Emerging trends in Statistical Process Control of Industrial Processes. Marco S. Reis

Transcription

1 Emerging trends in Statistical Process Control of Industrial Processes Marco S. Reis Guimarães, July 15 th, 16 Chemical Process Engineering and Forest Products Research Center CIEPQPF Department of Chemical Engineering University of Coimbra CIEPQPF/DEQ-FCTUC Outline 1. Introduction & Background on SPC. Current Trends & Examples From univariate, to multivariate, to high-dimensional ( megavariate ) From monitoring the mean, to dispersion, to correlation From stationary, to dynamic, to non-stationary From sensor data to higher-order profiles From detection, to diagnosis, to prognosis 3. Conclusions

2 1. Introduction & Background Statistical Process Control (SPC) (Statistical) Process Monitoring (SPM) Fault Detection and Diagnosis (FDD) ( ) 1. Introduction & Background Statistical Process Monitoring (SPM): Goal Verify if process behaviour is consistent with normal operating conditions. Detection: rapidly detect abnormalities in process operation Diagnosis: look for the root cause of abnormal behaviour Fault criticality assessment Decision: stop the process and fix the problem or accommodate the fault and proceed Rapidly detect and act on abnormalities in process operation.

3 The beginning Walter Shewhart first control chart: Western Electric (Hawthorne Works, Chicago, 194) 1. Introduction & Background,645,64,635,63,65 X-bar,6,615,61, Chance / Common Causes Process Variability Assignable / Special Causes Eliminate

4 1. Introduction & Background Benefits from SPM Increase safety of people Protect critical industrial assets Increase process eciency: out-of-spec product, scrap, Improve quality: product consistency, defects Improve economic results Reduce environmental impact... Goal Present an overview of some of the main trends on SPM over the last 9+ years 8

5 Topics From univariate, to multivariate, to high-dimensional From monitoring the mean, to dispersion, to correlation From stationary, to dynamic, to non-stationary From sensor data to higher-order profiles From detection, to diagnosis, to prognosis 9 From univariate, to multivariate, to high-dimensional ( megavariate ) 1

6 Univariate Megavariate Multivariate GEPSI PSE Group Process Chemometrics Lab. Matrix Plot X1 X X3 X4 X5 X6 X7 X8 X9 GEPSI PSE Group Process Chemometrics Lab.

7 T Hotelling s T (1931) T ( x x) S ( x x) = n 1 i i i H. Hotelling PCA

8 PC1 P PC C A PC X = PC1 + E

9 PCA-MSPC (1959/1991) X 3 Q Q X T T X 1 J. Edward Jackson J. F. MacGregor Example: Megavariate statistical process control in electronic devices assembling (M. Reis; P. Delgado) Solder Paste Deposits (SPD s) are of critical importance, because: They provide the necessary fixation for all the electronic components Functionalize the operation of electronic components Different shapes Different positions Reis, M. S., & Delgado, P. (1). A large-scale statistical process control approach for the monitoring of electronic devices ICQEM assemblage. 16 Computers and Chemical Engineering, GEPSI PSE Group 39, Process Chemometrics Lab. 18

10 The problem 1% inspection of Printed Circuit Boards (PCB s). Each PCB has more than 3 deposits (SPD s) of different shapes. Operators have less than 1 min to decide about the status of each PCB. Each solder deposit is evaluates according to 5 parameters obtained through Moiré interferometry Volume (V) Area (A) Height (H) Offset in the X coordinate (X) Offset in the Y coordinate (Y) > 15 measurements for each PCB! 19 Multivariate Statistical Process Control using Principal Components Analysis (PCA-MSPC*) * J.E. Jackson, Technometrics, 1:4 (1959) V H A X Y PCA V PCA H PCA A PCA X PCA Y T Q V T Q V H H T Q T Q TY Q A A X X Y Combined approach TC PCA C Q C FIRST LEVEL OF DETECTION

