CN102736546B  State monitoring device of complex electromechanical system for flow industry and method  Google Patents
State monitoring device of complex electromechanical system for flow industry and method Download PDFInfo
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 CN102736546B CN102736546B CN201210219078.3A CN201210219078A CN102736546B CN 102736546 B CN102736546 B CN 102736546B CN 201210219078 A CN201210219078 A CN 201210219078A CN 102736546 B CN102736546 B CN 102736546B
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Abstract
The invention relates to a state monitoring device of a complex electromechanical system for a flow industry and a method. The device comprises a manmachine interaction module, a data collecting module, a data preprocessing module, a data analyzing module and a failure case library. According to the device and the method provided by the invention, whether the system fails or is in abnormal states or not can be monitored and early warming for tripping accidents or other accidents of the flow industry system can be made. Meanwhile, a KPCA (Kernel Principal Component Analysis) method with double parameter optimization is used to overcome the deficiency that parameters are selected by empirical formula in conventional KPCA methods, thereby improving the state monitoring ability. Furthermore, the failure case database is adequately used in the historical production process so that failures of the system can be monitored more immediately and accurately.
Description
Technical field
The invention belongs to Mechatronic Systems monitoring technical field, relate to a kind of state monitoring apparatus and method, especially a kind of state monitoring apparatus of process industry complex electromechanical systems and method.
Background technology
In process industry, because industrial process scale constantly expands, complicacy increases day by day, the safety and reliability of production system requires also day by day to improve.The operation of production system longterm safety stability and high efficiency, avoids the generation of pernicious security incident to become a vital task of modern industry.For this reason, in system operational process, the generation of fault or abnormality need to be detected in time, and fault type is judged and source of trouble location, eliminate adverse effect factor.Traditional state monitoring method can be divided three classes: based on method, the method based on knowledge and the method based on datadriven of resolving.Method based on resolving is to be based upon on strict mathematical model basis, as methods such as Kalman filter, parameter estimation, equivalent spaces; Method based on knowledge is mainly to set up model according to technological process knowledge, as fault tree (FTA), decision tree (DT) etc.; Method based on data be mainly the process data that gathers be basis, excavate system status information implicit in data by various data processings and analytical approach, and then instruct production run, as multivariate statistical method, cluster analysis, spectrum analysis etc.Because the production system in process industry is increasingly sophisticated, obtain strict mathematical model and detailed systematic knowledge more difficult, therefore, be restricted based on method that resolve and based on knowledge; And, industrial system all gathers and record equipment running status data conventionally, these Condition Monitoring Datas have contained the essential information such as system conditions and system exception state evolution rule just, so the aspects such as the condition monitoring and fault diagnosis of the analytical approach based on datadriven in process industry are widely used.
From the angle of scientific research, the process industry production system take Chemical Manufacture as representative is a kind of distributed complex Mechatronic Systems being coupled to form by energy net, fluid network, Information Network, control net by many largesized power mechanized equipments, chemical reaction device and automation control system.In virtual condition observation process, such complex electromechanical systems faces 3 problems: (1) monitored parameters quantity is huge, has correlativity and strong coupling between variable, and manual type is difficult to monitor all variablees simultaneously.(2) feature that Monitoring Data presents gradual, magnanimity, many features such as nonlinear and atypical and deposits, lacks the equipment state characteristic information containing in effective means mining data.(3) net environment of modern process industry production system in a kind of multimedium coupling, also lacks apparatus system and the method for effectively carrying out status monitoring in system level at present.
Below the concept such as KPCA theory, wavelet denoising relating in the present invention is done to following simple introduction and definition:
Core principle component analysis (kernel principal component analysis), is called for short KPCA, is a kind of common method of the fault detect based on datadriven.The basic thought of core principle component analysis is first by a Nonlinear Mapping function Ф, the data matrix X of the input space to be mapped to a highdimensional feature space F, then the mapping (enum) data in higher dimensional space is done to pivot analysis, extract the linear feature of data at higher dimensional space, namely data are in the nonlinear characteristic of lower dimensional space.This Nonlinear Mapping is that the inner product of calculating data in the input space realizes by introducing kernel function.KPCA is the process statistics amount T based on process pivot characteristic signal subspace information by structure
^{2}with the statistic SPE of residual information subspace information, determine its control limit, and then realize status monitoring.
