Method for predicting failures in industrial systems

Abstract

A method for predicting failures in an industrial system (100), comprising: a) determining a plurality of data points (t 1,...,n ,y 1,...,n ), each data point having a timestamp (t i ) and each of the timestamps (t i ) the value of the variable W measured at i ), b) calculating fitting parameters (2) of a log-periodic power-law model function W(t) (3) that provides a minimum mean square error mse (4) for the input time series (1) or for one or more subsets (1a) of data points of the input time series (1) to obtain a fitted function (5); and c) finding a local maximum (N max ) and local minima (N min ) and d) identifying the identified local maxima (N max ) from at least some of the trends (T max ) to the identified local minimum (N min ) from at least some of the trends (T min ) respectively, and determining each of the trends (T max ,T min ) is the selected local maximum (N max ) and the local minimum (N min ) of the input time series (1), respectively determined by the slope of a linear fit to the given data point (t n ,y n ) is the critical point (t c ) or not, max ,T min ) for the given data point (t n ,y n The last point (t n-1 ,y n-1 ) is positive or negative for the given data point (t n ,y n ) is the critical point (t c ) and f) in step e), a critical point (tc and if a failure of one or more components (8) in the industrial system (100) is identified, outputting a signal (7) indicating that a failure of one or more components (8) in the industrial system (100) is predicted.

Description

[Technical Field]

[0001] The present invention relates to a method for predicting failures in an industrial system, an industrial system, a computer program and a computer-readable storage medium according to the independent claims. The present invention further relates to the use of the method disclosed herein for predicting failures in an industrial system, in particular in a reciprocating compressor. [Background technology]

[0002] The concept of predictive maintenance, i.e., the detection and prediction of future failures based on multivariate or univariate time series of data collected from industrial systems, has widespread significance and applicability in various industrial applications, as it allows necessary maintenance work to be planned in advance. By avoiding potential failures or machine breakdowns, machine uptime can be increased, reducing unscheduled downtime and the cost of standard service work.

[0003] The development of supervised predictive maintenance methods based on machine learning (ML) and machine operators training the algorithms is well known. However, in practice, the reliability and accuracy of predictive maintenance methods obtained in this way are often hindered by operators' misinterpretation and / or inaccurate description of failures. In most cases, it is impossible to accurately identify the cause of a failure over time based on the available data. This poses serious challenges for training ML models based on supervised methods and for detecting statistical shifts in the data. This requires frequent human intervention in the ML production pipeline.

[0004] The prior art is known from Non-Patent Document 1, which deals with critical phenomena involving a power law with a singularity at the critical point where a sudden change in the system state occurs. The authors of this paper report that lean blowout in a turbulent thermoacoustic system can be considered a critical phenomenon and that discrete-scale invariance exists as the system dynamics approach lean blowout. The presence of log-periodic oscillations in the time evolution of the amplitude of the dominant mode of low-frequency oscillations is present in pressure fluctuations preceding lean blowout. The presence of discrete-scale invariance indicates the recursive occurrence of blowouts. The authors further report that the amplitude of the dominant mode of low-frequency oscillations grows faster than exponentially and becomes singular when a blowout occurs. A model is presented that describes the evolution of the amplitude of the dominant mode of low-frequency oscillations based on a log-periodic correction to the power law associated with the growth of low-frequency oscillations. According to the authors, blowouts can be predicted several seconds in advance.

[0005] Also known from the prior art is US Pat. No. 5,629,999, which describes a computer program and method for detecting and predicting valve faults in complex machinery such as reciprocating compressors. The method is based on the fact that pressure signals have non-stationary waveforms. Features from the signals can be extracted using wavelet packet decomposition. The extracted features, together with temperature data from the reciprocating compressor, are used to train a logistic regression model for classifying between faulty and normal valve operation. For a given set of inputs, the model provides the probability that the input belongs to either the normal or faulty signature group. In other words, the logistic regression model is used as an indicator of system health.

