Design of Fault Diagnosis System of FPSO Production Process Based on MSPCA

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1 2009 Fifth International Conference on Information Assurance and Security Design of Fault Diagnosis System of FPSO Production Process Based on MSPCA GAO Qiang, HAN Miao, HU Shu-liang, DONG Hai-jie ianjin Key Laboratory for Control heory & Applications in Complicated Systems ianjin University of echnology ianjin, China Abstract-Based on the theory of wavelet analysis and principal component analysis,multi-scale PCA is introduced which combines the ability of PCA to decorrelate the variables by extracting a linear relationship, with that of wavelet analysis to extract deterministic features and approximately decorrelate autocorrelated measurements to improve the performance of PCA whose modeling is limited to a single scale. It is applied to the fault monitor and diagnose of Floating Production Storage and Off-loading System. he result show: the fault diagnose method based on multi-scale principal components analysis can realized FPSO earlier period fault monitor and diagnose accurately, and the capability of multi-scale principal components analysis fault diagnosis is better than the principal components analysis for the small disturbance. Key words-mspca; PCA; Fault diagnose;fpso I. INRODUCION With the development of the large-scale process industry, industry Process is in the direction of maximization and refinement, the requirement of system safety and reliability is higher and higher, monitoring the fault in time and diagnosing the source of fault have become a development direction in the fields of automation. he Principal component analysis (PCA) has been widely used in multivariable monitoring process, but the PCA is limited to the single-scale modeling, and collecting data is multi-scale in actual process. herefore, PCA analysis is not ideal in the most process data models. In addition, the ability of extracting decisive features and separating error message from important information is poor. Wavelet transform with the advantages of time-frequency analysis can extract information from the signals, and have multi-scale detailed analysis. Multi-scale PCA combines the ability of PCA to decorrelate the variables by extracting a linear relationship, with that of wavelet analysis to extract deterministic features and approximately decorrelate autocorrelated measurements, it not only improves capacity of detecting decisive changes, but also get autocorrelation variables monitoring more effective without augmented matrix or time series model. MSPCA is a significant improvement relative to existing his work is partially supported by the Fund of Science and echnology Development of High university of ianjin #2006BA22 methods, it is being paid wide attention in the fields of the academia and industry. II. PRINCIPAL COMPONEN ANALYSIS PCA is a statistical method, with which high dimensional variables were mapped to low dimensional space on the premise of ensuring minimum loss of data information. In fact, it selects some typical principal components to explain great varieties of process data. Consider a data matrix X (X R n m ) composed of n data sample and m process variables under normal operation condition. ransforming the matrix X into exterior product sum of based on m vectors as follows X t p1 t2 p2 tmp 1 (1) Where = [t 1 t 2 t m ] is score matrix, [p 1 p 2 p m ] is loading matrix, t i is score vectors, p i is loading vectors. When there is linear correlation in matrix X, former several loading vectors represent the main variety of matrix X, the projection of matrix X in latter several loading vectors is small. herefore PCA transforms the matrix X as follows X t p t p t p m E k k (2) Where E is residual subspace, it represents a variety of loading vectors from p k 1 to p m. Because E is caused by the noise, neglecting E will clear the noise. Matrix X can be transformed as follows X t1 p1 t2 p2 tk pk (3) Where X is principal components subspace. III. WAVELE RANSFORM Wavelet transform is a kind of integral transform both in time domain and frequency domain, it could extract information from signal effectively, and have multi-scale detailed analysis,thus it was used widely in many different kinds of fields. Wavelet transform theory is based on multi-resolution analysis, which could divide square integral functions L 2 R with limited energy into many multi-resolution subspaces defined by a series of orthogonal basis functions j,n x. In this space, square integrals function could be expressed as the linear combination of basis function /09 $ IEEE DOI /IAS

