct of improved core offset minimum binary, thereby set up the model bank of the penicillin fermentation process fault related direction of improved core offset minimum binary reconstruct,
Step 6: utilize the relevant direction model of penicillin fermentation process fault to carry out penicillin fermentation process fault diagnosis;
Step 6.1: according to the fault related direction of the principal component space of penicillin fermentation process performance variable off-line historical failure data set, calculate score matrix and the corresponding Hotelling statistic thereof of the principal component space of the penicillin fermentation process performance variable data of obtaining online;
Step 6.2: according to the fault related direction of the principal component space in the residual error space of penicillin fermentation process performance variable off-line historical failure data set, calculate score matrix and the corresponding Hotelling statistic thereof in the residual error space of the penicillin fermentation process performance variable data of obtaining online;
Step 6.3: according to the fault related direction in the residual error space in the residual error space of the historical normal data set of penicillin fermentation process performance variable off-line, calculate the SPE statistic in the residual error space of the penicillin fermentation process performance variable data of obtaining online;
Step 6.4: the Hotelling statistic of the principal component space of the penicillin fermentation process performance variable data obtained online of judgement, online the residual error space of the penicillin fermentation process performance variable data obtained Hotelling statistic, whether the SPE statistic in the residual error space of the penicillin fermentation process performance variable data obtained all lower than the confidence limit separately of setting online, be,, when prior fault is fault real in penicillin fermentation process, be out of order combination or new fault otherwise work as prior fault.
Beneficial effect:
1. in the monitoring of traditional kernel partial least squares: have some variablees and output orthogonal in (1) principal component space, these variablees are irrelevant with output; (2) kernel partial least squares is not as kernel principal component analysis, the method of successively decreasing according to eigenwert is extracted pivot, therefore the variable in residual error space is not applied the problem of SPE statistic monitoring for classic method, the present invention is divided into the input space: with the directly related principal component space of output, with the irrelevant principal component space (principal component space in residual error space) of output and with the irrelevant residual error space (the residual error space in residual error space) of output.Compared with classic method, both monitored the input variable relevant with output, monitor accurately again and input relevant variable.
2,, thus the method for improved Kernel partial least squares regression is reconstructed to the different faults type monitoring in penicillin fermentation process.By the method for improved Kernel partial least squares regression, the performance variable that production run is obtained has carried out correlativity processing, use data after treatment to be reconstructed and to set up improved core offset minimum binary reconstruct monitoring model, by the simulation experiment result, validity of the present invention and feasibility have been described.
Embodiment
Below in conjunction with accompanying drawing, the specific embodiment of the present invention is elaborated.
Because the fault in penicillin fermentation process is Protean, even if the input of the different faults of same performance variable is also different on the impact of state variable, but finally all can affect output and the quality of penicillin.
In present embodiment there is two kinds of dissimilar faults---Class1 and type 2 in the ventilation rate of penicillin fermentation process, represent respectively step fault and slope fault, the penicillin fermentation process method for diagnosing faults of application based on the reconstruct of core offset minimum binary diagnosed for the fault type 1 of ventilation rate and the penicillin fermentation process of 2 two kinds of different fault types of type.
Based on the penicillin fermentation process method for diagnosing faults of core offset minimum binary reconstruct, as shown in Figure 8, comprise the following steps:
Step 1: gather the historical normal data of off-line of penicillin fermentation process, comprise the historical normal data set Χ '=[x of penicillin fermentation process performance variable off-line
1..., x
b] ∈ (J × B) and the historical normal data set Y '=[y of penicillin fermentation process state variable off-line
1..., y
b] ∈ (J ' × B), wherein, the number that subscript B is data sampling, J ', J are variable number;
Penicillin fermentation process performance variable comprises the temperature of temperature, pH value and the fermentation reactor of flow velocity, the substrate feeding of ventilation rate, agitator power, substrate feeding;
Penicillin fermentation process state variable comprises the concentration of penicillin, the heat that penicillin reaction produces, concentration, the volume of nutrient culture media and the concentration of thalline of carbon dioxide;
The historical normal data set of each penicillin fermentation process performance variable off-line and the historical normal data set of penicillin fermentation process state variable off-line respectively comprise 300 samples;
Step 2: respectively to the historical normal data set Χ '=[x of penicillin fermentation process performance variable off-line
1..., x
b] and the historical normal data set Y '=[y of penicillin fermentation process state variable off-line
1..., y
b] carry out specification and standardization: make respectively the historical normal data set Χ '=[x of penicillin fermentation process performance variable off-line
1..., x
b] and the historical normal data set Y '=[y of penicillin fermentation process state variable off-line
1..., y
b] average be 0 and variance be 1, obtain the historical normal data set Χ=[x of specification and standardized penicillin fermentation process state variable off-line
1..., x
b] and specification and the historical normal data set Y=[y of standardized penicillin fermentation process state variable off-line
1..., y
b];
Step 3: utilize improved core offset minimum binary method to set up the malfunction monitoring model of penicillin fermentation process, this model be input as the historical normal data set Χ=[x of penicillin fermentation process performance variable off-line