11 SECOND LEVEL OF DETECTION Analysis of the residuals from the projection of each multivariate observation to the PCA subspace. 1 Residuals for observation:4 1 PCA projection residuals Index of SPD 1 RESULTS FOR THE FIRST LEVEL OF DETECTION Detection Statistics Measurements used to compute the relative area under the ROC curve (values in %) Height (H) Area (A) Volume (V) Offset X Offset Y Combined approach T Q PCB s classified as good were used to represent NOC data in SPC (estimate the PCA subspace, ) 16 PCB s classified as fail (16) and good (5) were used to test the procedure

12 RESULTS FOR THE SECOND LEVEL OF DETECTION Detection Statistics Measurements used to identify abnormal SPD s (values in %) Height (H) Area (A) Volume (V) Offset X Offset Y Combined approach Mean Standard Deviation Reis, M.S. and P. Delgado, A large-scale statistical process control approach for the monitoring of electronic devices assemblage. Computers and Chemical Engineering, 1. 39: p From monitoring the mean, to dispersion, to correlation

13 Monitoring the mean and dispersion Most MSPC schemes are focused on location (mean level); Shewhart EWMA CUSUM Hotelling s T PCA-MSPC 5 Monitoring the correlation Most industrial processes are heavily controlled Feedback control loops (PID) Cascade control Model predictive control When a fault arises, controllers fight to keep the mean levels on track: Faults are masked by the controller actions! But the correlation structure of the process variable changes!

14 SPM based on partial correlations Marginal correlations are unable to discern between direct and indirect associations between variables Partial correlations offer a better description of the process Normal Operating Conditions (NOC) network structure RMAX VnMAX max{ w( )} max w ( ) = r { } s = v

15 SPM based on partial correlations N C r1,chext R1MAX ChExt C r,chext RMAX ChExt C r,x W VMAX R1MAX X C r1,x C r1,ch E C r,ch RMAX X R1MAX Ch RMAX Ch PCA performs rather poorly in detecting localized changes in correlation A conventional approach, based on the marginal covariance (W), performs much better N Detection Rate W MSPC-PCA MSPC-PCA Ch W MSPC-PCA Ch MSPC-PCA

16 SPM based on partial correlations Rato, T. J., & Reis, M. S. (14a). Non-causal data-driven monitoring of the process correlation structure: a comparison study with new methods. Computers & Chemical Engineering, 71, Rato, T. J., & Reis, M. S. (14b). Sensitivity enhancing transformations for monitoring the process correlation structure. Journal of Process Control, 4, Rato, T. J., & Reis, M. S. (15a). Multiscale and Megavariate Monitoring of the Process Networked Structure: MNET. Journal of Chemometrics, 9(5), Rato, T. J., & Reis, M. S. (15b). On-line process monitoring using local measures of association. Part I: Detection performance. Chemometrics and Intelligent Laboratory Systems, 14, Rato, T. J., & Reis, M. S. (15c). On-line process monitoring using local measures of association. Part II: Design issues and fault diagnosis. Chemometrics and Intelligent Laboratory Systems, 14, From stationary, to dynamic, to non-stationary