[0006] However, the above publications did not lead to the invention as claimed. [Prior art documents] [Patent documents]

[0007] [Patent Document 1] US Patent Application Publication No. 2010 / 0106458 [Non-patent literature]

[0008] [Non-Patent Document 1] BANERJEE, A. et al., Imprints of log-periodicity in thermoacoustic systems close to lean blowout, ARXIV.ORG, Cornell University Library Summary of the Invention [Problem to be solved by the invention]

[0009] It is an object of the present invention to overcome these and other shortcomings of the prior art, and in particular to provide an improved method for predicting failures in industrial systems, such as reciprocating compressors, that is cost-effective, reliable, and easy to implement. It is a further object of the present invention to provide an industrial system, in particular a reciprocating compressor system, in which failures can be predicted in a cost-effective and reliable manner. [Means for solving the problem]

[0010] This object is achieved by a method for predicting failures in an industrial system, an industrial system, a computer program, a computer-readable storage medium and the use of the method disclosed herein for predicting failures in an industrial system according to the independent claims. Advantageous embodiments are the subject of the dependent claims.

[0011] The method for predicting a failure in an industrial system comprises the following steps a) to f). In step a), multiple data points (t 1,…,n ,y 1,…,n ), each of which is represented by a timestamp (t i ) and their respective timestamps (t i) the value of the variable W measured at i ), where index 1 denotes a first value and index n denotes a given value of the input time series. Index i denotes a value between the first value and the given value. In the present context, the term "given data point" refers to the data point under consideration, i.e., the data point for which it is determined whether it corresponds to a phase transition (critical point). The given data point may in particular be the most recent or the last point of the input time series.

[0012] In step b), fitting parameters of the log-periodic power-law model function W(t) are calculated for the input time series. Alternatively, the fitting may be performed for different time lengths or different numbers (L) of data points preceding a given data point of the input time series. In this alternative, the fitting parameters of the log-periodic power-law model function W(t) are calculated for one or more subsets of data points of the input time series, each subset consisting of several data points preceding a given data point of the input time series. In either case, the fitting is performed to obtain the minimum mean square error mse for the input time series or for each subset of data points considered, in order to obtain a fitted log-periodic power-law function.

[0013] In step c), the local extrema (N) of the best fitted function are identified. The local extrema (N) are the local maxima (N) of the best fitted function. max ) and local minima (N min ) consists of

[0014] In process d), the trend (T max ) is the local maximum (N max ) are determined from at least some of the identified local minima (N min ) from at least some of the trends (T min ) is determined. max ,T min ) are the selected local maxima (Nmax ) and local minima (N min ) is determined by the slope of the linear fit to

[0015] In step e), a given data point (t n ,y n ) is the critical point (t c ) is identified. n ,y n ) is the trend (T max ;T min ) for the given data point (t n ,y n The last point (t n-1 ,y n-1 ), i.e., positive or negative, the critical point (t c ). In the context of identifying whether a given data point is a critical point, the term "feature" as used herein refers to a mathematical sign, i.e., plus (positive) or minus (negative). Trend (T max ;T min ) is the time constant for a given data point (t n ,y n ) trend of the input time series (T max ;T min ), the next point (t n+k ,y n+k ) changes to the opposite characteristic or sign.

[0016] Critical point (t c If the critical point (t) is determined in step e), a signal indicating that a failure of one or more components in the industrial system is predicted is output in step f) of the method. Otherwise, if the critical point (t) is determined in step e), a signal indicating that a failure of one or more components in the industrial system is predicted is output in step f). c If no determination or identification has been made, the above procedure, i.e., at least method steps e) and f), is performed again at a later point in time to evaluate a new given input data point.

[0017] As outlined in the introductory part of this specification, in the case of supervised approaches for the development of predictive maintenance methods, poor quality training data often results in the resulting methods being unreliable or inappropriate. In contrast, the methods disclosed herein enable unsupervised prediction of failures in particular in industrial systems and are therefore better suited to building predictive maintenance processes.