1..., x
b], this model is output as the historical normal data set Y=[y of penicillin fermentation process state variable off-line
1..., y
b];
Step 3.1: data core mapping: historical penicillin fermentation process performance variable off-line normal data set is mapped to high-dimensional feature space by kernel function Φ from original data space, i.e. X → Φ (X);
Step 3.2: utilize kernel partial least squares that historical penicillin fermentation process performance variable off-line normal data set Χ and the historical normal data set Y of penicillin fermentation process state variable off-line are divided into respectively to principal component space and residual error space;
Step 3.3: utilize principal component space that kernel principal component analysis is residual error space by the residual error spatial division of historical penicillin fermentation process performance variable off-line normal data set Χ and the residual error space in residual error space, and then obtain the malfunction monitoring model of penicillin fermentation process: the data set that historical penicillin fermentation process performance variable off-line normal data set is expressed as to its principal component space, the data set sum in the residual error space in the data set of the principal component space in residual error space and residual error space, historical penicillin fermentation process state variable off-line normal data set is expressed as to the data set of its principal component space and the data set sum in residual error space,
Wherein, subscript T represents transposition, TP
tfor the data set of the principal component space of the historical normal data set Χ of penicillin fermentation process performance variable off-line,
for the data set in the residual error space of the historical normal data set Χ of penicillin fermentation process performance variable off-line, T
xp
x tfor the data set of the principal component space in the residual error space of the historical normal data set Χ of penicillin fermentation process performance variable off-line,
for the data set in the residual error space in the residual error space of the historical normal data set Χ of penicillin fermentation process performance variable off-line, TQ
tfor the data set of the principal component space of the historical normal data set Y of penicillin fermentation process state variable off-line,
for the data set in the residual error space of the historical normal data set Y of penicillin fermentation process state variable off-line; T is the score matrix of the principal component space of the historical normal data set Χ of penicillin fermentation process performance variable off-line, and P is the load matrix of the principal component space of the historical normal data set Χ of penicillin fermentation process performance variable off-line, T
xfor the score matrix of the principal component space in the residual error space of the historical normal data set Χ of penicillin fermentation process performance variable off-line, P
xfor the load matrix of the principal component space in the residual error space of the historical normal data set Χ of penicillin fermentation process performance variable off-line;
Step 4: utilize the malfunction monitoring model of penicillin fermentation process, the fault of on-line monitoring penicillin fermentation process;
Step 4.1: obtain online penicillin fermentation process performance variable data x '
new∈ (J × 1) and penicillin fermentation process state variable data y '
new∈ (J ' × 1);
Step 4.2: the penicillin fermentation process performance variable data of obtaining online and penicillin fermentation process state variable data are carried out to specification and standardization, obtain the penicillin fermentation process performance variable data x after specification and standardization
newpenicillin fermentation process state variable data y after ∈ (J × 1) and specification and standardization
new∈ (J ' × 1);
Step 4.3: data core mapping: the penicillin fermentation process performance variable data of obtaining are online mapped to high-dimensional feature space by kernel function Φ from original data space, i.e. x
new→ Φ (x
new);
Step 4.4: calculate the penicillin fermentation process performance variable data x obtaining online
newhotelling statistic (Hotelling-T in the principal component space of the historical normal data set Χ of penicillin fermentation process performance variable off-line
2), the penicillin fermentation process performance variable data x that obtains online
newhotelling statistic (Hotelling-T in the residual error space of the historical normal data set Χ of penicillin fermentation process performance variable off-line
2) and the penicillin fermentation process performance variable data x that obtains online
newat the historical normal data set x of penicillin fermentation process performance variable off-line
newresidual error space in SPE statistic;
The penicillin fermentation process performance variable data x obtaining online
newhotelling statistic in the principal component space of the historical normal data set Χ of penicillin fermentation process performance variable off-line is as follows:
In formula, t
newfor the penicillin fermentation process performance variable data x obtaining online
newnonlinear principal component in high-dimensional feature space; K
tfor the penicillin fermentation process performance variable data x obtaining online
newwith the inner product vector of the historical normal data set Χ of penicillin fermentation process performance variable off-line, u
kfor the latent variable of the historical normal data set Χ of penicillin fermentation process performance variable off-line; Λ is the covariance matrix of the historical normal data set Χ of penicillin fermentation process performance variable off-line; T
2represent the penicillin fermentation process performance variable data x obtaining online
newhotelling statistic (Hotelling-T in the principal component space of the historical normal data set Χ of penicillin fermentation process performance variable off-line
2);
The penicillin fermentation process performance variable data x obtaining online
newscore vector and Hotelling statistic in the residual error space of the historical normal data set Χ of penicillin fermentation process performance variable off-line are as follows:
In formula, t
x, newfor the penicillin fermentation process performance variable data x obtaining online
newresidual error
nonlinear principal component in high-dimensional feature space;
for x from original data space is mapped to high-dimensional feature space