2 Wavelet transform can be able to decompose multivariable signal X into 1-scale approximation coefficient A 1 and detail coefficient D 1. With the same transformation, A 1 could be further decomposed into 2-scale approximation coefficient A 2 and detail coefficient D 2. If decomposition scale is at L, the decomposition process lasts for L times, and then generates L approximation coefficients and one detail coefficient. Scaled signal sequences can be got by reconstruction algorithm based on the coefficient. IV. MULI-SCALE PRINCIPAL COMPONEN ANALYSIS Multi-scale PCA combines the ability of PCA to decorrelate the variables by extracting a linear relationship, with that of wavelet analysis to extract deterministic feature and approximately decorrelate auto-correlated measurements to improve the performance of PCA whose model is limited to a single scale. Consider a data matrix X (X R n m ) composed of n data sample and m process variables under normal operation condition. First of all, using wavelet transform for the decomposition of column vector of in matrix X, and decompose each column vector by wavelet transform based on the same decomposed depth, and then the m approximation coefficients of wavelet decomposition are gathered in a matrix. Similarly, the m wavelet decomposition s details are gathered in the L-matrix, as shown in Figure 1. Fig 2. Analysis step based on MSPCA V. ALGORIHM SIMULAION BASED ON MSPCA he separation process of Oil-gas-water mixture Based on FPSO is shown in Figure 3. Selecting 18 process variables as the research object to analyze 300 sets of history data of normal operational conditions, upon completion of the removal of variables, preprocessing the training set of data, decomposing standardized training data with three-tier wavelet, forming a approximation Coefficients matrix A1and three coefficient matrixes of details D 1, D 2, D 3 after the wavelet decomposition, analyzing the three matrixes by PCA. Getting three principle components according to the accumulation rate about the principle components model, and calculating 2 statistic and SPE statistics for each principle components model. o determine that if there is significant time on the three details scales in the light of the two statistics, the details scale and approximation scale could be composed for reconstruction of original signal. In order to determine that whether there is a fault, analyzing the original signal after reconstruction by PCA, and determining the source of fault based on fault contribution diagram. Fig 1. Wavelet decomposition of data matrix Each matrix could capture the variables trend on different scales. Using the PCA for the monitoring process of L wavelet coefficient matrixes of details. Determining the scale where there are significant events, combining the wavelet coefficient of details on the scale of significant event with A L for new reconstruction and then calculate the signal reconstruction after the PCA. In the process of MSPCA online application process, for each new collection of data, uses 2 statistic and SPE statistic to determine whether the process has changed. Analysis step is showed in Figure 2. Fig 3. he separation process of Oil-gas-water mixture Based on FPSO 5.1 he selection about optimum wavelet basis function Before the wavelet decomposition, the first thing to do is to choose optimum wavelet basis function. Analysis based on the same problem with different wavelet basis function usually has different results. At present, the most populur method is introduced as followed. Calculating the Maximum error value between the original signal and reconstructed signal, and selecting wavelet function with minimum error as practical wavelet basis function. he paper choose db5, db8, 730