[0018] The present inventors have surprisingly found that the proposed algorithm, based on fitting a logarithmic-periodic power law (LPPL), can reliably and well in advance predict failures, such as valve and piston rod packing failures in reciprocating compressor systems. Similar approaches, also based on the functional behavior of LPPL, have been proposed by Johansen, A. and Sornette, D. (Evaluation of Quantitative Prediction of Trend Reversals in the Japanese Stock Market in 1999, International Journal of Modern Physics C, 2000, Vol. 11, No. 2, pp. 359-364) and Sornette, D. (Critical Market Crashes, Physics Reports, 2003, Vol. 378, No. 1, pp. 1-98). In particular, known methods from the state of the art remain silent about the applicability of the log-periodic power-law method to determining critical points in univariate time series of measured variables, particularly those related to the condition of components in industrial systems such as reciprocating compressor systems. Unlike data describing financial markets, where the studied variables directly characterize changes or defects in the analyzed system, changes that cause failures (e.g., material degradation, cracks, etc.) in industrial systems such as reciprocating compressors—e.g., changes in the opening angle of the inlet or outlet valves in a cylinder as a function of the pressure in the cylinder chamber, or the vibration of a piston rod as a function of the angle of rotation of the crankshaft—cannot be measured directly, but only indirectly, making the applicability of the log-periodic power-law method particularly unpredictable. In other words, degrading (unmonitored) changes affect changes in the measured variables in a less visible (more distorted) way than in the case of direct variable measurement.

[0019] Analysis of data collected in the event of a reciprocating compressor failure has led to the conclusion that the machine's behavior is normal and usually shows no signs of failure until rupture (the onset of irreversible (deteriorating) processes at a critical point) occurs. However, after rupture occurs, changes in functional behavior are observable that indicate the occurrence of future problems. Surprisingly, it has been found that it is sufficient to determine whether a given (current) point in time is the moment of rupture. If the current point in time corresponds to rupture, based on knowledge of the time characteristics of the dynamics of the entire compressor system, it is possible to identify the period during which the failure will occur, i.e., the time when changes in operating parameters are significant enough to indicate the possibility of a machine failure or breakdown.

[0020] The log-periodic power law model applied in the methods disclosed herein describes a process near the critical point of a second-order phase transition. In the case of an industrial system, i.e., a machine or process, this is the point at which failure of one (or more) of the machine or process components occurs.

[0021] In a preferred embodiment of the method disclosed herein, the log-periodic power-law model function W(t) is Equation (1):

[0022]

number

[0023] In the above equation (1), the following parameters are used: W - vector of variables for which the industrial system is analyzed; t c = Critical point that is treated as the detection of future failures. t=[t n-1-pmax ,t n-pmax ,.,t n-2 ,t n-1 ] is the value p that reaches the minimum value of the error mse of the fitting of the function W(t) to the data used. max The past (t ≤ t) with a length determined by the parameter n-1 ) is the horizontal vector of the time from A,B,m,C1,ω,Φ,p max= Fitting parameters of the logarithmic periodic power law model function.

[0024] The inventors have found that the formula (1) can be used particularly well to find the points in the time series of input data indicating the failure of some component in the industrial system under study, particularly the reciprocating compressor system. However, it is understood by those skilled in the art that the above formula (1) can also be expressed differently and can be rearranged or modified into an equivalent form.

[0025] The following constraints are particularly preferred when the following fitting parameters in the above formula (1) are subject to the following constraints. A > 0 and / or 0 < m < 1 and / or 2 < ω < 8. In an even more preferred embodiment of the method disclosed herein, the following constraints are imposed on the following fitting parameters in the above formula (1). A > 0 and 0 < m < 1 and 2 < ω < 8.

[0026] The fitting parameter "A" is determined by the characteristics of the input data and is always a positive value in the applications presented herein. The preferred range of the parameter "m" ensures that the fitting value for the critical time (t c ) is greater than zero (m > 0) and changes faster than exponentially for times close to the critical point (m < 1). This increases the sensitivity of the method described herein. The preferred conditions for the parameter "ω" are, on the one hand, to avoid very fast logarithmic periodic oscillations that would otherwise fit the random component of the input data, and on the other hand, to avoid very slow logarithmic periodic oscillations that would otherwise contribute to the trend. The remaining fitting parameters "B" and "C1" of the formula (1) can be fitted without additional constraints.