newresidual error, Λ
xit is the covariance matrix in the residual error space of the historical normal data set Χ of penicillin operational process off-line;
represent x
newhotelling statistic in the residual error space of the historical normal data set Χ of penicillin operational process off-line;
The penicillin fermentation process performance variable data x obtaining online
newsPE statistic in the residual error space of the historical normal data set Χ of penicillin operational process off-line is as follows:
In formula, e
x, newfor the penicillin fermentation process performance variable data x obtaining online
newresidual error
residual error in high-dimensional feature space, SPE
xfor the penicillin fermentation process performance variable data x obtaining online
newsPE statistic in the residual error space of the historical normal data set Χ of penicillin operational process off-line;
Step 4.5: the penicillin fermentation process performance variable data x obtaining online that judgement calculates
newhotelling statistic T in the principal component space of the historical normal data set Χ of penicillin fermentation process performance variable off-line
2, the penicillin fermentation process performance variable data x that obtains online
newhotelling statistic in the residual error space of the historical normal data set Χ of penicillin fermentation process performance variable off-line
the penicillin fermentation process performance variable data x obtaining online
newsPE statistic SPE in the residual error space of the historical normal data set Χ of penicillin fermentation process performance variable off-line
xin whether have at least one statistic higher than its corresponding confidence limit: be, current penicillin fermentation process breaks down, execution step 5, otherwise return to step 4.1;
Step 5: set up the relevant direction model of penicillin fermentation process fault based on the reconstruct of improved core offset minimum binary;
Step 5.1: gather the off-line historical failure data of penicillin fermentation process, comprise penicillin fermentation process performance variable off-line historical failure data set Χ '
f=[x
1f..., x
bf] ∈ (J × B) and penicillin fermentation process state variable off-line historical failure data set Y
f'=[y
1f..., y
bf] ∈ (J ' × B);
Step 5.2: to penicillin fermentation process performance variable off-line historical failure data set Χ '
f=[x
1f..., x
bf] and penicillin fermentation process state variable off-line historical failure data set Y
f'=[y
1f..., y
bf] carry out specification and standardization:
Make respectively penicillin fermentation process performance variable off-line historical failure data set Χ '
f=[x
1f..., x
bf] and penicillin fermentation process state variable off-line historical failure data set Y
f'=[y
1f..., y
bf] average be 0 and variance be 1, obtain specification and standardized penicillin fermentation process performance variable off-line historical failure data set Χ
f=[x
1f..., x
bf] and specification and standardized penicillin fermentation process state variable off-line historical failure data set Y
f=[y
1f..., y
bf];
Step 5.3: penicillin fermentation process performance variable off-line historical failure data set is mapped to high-dimensional feature space by kernel function Φ from original data space, i.e. X
f→ Φ (X
f);
Step 5.4: according to the historical normal data set Χ of penicillin fermentation process performance variable off-line and penicillin fermentation process performance variable off-line historical failure data set Χ
f, reconstruct penicillin fermentation process performance variable off-line historical failure data set Χ
fthe fault related direction of principal component space;
Step 5.4.1: utilize core offset minimum binary method by penicillin fermentation process performance variable off-line historical failure data set Χ
fhistorical normal data set Χ divides respectively principal component space and residual error space with penicillin fermentation process performance variable off-line, obtains respectively penicillin fermentation process performance variable off-line historical failure data set Χ
fcore partial least square model Φ (X
f)
tcore partial least square model Φ (X) with the historical normal data set Χ of penicillin fermentation process performance variable off-line
t;
In formula,
for the data set of the principal component space of the historical normal data set Χ of penicillin fermentation process performance variable off-line,
for the data set in the residual error space of the historical normal data set Χ of penicillin fermentation process performance variable off-line,
for penicillin fermentation process performance variable off-line historical failure data set Χ
fthe data set of principal component space,
for penicillin fermentation process performance variable off-line historical failure data set Χ
fthe data set in residual error space, α is the proper vector of the principal component space of Φ (X), α
ffor Φ (X
f) the proper vector of principal component space, P
ffor penicillin fermentation process performance variable off-line historical failure data set Χ
fthe load matrix of principal component space,
for penicillin fermentation process performance variable off-line historical failure data set Χ
fthe load matrix in residual error space, K is the historical normal data set Χ of penicillin fermentation process performance variable off-line and the interior product matrix of penicillin fermentation process performance variable off-line history normal data set Χ, K
ffor penicillin fermentation process performance variable off-line historical failure data set Χ
fwith penicillin fermentation process performance variable off-line historical failure data set Χ
finterior product matrix, and P=Φ (X) α, K=Φ (X)
tΦ (X), P
f=Φ (X
f) α
f, K
f=Φ (X
f)
tΦ (X
f);
Step 5.4.2: the data set of the principal component space of the historical normal data set Χ of penicillin fermentation process performance variable off-line
orthogonal mapping is to penicillin operational process performance variable off-line historical failure data set Χ respectively
fthe load matrix P of principal component space
fwith penicillin operational process performance variable off-line historical failure data set Χ
fthe load matrix P in residual error space
f *, obtain the books of the principal component space of the principal component space of the historical normal data set Χ of penicillin fermentation process performance variable off-line after orthogonal mapping
data set with the residual error space of the principal component space of the historical normal data set Χ of penicillin fermentation process performance variable off-line after orthogonal mapping
