WO1997049011A9 - Industrial process surveillance system - Google Patents
Industrial process surveillance systemInfo
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- WO1997049011A9 WO1997049011A9 PCT/US1997/010430 US9710430W WO9749011A9 WO 1997049011 A9 WO1997049011 A9 WO 1997049011A9 US 9710430 W US9710430 W US 9710430W WO 9749011 A9 WO9749011 A9 WO 9749011A9
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Classifications
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- G—PHYSICS
- G05—CONTROLLING; REGULATING
- G05B—CONTROL OR REGULATING SYSTEMS IN GENERAL; FUNCTIONAL ELEMENTS OF SUCH SYSTEMS; MONITORING OR TESTING ARRANGEMENTS FOR SUCH SYSTEMS OR ELEMENTS
- G05B13/00—Adaptive control systems, i.e. systems automatically adjusting themselves to have a performance which is optimum according to some preassigned criterion
- G05B13/02—Adaptive control systems, i.e. systems automatically adjusting themselves to have a performance which is optimum according to some preassigned criterion electric
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- G—PHYSICS
- G05—CONTROLLING; REGULATING
- G05B—CONTROL OR REGULATING SYSTEMS IN GENERAL; FUNCTIONAL ELEMENTS OF SUCH SYSTEMS; MONITORING OR TESTING ARRANGEMENTS FOR SUCH SYSTEMS OR ELEMENTS
- G05B23/00—Testing or monitoring of control systems or parts thereof
- G05B23/02—Electric testing or monitoring
- G05B23/0205—Electric testing or monitoring by means of a monitoring system capable of detecting and responding to faults
- G05B23/0218—Electric testing or monitoring by means of a monitoring system capable of detecting and responding to faults characterised by the fault detection method dealing with either existing or incipient faults
- G05B23/0243—Electric testing or monitoring by means of a monitoring system capable of detecting and responding to faults characterised by the fault detection method dealing with either existing or incipient faults model based detection method, e.g. first-principles knowledge model
- G05B23/0254—Electric testing or monitoring by means of a monitoring system capable of detecting and responding to faults characterised by the fault detection method dealing with either existing or incipient faults model based detection method, e.g. first-principles knowledge model based on a quantitative model, e.g. mathematical relationships between inputs and outputs; functions: observer, Kalman filter, residual calculation, Neural Networks
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- G—PHYSICS
- G05—CONTROLLING; REGULATING
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- G05B23/00—Testing or monitoring of control systems or parts thereof
- G05B23/02—Electric testing or monitoring
- G05B23/0205—Electric testing or monitoring by means of a monitoring system capable of detecting and responding to faults
- G05B23/0259—Electric testing or monitoring by means of a monitoring system capable of detecting and responding to faults characterized by the response to fault detection
- G05B23/0262—Confirmation of fault detection, e.g. extra checks to confirm that a failure has indeed occurred
Definitions
- the present invention is related generally to a method and system for carrying out surveillance of industrial processes using sensor or data source outputs. More particularly, the invention is concerned with a method and system for processing sensor data and using virtual data as an improved methodology over basic statistical approaches to industrial process surveillance. Further, the invention involves use of a plurality of techniques coupled for enhanced analysis of industrial process data.
- SPRT sequential probability ratio test
- the SPRT method is a pattern recognition technique which processes the stochastic components associated with physical process variables and has high sensitivity for the onset of subtle disturbances in those variables.
- Two features of the conventional SPRT technique make it attractive for parameter surveillance and fault detection: (1) early annunciation of the onset of a disturbance in noisy process variables, and (2) the SPRT technique has user-specificable false alarm and missed-alarm probabilities.
- SPRT techniques are primarily directed to the analysis of data from paired or multiple pairs of sensors in contrast to a large number of different process sensor data points. SPRT is also typically dependent on assumptions of the data being independent of other data sources and being Gaussian distributed data. The SPRT technique used alone therefore has certain shortcomings in identifying anomalies in processes.