[0027] In a preferred embodiment of the method described herein, the trends of each of the local maxima (T max ) and local minima (T min ) are each determined as follows in step d).

[0028] In step d1), the critical point (t c ) is determined to correspond to a given data point (t n ,y n ) are selected from the local extrema (N) identified in step c).

[0029] In step d2), the selected N-1 extreme values ​​are fitted using linear regression to obtain a regression line, and the slope of said regression line is determined. The slope is calculated by multiplying the local maximum (T max ) and local minima (T min ) Determine the trend (T) for each.

[0030] The trend finding procedure, i.e. steps d1) and d2), may be performed separately, simultaneously or sequentially for the maximum and minimum values. Due to the large number of parameters that need to be determined during the fitting procedure of the log-periodic power-law function and the existence of many local extrema (N), the entire procedure of obtaining the best fitting function of the log-periodic power-law function can be difficult and computationally expensive.

[0031] Therefore, in a preferred embodiment of the method disclosed herein, fitting parameters of the log-periodic power-law model function W(t) are calculated in step b) for multiple subsets of the input time series provided in step a). The fitted function is calculated as p max ≧L min , p max ≦L max , and t ≤ t n The subset (p max ) is obtained from

[0032] In this way, the computational power and time required to carry out the method can be reduced. However, the small amount of past data (L min), i.e., in step e), the critical point (t c ) is determined to correspond to a given data point (t n ,y n Note that using data points preceding L for the best fit may result in a (very) large number of good fits (with very small fitting errors), which may correspond to random correlations between the input data and the shape of the fitted function. max ) is due to the fact that the probability of finding a good match becomes smaller and smaller with increasing number of data points.

[0033] Therefore, in a further preferred embodiment of the method disclosed herein, the minimum number of preceding data points (L min ) is 40, and the maximum number of preceding data points (L max ) is 101. In this embodiment, the best past data length (p max ) may in particular be in units of days.

[0034] Critical point (t c When the predicted failure time of the one or more components of the industrial system is determined in step e), a preferred embodiment of the method disclosed herein further comprises step g), in which a predicted failure time period of the one or more components of the industrial system is output based on the mean square error mse obtained in step b).

[0035] Critical point (t cThe accuracy of determining W(t) depends on the error of fitting the log-periodic power-law model function W(t) to the input data. The smaller the mean squared error mse, the higher the confidence that a given point in the input time series is actually a critical point (or not). Furthermore, clusters of points with good fits, i.e., small mean squared errors mse, are observed near critical points. Such groupings of points with similar match errors occur, for example, when repairs are made to a monitored industrial system some time before the predicted fault is actually identified. In the case of a reciprocating compressor system, this grouping of points with similar match errors can occur approximately 40 days before the fault identification time, as explained in more detail below.

[0036] Step g) may be carried out simultaneously with or after step f). Not all failures require corrective action for various reasons (economic, production, etc.). Sometimes, a minor failure may not be a justification for shutting down an industrial system or process.

[0037] In preferred embodiments of the method disclosed herein, the output signal further indicates the severity of the detected fault, thus increasing the profitability of the method, as the user can easily determine, for example, whether further action is immediately required at some point in the future, or whether operation of the system is likely to continue without breakdown.

[0038] By comparing the faults detected by the method disclosed herein with the resulting system operational behavior and / or the actual occurrence of the detected faults as assessed by experts in the monitored industrial system, it was found that the match error, i.e., the mean squared error (MSE), depends on the criticality (severity) of the faults actually identified in the future. Therefore, a threshold value for the mean squared error (MSE) and the corresponding criticality or severity of the predicted faults can be defined to keep the number of detected faults and corresponding output signals (e.g., error messages) within limits, and in particular to reduce them to truly relevant events.

[0039] By way of example, and particularly where the industrial system is a reciprocating compressor stem, the following classification of predicted failures may apply: 1. Criticality event: mse<6·10 -5 A serious malfunction is expected and the system should be checked and repairs made.