In formula,
for Φ (X
f) the proper vector in residual error space, Κ
nfor the historical normal data set Χ of penicillin fermentation process performance variable off-line and penicillin operational process performance variable off-line historical failure data set Χ
finterior product matrix,
k
n=Φ (X)
tΦ (X
f);
Step 5.4.3: utilize kernel principal component analysis to determine the principal component space data set of the principal component space of the historical normal data set Χ of penicillin fermentation process performance variable off-line after orthogonal mapping
pivot T
cresidual error space data sets with the principal component space of the historical normal data set Χ of penicillin fermentation process performance variable off-line after orthogonal mapping
pivot
In above formula, α
cfor
the proper vector of principal component space,
for
the proper vector of principal component space, P
cfor
load matrix,
for
load matrix,
Step 5.4.4: ask respectively penicillin fermentation process performance variable off-line historical failure data set Χ
fthe data set of principal component space
the load matrix P of the principal component space of the principal component space of the historical normal data set Χ of penicillin fermentation process performance variable off-line after orthogonal mapping
cpivot in direction and penicillin fermentation process performance variable off-line historical failure data set Χ
fthe data set in residual error space
the load matrix in the residual error space of the principal component space of the historical normal data set of penicillin fermentation process performance variable off-line after orthogonal mapping
pivot in direction, obtains respectively the fault pivot T of the principal component space of penicillin fermentation process performance variable off-line historical failure data set
fcfault pivot T with the residual error space of penicillin fermentation process performance variable off-line historical failure data set
fc *;
Step 5.4.5: the fault pivot T that calculates the principal component space of penicillin fermentation process performance variable off-line historical failure data set
fcthe pivot T of the principal component space of the principal component space of the historical normal data set of penicillin fermentation process performance variable off-line after orthogonal mapping
cmiddle proportion RT
fc, i, calculate the fault pivot T in the residual error space of penicillin fermentation process performance variable off-line historical failure data set
fc *the pivot T in the residual error space of the principal component space of the historical normal data set of penicillin fermentation process performance variable off-line after orthogonal mapping
c *middle proportion
In formula, var () represents variance, (:, i) represent that the i of a matrix is listed as, the fault pivot T in above formula
fcat pivot T
cmiddle proportion RT
fc, iwith fault pivot T
fc *at pivot T
c *middle proportion
larger, represent fault data principal component space
larger to the contribution of Hotelling statistic along each load direction (being the direction of the load vector representative in load matrix);
Step 5.4.6: the fault pivot that is greater than the residual error space of the historical normal data set of penicillin fermentation process performance variable off-line after fault pivot and the orthogonal mapping of principal component space of the corresponding penicillin fermentation process performance variable of the each ratio value off-line historical failure data set of the ratio lower limit of setting in two class ratio values forms respectively the pivot direction R of the principal component space of new penicillin fermentation process performance variable off-line historical failure data set
fcpivot direction with the residual error space of new penicillin fermentation process performance variable off-line historical failure data set
Step 5.4.7: the pivot direction R that utilizes the principal component space of new penicillin fermentation process performance variable off-line historical failure data set
fccorresponding load matrix P
fcpivot direction with the residual error space of new penicillin fermentation process performance variable off-line historical failure data set
corresponding load matrix P
fc *, the load matrix P of the principal component space of the principal component space of the historical normal data set Χ of reconstruct penicillin fermentation process performance variable off-line
cload matrix P with the residual error space of the principal component space of the historical normal data set of penicillin fermentation process performance variable off-line
c *, i.e. the fault related direction P of the principal component space of penicillin fermentation process performance variable off-line historical failure data set
rec, c;
Wherein, α
fcfor with pivot direction R
fccharacteristic of correspondence vector, α
fc *for with pivot direction
characteristic of correspondence vector;
Step 5.5: according to the historical normal data set Χ of penicillin fermentation process performance variable off-line and penicillin fermentation process performance variable off-line historical failure data set Χ
freconstruct penicillin fermentation process performance variable off-line historical failure data set Χ
fthe fault related direction of principal component space in residual error space;
Step 5.5.1: utilize core pivot element analysis method, respectively by penicillin fermentation process performance variable off-line historical failure data set Χ
fresidual error space and the residual error spatial division of the historical normal data set Χ of penicillin fermentation process performance variable off-line be the principal component space in residual error space and the residual error space in residual error space, obtain respectively the kernel pivot model in the residual error space of penicillin fermentation process performance variable off-line historical failure data set
kernel pivot model with the residual error space of the historical normal data set of penicillin fermentation process performance variable off-line
In formula,
for the data set of the principal component space in the residual error space of the historical normal data set Χ of penicillin fermentation process performance variable off-line,
for the data set in the residual error space in the residual error space of the historical normal data set Χ of penicillin fermentation process performance variable off-line,
for penicillin fermentation process performance variable off-line historical failure data set Χ
fthe data set of principal component space in residual error space, E
