System for detecting occurrence of an event when the slope of change based upon difference of short and long term averages exceeds a predetermined limit

[0002] This application claims the priority of provisional application No. 60/096,004 filed on Aug. 10, 1998.

[0003] 1. Field of the Invention

[0004] This invention relates broadly to monitoring systems. More specifically, this invention relates to a system and method for monitoring a dynamic system, such as a boiler or heat exchanger, which tends to undergo operational fluctuations, and for detecting quickly and accurately the occurrence of an event, such as a leak or lost efficiency, which may otherwise be masked or falsely implied by the operational fluctuations.

[0005] 2. Background

[0006] The early detection of an event such as a leak or malfunction can be critical in many applications. As used herein, the term “event” broadly refers to an occurrence which impacts the normal operational of a particular system, and which, in many cases, tends to grow worse or more intense if left unattended. For example, in the case of black liquor recovery boilers used in the paper industry, detecting a leak in the boiler tubes early often is the difference between a controlled shut down and a catastrophic explosion. Such explosions not only result in the destruction of the boiler, but also frequently in severe injury and death.

[0007] Detecting the occurrence of a real and significant event in a system, particularly a complex system like a black liquor recovery boiler, poses a challenging task. Often such systems have many variables and their operation is subject to considerable, yet normal, changes and fluctuations. These normal operational changes and fluctuations tend to mask events or create the false appear of one. Therefore, a monitoring system for detecting the occurrence of an event must be able to filter out these normal fluctuations, but nevertheless remain sensitive enough to provide an early indication of an event.

[0008] In the case of recovery boilers, methods to detect water leaks have been proposed and tested by researchers for several years. Most leak detection schemes monitor the total airborne or structural acoustic energy levels within the boiler to determine if a leak is present. Such acoustic leak detection strategies, however, face significant limitations. These limitations include the interference presented by high background noise levels, the attenuation of acoustic energy occurring within the boiler, and the limited durability of acoustic sensors in the harsh environment of the boiler.

[0009] A more recent improvement of acoustic leak detection systems, developed by Westvaco Corporation, utilizes spectral analysis techniques (TAPPI Journal(July 1990)). While the Westvaco system appears to be an improvement over previous acoustic leak detection systems, it still, to some extent, is subject to the above-identified disadvantages of acoustic leak detection technology. Moreover, spectral-analysis, acoustic leak detection systems tend to be expensive to purchase, implement and maintain.

[0010] A difference approach to leak detection system, which was introduced by the Applicant in U.S. Pat. No. 5,363,693, detects a leak by striking a mass balance around the recovery boiler. By measuring the fluid flowing in to and out of the recovery boiler system, fluid leakage loss based on the difference between the input and output can be calculated. If the difference is determined to be significant, a leak is indicated.

[0011] Although this leak detection system represents a marked improvement over existing acoustic methods, an on-going need exists to improve the sensitivity and reliability of a leak detection system. Moreover, the Applicant perceives a general need for a system that can quickly and accurately detect an occurrence of an event or significant change in all types of dynamic systems which undergo normal fluctuations. The present invention fulfills these needs among others.

[0012] The present invention provides for the early and accurate detection of an event or significant change in a target system by monitoring and statically evaluating at least one operational variable of the target system. The operational variable may be related to mass, volume, energy, momentum, time, money, quality, or any other quantitative measurement or calculation that provides an indication of one or more conditions of the target system which change in response to the event. The operational variable is evaluated by periodically averaging its values over relatively short and long terms. By comparing the long and short term averages using convenient, readily-implemented statistical techniques, the occurrence of an event can be determined with a high degree of confidence despite the target system's normal fluctuations.

[0013] One aspect of the present invention is a method for detecting an occurrence of an event in a target system. In a preferred embodiment, the method comprises the steps of: (a) calculating short and long term averages of sequentially recorded values of an operational variable wherein the long term average includes at least one values in addition to those included in the short term average; (b) calculating a difference, Δ, between the short and long term averages; and (c) statistically evaluating whether Δ is significant and indicative of an event occurrence.

[0014] In one embodiment, the statistical evaluation of step (c) comprises an analysis of Δ to determine its significance given the number of values considered in the averages and the variation between the values. The reliability of the indication is increased by repeatedly calculating whether a significant Δ exists. As the number of sequential significant Δs increases, so does the certainty that an event has occurred.

[0015] A preferred technique for determining the significance of A comprises calculating t_test. This calculation provides an important correlation between the sampling size and the certainty that a Δ is real as opposed to just a random anomaly or “noise.”

[0016] In another embodiment, the statistical evaluation of step (c) comprises an analysis of the change in a over time. By analyzing the dynamics of Δ, a trend indicative of the event can be determined well before the event's full effect is realized by static measurements. In other words, the present invention anticipates an event based upon the trend of Δs, rather than waiting until Δ reaches a predetermined limit. This approach not only shortens the time in which an event can be determined over prior art methods, but also improves the accuracy of such determinations and reduces the occurrence of false positive alarms.