Traditional KPCA method has the following disadvantages in actual applications: (1) KPCA nuclear parameter and pivot number choose very internalise, at present choosing of nuclear parameter do not had to unified criterion, mostly take the method for experimental formula.In KPCA, pivot number chooses simple conventional pivot accumulation contribution rate method (the Cumulative percent variance of general employing, CPV), but contribution rate is got how many most suitable not unified standards, and while adopting pivot accumulation contribution rate to ask pivot number in KPCA, first can be subject to the impact that nuclear parameter is chosen; (2) whole observation process does not utilize known fault case data, but sets up a KPCA model and detect the fault of all kinds according to given parameter.But a fixing system model can not have good detection effect to all faults, can only be to wherein a certain, or a certain class fault is very responsive.The present invention, by the basis of the KPCA model in improved twoparameter optimization, proposes a set of device and method and overcomes above problem.
Wavelet denoising: the data that gather in actual industrial process are often subject to pollution and the interference of noise, as white noise and electromagnetic interference (EMI) etc., wherein useful signal is usually expressed as low frequency signal or some signals more stably, and noise signal is usually expressed as highfrequency signal.When the data of actual acquisition are carried out to wavelet decomposition, noise section is mainly included in high frequency wavelet coefficient, thereby, can apply the forms such as threshold value processes wavelet coefficient, then signal is reconstructed and can reaches noise reduction, jamproof object, and then the raising quality of data, improve fault Detection capability and accuracy.
Summary of the invention
The object of the invention is to overcome the shortcoming of abovementioned prior art, a kind of state monitoring apparatus and method of process industry complex electromechanical systems are provided, its multivariate for process industry complex electromechanical systems Monitoring Data, magnanimity, the feature such as nonlinear, realize the status monitoring production run from system level, can improve status monitoring ability, find in time the generation of fault and abnormality.
The object of the invention is to solve by the following technical programs:
The state monitoring apparatus of this process industry complex electromechanical systems, comprising:
Humancomputer interaction module: for realizing the mutual of user and condition monitoring system, comprise the input and output of system state monitoring information, calling data acquisition module, data preprocessing module and data analysis module;
Data acquisition module: extract for system historic state being detected to the real time data that data and DCS control system operational process produce;
Data preprocessing module: for removing the white Gaussian noise of monitored parameters data, and the data that gather are carried out to standardization, remove the impact of dimension, so that followup analysis;
Data analysis module: for the modeling to monitoring system, and by Realtime Monitoring Data and institute's established model contrast, detection system abnormality;
Fault case storehouse: for storing, manage the historical failure information of monitored system, comprise faulttime, failure cause and fault mode;
Described humancomputer interaction module is connected with data acquisition module, data preprocessing module and data analysis module respectively, the carrier transmitting as information; Meanwhile, data acquisition module, data preprocessing module and data analysis module are connected with fault case storehouse respectively, and information extraction from fault case storehouse completes the function of modeling and analysis.
Function in abovementioned data analysis module comprises: the analytical approach of the KPCA model of twoparameter optimization; The data message of coupling system case library, sets up the KPCA Models Sets of monitoring system; The KPCA Models Sets contrast of Realtime Monitoring Data and foundation, detection system abnormality; Ruuning situation to whole process industry system judges, and safe early warning information is pointedly provided.
The present invention also proposes a kind of state monitoring method of the process industry complex electromechanical systems based on said apparatus, comprises the following steps:
1) data acquisition: extract the nominal situation historical data of monitored target and gather the Realtime Monitoring Data of monitoring target from fault case storehouse; Wherein historical data is used for setting up system model, and real time data is for the monitoring to system state;
2) data preservice: the Realtime Monitoring Data of the monitoring target of the method that first adopts Wavelet Denoising Method to the nominal situation historical data of extracting and collection carries out noise reduction process; Then the data after noise reduction are carried out to standardization, eliminate the inconsistent impact of each monitored parameters dimension;
3) set up system model: the core pivot element analysis method that adopts twoparameter optimization, set up KPCA model according to nominal situation historical data, and in conjunction with known fault case data, the nuclear parameter in KPCA model and pivot number are optimized, obtain KPCA Models Sets, for detection of system whether in abnormality;
4) monitoring abnormal state: calculate the monitoring and statistics amount of the Realtime Monitoring Data gathering under set up model, and make comparisons with the monitoring and statistics amount higher limit of model, if exceeded statistic higher limit, can judge that abnormality has appearred in system in statistical significance;
5) analysis result and effective early warning information are shown by humancomputer interaction module.