f tfor penicillin fermentation process performance variable off-line historical failure data set Χ
fthe data set in residual error space in residual error space, P
xfor the load matrix in the residual error space of the historical normal data set Χ of penicillin fermentation process performance variable off-line, P
x *for penicillin fermentation process performance variable off-line historical failure data set Χ
fthe load matrix in residual error space, α
ifor
the proper vector of principal component space, α
i *for
the proper vector in residual error space, α
iffor
the proper vector of principal component space, α
if *for
the proper vector in residual error space, P
x,ffor penicillin fermentation process performance variable off-line historical failure data set Χ
fthe load matrix of principal component space in residual error space, P
x,f *for penicillin fermentation process performance variable off-line historical failure data set Χ
fthe load matrix in residual error space in residual error space, K
ifor the data set in the residual error space of the historical normal data set Χ of penicillin fermentation process performance variable off-line
data set with the residual error space of the historical normal data set Χ of penicillin fermentation process performance variable off-line
interior product matrix, K
iffor penicillin fermentation process performance variable off-line historical failure data set Χ
fthe data set in residual error space
with penicillin fermentation process performance variable off-line historical failure data set Χ
fthe data set in residual error space
interior product matrix, and
Step 5.5.2: the data set of the principal component space in the residual error space of the historical normal data set Χ of penicillin fermentation process performance variable off-line
orthogonal mapping is to penicillin fermentation process performance variable off-line historical failure data set Χ respectively
fthe load matrix P of principal component space in residual error space
x,fwith penicillin fermentation process performance variable off-line historical failure data set Χ
fthe load matrix P in residual error space in residual error space
x,f *, obtain the data set of the principal component space in the residual error space of the historical normal data set Χ of penicillin fermentation process performance variable off-line after orthogonal mapping
data set with the residual error space in the residual error space of the historical normal data set of penicillin fermentation process performance variable off-line after orthogonal mapping
In formula, Κ
mfor the data set in the residual error space of the historical normal data set Χ of penicillin fermentation process performance variable off-line
with penicillin fermentation process performance variable off-line historical failure data set Χ
fresidual error space data sets
interior product matrix, and
Step 5.5.3: utilize kernel principal component analysis to determine the data set of the principal component space in the residual error space of the historical normal data set of penicillin fermentation process performance variable off-line after orthogonal mapping
pivot T
pdata set with the residual error space in the residual error space of the penicillin fermentation process performance variable off-line historical failure data set after orthogonal mapping
pivot T
p *;
In formula, α
pfor
the proper vector of principal component space,
for
the proper vector of principal component space, P
pfor
load matrix,
for
load matrix,
Step 5.5.4: the data set of asking the principal component space in the residual error space of the historical normal data set of penicillin fermentation process performance variable off-line
the load matrix P of the principal component space in the residual error space of the historical normal data set of penicillin fermentation process performance variable off-line after orthogonal mapping
ppivot in direction, asks the data set in the residual error space in the residual error space of the historical normal data set of penicillin fermentation process performance variable off-line
the load matrix in the residual error space in the residual error space of the penicillin fermentation process performance variable off-line historical failure data set after orthogonal mapping
pivot in direction, i.e. the fault pivot T of the principal component space in the residual error space of the historical normal data set of penicillin fermentation process performance variable off-line
fpfault pivot T with the residual error space in the residual error space of the historical normal data set of penicillin fermentation process performance variable off-line
fp *;
Step 5.5.5: the fault pivot T that calculates the principal component space in the residual error space of the historical normal data set of penicillin fermentation process performance variable off-line
fpthe pivot T of the principal component space in the residual error space of the historical normal data set of penicillin fermentation process performance variable off-line after orthogonal mapping
pmiddle proportion, calculates the fault pivot in the residual error space in the residual error space of the historical normal data set of penicillin fermentation process performance variable off-line
the pivot of the principal component space in the residual error space of penicillin fermentation process performance variable off-line historical failure data set after orthogonal mapping
middle proportion;
In above formula, fault pivot T
fpat pivot T
pmiddle proportion RT
fp, iwith fault pivot
in pivot
middle proportion
larger, the residual error space of expression penicillin fermentation process performance variable off-line historical failure data set
along each load direction to Hotelling statistic
contribute larger;
Step 5.5.6: the fault pivot that is greater than the fault pivot of principal component space in the residual error space of the corresponding penicillin fermentation process performance variable of the each ratio value off-line historical failure data set of the ratio lower limit of setting and the residual error space in the residual error space of the historical normal data set of penicillin fermentation process performance variable off-line in two class ratio values forms respectively the pivot direction R of the principal component space in the residual error space of new penicillin fermentation process performance variable off-line historical failure data set
fppivot direction with the residual error space in the residual error space of new penicillin fermentation process performance variable off-line historical failure data set