[0017] The dynamic analysis mentioned above may be performed by repeating steps (a) and (b) at least once, wherein the short and long term averages include at least one value more recent than any values considered in a previously calculated short and long term average, and then calculating the change in Δ over the change in sequence of the recorded values. If the change in Δ exceeds a predetermined value, then the occurrence of an event is likely.

[0018] Another aspect of the present invention is a system for detecting an occurrence of an event in a target system. In a preferred embodiment, the system comprises a central processing unit (CPU), user interface means operatively connected to the CPU for inputing the target system's operational variable(s) and for outputing an indication of an occurrence of an event, and memory which contains a program of instructional means for the system to perform the above-mentioned process. The system may also comprise measurement means for measuring the target system's inputs and outputs.

[0019] Still another aspect of the present invention is a computer readable medium, such as a floppy disk or CD ROM. The computer readable medium contains a program of instructional means for the above-mentioned system to perform the above-mentioned process. In accordance with the present invention, the method and system provided enable a user to monitor a dynamic system which tends to undergo operational fluctuations, and to detect quickly and accurately the occurrence of a significant event which may otherwise be masked or falsely implied by the operational fluctuations. Applications for the present invention are widespread and include, for example, monitoring a mass balance around a boiler to detect a leak; monitoring the heat transfer of a heat exchanger to detect excess scale build up; monitoring a motor's power consumption to detect bearing failure; monitoring overtime to detect an under-staffing condition; monitoring service calls to detect a defective product; and monitoring quality on an assembly line to detect low moral. Indeed, the present invention can be applied to any target system or situation having at least one operation variable that changes in response to an event.

[0020] FIG. 1 is a flow chart depicting a preferred process embodiment of the invention;

[0021] FIG. 2 is a schematic diagram of a preferred system embodiment of the invention;

[0022] FIG. 3 is a schematic diagram of a preferred embodiment of the system applied to a chemical recovery boiler;

[0023] FIG. 4 is a chart showing drum balances over time in relation to various time frames;

[0024] FIG. 5 is a flow chart of a preferred process embodiment of the invention in which a pattern of significant As are monitored; and

[0025] FIG. 6 is a chart of values of system balances as a function of sequential recordings.

[0026] The present invention provides a system and method for quickly and accurately detecting the occurrence of an event in a target system. The present invention may be practiced on any target system having one or more operational variables that change in response to an event occurring in or around the target system. Suitable target systems include, for example, apparatus such as boilers, heat exchangers, or reactors; combinations of components such as electrical distribution systems, fresh water cooling systems, or assembly lines; and even personnel such as a sales department, clerical staff, or city population.

[0027] A process embodiment of the invention is depicted in FIG. 1 as a flow chart. Referring to that figure, in Block 101, operational variable values are periodically measured or calculated and recorded sequentially. Block 102 then calculates and records short and long term averages for these values. The short and long term averages are moving averages of the operational variable values, and are typically recalculated once a new operational variable value is recorded. The short term average is based upon a sampling size which is a fraction of the sampling size used for the long term average. In Block 103, the difference between each corresponding set of short and long term averages, herein “Δ”, is determined. In a preferred embodiment, Block 104 determines if Δ is over a predetermined limit. This step avoids unnecessary statistical evaluation in Block 105 if Δ is insignificant. If Δ does exceed a predetermined limit or if the optional Block 104 is not employed, then the process proceeds to Block 105 where the short and long term averages are evaluated using statistical techniques to determine whether Δ is real and significant and, therefore, indicative of an event. The statistical evaluation techniques used in this process represent an important aspect of the invention and are considered in more detail below. After evaluation, if Δ is determined not to be significant in Block 106, the interrogation of a particular Δ ends. If Δ is significant, then Block 107 indicates the probable occurrence of an event.

[0028] A system embodiment of the invention is depicted schematically in FIG. 2. As shown, a system 200 comprises a central processing unit (CPU) 201 which may be a discrete processor, or a combination of processors, configured in a personal computer, controller, work station, main frame or the like. Such CPUs are known in the art. operatively connected to the CPU 201 is a user interface 202. The user interface may contain input means, such as a mouse or keyboard, which enables the user to input information into the system 200. It may also include output means, such as a display monitor, printer or audio alarm mechanism, which provides the user with an indication of the system's output. The system 200 may also comprise measurement means 205 operatively connected to the CPU 200. The measurement means 205 measures one or more operational variables of a target system 150. In the embodiment depicted in FIG. 2., the target system 150 has an input 151, an output 152, and a potential event 153 (phantom line) which may be an unaccounted for leak, waste, or inefficiency. It should be noted that measurement of an operation variable may be performed by equipment outside the system of the present invention and provided to the CPU 201 by means known in the art. Also operatively connected to the CPU 201 is memory 204 which contains a program of instructional means for the system 200 to perform the process of the present invention as described above. Memory 204 can be any known memory medium such as RAM or PROM.