17 PCA assumes i.i.d. observations X1 X X3 X4 Xm X1() X() X3() X4() Xm() X1(1) X(1) X3(1) X4(1) Xm(1) X1() X() X3() X4() Xm() X1(3) X(3) X3(3) X4(3) Xm(3) X1(4) X1(5) X(4) X(5) X3(4) X3(5) X4(4) X4(5) Xm(4) Xm(5) PCA X1(6) X(6) X3(6) X4(6) Xm(6) X1(7) X(7) X3(7) X4(7) Xm(7) X1(8) X(8) X3(8) X4(8) Xm(8) X1(9) X(9) X3(9) X4(9) Xm(9) Dynamic PCA Ku et al. (1995) X1 X1() X1 X1 (L=1) (L=) X X() X X (L=1) (L=) Xm Xm() Xm (L=1) Xm (L=) X1(1) X1() X(1) X() Xm(1) Xm() X1() X1(1) X1() X() X(1) X() Xm() Xm(1) Xm() X1(3) X1() X1(1) X(3) X() X(1) Xm(3) Xm() Xm(1) X1(4) X1(5) X1(3) X1(4) X1() X1(3) X(4) X(5) X(3) X(4) X() X(3) Xm(4) Xm(5) Xm(3) Xm(4) Xm() Xm(3) PCA X1(6) X1(5) X1(4) X(6) X(5) X(4) Xm(6) Xm(5) Xm(4) X1(7) X1(6) X1(5) X(7) X(6) X(5) Xm(7) Xm(6) Xm(5) X1(8) X1(7) X1(6) X(8) X(7) X(6) Xm(8) Xm(7) Xm(6) X1(9) X1(8) X1(7) X(9) X(8) X(7) Xm(9) Xm(8) Xm(7) X1(9) X1(8) X(9) X(8) Xm(9) Xm(8) X1(9) X(9) Xm(9)

18 Dynamic Principal Components Analysis (DPCA) However, the DPCA scores still present autocorrelation DPCA-LS1--S1 Sample Autocorrelation DPCA-LS1--R1 Sample Autocorrelation Lag Lag Figure. Sample autocorrelation function for the DPCA-LS1--S1 and DPCA-LS1--R1 statistics. Dynamic PCA with Decorrelated Residuals: DPCA-DR (Rato & Reis) X =[X(k) X(k 1) X(k l)]; # # x T P x=, =, = * S PP P * x P ( ) 1 *T * *T * tˆ 1: k I k k ( n k ) P P P x = Scores T PREV T 1 ( tt) S ( tt) ˆ = t t ˆ ˆ Residuals T RES T 1 ( xpt) Sˆ ( xpt) = t ˆ ˆ

19 Tennessee Eastman process 8 6 T PCA 6 4 Q PCA Time (hr) Time (hr) 1 T DPCA 5 Q DPCA Time (hr) Time (hr) 8 x 15 6 T PREV 6 4 T RES Time (hr) Time (hr) 37 Dynamic DPCA-DR DPCA-MD scores for the same system present a significantly lower level of autocorrelation. DPCA-LS-MD-S3 Sample Autocorrelation DPCA-LS-MD-R Sample Autocorrelation Lag Lag Figure. Sample autocorrelation function for T Prev and T Res statistics.

20 From sensor data to higher-order profiles Monitoring Profiles (1D, D, 3D, ) ( ) We view the monitoring of process and product profiles as the most promising area of research in statistical process control. ( ) Woodall, W. H., Spitzner, D. J., Montgomery, D. C., and Gupta, S. (4). Using Control Charts to Monitor Process and Product Quality Profiles. Journal of Quality Technology, 36(3),

21 Definition [Profile, P]: An array of data, indexed by time and/or space, that characterizes a given entity (product, process). P ( ix iy iz it) { Y } :,,, { Y} ix, iy, yz, it n ix, iy, iz, it Spatial indices Time index x y z t Frequency domain localization High Low Dual domain classification Frequency Localized Random Profiles Delocalized Random Profiles Low More: Analysis of Coherent I Images Perfusion experiments fmri, Time/Space localization Fully Localized Profiles More: Acoustic signals Seismic signals Hard constraint: ( g) ( gˆ) Time-Space Localized Random Profiles High 1

22 Monitoring paper formation* (Reis, MS & Bauer, A.) Currently is evaluated off-line: few times per day (e.g. after each paper reel production) Very high delay, regarding the production speed of current paper machines (~1 Km/h!) * Level of uniformity in the way fibres are distributed across the paper surface. 43 Goal Develop a technology for on-line monitoring of the paper formation.