- FIGURE 1 illustrates a schematic functional flow diagram of a preferred embodiment of the invention
- FIGURE 2 illustrates a functional flow diagram of a time lead-lag correlation methodology
- FIGURE 3 illustrates a functional flow diagram of a method of determining a full range of data by searching normal state training data
- FIGURE 4 illustrates a functional flow diagram of a method for modeling behavior of commercial system operating states
- FIGURE 5 illustrates a functional flow diagram of a method for performing pattern recognition
- FIGURE 6A illustrates sensor signals having a four second delay before applying a lead-lag method
- FIG. 6B illustrates the sensor signals after applying the lead-lag method
- FIGURE 7A illustrates sensor signal data from pump 1 power with an SMSET estimate superimposed thereon;
- FIG. 7B illustrates the SMSET estimation error between the SMSET estimate and the sensor signal data;
- FIG. IC illustrates a histogram of the error;
- FIGURE 8A illustrates sensor signal data from pump 2 power with an SMSET estimate superimposed thereon;
- FIG. 8B illustrates the SMSET estimation error between the SMSET estimate and the sensor signal data;
- FIG. 8C illustrates a histogram of the error;
- FIGURE 9A illustrates sensor signal data from pump 1 speed with an SMSET estimate superimposed thereon;
- FIG. 9B illustrates the SMSET estimation error between the SMSET estimate and the sensor signal data;
- FIG. 9C illustrates a histogram of the error;
- FIGURE 10A illustrates sensor signal data from pump 2 speed with an SMSET estimate superimposed thereon;
- FIG. 1OB illustrates the SMSET estimation error between the SMSET estimate and the sensor signal data;
- FIG. IOC illustrates a histogram of the error;
- FIGURE 11 A illustrates sensor signal data for reactor outlet flow rate
- FIG. 11B illustrates the SMSET estimation error between the SMSET estimate and the sensor signal data
- FIG. 11C illustrates a histogram of the error
- FIGURE 12A illustrates sensor signal data for primary pump 2 flow rate
- FIG. 12B illustrates the SMSET estimation error between the SMSET estimate and the sensor signal data
- FIG. 12C illustrates a histogram of the error
- FIGURE 13 A illustrates sensor signal data for subassembly outlet temperature 1A1;
- FIG. 13B illustrates the SMSET estimation error between the SMSET estimate and the sensor signal data; and
- FIG. 13C illustrates a histogram of the error;
- FIGURE 14A illustrates sensor signal data for subassembly outlet temperature 2B1;
- FIG. 14B illustrates the SMSET estimation error between the SMSET estimate and the sensor signal data;
- FIG. 14C illustrates a histogram of the error;
- FIGURE 15A illustrates sensor signal data for subassembly outlet temperature 4E1;
- FIG. 15B illustrates the SMSET estimation error between the SMSET estimate and the sensor signal data;
- FIG. 15C illustrates a histogram of the error;
- FIGURE 16A illustrates sensor signal data for subassembly outlet temperature 4F1;
- FIG. 16B illustrates the SMSET estimation error between the SMSET estimate and the sensor signal data; and
- FIG. 16C illustrates a histogram of the error;
- FIGURE 17A illustrates sensor signal data for reactor outlet temperature 1534CF;
- FIG. 17B illustrates the SMSET estimation error between the SMSET estimate and the sensor signal data;
- FIG. 17C illustrates a histogram of the error;
- FIGURE 18A illustrates sensor signal data for primary tank sodium level 530 Float
- FIG. 18B illustrates the SMSET estimation error between the SMSET estimate and the sensor signal data
- FIG. 18C illustrates a histogram of the error
- FIGURE 19 A illustrates sensor signal data for primary tank sodium level 531 induction
- FIG. 19B illustrates the SMSET estimation error between the SMSET estimate and the sensor signal data
- FIG. 19C illustrates a histogram of the error
- FIGURE 20A illustrates standard deviation of SMSET errors for each of the data in FIG. 7-19