Further, in above step 3), specifically comprise the following steps:
A) set up a twoparameter objective optimization problem, ask and make statistic T
^{2}nuclear parameter σ and pivot number p when statistic recall rate and SPE statistic recall rate are maximum, be expressed as with following formula:
Wherein:
σnuclear parameter;
Ppivot number;
Nthe pivot number while getting 85% accumulation contribution rate;
The dimension of mthe input space, i.e. variable number;
F
_{t}(σ, p)the T under given nuclear parameter and a pivot said conditions
^{2}statistic recall rate;
F
_{s}(σ, p)the SPE statistic recall rate under given nuclear parameter and a pivot said conditions;
B) obtain data under nominal situation as training sample standardization, set up KPCA model by incipient nucleus parameter and pivot number; Incipient nucleus parameter σ=10m, m is input space dimension, namely variable number; Initial pivot number is chosen according to the method for accumulation contribution rate to 85%;
C) try to achieve the T under insolation level α=99% by initial pivot number
^{2}statistic and SPE statistic higher limit;
D) obtain fault case data, and standard deviation and the average standardization with the corresponding vector of training data to each variable;
E) ask for the principal component vector of these fault case data under initial parameter, obtain T
^{2}statistic and SPE statistic;
F) comparative statistics value sum test statistics higher limit, calculates respectively T
^{2}statistic and SPE statistic exceed the shared number percent of sample of higher limit, obtain average recall rate;
G) change initial parameter, and calculate the average recall rate of statistic under new argument by abovementioned steps, with a upper average recall rate comparison, retain nuclear parameter and pivot number that average recall rate is higher;
H) repeat abovementioned steps, until average recall rate meets a certain recall rate of fault detect requirement, or obtain a convergence solution; Nuclear parameter now and pivot number are the optimum KPCA model parameters for this fault.
The present invention has following beneficial effect:
Adopt a kind of process industry complex electromechanical systems state monitoring apparatus of the present invention and method can monitoring system whether have fault or abnormality to occur, can the jumping car accident of process industry system or other security incidents be made and being given warning in advance.Meanwhile, utilize the KPCA method of twoparameter optimization, improved the faultdetecting ability of traditional KPCA monitoring method.Moreover, owing to making full use of the fault case database of setting up in process flow industry process system, make the monitoring of the system failure more in time with accurate.
Accompanying drawing explanation
Fig. 1 is the structural representation of device of the present invention;
Fig. 2 is workflow diagram of the present invention;
Fig. 3 is that the KPCA method of twoparameter optimization solves flow process;
Fig. 4 is embodiment of the present invention subsystem structure figure;
Fig. 5 is the status monitoring figure of the present invention to system.
Embodiment
Referring to Fig. 1, the state monitoring apparatus of process industry complex electromechanical systems of the present invention, comprising:
Humancomputer interaction module: for realizing the mutual of user and condition monitoring system, comprise the input and output of system state monitoring information, calling data acquisition module, data preprocessing module and data analysis module.Can revise, upgrade system failure case library, management history/Realtime Monitoring Data and calling data analysis module carry out status monitoring.
Data acquisition module: for the Realtime Monitoring Data of system historic state Monitoring Data and the generation of system operational process DCS control system is extracted.
Data preprocessing module: for removing the white Gaussian noise of monitored parameters data, and the data that gather are carried out to standardization, remove the impact of dimension, so that followup analysis.
Data analysis module: this module is the core of apparatus of the present invention.The data message of coupling system case library, on the basis of the KPCA modeling to monitoring system, Realtime Monitoring Data and the KPCA Models Sets of building are contrasted, fast and effeciently detection system abnormality, and the ruuning situation of whole process industry system is judged, safe early warning information is effectively provided.
Fault case storehouse: for storing, manage the historical failure information of monitored system, comprise the relevant informations such as faulttime, failure cause and fault mode.
Described humancomputer interaction module is connected with data acquisition module, data preprocessing module and data analysis module respectively, the carrier transmitting as information; Meanwhile, data acquisition module, data preprocessing module and data analysis module are connected with fault case storehouse respectively, and information extraction from fault case storehouse completes the function of modeling and analysis.