23 Experimental: Measurement Sensor Digital camera Housing with a rotating head Light source :1 ( ) : : Experimental 1: : Image set: 4 images, representing different levels :3 of formation quality :1 353: 3: : : 4 4: GEPSI PSE Group 5 Process Chemometrics 5 Lab ( ) 1 3

24 Paper web Methods Acquire Image Raw image Image pre-processing = (Raw image) Pre-processed image (luminosity corrected) (Illumination pattern) (Pre-processed image) Wavelet Transform D Wavelet transform Features computation WTA features profiles Process Monitoring Grade evaluation Status of the process (normal / abnormal) Quality Grade Results (RQ1) PCA analysis of wavelet signatures PC PC Scores plot PC s 97.96% of the overall variability 3 A B

25 Results (RQ1) Prototypes of clusters A and B A heterogeneity through smaller and more frequent irregularities. B - cloudy texture. Analysis (sub-images) Grade 1 Others Control limits (99%) Results (RQ) Q Note: Half of the Grade 1 samples were used to estimate the NOC region. T

26 From detection, to diagnosis, to prognosis Detection Basic requirement: a good description of the Normal Operating Conditions Mean levels and main correlations between variables Non-causal associations

27 Diagnosis To find the root cause, causal information is needed! However, most SPM models are acausal, and therefore cannot provide all the information required for a thorough diagnosis They may also point to variables that are not directly involved in the fault The smearing-out effect of PCA-MSPC is a wellknown manifestation 1 11 C 8 A B D One solution Plug-in causality into conventional NOC models through an adequate pre-processing of the variables This can be done using the concept of Sensitivity Enhancing Transformations (SET) Rato, T. J., & Reis, M. S. (14a). Non-causal data-driven monitoring of the process correlation structure: a comparison study with new methods. Computers & Chemical Engineering, 71, Rato, T. J., & Reis, M. S. (14b). Sensitivity enhancing transformations for monitoring the process correlation structure. Journal of Process Control, 4,

28 Sensitivity enhancing transformation (SET) 1. Network Identification x x x x x x Regress each variable onto its parents y1 = x1 y = x y = x xb x b y = x x b ,3, ,4 4. Apply the Cholesky decomposition to the regression residuals thus obtained. B 3. Final model Y = XB 1 b1,3 1 b,3 = 1 b3,4 1 Process Data Plug-in approach: SET Uncorrelated data Monitoring statistics (PC, T ) Statistics MSPC Process State (Normal / Abnormal)

29 Detection 1 1 C 8 A B Detection Rate.6.4 D W E RMAX-SET Rato, T.J. and M.S. Reis, Sensitivity enhancing transformations for monitoring the process correlation structure. Journal of Process Control, 14. 4: p Rato, T.J. and M.S. Reis, On-line process monitoring using local measures of association. Part I: Detection performance. Chemometrics and Intelligent Laboratory Systems, : p C 8 A Diagnosis 16 3 B D % 1 % variable (a) variable Figure. Percentage of times that each variable was considered as the faults root cause by the marginal correlation procedure on a fault in the relationship between variables 1 and 8: (a) marginal correlation of the original variables; (b) marginal correlation of the transformed variables. (b)

30 SPM in the big data era Data Big Data Technology Analytics 59 Typology of SPM applications Statistical Process Monitoring 6

31 Conclusions 9+ years after its introduction, SPC is still an exciting and evolving field! SPC should be complemented with effective Diagnosis tools New challenges include Move focus from Detection to Diagnosis Handling complex dynamics: multiscale methods Integrating the structure of the system and existing domain knowledge: SET, Bayesian methods Handling multiple data structures (profiles): multi-block methods Monitoring time-varying systems: adaptive methods, and making everything simple to use and robust! 61 Acknowledgements Pedro Saraiva Pedro Delgado Tiago Rato Ricardo Rendall Maria Campos Veronique Medeiros 6

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