- FIG. 20B illustrates the mean value of SMSET errors for each of the data in FIG. 7-19
- FIGURE 21 shows subassembly outlet temperature ("SOT") and SMSET estimates and in particular FIG. 21 A illustrates time dependent normal SOT for 3F1 in the EBR-II nuclear reactor; FIG. 21B illustrates normal SOT for 3C1; FIG. 21C illustrates normal SOT for 5C2 and FIG. 21D illustrates normal SOT for 7A3;
- SOT subassembly outlet temperature
- FIGURE 22A-D illustrates SMSET estimation error for each of the data of FIGS. 21A-D, respectively;
- FIGURE 23A-D illustrates SPRT results for each of the data of FIGS. 21A-D, respectively;
- FIGURE 24 A corresponds exactly to FIG. 21 A;
- FIG. 24B includes a linear drift component compared to FIG. 21B; and
- FIGS. 24C and 24D correspond exactly to FIG. 21C and 21D, respectively;
- FIGURE 25A corresponds exactly to FIG. 22A;
- FIG. 25B includes the effect on SMET estimation error of the linear drift of FIG. 24B; and
- FIGS. 24C and 24D correspond exactly to FIGS. 22C and 22D, respectively;
- FIGURE 26A corresponds exactly to FIG. 23A
- FIG. 26B illustrates the SPRT results for the linear drift error of FIG. 24B
- FIGS. 26C and D corresponds exactly to FIG. 23C and D, respectively;
- FIGURES 27A and 28B corresponds exactly to FIGS. 21A and 21B, respectively;
- FIG. 27C includes a temporary amplitude pulse of 0.25% of the signal magnitude; and
- FIG. 27D corresponds exactly to FIG. 2 ID;
- FIGURES 28A and 28B corresponds exactly to FIGS. 22A and 22B;
- FIG. 28C illustrates SMSET estimation error for the amplitude pulse effect of FIG. 27C and
- FIG. 27D corresponds exactly to FIG. 22D;
- FIGURES 29A and 29B corresponds exactly to FIGS. 23A and 23B;
- FIG. 29C illustrates SPRT results ' of the amplitude pulse in FIG. 27C; and
- FIG. 29D corresponds exactly to FIG. 23D;
- FIGURE 30A illustrates EBRII subassembly temperature data 3F1 but includes a uniform gain change compared to FIG. 21A and FIGS. 30B-D correspond exactly to FIGS. 21B-D;
- FIGURE 31A illustrates the SMSET estimation error for the gain change of FIG. 30A; and FIGS. 31B-D correspond exactly to FIGS. 22B-D, respectively; and
- FIGURE 32 A illustrates the SPRT results for the gain change of FIG. 30A and SMSET analysis of FIG. 31A; and FIGS. 32B-D correspond exactly to FIGS. 23B-D, respectively.
- the system 10 herein includes a methodology (see FIG. 1) and apparatus for surveillance of sensor or data accumulation configurations in industrial, utility, business, medical, investment and transportation applications.
- the system 10 is useful for sensitive identification of the onset of sensor or data source degradation, process or system anomalies, or the onset of change to a different operational state.
- the most preferred form of the system 10 comprises a synergistic integration of four techniques to provide enhanced surveillance capabilities compared to conventional approaches (including neural networks), and also provide enhanced reliability and improved computational efficiency.
- the four elements that make up the most preferred surveillance form of the system 10 are embodied in four different methodologies generally characterized as a time correlation module 20, a training module 30, a system state estimation module 40 and a pattern recognition module 50.
- TCs thermocouples
- TC(N) At any given instant in time, TC(N), at the outlet end of the pipe, is seeing fluctuations that passed TC(1) ten seconds ago.
- TCs may still contain a small degree of correlation due to gross changes in fluid temperature from a heat source or sink that is upstream of the pipe; however, the more valuable intersensor correlation that arises from local temperature perturbations carried along the pipe will be lost. This same phenomenon degrades the performance of neural networks and other pattern-recognition paradigms applied to any processes wherein the physical sensors or data sources are displaced in time across the process they are monitoring.