Step 5.5.7: the pivot direction R that utilizes the principal component space in the residual error space of new penicillin fermentation process performance variable off-line historical failure data set
fpcorresponding load matrix P
fppivot direction with the residual error space in the residual error space of new penicillin fermentation process performance variable off-line historical failure data set
corresponding load matrix
the load matrix P of the principal component space in the residual error space of reconstruct penicillin fermentation process performance variable off-line historical failure data set
pload matrix with the residual error space in the residual error space of penicillin fermentation process performance variable off-line historical failure data set
be the fault related direction P of the principal component space in the residual error space of penicillin fermentation process performance variable off-line historical failure data set
rec, p;
Wherein, α
fpfor with R
fpcharacteristic of correspondence vector, α
fp *for with
characteristic of correspondence vector;
Step 5.6: according to the historical normal data set Χ of penicillin fermentation process performance variable off-line and penicillin fermentation process performance variable off-line historical failure data set Χ
freconstruct penicillin fermentation process performance variable off-line historical failure data set Χ
fthe fault related direction in residual error space in residual error space;
Step 5.6.1: by the data set E in the residual error space in the residual error space of the historical normal data set Χ of penicillin fermentation process performance variable off-line
torthogonal mapping is to penicillin fermentation process performance variable off-line historical failure data set Χ respectively
fthe load matrix P of principal component space in residual error space
x,fload matrix P with the residual error space in the residual error space of penicillin fermentation process performance variable off-line historical failure data set
x,f *, obtain the principal component space in the residual error space in the residual error space of the historical normal data set Χ of penicillin fermentation process performance variable off-line after orthogonal mapping
residual error space with the residual error space in the residual error space of the historical normal data set Χ of penicillin fermentation process performance variable off-line after orthogonal mapping
Step 5.6.2: utilize kernel principal component analysis to determine the data set of the principal component space in the residual error space in the residual error space of the historical normal data set of penicillin fermentation process performance variable off-line after orthogonal mapping
pivot T
edata set with the residual error space in the residual error space in the residual error space of the historical normal data set of penicillin fermentation process performance variable off-line after orthogonal mapping
pivot
In formula, α
nffor Ε
nfthe proper vector of principal component space,
for Ε
nf *the proper vector of principal component space, P
efor E
nfthe load matrix of principal component space,
for Ε
nf *the load matrix of principal component space, P
e=E
nfα
nf,
Step 5.6.3: the data set of the principal component space in the residual error space of penicillin fermentation process performance variable off-line historical failure data set
be mapped to the load matrix P of the principal component space in the residual error space in the residual error space of the penicillin fermentation process performance variable off-line historical failure data set after orthogonal mapping
e, the data set E in the residual error space in the residual error space of the historical normal data set of penicillin fermentation process performance variable off-line
f tbe mapped to the load matrix in the residual error space in the residual error space in the residual error space of the historical normal data set of penicillin fermentation process performance variable off-line after orthogonal mapping
obtain the data set of the mapping space of the principal component space in the residual error space in the residual error space of the historical normal data set of penicillin fermentation process performance variable off-line
data set E with the mapping space in the residual error space in the residual error space in the residual error space of the historical normal data set of penicillin fermentation process performance variable off-line
f,e;
Step 5.6.4: calculate penicillin fermentation process performance variable off-line historical failure data set Χ
fthe data set of principal component space in residual error space
arrive the data set of the mapping space of the principal component space in the residual error space in the residual error space of the historical normal data set of penicillin fermentation process performance variable off-line
the distance of load matrix, calculate the data set E in residual error space in the residual error space of the historical normal data set Χ of penicillin fermentation process performance variable off-line to the data set of the mapping space in the residual error space in the residual error space in the residual error space of penicillin fermentation process performance variable off-line history normal data set
the distance of load matrix, and calculate the ratio R T of two distances
f,
e;
Step 5.6.5: calculate penicillin fermentation process performance variable off-line historical failure data set Χ
fthe data set E in residual error space in residual error space
farrive the data set of the mapping space of the principal component space in the residual error space in the residual error space of the historical normal data set of penicillin fermentation process performance variable off-line
the distance of load matrix, calculate the data set E in residual error space in the residual error space of the historical normal data set Χ of penicillin fermentation process performance variable off-line to the data set of the mapping space in the residual error space in the residual error space in the residual error space of penicillin fermentation process performance variable off-line history normal data set
the distance of load matrix, and calculate the ratio of two distances
In formula, || || represent Euclid's length, P
f,efor mapping space
load matrix,
for mapping space E
f,eload matrix, this ratio of distances constant is larger, represents the residual error space of penicillin fermentation process performance variable off-line historical failure data set
larger to the contribution of SPE statistic along each load direction;