[0029] The program of instructional means may be integral to the system of the present invention or a discrete aspect of the present invention. The program may be adapted to function on known operating platforms and is anticipated to be compatible with emerging operating platforms as well. The program may be stored on any computer readable medium such as a disk, tape, CD ROM, RAM or PROM.

[0030] A particular embodiment of the system of the present invention as applied to a chemical recovery boiler is shown in FIG. 3. Referring to that figure, a system 310 for detecting leakage from a chemical recovery boiler system 312 of the type which includes a recovery boiler drum 314 and associated steam output piping 316 is shown. Recovery boiler system 312 typically includes a feed water line 318 for supplying water to the recovery boiler drum 314 and an outlet line 320 for “blow-down” flow. Boiler system 312 further includes steam output piping 316, which typically leads to a turbine for electricity generation. An inflow line 322 for introducing attemperator fluid, usually water, into the steam piping 316 is also illustrated in FIG. 3. The purpose of the attemperator fluid is to cool down steam which has been heated beyond a predetermined level. Primary and secondary superheaters 324, 326 may also be positioned in the steam output line 316.

[0031] The system 310 according to the preferred embodiment of the invention includes a first monitor 328 that interposed within the feed water line 318 for measuring the mass flow of feed water into the recovery boiler drum 314. A second monitor 330 is interposed in the blowdown output line 320 for measuring the mass flow of blow-down which may be expelled from the recovery boiler drum 314. A third monitor 332 is interposed in the attemperator fluid inflow line 322 for measuring the mass flow of attemperator fluid into the steam output piping 316. A fourth monitor 334 is provided in the outflow portion of steam piping 316 for measuring the mass output from the steam piping 316. A fifth monitor 343 is operatively connected to the boiler drum 314 for measuring the level of fluid in the drum, herein referred to as the “drum level”. The monitors 328, 330, 332, 334, and 343 are all preferably electronic in nature, and all are constructed and arranged to report electronically to a controller 336, as is schematically depicted in FIG. 3.

[0032] The process of the present invention is addressed below in greater detail and in regard to a specific target system, namely, the chemical recovery boiler as described above. It should be understood, however, that the process may be applied to any target system having one or more operational variables that change upon the occurrence of an event.

[0033] The first step involves sequentially recording values of one or more operational variables of the system. As mentioned above, the operational variable may be related to mass, volume, energy, momentum, time, money, quality, or any other quantitative measurement or calculation that provides an indication of one or more conditions of the target system which change in response to the event. In a preferred embodiment, the operational variable relates to a system balance which may be calculated by equating inputs to outputs. For example, the input may be raw materials, energy, water, steam, etc, and the output may be a finished product, steam, energy, etc. In a simple target system, there is a one to one correspondence between input operational variables and output operational variables, meaning units going in directly correspond to unit going out, e.g., gallons of water in/gallons of water out. In a more complicated target system, the input and output must be equated. For example, an input of a certain amount of water and energy corresponds to an output of steam at a certain pressure and temperature. Equating such inputs and outputs is known in the art.

[0034] Referring to FIG. 3, during operation of the recovery boiler system 312, the monitors 328, 330, 332, 334 report continuously to controller 336, which samples such data periodically, preferably about every second. From this data, controller 36 calculates a system balance, which in this case is the drum balance (DB) expressed in units of mass per unit time. This calculation, depicted as Block 101 in the flow chart illustrated in FIG. 1, may be expressed as follows:

[0035] DB=Feed Water Flow+Attemperator Flow−(Steam Flow+Blow Down Flow)  Equation (1)

[0036] According to a preferred embodiment of the invention, the accuracy of detecting a significant change in a system balance can be improved by compensating for normal fluctuations within the system. To this end, a relationship is struck between the system balance and one or more operational variables that to impact it. The correlation between the operational variable(s) and the system balance can be used to generate a correction or compensation factor that can be applied to the system balance to correct expected fluctuations.

[0037] For example, in a chemical recovery boiler, the drum balance calculation is improved by compensating for the swelling and shrinking of the boiler drum 14 caused by pressure changes in the system 10 and other factors. The swelling and shrinking of the boiler drum can conceal or suggest a leak erroneously. That is, when a boiler swells, its volume increases and retains more fluid. This gives the indication that the amount of fluid entering the boiler is less than the fluid exiting, which therefore suggests a leak. Conversely, when the boiler shrinks, its capacity is diminished. This results in increased fluid relative to the boiler system. If a leak exists, the increased fluid may serve to mask it since the fluid output may not change or may even increase vis a vis the fluid input. Therefore, a more accurate drum balance can be calculated by compensating for boiler shrinking/swelling.