- time delays in correlated systems include: systems with slow data flow rates and/or large physical distances (oil refineries, power plants, HVAC systems, and financial systems), delays due to analog or digital electronics (noise filters and large capacitors) or transmission delays (satellite communications, or transmitting data over different BUS systems.
- a Leadlag component of the invention performs dynamic, real-time intersensor lead-lag adjustments.
- the Leadlag module 20 performs adjustments so that the output signals, which are then input subsequently into the SMSET routine (the system state estimation module 40), are optimally correlated and impart the maximum information content to the pattern recognition module 50.
- the Leadlag module 20 is attached hereto as a computer software Appendix A.
- the Leadlag module 20 accomplishes the adjustment function by performing, for each pair of signals, an iterative regression procedure that generates a vector of correlation coefficients with respect to lag time. This vector of correlation coefficients is a unimodal concave function of lag time.
- the optimal lag time between the pair of signals is identified simply by searching for the zero-crossing of the first derivative of the vector with respect to the lag time.
- the Leadlag module 20 is not utilized or the data has already been processed by the Leadlag module 20, the data is preferably input to a training module 30.
- this training module is a MiniMax module 30 which searches through all the observations for all signals or data during a training time period to construct training vectors that include the highest point and lowest point for each signal or data space under surveillance.
- a computer software Appendix B sets forth the MiniMax module 30.
- the MiniMax module 30 produces an "optimal" training set. It is optimal in the sense that it contains only, at most, 2N vectors, where N is the number of signals or data points in the system; and these vectors span the full range that all sensors or data sources have noted during the available training period. Wherever two or more sensors or data sources simultaneously attain maxima or minima, the resulting number of training vectors will be less than 2N.
- both the Leadlag module 20 and the MiniMax module 30 can be skipped, and the data can be input directly to the system state module 40.
- the system state estimation module 40 (such as the preferred Subsystem Multivariate State Estimation Technique ("SMSET") module) models the behavior of a system through examples of the operating states of the commercial system being modeled.
- SMSET Subsystem Multivariate State Estimation Technique
- a computer sofflvare Appendix C sets forth the SMSET module 40.
- the system state estimation module 40 can be any one of a variety of modeling methodologies, such as auto regressive moving average, a neural network, or a Kalman filtering technique or an empirical methodology.
- the SMSET module 40 utilizes its memory of the learned states of the commercial system in conjunction with a single new observation to provide an estimate of the current "true" system state. States of the system are represented by vectors whose elements are comprised of direct values of system parameters (measured signals) as well as any transformation of these system parameters that produce scalar values, e.g. calculated parameters based upon measured data.
- the SMSET module 40 does not require the state vector elements to be linearly independent as do most other types of estimation techniques.
- the learning process which results in a "learned-state" matrix, is performed according to the MiniMax module 30 and the Leadlag module 20 described hereinbefore.
- the basic methodology of the SMSET module 40 involves the input of a new observation of the behavior of a system that is compared with the "memory" of previous system behavior embodied in the learned-state matrix. A series of mathematical operations are performed that generates an estimate of the states in the system's memory that is "closest" to the new observation.
- the definition of "closest” that is used by the SMSET module 40 is the state that is lying closest to the new observation from the point of view of a set of rules that determine the association of two vectors. From this closest state, an estimate of the "true” state of the system is performed for each and every element of the state vector.
- the SMSET module 40 provides an estimate of the current true state of the system.
- the value of this method is that an estimate of all of the values of the system parameters in the state vector can be provided even if the current observation vector is incomplete ( " e.g. some sensors or data sources may have failed or are no longer available), contains erroneous or faulty elements (some sensors may have drifted, become uncalibrated, become contaminated with high noise levels, etc.), or even if the new system state does not coincide with previous operating states.
- the new system state must, in a general sense, be bounded by the domain of the states used to develop the system memory (learned-state matrix).
- This estimation of the true current state of the commercial system is used in conjunction with the actual measured system parameters to ascertain the operability of sensors (or other data sources) and disturbances in the system state.