Step 5.6.6: the ratio of this two classes distance is greater than the pivot direction V that the principal component space in residual error space of penicillin fermentation process performance variable off-line historical failure data set that the ratio of its all distances of setting ratio lower limit is corresponding and the residual error space in the residual error space of penicillin fermentation process performance variable off-line historical failure data set form respectively the principal component space in the residual error space in the residual error space of new penicillin fermentation process performance variable off-line historical failure data set
fepivot direction with the residual error space in the residual error space in the residual error space of new penicillin fermentation process performance variable off-line historical failure data set
Step 5.6.7: the pivot direction V that utilizes the principal component space in the residual error space in the residual error space of new penicillin fermentation process performance variable off-line historical failure data set
fepivot direction with the residual error space in the residual error space in the residual error space of new penicillin fermentation process performance variable off-line historical failure data set
the fault related direction P in the residual error space in the residual error space of the historical normal data set of reconstruct penicillin fermentation process performance variable off-line
rec, e;
Wherein, α
fefor pivot direction V
fecharacteristic of correspondence vector,
for pivot direction
characteristic of correspondence vector;
Step 5.7: for all faults of penicillin fermentation process, applying step 5.1-5.6 reconstructs respectively the fault related direction P of the principal component space of penicillin fermentation process performance variable off-line historical failure data set
rec, c, penicillin fermentation process performance variable off-line historical failure data set the fault related direction P of principal component space in residual error space
rec, p, the historical normal data set of penicillin fermentation process performance variable off-line the fault related direction P in residual error space in residual error space
rec, eform the penicillin fermentation process fault related direction based on the reconstruct of improved core offset minimum binary, thereby set up the model bank of the penicillin fermentation process fault related direction of improved core offset minimum binary reconstruct;
Step 6: utilize the relevant direction model of penicillin fermentation process fault to carry out penicillin fermentation process fault diagnosis;
Step 6.1: according to the fault related direction P of the principal component space of penicillin fermentation process performance variable off-line historical failure data set
rec, c, the score matrix Τ of the principal component space of the penicillin fermentation process performance variable data that calculating is obtained online
foand corresponding Hotelling statistic
In formula,
for x
newthe set of principal component space, t
fofor score matrix Τ
forow vector, Λ
fofor the covariance matrix of the principal component space of penicillin fermentation process performance variable off-line historical failure data set, J
newfor the number of samples of the penicillin fermentation process performance variable data obtained online, K
f, newfor the penicillin fermentation process performance variable data x obtaining online
newset X
newwith the penicillin fermentation process performance variable data x obtaining online
newset X
newinterior product matrix, K
n, newfor the historical normal data set Χ of penicillin fermentation process performance variable off-line and the penicillin fermentation process performance variable data x obtaining online
newset X
newinterior product matrix, K
f, c, newfor the penicillin fermentation process performance variable data x obtaining online
newset X
newprincipal component space data set and penicillin fermentation process performance variable off-line historical failure data set Χ
finterior product matrix, α
f, newfor Φ (X
f, new) the proper vector of principal component space;
Step 6.2: according to the fault related direction of the principal component space in the residual error space of penicillin fermentation process performance variable off-line historical failure data set, calculate the score matrix Τ in the residual error space of the penicillin fermentation process performance variable data of obtaining online
x, foand corresponding Hotelling statistic
In formula, t
x, fofor score matrix Τ
x, forow vector, Λ
x, fofor the covariance matrix in the residual error space of penicillin fermentation process performance variable off-line historical failure data set, K
if, newfor the penicillin fermentation process performance variable data x obtaining online
newset X
newresidual error space data sets
with the penicillin fermentation process performance variable data x obtaining online
newset X
newresidual error space data sets
interior product matrix, K
i, newfor the residual error space data sets of the historical normal data set Χ of penicillin operational process off-line
with the penicillin fermentation process performance variable data x obtaining online
newset X
newresidual error space data sets
interior product matrix, K
f, p, newfor the penicillin fermentation process performance variable data x obtaining online
newset X
newthe principal component space data set in residual error space
with penicillin fermentation process performance variable off-line historical failure data set Χ
fthe data in residual error space
interior product matrix, α
if, newfor
the proper vector of principal component space;
Step 6.3: according to the barrier related direction in the residual error space in the residual error space of the historical normal data set of penicillin fermentation process performance variable off-line, calculate the SPE statistic in the residual error space of the penicillin fermentation process performance variable data of obtaining online;
In formula, e
x, fofor score matrix Ε
x, forow vector;
Step 6.4: the Hotelling statistic of the principal component space of the penicillin fermentation process performance variable data that judgement is obtained online
the Hotelling statistic in the residual error space of the penicillin fermentation process performance variable data of obtaining online
whether the SPE statistic in the residual error space of the penicillin fermentation process performance variable data of obtaining is online all lower than the confidence limit separately of setting, be,, when prior fault is fault real in penicillin fermentation process, be out of order combination or new fault otherwise work as prior fault.