[0038] To this end, the present invention draws a relationship between drum balance and drum level. It has been found that drum level provides a simple and accurate correlation to drum balance (although other variables such as system pressure and temperature can be used individually or in combination to provide an indication of drum balance). Theoretically, the drum level and drum balance should be mirror images of one another—as the drum balance increases and decreases, drum level should drop and rise respectively. Based on this relationship, the controller 334 receives a signal from monitor 343 and calculates a compensated drum balance (DB_C) using the following equation:

[0039] DB_C=DB−DB_P  Equation (2)

[0040] wherein DB is calculated according to Equation (1), and DB_Pis the compensation factor based on drum level. The compensation factor has the following correlation equation:

[0041] DB_P=a+DL*b  Equation (3)

[0042] wherein a is a moving intercept, b is a moving slope for a particular set of data, and DL is the drum level.

[0043] In one embodiment, the correlation equation is generated using neural network logic. Neural systems are known in the art and can train themselves to predict process behavior using on-line data. Using neural lines correlation techniques therefore enables the compensation factor to be updated periodically, for example, every second, to account for fluctuations caused by boiler swelling and shrinking in the drum balance, thereby minimizing erroneous measurements. Although neural networks provide a powerful tool to predict output, it should be understood that other conventional correlation techniques can be used. Moreover, it is anticipated that future correlation techniques used to predict one variable based on another variable, or a group of variables, will find application in this leak detection system.

[0044] The present invention uses a comparison of long term sampling and short term sampling in its statistical evaluation of one or more operational variables. More specifically, a long term moving average of a operational variable is calculated over a particular time frame or “window.” The window contains a particular sampling size of sequentially recorded values of an operational variable. The sampling of data in this window changes as new operational variable values are recorded. These new values enter the window while older values leave. A short term moving average of the operational variable is calculated over just a portion of this window.

[0045] Averaging data is well known in the art and any known technique may be practiced within the scope of this invention. In the chemical recovery boiler, for example, controller 336 uses long term sampling and short term sampling in its statistical analysis of the data received from the monitors 328, 330, 332, 334. As represented below in equation (4) and (5), controller 336 calculates short term and long term drum balance averages {overscore (DB₁)} and {overscore (DB₂)} periodically, for each data sampling, wherein Ts represents current time in seconds, N₁represents the number of samples included in the short term average, and N₂refers to the number of samples included in the long term average: $\begin{array}{cc}\stackrel{\_}{{\mathrm{DB}}_1}=\frac{\sum _{i=T_s-N_1}^{N_1}\mathrm{DB}\left(i\right)}{N_1}& \text{Equation (4)}\\ \stackrel{\_}{{\mathrm{DB}}_2}=\frac{\sum _{i=T_s-N_2}^{N_2}\mathrm{DB}\left(i\right)}{N_2}& \text{Equation (5)}\end{array}$

[0046] Rather than relying on a single window, a preferred embodiment of the present invention uses a plurality of windows of varying duration or sampling size. Each window corresponds to a pair (herein “window pair”) of short and long term averages.

[0047] Multiple window pairs allow the system and method of the present invention to strike a balance between responsiveness and accuracy. A window pair taken over a relatively short time frame allows for a relatively quick indication of a leak. However, the risk of a false alarm is greater due to the relatively small data sampling failing to transcend an otherwise benign system fluctuation. on the other hand, a longer time frame involves a greater sampling size and tends to reduce the effects of transient fluctuations. The cost of such accuracy, however, is decreased response time. Therefore, the present invention provides for a variety of time frames to satisfy response time and accuracy needs.

[0048] An example of a multiple window pair system for a recovery boiler system is shown in FIG. 4. That figure depicts drum balance data over time in relation to a leak detection system having three independent window pairs—a first pair 401, a second pair 402, and a third pair 403. The right side of the chart indicates time zero or present time, and towards the left side of the chart, the drum balance data becomes more dated. It should be apparent from the depiction of FIG. 4 that with every update, new drum balance datum enters the window pairs simultaneously from the right, while various older drum balance data exit the window pairs to their left. The duration that a particular drum balance datum remains in a window pair depends entirely on the window size.

[0049] The first window pair 401 corresponds to a short term average drum balance that extends back in time for a short term 404. The short term average drum balance of the second window pair 402 extends back in time for a short term 405 which is longer than the short term 404. Likewise, the third window pair 403 corresponds to a short term average drum balance that extends back in time for a short term 406 which is longer yet than that the short term 405. The long term average drum balances corresponding to the first 401, second 402, and third 403 window pairs extend back for long terms 407, 408, and 409 respectively.

[0050] The short term over which a particular short term average is calculated, or, in other words, the number of data considered, preferably relates to the cyclic tendency of the system being monitored. Due to various operating conditions, for example, pumps turning on/off and changing steam demands, a given operational variable tends to cycle. It is therefore preferred that the short term averages be taken over a period corresponding to a portion of the cycle that roughly provides a range of operational variable value magnitudes expected to occur in a typical cycle, for example, a quarter cycle. In this way, the short term average includes both cyclic highs and lows, and consequently, tends to avoid false leak indications caused by ordinary cycling.