- This state estimation process can further be described as an inference engine that accepts as input a set of learned states and a new observation of the commercial system. After a series of operations are performed by the inference engine on this input, the result is an estimate of the learned state "closest" to the new observation.
- the definition of "closest” used here is the state lying closest to the new observation from the point of view of a set of rules that determine the association (overlap) of any two vectors.
- Another result is the estimation of the "true” value of each and every element in the new observation vector in the form of an estimated state vector.
- the series of operations performed in the inference engine consist of various matrix operations. First, all pairs of learned states are preferably associated two at a time using a rule set to create the elements of a recognition matrix. Next, the new observation is associated with each learned state using the rule set to produce a vector that has the same number of elements as the number of learned states. The largest element value in this vector identifies the "closest" learned state to the new observation. Finally, the normal matrix product of this vector with the recognition matrix produces a set of linear combination coefficients for combining the learned states into the estimated state vector.
- the SMSET module 40 Once the SMSET module 40 has modeled the data as described hereinbefore, the data is input to a pattern recognition module 50, such as the Sequential Probability Ratio Test ("SPRT") module.
- SPRT Sequential Probability Ratio Test
- the computer software for the SPRT module 50 is in Appendix D.
- This SPRT module 50 is a sensitive pattern recognition method that can detect the onset of subtle degradation in noisy signals with high reliability, and with quantitative false-alarm and missed-alarm probabilities.
- Output from the SMSET module 40 is provided as a set of estimated signals (also called "virtual signals") for each sensor under surveillance. These virtual signals are fed into a network of interacting SPRT modules 50 together with the actual sensor readings.
- Each of the SPRT modules 50 receives one sensor-signal, virtual-signal pair.
- the SPRT module(s) 50 provide an annunciation to the operator and an actuator signal to the control system, which can selectively as needed automatically swap in the virtual signal to replace the degrading sensor signal, or data source. Further details of the SPRT module 50 are described in USPN 5,459,675, which is incorporated by reference herein.
- the user can continue operating the commercial system or process if the sensor or data source were operating normally.
- the system 10 can operate to substitute in a modeled estimate into a actual commercial system or process as input to replace a failed sensor or failed data source. This allows the commercial system or process to keep operating.
- the system 10 does not rely on analytical modeling by itself, it is applicable to a wide variety of processes and systems, such as petro-chemical, power generation, automotive, manufacturing, medical, aeronautical, financial and any system in which signals are available for processing that are related to the commercial system process operation or performance.
- the only requirement of the system 10 is that there is some type of cross-correlation, be it linear or nonlinear, between the signals used as input to the system 10.
- the signals can be linear, nonlinear, stationary, nonstationary, clean or noisy (with an arbitrary distribution).
- the system 10 uses a database of historical operation data to model the commercial system or process.
- the database is assumed to contain data from all relevant operating modes of the system; however, if a new mode of operation is encountered and is determined not to be a result of commercial system or sensor failures, a new vector can be added to the existing training matrix to incorporate the unanticipated operating mode in the system model.
- the following nonlimiting examples illustrate various aspects of the invention described herein.
- the data used is all taken from the EBR-II reactor at Argonne National Laboratory (West).
- FIGS. 6A and 6B show two voltage signals with a four second delay between them.
- the correlation coefficient is 0.0182 which implies no correlation versus processing through the Leadlag module 20 to obtain a correlation of 0.9209 (see FIG. 6B).
- the set of signals, or data, being used is more than two, all the possible pair combinations are used to calculate maximum possible correlation coefficients so all signals can be properly correlated.
- the SMSET methodology generally was carried out using sensor data from the Experimental Breeder Reactor II (EBR-II) at Argonne National Laboratory (U558).
- the sensor data set contained 13 signals from sensors monitoring EBR-II.
- Table I shows the SMSET Estimation accuracy for EBR-II Data. Table I includes the channel numbers and descriptions for each of the sensor signals used in the analysis.
- the experiment was conducted in three steps; first the SMSET module was trained using two days worth of EBR-II data, next the trained SMSET module was used to estimate the state of approximately 110 hours worth of EBR-II data, and then the accuracy of the estimates was analyzed.