Function in described data analysis module comprises: the analytical approach of the KPCA model of twoparameter optimization; The data message of coupling system case library, sets up the KPCA Models Sets of monitoring system; The KPCA Models Sets contrast of Realtime Monitoring Data and foundation, detection system abnormality; Ruuning situation to whole process industry system judges, and safe early warning information is pointedly provided.
The present invention can adopt computer memory to store system failure case data information, monitoring historical data, real time data and data analysis flow process, and adopting IO interface to connect keyboard, external memory storage and display, the KPCA Models Sets information and the analysis result etc. that in analytic process, generate can adopt the form of manmachine interaction to express in display.
Based on above device, as shown in Figure 2, concrete steps are as follows for the workflow of process industry complex electromechanical systems status monitoring analytical approach of the present invention:
Step 1: the data of monitored target are extracted, according to concrete monitored target, in conjunction with monitoring objective, effectively extracts the data of the nominal situation of storing in historical data base, and can extract and the real time data of the corresponding monitored parameters of historical data.
Step 2: to extract in real time/preservice of historical data; The preservice of data comprises wavelet denoising and standardization (making average is zero, and variance is 1).This step specifically comprises:
(a) to extract in real time/historical data carries out wavelet denoising.According to the principle of Wavelet Transform Threshold denoising, Wavelet Transform Threshold denoising comprises following 3 steps conventionally: (1) is selected a suitable wavelet basis and determined that the level decomposing carries out wavelet decomposition to signal; (2) determine the threshold value of each layer of detail coefficients, process wavelet coefficient by the method for softthreshold or hardthreshold; (3) wavelet inverse transformation reconstruction signal.
(b) data after Wavelet Transform Threshold denoising are carried out to standardization.Different variablees usually have different dimensions and the order of magnitude.For the intensity of variation of more different variablees on the same order of magnitude, need to eliminate the impact of dimension, therefore by data normalization.After standardization, the average of data is 0, and variance is 1.
Step 3: set up KPCA model based on historical nominal situation data.Original input data matrix X ∈ R
^{n × m}(m observational variable, n sampling number) is n sample under normal operating condition, through the pretreated data matrix of step 2 is
adopt gaussian radial basis function kernel function
calculate nuclear matrix K.
To nuclear matrix K centralization, and solve eigenwert and the proper vector a of K
_{k}, to proper vector standardization, make <a
_{k}, a
_{k}>=1/ λ
_{k}.Wherein λ
_{k}it is characteristic of correspondence value.
Calculate nonlinear principal component t
_{k}:
Wherein,
standardization proper vector afterwards,
centralization nuclear matrix K afterwards.
Step 4: in conjunction with fault case storehouse, build the KPCA Models Sets of twoparameter optimization.To each fault in fault case storehouse, the nuclear parameter to KPCA and pivot number are optimized, and obtain the KPCA model of corresponding every kind of fault.Concrete optimization method is referring to explanation (3).
Step 5: the KPCA status monitoring based on twoparameter optimization.For the sampled data sample x of a new RealTime Monitoring
_{new}∈ R
^{1 × m}, construct corresponding statistic T
^{2}with SPE and corresponding control limit threshold values T thereof
_{α} ^{2}and SPE
_{α}monitoring system state.Statistic T
^{2}and corresponding control limit threshold values T
_{α} ^{2}can be determined by following formula:
T
^{2}=[t
_{1},.,t
_{p}]Λ
^{1}[t
_{1}，…,t
_{p}]
^{T} （2）
Wherein Λ
^{1}the inverse matrix of the diagonal matrix of the corresponding eigenwert formation of pivot, F
_{α}(k, nk) for degree of confidence be α, degree of freedom be respectively p and np F distribute higher limit, the acquisition of can tabling lookup.SPE is defined as:
In the time that insolation level is α, SPE controls and is limited to
sPE controls limit and obeys the χ that degree of freedom is h
^{2}distribute.If a, b is respectively average and the variance of SPE, g=b/2a, h=2a
^{2}/ b.
Step 6: analysis result and effectively early warning information show.The contrast statistics value of Realtime Monitoring Data and the statistic higher limit of KPCA model, if T
_{a}<T or SPE
_{a}<SPE, there is abnormality in illustrative system.Even if analysis result shows by humancomputer interaction module, gives operating personnel's system exception condition prompting.