[0051] The cycle can be determined either by examining the system data over time or, preferably, by calculating it online in the system CPU using contemporaneous recorded data. The latter can be undertaken using known correlation or curve fitting software. By having the operational variable cycle updated continuously in the CPU, the system can adjust the short term drum balance averages to cover relevant portions of the cycle as the cycle itself varies.

[0052] The long term over which a particular long term average is taken depends in part upon the short term of its paired short term average. That is, the long term average should be long enough to transcend operational conditions affecting the short term average, but not so long as to average out all drum balance anomalies. As used in this disclosure, R refers to the ratio of N₂divided by N₁. It has been found that a preferred R or the ratio of N₂to N, is about 8:1 to about 12:1, and, more preferably, about 10:1. Moreover, with particular regard to longer time frames, it may be beneficial to extend the long term average beyond a typical work shift. This way, operational differences between different shifts can be averaged out thereby reducing the likelihood of a false positive alarm signal.

[0053] Referring back to FIG. 4, the first 401, second 402 and third 403 window pairs have short terms corresponding to approximately one quarter, one half and a full boiler cycle respectively. The long terms are approximately ten times as long. Thus, in a system with a drum balance cycle of approximately 40 minutes, controller 336 conducts short term averaging over 10, 20, and 40 minute terms for the first, second and third time frames respectively. The long term average drum balances would be calculated over approximately 100, 200, and 400 minute terms for the first, second, and third time frames respectively. It may be beneficial to extend the long term of the third time frame to approximately 600 minutes, or so, to span between multiple operation shifts. For the first window pair, N₁and N₂would be 120 and 1200 respectively for sampling every 5 seconds. The numbers of drum balance data used in the second and third time frames would be calculated in a similar manner.

[0054] After calculating long and short term value averages of a operational variable, the CPU calculates the difference (herein “Δ”) between them in Block 203 to determine the possibility of an event. If Δ does not exceed a maximum tolerable difference, Δ_max, then the process waits until the long and short term averages are updated and recalculates Δ. If Δ_maxis exceeded, however, Δ may be indicative of an event, and the process proceeds to Block 205. Δ_maxmay be determined empirically based upon the desired sensitivity of the system and method. It should be understood that although determining the significance of Δ before embarking on its statistical evaluation is preferable from the standpoint of conserving computer resources, it is not required.

[0055] In the case of the recovery boiler, for example, controller 336 calculates Δ between the short and long term average drum balances {overscore (DB₁)} and {overscore (DB₂)} for each window pair for each sampling period using the following calculation:

[0056] Δ={overscore (DB₁)}−{overscore (DB  Equation (6)

[0057] In Block 204, the controller 336 next compares Δ with a predetermined maximum limit Δ_maxas described above. A Δ in excess of Δ_maxmay be indicative of a leak.

[0058] An essential aspect of the present invention is determining whether Δ is “real” and indicative of an event, such as a leak. To this end, the present invention employs a variety of statistical techniques, individually and in combination. These techniques include but are not limited to the following:

[0059] a. Determining the significance of Δ,

[0060] b. Monitoring a particular pattern of significant Δs, and

[0061] c. Monitoring change in Δ.

[0062] a. Determining the Significance of Δ

[0063] One approach in evaluating Δ is to determine if it is significant given the variations in the sample data and the size of the sample. A preferred technique for determining this is calculating t_test. Those skilled in the art of statistics will recognize that t_testprovides an important correlation between the sampling size and the certainty that a Δ is real as opposed to just a random anomaly or “noise.”

[0064] A flow chart of processes involving the calculation and use of t_testis shown in FIG. 5. Determining t_testrequires calculating the pooled standard deviation of the long and short term averages in Block 501. Such a calculation is well known in the art. For example, the controller 336 may first calculate the standard deviations σ₁, σ₂for the short and long term samples of each window pair, respectively, using equations (7) and (8): $\begin{array}{cc}{\sigma }_1=\sqrt{\frac{\sum _{i=T_s-N_1}^{N_1}{\left(\mathrm{DB}\left(i\right)-\stackrel{\_}{{\mathrm{DB}}_1}\right)}^2}{N_1-1}}& \text{Equation (7)}\\ {\sigma }_2=\sqrt{\frac{\sum _{i=T_s-N_2}^{N_2}{\left(\mathrm{DB}\left(i\right)-\stackrel{\_}{{\mathrm{DB}}_2}\right)}^2}{N_2-1}}& \text{Equation (8)}\end{array}$

[0065] In Block 502, the controller 336 then calculates the pooled estimated standard deviation {overscore (S)} for the entire data set for each time frame 204 using the following equation: $\begin{array}{cc}\stackrel{\_}{S}=\sqrt{\frac{\left(N_1-1\right){\sigma }_1^2+\left(N_2-1\right){\sigma }_2^2}{\left(N_1-1\right)+\left(N_2-1\right)}}& \text{Equation (9)}\end{array}$