- FIGS 7-19 show the sensor signal (top plot) and SMSET estimate superimposed, the middle plot shows error between the SMSET and the sensor signal (in percent of the signal magnitude), ad a histogram (bottom plot) of the error.
- the histogram plots are compared to a Gaussian distribution with the same mean ad variance to give an idea of how Gaussian the error signals.
- FIG. 20 provide a summary of the data of FIGS. 7-19.
- a methodology entitled MiniMax was used to train the system using the two days of training data cited above. After the MiniMax method was applied, a training matrix was constructed consisting of twenty-five unique vectors constituting an empirical model of the overall system. After creating the model, the methodology was then applied to the signals listed in the accuracy table. Each signal in the system has its own estimation error signal that is a measure of how close the pattern recognition model is representing the system relative to the sensor readings.
- the second column of Table I lists the standard deviation of the estimate error for all of the signals in the experiment in terms of each of the signals' magnitude. The magnitude of the signal is defined by its mean during normal operation.
- the third column in Table I lists the mean of the estimate error for all of the signals also in terms of the signal magnitude. In general the estimate error standard deviations are in the range of 0.01 % to 0.1 % and the estimate error means are centered around 0. Bar graphs of the tabular information are shown in FIGS. 20 A and 20B as graphic representation of the accuracy information.
- FIGS. 21-32 examples of different sensor failure modes are shown along with how the system reacts to the failures.
- the preferred method of FIG. 1 is applied to the data.
- the sensor signals used in these examples are from a subset of 22 sensor signals used in the system.
- the 22 sensors monitored the EBR-II subassembly system at Argonne National Laboratory (West).
- Each of FIGS. 21-32 contains four subplots in which the upper most plot is related to Subassembly Outlet temperature ("SOT") 3F1, the upper middle plot is related to SOT 3C1, the lower middle plot is related to SOT 5C2, and the bottom plot is related to SOT 7A3.
- the system applied in each of the examples uses the same training matrix, which consists of 83 vectors selected from a training data base containing almost a weeks worth of data taken once every minute.
- FIGS. 21-23 are shown the results of using the system 10 during approximately 5.5 days of normal operation of EBR-II.
- FIG. 21 shows the SOT signals with their corresponding SMSET estimates (signal being the circles and the lines being the estimate).
- FIG. 22 shows the respective raw estimate errors (not in terms of the signal magnitude) derived by taking the difference between the SOR signals and corresponding SMSET estimates.
- FIG. 23 the results are shown from applying the decision making module of the system 10 (the SPRT module 50- see Appendix D) to the SMSET estimation errors of FIG. 22.
- the SPRT plots show a total of only three false alarms which is a false alarm rate of 9.4 x 10 "s , and this is well within the specified false alarm rate of 1.0 x 10 "3 .
- FIGS. 24-26 illustrate a comparative example of processing data from this type of failure and failure identification.
- Signal #2 (FIG. 24B) has a 0.2% linear drift in it's mean over the 2.75 day period starting at 4000 minutes into the signal. The other sensors are operating normally.
- FIG. 25 shows the resulting SMSET estimation errors for each sensor signal.
- the error plot for signal #2 (FIG. 25B) shows evidence of drifting after the sensor signal has drifted approximately 0.05%.
- the SPRT method has determined that #2 (FIG. 26B) is drifting after approximately 0.05% of drift and that all other sensors are operating normally.
- FIGS. 27-29 show a example of this type of failure for the SOT measurements.
- sensor signal #3 (FIG. 27C) contains a pulse with an amplitude of 0.25 % of the signal magnitude. The pulse starts at 4000 minutes and lasts for 2000 minutes.
- FIG. 27 shows the sensor signals and the SMSET estimates for the four SOT signals.
- FIG. 28 shows the resulting SMSET estimation errors.
- the error signal for #3 (FIG. 28C) shows that there is a problem starting at 4000 minutes and ending at 6000 minutes.
- the error signals are fed through the SPRT module 50, and the results are plotted in FIG. 29.