[0040] 2. Monitoring events: 6-10 -5 ≦mse<10 10 -5 ;anticipating potential problems and monitoring required system behavior. 3. Unrelated events: 10 10 -5 < mse; not a meaningful prediction, and monitoring of system behavior is optional.

[0041] Therefore, in a preferred embodiment of the method disclosed herein, the signal is output in step f) only if the mean square error mse is less than or equal to a predetermined threshold. In an even more preferred embodiment of the method disclosed herein, the signal is output in step f) only if the mean square error mse is less than or equal to a predetermined threshold. -5 In an even more preferred embodiment of the method disclosed herein, the signal is output in step f) only if the mean square error mse is less than 10 10 -5 It is output in step f) only if it is less than .

[0042] According to the methods described herein, more accurate identification of anticipated problems can be achieved when the input data or input time series, respectively, relate to a specific part of the monitored industrial system, in particular a reciprocating compressor.

[0043] In a preferred embodiment of the method disclosed herein, the input time series relates to the opening angle of one or more intake valves in a cylinder of a reciprocating compressor, where the opening angle is given as a function of pressure expressed or expressible in terms of crankshaft rotation angle.

[0044] In another preferred embodiment of the above method, the reciprocating compressor is a double-acting reciprocating compressor comprising a double-acting cylinder having a crank end and a head end, wherein one or more intake valves are located at the crank end and one or more intake valves are located at the head end of the double-acting cylinder.

[0045] In this way, any detected critical point t c indicates a potential future failure in a localized portion of the cylinder. For example, for an input time series for an intake valve located at the crank end of a double-acting cylinder, a predicted trend in the intake valve opening angle is decreasing, which could indicate an intake valve failure or piston rod packing damage. If the trend suggests an increasing angle, the problem is with the exhaust valve. Similarly, for an input time series for an intake valve located at the head end of a double-acting cylinder, a decreasing trend in the intake valve opening angle could indicate an intake valve failure or cylinder seal damage. On the other hand, an increasing trend in the opening angle could indicate an exhaust valve failure.

[0046] Thus, based on the methods disclosed herein, the algorithm is able to predict both the time period for failure occurrence and the group of parts that may fail. This object is further achieved by an industrial system comprising one or more components for which future failure is predicted, one or more sensors, a condition monitoring unit, and means for outputting a signal indicating that failure of the component is predicted. The one or more sensors are configured to provide an input time series to the condition monitoring unit, the input time series including a plurality of data points, each data point including a timestamp and a value of a variable W measured at the respective timestamp. The condition monitoring unit is configured to perform any one of the steps of the methods disclosed herein.

[0047] The beneficial effects of such industrial systems are essentially the same as those already described for the methods disclosed herein: in particular, such industrial systems are characterized by a high reliability of operational readiness and a generally increased service life, since the predictive maintenance methods disclosed herein also prevent or at least reduce cascading errors or failures with any resulting damage.

[0048] In a preferred embodiment of the industrial system disclosed above, the industrial system is a reciprocating compressor including a crankshaft and a cylinder having one or more intake valves, and the one or more sensors are configured to measure an opening angle of one or more of said intake valves as a function of pressure represented or representable by an angle of crankshaft rotation.

[0049] In a further preferred embodiment of the reciprocating compressor system disclosed above, the reciprocating compressor is a double-acting reciprocating compressor including a double-acting cylinder having a crank end and a head end, wherein one or more intake valves are disposed at the crank end and one or more intake valves are disposed at the head end of the double-acting cylinder.

[0050] This object is further solved by a computer program comprising instructions which, when said program is executed by a computer, cause said computer to carry out the steps of the methods disclosed herein.

[0051] This object is further achieved by means of a computer readable storage medium embodying a computer program comprising instructions which, when executed by a computer, cause the computer to perform the steps of the methods disclosed herein.

[0052] In the context of the present invention, the term "storage medium" includes, among others, cloud storage, flash storage, and embedded storage. This object is further achieved by the use of the method disclosed herein for predicting failures in an industrial system, particularly an industrial system comprising or consisting of a reciprocating compressor system.