[0066] In Block 503, the significance of Δ for each time frame is determined using t_test, which may be calculated in any manner known in the art. For example, the controller 336 may calculate t_testusing the following equation: $\begin{array}{cc}{t}_{\mathrm{test}}=\frac{\stackrel{\_}{{\mathrm{DB}}_1}-\stackrel{\_}{{\mathrm{DB}}_2}}{\stackrel{\_}{S}\sqrt{\frac{1}{N_1}+\frac{1}{N_2}}}& \text{Equation (10)}\end{array}$

[0067] In Block 504, the CPU determines whether t_testexceeds a predetermined maximum, t_max. If t_maxis exceeded, then Δ is considered to be significant at a corresponding confidence limit. In one embodiment of the invention, the controller 336 signals an alarm in Block 107 (FIG. 1) if the t_maxwas exceeded.

[0068] b. Monitoring a Pattern of Significant Δs

[0069] To improve the accuracy of determining the occurrence of an event, significant Δs (as calculated by t_test, for example) are monitored to determine if a predetermined limit is exceeded. This predetermined limit is user defined and may include a given number of significant Δs over a certain period, a particular pattern of significant Δs, or a predetermined succession of significant Δs. Of these, a predetermined limit of consecutive significant Δs is preferred.

[0070] A succession of significant Δs in the average drum balances offers a higher degree of reliability that a leak actually exists than just one occurrence. By analogy, flipping a coin just once and having it land heads-up indicates very little about its tendency to be fair and land either heads-up or heads-down with equal probability. If, on the other hand, a coin is flipped repeatedly and continues to land heads-up, the likelihood that the coin is not fair increases exponentially as the succession of heads-up landings increases.

[0071] By increasing the reliability of an alarm condition, the improved system offers two distinct advantages over the prior art. First, higher reliability equates to fewer false alarms. False alarms may not only precipitate a costly shut-down, but also “desensitize” the operators causing them to react indifferent to a real leak. Second, higher reliability allows for a more sensitive system. That is, since the chance of a false alarm is greatly diminished, the t_maxcan be lower. It need not be maintained at a relatively high level to act filter for peak normal values.

[0072] Referring back to FIG. 5, one preferred embodiment of the invention is shown for monitoring a pattern of significant Δs in a recovery boiler. If t_testis not greater than t_maxin Block 504, then controller 336 resets the number or the indicator of consecutive significant Δs (n) to zero in Block 505, and waits to repeat the above-described calculations with respect to the data which is received from the sensors 328, 330, 332, and 334 in the next sampling period. On the other hand, if t_testis greater than t_max, controller 336 increases the number of significant Δs by one in Block 506, and then determines whether a predetermined succession of significant Δs has been reached in Block 507. If the number of significant Δs is reached, an alarm 338 is signaled in Block 207.

[0073] C. Monitoring Change in Δ

[0074] Another statistical techniques for determining the significance of Δ is evaluating the dynamics of Δ as new operational variable values are periodically recorded. An event, such as a leak, will produce a predictable Δ slope over time. By monitoring Δ slope, a highly reliable determination can be made as to the occurrence of an event.

[0075] FIG. 6 shows a graphical representation of recorded values of an operational variable, in this case a system balance 601, as a function of time or sequential recordations. The figure also shows short term average system balance 602, long term balance average system balance 603, and Δ 604 as system balance are periodically recorded. Although system balance is represented in FIG. 6 and the following equations, it should be noted that any operational variable may be similarly used.

[0076] An event at the origin 605 causes the initial system balance SB_Oto increase sharply to SB_E606. As a result, the short term average begins to increase at a rate of SB_E/N₁, where N₁is the number of system balances considered in the short term average. The short term average increases until reaching its maximum at a point equal to N₁after the event. The long term average increases at a lower rate of SB_E/N₂where N₂is the number of system balances considered in the long term average. In similar fashion to the short term average, the long term average increases until reaching its maximum at a point equal to N₂after the event. After such time, SB₁is considered in all the system balances used in both the short and long term averages and Δ is minimized.

[0077] The difference in the rate of increase between the short and long term averages produces a Δ with a characteristic slope. As a result of the event, Δ increases with a slope having the following equation: $\begin{array}{cc}{\mathrm{SLOPE}}_{{\Delta }_{\mathrm{theoretical}\mathrm{up}}}=\frac{\frac{N_2-N_1}{N_2}*{\mathrm{SB}}_E}{N_1}& \text{Equation (11)}\end{array}$

[0078] The slope of Δ continues to increase according to Equation 11 for a period equal to N₁, at which point, Δ reaches its maximum value. Then, Δ begins a slow decrease with a slope having the following equation: $\begin{array}{cc}{\mathrm{Slope}}_{{\Delta }_{\mathrm{theoretical}\mathrm{down}}}=\frac{\frac{N_2-N_1}{N_2}*{\mathrm{SB}}_E}{N_2-N_1}& \text{Equation (12)}\end{array}$

[0079] This slope lasts until reaching a steady state after a period equal to N₂from the point of the event.