3 sym5, sym8 for comparison, the results are shown in able 1. ABLE1. HE MAXIMUM ERROR VALUE OF RECONSRUCED SIGNAL It can be seen from the table, selecting sym8 as basis function is comparative ideal. 5.2 Calculation about the control limits Building offline principal component models based on three scales by coefficient matrix of three-ply wavelet decomposition, calculating the control limits of Hotelling and SPE on each scale according to the eigenvalue of covariance matrix,as well as corresponding eigenvector. he result is shown in able 2. ABLE2. HE VALUE OF CONROL LIMI FOR EACH SCALE 1-Scale 2-Scale 3-Scale Getting single scale offline PCA model by the reconstruction between A L and details wavelet coefficients of scale on which there are significant events. 5.4 Online fault diagnosis On the basis of FPSO typical data of the history database, we can set up 5 sets of data through the FPSO simulation system, the total number of fault data in each set is 150. he simulation results show that fault data 1 and data 4 are representative, so we select the two sets of data as detailed studies, assess and compare the Diagnosis results based on MSPCA and PCA 1) Data 1 Data 1 simulation system fault caused by the low pressure of the first level separator the fault data deviated from the normal properties of operation clearly. Such process fault could easily be detected. he statistics which have unobvious effect on fault 1 in process monitoring might be bad for other faults. Figure 5 and Figure 6 show the results of fault monitor based on PCA and MSPCA respectively. he dotted line shows the 95% control limits of the statistic, there is a fault when the statistics outrun the control limits. he system lies in normal operation process in the former 30 seconds, so the former 30 statistics are under the control limit SPE Online monitoring With the projection of online data worked onto offline model on each scale, calculating the statistics of Hotelling and SPE on each scale, and then comparing the statistics with respective control limit in order to determine if there are significant events. When the process appears abnormal, abnormal condition is first detected by fine scale wave coefficient, if the abnormal continues, coarse scale wave coefficient can detect it, if the abnormal lasts all the time, even low frequency coefficient on the coarsest scale can found the change. he result is shown in Figure 4. Fig 5. he results of fault monitor based on PCA Fig 6. he results of fault monitor based on MSPCA Calculating contribution value of process monitoring statistics both in principle components subspace and residual subspace, contribution values based on the two different ways are given in Figure 7 and 8. From the two diagrams, we can see that the contribution value of the ninth Process variable both in principle components subspace and residual subspace exceeds the others to a large extent, we can find out the fault source easily by combining process experience knowledge with analysis result. he undetected rate is close to zero with PCA and MSPCA. Both PCA and the MSPCA Fig 4. Online monitoring based on MSPCA 731

4 can accurately detect the fault deviating from control target obviously. contribution values based on the two different ways are given in Figure 11 and 12. Fig 7. Contribution value based on PCA in principle Fig 11. Contribution value based on PCA in principle Fig 8. Contribution value based on MSPCA in principle 2) Data 2 Data 2 simulates the changes of original export temperature in crude oil - water entrance exchanger, fault data produce a concussion in the vicinity of the targets. Since the fault doesn t deviate from the control targets apparently, it is more difficult to detect and diagnose the fault. Figure 9 and Figure 10 show the results of fault monitor based on PCA and MSPCA respectively. Fig 9. he results of fault monitor based on PCA Fig 10. he results of fault monitor based on MSPCA On the whole, there is no detected fault about 2 statistic and SPE statistic in the monitoring process from Figure 9. But can be seen from Figure 10, fault detected rate about the two statistics increase significantly. Calculating contribution value of process monitoring in principle, Fig 12. Contribution value based on MSPCA in principle. Since the PCA did not detect the fault, it is difficult to distinguish fault variables both in principal component space and residual space with PCA method, whereas the fault contribution of the second variable is higher than other variables significantly in MSPCA. So we can attribute the root of the system fault to the original export temperature of crude oil - water heat exchanger entrance (I_2110A). VI. CONCLUSION From the above analysis we can see that there will be inevitable time-varying and uncertain, measuring noise and signal interference in industrial process data of actual production process, they will have an impact on the normal process model, real-time monitoring, and fault diagnosis. It is evident that PCA whose model is limited to a single scale can t detect the fault occurrence effectively. he multi-scale principal component analysis (MSPCA) combines ability of breaking down data into multiple time scale with reducing the PCA data dimension, It can make full use of the advantages of multi-scale model, it can not only be able to detect changes in the more significant fault but also detect a slight slow fault. Compared with the PCA, MSPCA can detect the changes among the variables accurately, and find out the abnormal circumstances in time, it is effective in the monitoring process. REFERENCE [1] CHANGKYU L, SANG W C, LEE I B. Sensor fault identification based on time-lagged PCA in dynamic process. Chemo metrics and Intelligent Laboratory Systems. 2004, 70:l65-l78 [2] CHEN Guojin, LIANG Jun, Liu Yuming, et. Process monitoring based on multivariate statistical projection 732

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