- Clearly, there has been a disturbance in sensor #3 (FIG. 29C) beginning at time 4000 minutes and ending at 6000 minutes.
- FIGS. 30-32 an example of a failure mode related to the sensor gain is shown.
- the gain of the sensor signal changes over tune, i.e., the amplitude is increasing over time.
- the gain begins changing linearly over time from a beginning value of 1 to a final value of 1 +0.075% of the sensor magnitude.
- the system 10 for the estimation error is applied to the signals, and the results are shown in FIG. 31.
- a human operator would most likely not be able to tell that there is a problem even after 8000 minutes by looking at the sensor signal.
- FIG. 31 A it is apparent that signal #1 is operating abnormally. This is confirmed in FIG. 32A by the SPRT results, showing a steadily increasing number of SPRT alarms over the 8000 minute period.
- Appendix A Computer software for Leadlag module which performs dynamic, real-time intersensor lead-lag time correlation adjustments.
- L lengthFile (Train) ; f seek (Train, OL,0) ; ⁇
- MinMa ( ) ⁇ void extendD ( float ex) ⁇ int i , j ; float mn[MAXSENS/*RowsD*/] , std[MAXSENS/*RowsD*/] , tp;
- F2 F2-1; */ Appendix C Computer software for modeling behavior for examples of the operating states ommercial system.
- % function [Erms, X_hat, Err, W2,WW] mset (Input, rangeL, rangeU, D, DDi, ...
- % X_hat Estimated states for variables specified by prt_cols.
- % Err Estimation error for variables specified by prt_cols.
- Input input state matrix: an N by M+l array with the first column containing a timestamp.
- the array contains n observation vectors, with m dependent variables in each vector.
- rangeL Length M vector, where each element sets the lower limit of data for a corresponding variable.
- % rangeU Length M vector, where each element sets the upper limit of
- % D Training set, an M by N array.
- % DDi Inverse of the similarity matrix (from auto_trannsa) .
- % alpha Multiplicative factor the vprprod nonlinear operator.
- % beta Power factor in the vprprod nonlinear operator.
- V p_flag Print/don't print run progress data for 0/1.
- % thrsh Cutoff threshold for weighting vector H (default 0) %
- the rangeL and rangeU vectors are used to specify the anticipated range of % the variables. Data is linearly scaled from the ranges specified by these % vectors to the range 0:1. If the rangeL vector specifies the lower limit of % the data while rangeU is 0, then the code will shift the data by subtracting % the rangeL values from each element in a corresponding column of the data. % If both of the rangeL and rangeU vectors are set to a scalar value of 0, % the data will not be scaled.
- V Scale each observation vector in the training matrix.
- Y (Y-rangeL' ⁇ ones(l,N)) ./...
- V D and Y matrices V D and Y matrices .
- DtY vprprod (D_pro ⁇ ' , Yjpro ⁇ ( : , ⁇ ) , alpha, beta) ; W . DDi ⁇ DtY;
- MOIN length (rangeU(prt_cols) ) ;
- X_hat(i,:) (rangeU(prt_cols (i) ) - rangeL (prt_cols(i) ) ) * ... X_hat (i , : ) + rangeL (prt_cols (i) ) ,- end end
- NNN «length(prt_cols) ;
- Y Input ( : ,2:s ⁇ ze(Input,2) ) ';
- % function [z, ⁇ orm_dist] vprprod [x, y, alpha, beta) ;
- diet is the normalized distance between a vector in y and each
- Appendix D Computer software for performing pattern recognition by detecting onset of degradation in noisy signals.
- f gets (buf , 13. rxox2 ) ; taap-a c (buf) ; maaa2+-tasp/calcX ⁇ ength;
- fprintf (sprtposl, ⁇ %£ ⁇ n* . Sposl) ; fprintf (aprtpos2. a %£ ⁇ n a ,Spos2) ; fprintf (sprta ⁇ gl. "%f ⁇ n a , Snegl) ; fprintf (eprtneg2. •%£ ⁇ a" ,S ⁇ eg2) ; scan (flowl. a %f ⁇ n a .