[0080] The present invention recognizes the dynamic relationship between Δ and the occurrence of an event. Based on this relationship, a preferred embodiment of the present invention plots Δs as a function of the periodic calculation of system balances to provide an indication of an occurrence. Once Δ exceeds a predetermined limit as described in Block 106 above, is the positive slope of Δs (herein “slope_Δup”) is calculated. The calculation of slope_Δupmay be performed using any known slope calculation means. In one preferred embodiment, slope_Δupis calculated in accordance with the follow formula: $\begin{array}{cc}{\mathrm{Slope}}_{{\Delta }_{\mathrm{up}}}=\frac{{\Delta }_i-{\Delta }_o}{N_i-N_o}& \text{Equation (13)}\end{array}$

[0081] In this equation, N_orepresents a point in time or other sequential index identifying a corresponding recordation of an operational variable value just prior to the occurrence of an event. N_ocorrelates to Δ_owhich represents the calculated difference between the short and the long term just prior to the occurrence of an event. In a preferred embodiment, N_oand Δ_oare the N and Δ values just prior to Δ exceeding Δ_max. N_iand Δ_irespectively represent the sequential index and Δ pertaining to a particular recorded value. Aside from Equation 13, other, conventional curve fitting software may be employed to determining Δ slope, such as least squares. The slope_Δupis compared to a slope limit or slope_{Δup max}. If the value of the slope equals or exceeds slope_{Δup max}, than the occurrence of an event is likely.

[0082] Establishing slope_{Δup max}is similar to establishing Δ_maxand may be done through empirical testing to determine the optimum value for sensitive yet reliable results. In a preferred embodiment, Δ_maxis substituted in Equation (11) and the resulting slope is slope_{Δup max}. For example, if N₁is 10, N₂is 100 and Δ_maxis 5 gallons/minute, then slope_{Δup max}would be (0.45 gallons/minute)/(change in N). Therefore, in this example, if the slope equals or exceeds 0.45 gallons/minute)/(change in N), then an event is likely to have occurred.

[0083] After it is determined that slope_Δupis equal to or exceeds slope_{Δup max}, optional, additional statistical evaluations may be performed to ensure accuracy and to avoid a false positive indication of an event. One such statistical evaluation involves, again, the use of t_test. In this situation, t_testmay be determined using the following equation: $\begin{array}{cc}{t}_{\mathrm{test}}=\frac{{\mathrm{Slope}}_{\Delta \mathrm{up}}-{\mathrm{Slope}}_{\Delta \mathrm{up}\max }}{{\sigma }_{{\mathrm{Slope}}_{\Delta }}\sqrt{\frac{1}{N_i-N_o}}}& \text{Equation (14)}\end{array}$

[0084] wherein σ_{slope Δ} represents the standard deviation for the Δs used in the calculation of slope_Δ. If t_testexceeds a predetermined value of t_test, t_max, then the certainty of an event is established at a particular confidence level. For example, a positive t_testof over 2.94 indicates an event with 99% probability. The probability increases as successive, new t_test, that exceed t_maxare calculated (as described above).

[0085] Another approach to increase confidence that an event has occurred is to calculate successive values of slope_Δups and determine if each successive value is equal to or exceeds slope_Δmax. The probability of an event increases as the number of successive slope_Δupvalues that exceed slope_Δmaxincreases. The optimum number of values considered for a particular confidence level can be determined by someone skilled in the art without undue experimentation.

[0086] Yet another approach to increase confidence that an event has occurred is to calculate not only the slope_Δupbut also slope_Δdown. If the slope of Δs follows the theoretical down slope of Equation 12 after a period N₁following the excessive Δ, then the occurrence of an event is almost certain. The down slope of Δ may calculated in accordance with the follow formula: $\begin{array}{cc}{\mathrm{Slope}}_{{\Delta }_{\mathrm{down}}}=\frac{{\Delta }_i-{\Delta }_{o+N_2}}{N_i-N_{o+N_i}}& \text{Equation (15)}\end{array}$

[0087] The slopes_Δdownis compared to a down slope limit (herein “slopes_{Δdown max}”) If the value of the slope equals or exceeds slope_{Δdown max}, than the occurrence of an event is likely. Like slope_max, slope_{down max}can be determined by empirical means or by substituting Δ_maxin Equation 12. For example, in the case where N₁is 10, N₂is 100 and Δ_maxis 5 gallons/minute, then slope_{Δdown max}would be (0.1 gallons/minute)/(change in N). Therefore, in this example, if the slope equals or exceeds−0.1 gallons/minute)/(change in N), then an event is likely to have occurred.

[0088] The relationship of slopes down to slope_{Δdown max}is analogous to the relationship of slope_Δupto slope_{Δup max}in regard to the improving detection confidence levels. For example, t_testmay be calculated in accordance with Equation 14 modified for slopes down rather than slope_Δup.