In present embodiment, first choose 300 sampled points of the historical normal data of off-line of penicillin fermentation process, utilize improved core offset minimum binary method to set up the malfunction monitoring model of penicillin fermentation process, then on-line monitoring fault type 1 and fault type 2, the data of table 1~table 5 are partial data:
Table 1 is set up four groups of data in penicillin fermentation process malfunction monitoring model
Table 2 is set up four groups of data in the fault data 1 in the relevant direction model of penicillin fermentation process fault of improved core offset minimum binary reconstruct
Table 3 is set up four groups of data in the fault data 2 in the relevant direction model of penicillin fermentation process fault of improved core offset minimum binary reconstruct
Table 4 is monitored one group of data in the fault data 1 of penicillin fermentation process
Table 5 is monitored one group of data in the fault data 2 of penicillin fermentation process
Can find out the Hotelling statistic of the performance variable principal component space in penicillin fermentation process and the Hotelling statistic in process variable residual error space by Fig. 2 and Fig. 3
in 200 points, all do not exceed confidence limit with SPE statistic, since the 300th sampled point, there is significantly transfiniting phenomenon in above-mentioned three statistics, and this is true to life.Illustrate that the penicillin fermentation process method for diagnosing faults based on the reconstruct of core offset minimum binary can be good at diagnosing out the fault in Penicillium sweat.
Then, the reconstruct fault related direction that 300 history samples points of fault type 1 carry out, inline diagnosis fault type 1, as seen from Figure 4, the Hotelling statistic in the Hotelling statistic of the principal component space of the performance variable in penicillin fermentation process and the residual error space of performance variable
all lower than confidence limit, illustrate that fault type 1 is for current fault with SPE statistic, and the relevant direction model of this fault can be good at diagnosis and is out of order.
With the fault related direction on-line monitoring fault type 2 of 300 sampled point reconstruct of fault type 1, as seen from Figure 7, the Hotelling statistic (Hotelling-T of the principal component space of the performance variable in penicillin fermentation process
2) and the Hotelling statistic in the residual error space of performance variable
all higher than confidence limit, the relevant direction model of the fault of application fault type 1 can not be diagnosed fault type 2 with SPE statistic.
Utilize equally 300 sampled points of fault type 2 to be reconstructed fault related direction, inline diagnosis fault type 2, as seen from Figure 6, the Hotelling statistic in the Hotelling statistic of the principal component space of the performance variable in penicillin fermentation process and the residual error space of performance variable
all lower than confidence limit, explanation fault type 1 is current fault with SPE statistic, and the relevant direction model of this fault can be good at diagnosis and is out of order.
Next, use the fault related direction on-line monitoring fault type 1 of 300 sampled point reconstruct of fault type 2, as seen from Figure 5, the Hotelling statistic (Hotelling-T of the principal component space of the performance variable in penicillin fermentation process
2) and the Hotelling statistic in the residual error space of performance variable
all higher than confidence limit, the relevant direction model of the fault of application fault type 2 can not be diagnosed fault type 1 with SPE statistic.
Comparison diagram 4 and Fig. 5 or (Fig. 6 and Fig. 7) can find out that the present invention is to diagnosing the different faults of same performance variable.
Can be obtained by the above results, by penicillin fermentation process method for diagnosing faults of the present invention, can effectively monitor the different faults type of same process variable.
Although more than described the specific embodiment of the present invention, the those skilled in the art in this area should be appreciated that these only illustrate, and can make various changes or modifications to these embodiments, and not deviate from principle of the present invention and essence.Scope of the present invention is only limited by appended claims.