[0053] The present invention will be better understood with reference to the following description of preferred embodiments and the accompanying drawings, in which the same reference numerals are used to denote the same or equivalent features among different embodiments and examples. [Brief explanation of the drawings]

[0054] [Figure 1] 1 is a flowchart illustrating a processing sequence of one embodiment of the method disclosed herein. [Figure 2a] FIG. 10 shows an example of a fitted LPPL function with a positive trend for selected data points. [Figure 2b] FIG. 10 shows an example of a fitted LPPL function with a negative trend for selected data points. [Figure 3] FIG. 10 is a diagram illustrating an example of detecting time points corresponding to critical points in an input time series. [Figure 4] FIG. 4 is a diagram showing an example of a predicted period of failure occurrence for the critical point determined in the example of FIG. 3; DETAILED DESCRIPTION OF THE INVENTION

[0055] Figure 1 shows the time series of input data 1 for a given data point (t n ,y n ) (not shown separately in FIG. 1) is the critical point t c 1 shows a sequence of steps of an embodiment of a method described herein for determining whether a critical point t cThe detection of is treated as the detection of a future failure of one or more components 8 of the industrial system 100. The algorithm is executed by a condition monitoring unit 10 that is part of the industrial system 100, but the condition monitoring unit 10 may be located physically separate from the industrial system 100. For clarity, in FIG. 1 the respective maximum and minimum values ​​of the regression lines 6 and their slopes s, as well as of the trends T, and of the local extrema N are not separately designated (subscripts max or min (Not shown in FIG. 1). However, as will be apparent from this specification, the above elements refer to both their respective maximum and minimum values.

[0056] The method comprises steps a) to f). In step a), an input time series 1 is provided relating to the state of one or more components 8 of an industrial system 100 for which a future failure is predicted. The input time series 1 includes a plurality of data points (t1, ..., n ,y1,…, n ), where each data point is at timestamp t i and each timestamp t i The value y of the variable W measured at i The input time series 1 may optionally be reduced to one or more subsets 1a of data points, each subset consisting of L data points preceding a given data point, i.e., the data point under consideration, which is to be determined as being a critical point or not. This alternative using a subset 1a of the input time series 1 is indicated by the dashed arrow in Fig. 1. In step b), a best fit 5 of the log-periodic power-law model function W(t)3 is determined by calculating fitting parameters 2 of said function W(t)3. The best fit 5 is determined by calculating fitting parameters 2 of the input time series 1 or a subset of the input data 1a, in particular the time length p that gave the overall smallest mean squared error mse (not shown). max Then, local extrema N of the fitted function 5 are identified in step c). The local extrema N are local maxima N of the fitted function 5. max and the local minimum Nmin In step d), which in the embodiment shown in FIG. 1 includes steps d1) and d2), a trend T of the identified local extrema N is identified. More specifically, a first trend T max is the identified local maximum N max and a second trend T min is the identified local minimum N min In this example, the trend T max is the local maximum N identified in step c) in step d1). max From the above, in step e), the critical point t c A given data point (t n ,y n In step d2), the selected N-1 local maxima are determined by selecting the N-1 local maxima that are closest to the regression line 6. max The regression line 6 is fitted using linear regression to obtain max The slope of s max is determined. The slope s max is the trend of the local maximum T max Determine the trend of the local minimum, T min Similarly, the selected N-1 local minima and their respective regression lines 6 min The slope of s min In step e), a given data point (t n ,y n ) is the critical point t c and the given data point (t n ,y n ) are the trends of both, i.e., the identified local maxima N max A trend T determined from at least some of max and the identified local minimum N min A trend T determined from at least some of min is the given data point (t n ,y n The last point (t n-1 ,yn-1 ) have the same characteristics (i.e., both slopes are positive or both slopes are negative), the critical point t c In step e), for a given data point (t n ,y n ) is the critical point t c If so, a signal 7 is output indicating that a failure of one or more components 8 in the industrial system 100 has been predicted.