[0089] It should be understood that a preferred embodiment of the invention involves a combination of the aforementioned techniques for evaluating Δ.

[0090] Once the Δ is determined to be real and indicative of an event, such as a leak, an indication or warning is given to the user via the user interface. The indication of an event can be audio, visual or both. Moreover, in an embodiment using multiple window pairs, a different alarm condition can be indicated for a particular window pair. The severity of the alarm can be tailored to the length of the window indicating an event—the longer the window, the more urgent the warning.

[0091] Once a leak is detected, controller 336 (FIG. 3) in turn provides control signals to alarm 338 and, optionally, to a warning lamp 340. For shorter window pairs, the alarm indicate that a potential leak has been detected. This puts the operators on notice that a leak is likely, and affirmative action should be taken such as inspecting the boiler for confirmation. As the anomalous drum balance data subsequently affect the longer window pairs thereby triggering their alarms, the condition should be treated as much more serious. A long term alarm may require emergency action such as shutting off the feed water.

[0092] In one embodiment of the invention, the leak detection system not only signals an alarm condition, but also takes action to avert a catastrophic failure. Referring back to FIG. 5, controller 336 calculates leakage rate Δ for the next data set in Block 610, and for subsequent data sets. At the end of such calculations, controller 336 will determine if the calculated leakage rate Δ has increased with respect to previous measurements in Block 611. If Δ has not increased, the process is repeated. If Δ does increase, controller 336 then determines if a predetermined minimum time T_Bhas elapsed in Block 612. If time equal to T_Bhas not elapsed, the sampling and calculation process is again repeated. If a period of time greater than TB has elapsed, controller 336 in Block 613 will activate shutoff valve 342 in feed water line 318, to cut off feed water to the recovery boiler 314, thereby shutting down the recovery boiler system 312 automatically. Thus, if the leakage rate continues to increase over a predetermined period of time without human intervention, system 310 act to automatically prevent a leak created explosion from taking place in the recovery boiler system 12.

[0093] This example illustrates the practice of the present invention on a target system having equatable input(s) and output(s) such that a system balance (SB) can be drawn around it. As shown in Table 1, theoretical inputs (in) and outputs (out) were entered sequentially at various intervals (N). For simplicity, no units are assigned to the input and output. The output was subtracted from the input to calculate SB. Short and long term averages, SB₁and SB₂, respectively, were calculated based upon a short term sampling, N₁, of 5, and a long term sampling, N₂, of 15. It should be noted that these samplings are typically longer, but were shorted herein to render the size of the example more manageable.

[0094] At interval 16, an event occurs wherein the output drops sharply to only about one (1) causing SB to increase dramatically. Initially, this change is realized to a greater extent by SB₁than by SB₂due to the greater impact the change has in the smaller sampling of SB₁. The difference in the averages is recorded as Δ.

[0095] A preferred embodiment of the present invention determines whether Δ is excessive before statistically evaluating it. In this case, a Δ of greater than 5 is considered excessive and will trigger the statistical evaluation of Δ to determine the likelihood of an event. Δ exceeds this limit at interval 19.

[0096] One approach to statistically evaluating Δ is to determine whether it is significant by calculating its t_test. In a preferred embodiment, this is performed at interval 19 (excessive Δ), however, if computational resources are not an issue, t_testcan be calculated for each Δ (as shown in Table 1). Determining t_testfirst requires calculating the standard deviation for the short and long term averages, σ₁and σ₂, respectively. A t_testof 2.94 suggests a 99% likelihood that the event is real. Therefore, at interval 20, a determination is made that the occurrence of an event is extremely likely.

[0097] Another approach to the statistically evaluation of Δ comprises monitoring successive, significant Δs. In intervals 21 through 26, successive, significant As are calculated. This virtually assures that an event has occurred.

[0098] Yet another approach to evaluate Δ comprises monitoring the change in Δ. The change in Δ is calculated in terms of its slope using Equation (13) wherein Δ_ois assumed to be 0 prior to the event occurring. In this example, N_ois taken at N=15, just prior to the event's occurrence. The slope of Δ immediately increases to about 1.5 and remains for a period equal to the number of values considered in the short term average, in this case, 5. A slope of 1.5 exceeds a maximum slope of ⅔ which is calculated using Equation (11) and a Δ_maxof 5. The confidence level of an event detection can be increased by utilizing t_test, one equation for which is shown in Equation 14. As indicated in intervals 18 through 20, extremely high t_tests are calculated which virtually assures the probability of an event.

[0099] It is to be understood, however, that even though numerous characteristics and advantages of the present invention have been set forth in the foregoing description, together with details of the structure and function of the invention, the disclosure is illustrative only, and changes may be made in detail, especially in matters of shape, size and arrangement of parts within the principles of the invention to the full extent indicated by the broad general meaning of the terms in which the appended claims are expressed.