The KPCA method optimizing process of twoparameter optimization is as follows above:
Consult Fig. 3, the KPCA method that Fig. 3 is twoparameter optimization solves schematic flow sheet.In conjunction with fault case storehouse, every kind of fault in case library is built to the KPCA model of twoparameter optimization.Set up a twoparameter objective optimization problem, ask and make T
^{2}nuclear parameter σ and pivot number p when recall rate and SPE recall rate are maximum, available following formula is expressed as:
Wherein:
σnuclear parameter;
Ppivot number;
Nthe pivot number while getting 85% accumulation contribution rate;
The dimension of mthe input space, namely variable number;
F
_{t}(σ, p)the T under given nuclear parameter and a pivot said conditions
^{2}statistic recall rate;
F
_{s}(σ, p)the SPE statistic recall rate under given nuclear parameter and a pivot said conditions;
To twoparameter objective optimization problem, it specifically solves and comprises the steps:
Step 1: obtain data under nominal situation as training sample standardization, set up KPCA model by incipient nucleus parameter and pivot number.Incipient nucleus parameter σ=10m, m is input space dimension, namely variable number.Initial pivot number is chosen according to the method for accumulation contribution rate to 85%.
Step 2 is tried to achieve the T under insolation level α=99% by initial pivot number
^{2}statistic and SPE statistic higher limit.
Step 3: obtain fault case data, and standard deviation and the average standardization with the corresponding vector of training data to each variable.
Step 4: ask for the principal component vector of these fault case data under initial parameter, obtain T
^{2}statistic and SPE statistic.
Step 5: comparative statistics value sum test statistics higher limit, calculate respectively T
^{2}statistic and SPE statistic exceed the shared number percent of sample of higher limit, obtain average recall rate.
Step 6: change initial parameter, and calculate the average recall rate of statistic under new argument by abovementioned steps, with a upper average recall rate comparison, retain nuclear parameter and pivot number that average recall rate is higher.
Step 7: repeat abovementioned steps, until average recall rate meets a certain recall rate of fault detect requirement, or obtain a convergence solution.Nuclear parameter now and pivot number are the optimum KPCA model parameters for this fault.
In the solution procedure of this optimization problem, need to consider that nuclear parameter σ can not get excessive, too extensive to prevent kernel function, lose the advantage of extracting nonlinear characteristic.In the time asking pivot number p, if it is larger that pivot number occurs, the situation that fault recall rate is higher, needs consider to promote dimensionality reduction effect and improve the balance between fault recall rate.
The twoparameter optimization KPCA method that the present invention adopts combines fault case data, and known fault is had more to specific aim.When in system operational process, occur with fault case storehouse in similarly when fault, the KPCA method of twoparameter optimization can make fault detect effect reach best.
Consult Fig. 4Fig. 5, Fig. 4 is compressor train structural representation.This compressor unit system is by 5EH8BD steam turbine, and RIK1004 is isothermal compact lost press radially, and RBZ457 is cartridge type supercharger and TX36/1C wheel box and some servicing units and equipment composition radially.Choose with closelyrelated 70 monitored parameterses of compressor unit system running status as observational variable.
Fig. 5 is the detection figure of twoparameter optimization KPCA to the system failure.This fault causes air compressor machine underrun because of steam pipe system pressure drop.After optimizing, selecting nuclear parameter is 495, and pivot number is 8, sets up the running status of KPCA model monitoring compressor group.As we can see from the figure, near the 800th sample, two statistics all show significantly and transfinite, and two statistics can effectively detect this fault.Wherein, T
^{2}the recall rate of statistic is that the recall rate of 94.2%, SPE statistic is 99.4%, and average recall rate is 96.8%.
Systematic comparison complexity, system failure situation in actual flow process commercial production are many, therefore need to set up abundant fault case database, and the abnormality of system is made to early warning targetedly.Utilize on this basis technician's experimental knowledge to do and further accept or reject and analyze status monitoring result, do further fault diagnosis.