[0057] Figures 2a and 2b show the time length p max 5 shows an example of a log-periodic power-law function fitted to a subset of the input time series with max have a positive trend (Fig. 2a) and a negative trend (Fig. 2b) for a given data point, respectively. As can be seen from Fig. 2a and Fig. 2b, for a given data point (t n ,y n ) is the determined trend T max and the determined trend T min Both have the same characteristics, i.e., regression line 6 max and 6 min The critical point t is determined by the slope of the input time series, which is positive (Fig. 2a) or negative (Fig. 2b) for the last point in the input time series preceding a given data point. c The examples presented in Figures 2a and 2b are from backtests of the forecasting method disclosed herein on historical data for periods of one and two years, respectively, from which critical points were calculated. start Starting from , for each next timestamp of the input time series, a best-fit LPPL function 5, characterized by the smallest mean squared error mse, relative to the input time series 1, is calculated. The resulting graphs 5, shown in Figures 2a and 2b, show the results over time in days.

[0058] Figure 3 shows the critical point t for a given input time series 1. c An example of predicted future failures corresponding to t is shown in Figure 3. The input time series in Figure 3 is the solid line with measurement points marked by reference numeral 1. cThe vertical line marked by c The critical point t c For each time point, moving from left to right in Figure 3, the average value of the LPPL function fitting error (mean squared error mse) is annotated. The four vertical lines in Figure 3, marked by thick arrows, indicate the dates of compressor repairs (diagnosed breakpoints), which typically occurred several weeks to several weeks after failure was predicted by the condition monitoring system using the methods disclosed herein. c Detected critical points t , except for the detected critical points marked with * and the prediction determined by the maximum error (mse=0.000249). c The correlation between the determined breakpoint and the c * indicates that the mean square error mse is 10 10 -5 can be classified as an unrelated event due to the mse being equal to or greater than the corresponding mse threshold for unrelated events.

[0059] FIG. 4 shows the critical point t determined in the example of FIG. c Each of the three diagrams a), b) and c) of FIG. 4 shows the same input time series marked with reference number 1 and the critical point t determined for said input time series 1. c and the critical point t c are further labeled A to F in time progression from left to right in each diagram. c For each, a corresponding time period 11 (area bounded by vertical dashed lines) is provided that indicates when the monitored component is expected to fail. In particular, in Figure 4, the categorization of the criticality of the predicted failures is represented by dividing them into three separate diagrams: a) the critical point T c A to C and T c The graph shows the corresponding periods 11A-C and 11E-F that fall into the category of "critical events." In this example, the "critical events" class is <6·10 -5Figure b) shows the mean square error mse of the -5 ≦mse<10 10 -5 In this example, we show that the algorithm finds a critical point t that satisfies this requirement for the mean squared error mse. c Since the value of 10·10 has not been determined, the "Monitoring Event" class remains without a vertical line. Finally, Figure c) shows the value of 10·10 in this example. -5 As can be seen in Figure 4, panel c), there is only one critical point t that satisfies this requirement for the mean squared error mse. c Although the algorithm determined the failure period 11D, no actual failure occurred during the corresponding prediction period 11D. Therefore, no compressor repairs were performed. The repair (maintenance) time is indicated by the black arrow in Figure 4. Furthermore, the gray areas in Figure a) without reference numbers indicate periods during which abnormal compressor behavior was observed, which should be monitored by a qualified technician. As can be seen from Figure 4, the correlation between the prediction of the failure period 11 and the actual repair date, as well as the period during which the abnormal compressor behavior was detected by a qualified technician, is very good for the "criticality event" and "monitoring event" categories. The predictions in the "unrelated event" category were not followed up or confirmed by any repair and diagnostic records, further demonstrating the effectiveness of the method disclosed herein.