- &teapl scanf ( asti, ".£ ⁇ n- , &temp2) ; if (subl) fprintf (coabl, ⁇ %£ ⁇ n a , teap2)-; else fprint (ccabl, *S£ ⁇ &' . tempi) ; fscsn£ (flow2. , %f ⁇ n a , &ta ⁇ pl) ; fscan (feat2, * t ⁇ n" , &teap2) ; if (sub2) fprintf (ceab2, ⁇ *.f ⁇ n a , taap2) ; else fprintf (c ⁇ mb2.
Abstract
Description
Claims
Priority Applications (6)
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CA002257881A CA2257881C (en) | 1996-06-19 | 1997-06-13 | Industrial process surveillance system |
JP50322398A JP3449560B2 (en) | 1996-06-19 | 1997-06-13 | Industrial process monitoring system |
EP97930046A EP0906593B1 (en) | 1996-06-19 | 1997-06-13 | Industrial process surveillance system |
DE69723839T DE69723839T2 (en) | 1996-06-19 | 1997-06-13 | MONITORING SYSTEM FOR INDUSTRIAL SYSTEM |
KR1019980710448A KR100313067B1 (en) | 1996-06-19 | 1997-06-13 | Industrial process surveillance system |
AU33967/97A AU3396797A (en) | 1996-06-19 | 1997-06-13 | Industrial process surveillance system |
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US08/666,938 US5764509A (en) | 1996-06-19 | 1996-06-19 | Industrial process surveillance system |
US08/666,938 | 1996-06-19 |
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WO1997049011A1 WO1997049011A1 (en) | 1997-12-24 |
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PCT/US1997/010430 WO1997049011A1 (en) | 1996-06-19 | 1997-06-13 | Industrial process surveillance system |
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US (2) | US5764509A (en) |
EP (1) | EP0906593B1 (en) |
JP (1) | JP3449560B2 (en) |
KR (1) | KR100313067B1 (en) |
AU (1) | AU3396797A (en) |
CA (1) | CA2257881C (en) |
DE (1) | DE69723839T2 (en) |
ES (1) | ES2205244T3 (en) |
WO (1) | WO1997049011A1 (en) |
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1996
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-
1997
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- 1997-06-13 KR KR1019980710448A patent/KR100313067B1/en not_active IP Right Cessation
- 1997-06-13 ES ES97930046T patent/ES2205244T3/en not_active Expired - Lifetime
- 1997-06-13 WO PCT/US1997/010430 patent/WO1997049011A1/en active IP Right Grant
- 1997-06-13 DE DE69723839T patent/DE69723839T2/en not_active Expired - Lifetime
- 1997-06-13 EP EP97930046A patent/EP0906593B1/en not_active Expired - Lifetime
- 1997-06-13 CA CA002257881A patent/CA2257881C/en not_active Expired - Lifetime
- 1997-06-13 AU AU33967/97A patent/AU3396797A/en not_active Abandoned
-
1998
- 1998-02-24 US US09/028,443 patent/US6181975B1/en not_active Expired - Lifetime
Also Published As
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JP3449560B2 (en) | 2003-09-22 |
KR20000022050A (en) | 2000-04-25 |
JP2000505221A (en) | 2000-04-25 |
KR100313067B1 (en) | 2001-12-12 |
US5764509A (en) | 1998-06-09 |
WO1997049011A1 (en) | 1997-12-24 |
DE69723839D1 (en) | 2003-09-04 |
CA2257881C (en) | 2004-02-10 |
US6181975B1 (en) | 2001-01-30 |
ES2205244T3 (en) | 2004-05-01 |
EP0906593B1 (en) | 2003-07-30 |
AU3396797A (en) | 1998-01-07 |
EP0906593A4 (en) | 1999-09-15 |
EP0906593A1 (en) | 1999-04-07 |
DE69723839T2 (en) | 2004-04-22 |
CA2257881A1 (en) | 1997-12-24 |
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