Claims (3)
1. a state monitoring apparatus for process industry complex electromechanical systems, is characterized in that, comprising:
Humancomputer interaction module: for realizing the mutual of user and condition monitoring system, comprise the input and output of system state monitoring information, calling data acquisition module, data preprocessing module and data analysis module;
Data acquisition module: extract for system historic state being detected to the real time data that data and DCS control system operational process produce;
Data preprocessing module: for removing the white Gaussian noise of monitored parameters data, and the data that gather are carried out to standardization, remove the impact of dimension, so that followup analysis;
Data analysis module: for the modeling to monitoring system, and by Realtime Monitoring Data and institute's established model contrast, detection system abnormality;
Fault case storehouse: for storing, manage the historical failure information of monitored system, comprise faulttime, failure cause and fault mode;
Described humancomputer interaction module is connected with data acquisition module, data preprocessing module and data analysis module respectively, the carrier transmitting as information; Meanwhile, data acquisition module, data preprocessing module and data analysis module are connected with fault case storehouse respectively, and information extraction from fault case storehouse completes the function of modeling and analysis;
Function in described data analysis module comprises: the analytical approach of the KPCA model of twoparameter optimization; In conjunction with the data message in fault case storehouse, set up the KPCA Models Sets of monitoring system; The KPCA Models Sets contrast of Realtime Monitoring Data and foundation, detection system abnormality; Ruuning situation to whole process industry system judges, and safe early warning information is provided.
2. the state monitoring method based on the process industry complex electromechanical systems of device described in claim 1, is characterized in that, comprises the following steps:
1) data acquisition: extract the nominal situation historical data of monitored target and gather the Realtime Monitoring Data of monitoring target from fault case storehouse; Wherein historical data is used for setting up system model, and real time data is for the monitoring to system state;
2) data preservice: the Realtime Monitoring Data of the monitoring target of the method that first adopts Wavelet Denoising Method to the nominal situation historical data of extracting and collection carries out noise reduction process; Then the data after noise reduction are carried out to standardization, eliminate the inconsistent impact of each monitored parameters dimension;
3) set up system model: the core pivot element analysis method that adopts twoparameter optimization, set up KPCA model according to nominal situation historical data, and in conjunction with known fault case data, the nuclear parameter in KPCA model and pivot number are optimized, obtain KPCA Models Sets, for detection of system whether in abnormality;
4) monitoring abnormal state: calculate the monitoring and statistics amount of the Realtime Monitoring Data gathering under set up model, and make comparisons with the monitoring and statistics amount higher limit of model, if exceeded statistic higher limit, can judge that abnormality has appearred in system in statistical significance;
5) analysis result and effective early warning information are shown by humancomputer interaction module.
3. the state monitoring method of process industry complex electromechanical systems according to claim 2, is characterized in that, in step 3), specifically comprises the following steps:
A) set up a twoparameter objective optimization problem, ask and make T
^{2}nuclear parameter σ and pivot number p when statistic recall rate and SPE statistic recall rate are maximum, be expressed as with following formula:
Wherein:
σnuclear parameter;
Ppivot number;
Nthe pivot number while getting 85% accumulation contribution rate;
The dimension of mthe input space, i.e. variable number;
F
_{t}(σ, p)the T under given nuclear parameter and a pivot said conditions
^{2}statistic recall rate;
F
_{s}(σ, p)the SPE statistic recall rate under given nuclear parameter and a pivot said conditions;
B) obtain data under nominal situation as training sample standardization, set up KPCA model by incipient nucleus parameter and pivot number; Incipient nucleus parameter σ=10m, m is input space dimension, namely variable number; Initial pivot number is chosen according to the method for accumulation contribution rate to 85%;
C) try to achieve the T under insolation level α=99% by initial pivot number
^{2}statistic and SPE statistic higher limit;
D) obtain fault case data, and standard deviation and the average standardization with the corresponding vector of training data to each variable;
E) ask for the principal component vector of these fault case data under initial parameter, obtain T
^{2}statistic and SPE statistic;
F) comparative statistics value sum test statistics higher limit, calculates respectively T
^{2}statistic and SPE statistic exceed the shared number percent of sample of higher limit, obtain average recall rate;
G) change initial parameter, and calculate the average recall rate of statistic under new argument by abovementioned steps, with a upper average recall rate comparison, retain nuclear parameter and pivot number that average recall rate is higher;
H) repeat abovementioned steps, until average recall rate meets a certain recall rate of fault detect requirement, or obtain a convergence solution; Nuclear parameter now and pivot number are the optimum KPCA model parameters for this fault.
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