[0060] The following embodiments are possible: 1. A method for predicting failures in an industrial system (100), particularly a reciprocating compressor (100), comprising: a) Multiple data points (t 1,...,n ,y 1,...,n ), each data point having a timestamp (t i ) and each of the timestamps (t i ) the value of the variable W measured at i), where index 1 denotes a first value, index n denotes a given value, and index i denotes a value between the first value and the given value of the input time series (1); b) calculating fitting parameters (2) of a log-periodic power-law model function W(t) (3) that provides a minimum mean square error mse (4) for the input time series (1) or for one or more subsets (1a) of data points of the input time series (1), to obtain a fitted function (5), wherein each subset (1a) is a function of the given data point (t) of the input time series (1). n ,y n ) preceded by a number (L) of data points (t i,...,n-1 ,y i,...,n-1 ) a process comprising: c) identifying local extrema (N) of the fitted function (5), wherein the local extrema (N) are local maxima (N) of the fitted function (5); max ) and local minima (N min ) a process comprising: The identified local maxima (N max ) from at least some of the trends (T max ) to the identified local minimum (N min ) from at least some of the trends (T min ) respectively; e) the given data point (t n ,y n ) is the critical point (t c ) determined in step d), max ;T min ) for the given data point (t n ,y n The last point (t n-1 ,y n-1 ) have the same characteristics for the given data point (t n ,y n ) is the critical point (t c ) and f) In step e), the critical point (t cand if a failure is identified, outputting a signal (7) indicating that a future failure of one or more components (8) in the industrial system (100) is predicted.

[0061] This embodiment may be combined with any of the embodiments disclosed above.

Claims

1. A method for predicting failures in an industrial system (100), in particular in a reciprocating compressor (100), comprising: a) Multiple data points (t １，．．．，ｎ , y １，．．．，ｎ ), each data point having a timestamp (t ｉ ) and each of the timestamps (t ｉ ) the value of the variable W (y ｉ ), where index 1 denotes a first value, index n denotes a given value, and index i denotes a value between the first value and the given value of the input time series (1); b) calculating fitting parameters (2) of a log-periodic power-law model function W(t) (3) that provides a minimum mean square error mse (4) for the input time series (1) or for one or more subsets (1a) of data points of the input time series (1), to obtain a fitted function (5), wherein each subset (1a) is a function of the given data point (t) of the input time series (1). ｎ , y ｎ ) precedes a number (L) of data points (t ｉ，．．．，ｎ－１ , y ｉ，．．．，ｎ－１ and c) identifying local extrema (N) of the fitted function (5), wherein the local extrema (N) are local maxima (N) of the fitted function (5); ｍａｘ ) and local minimum (N ｍｉｎ ) a step of d) the identified local maxima (N ｍａｘ ) from at least some of the trends (T ｍａｘ ) to the identified local minimum (N ｍｉｎ ) from at least some of the trends (T ｍｉｎ ) respectively, and determining each of the trends (T ｍａｘ , T ｍｉｎ ) is the selected local maximum (N ｍａｘ ) and the local minimum (N ｍｉｎ ) respectively determined by the slope of a linear fit to e) the given data point (t ｎ , y ｎ ) is the critical point (t ｃ ) determined in step d), ｍａｘ , T ｍｉｎ ) are both at the given data point (t ｎ , y ｎ ) of the input time series. ｎ－１ , y ｎ－１ ) is positive or negative for the given data point (t ｎ , y ｎ ) is the critical point (t ｃ ) and f) In step e), the critical point (t ｃ ) is identified, outputting a signal (7) indicating that a future failure of one or more components (8) in the industrial system (100) is predicted.

2. The log-periodic power-law model function W(t) (3) is expressed by the following equation (1): [Equation 1] and W = the vector of variables for which the industrial system (100) is analyzed; t ｃ = critical point treated as detection of future failure events, t = [t ｎ－１－ｐｍａｘ , t ｎ－ｐｍａｘ ,... ,t ｎ－２ , t ｎ－１ ] - p in units of time ｍａｘ a horizontal vector of time points with length A, B, m, C １ , ω, Φ, p ｍａｘ The method of claim 1 , wherein: is a fitting parameter (2).

3. The following constraints are imposed on the following of the fitting parameters (2): A>0, 0<m<1, 2<ω<8, Preferably, the following constraints are imposed on the following of said fitting parameters (2): A>0, and 0<m<1, and The method of claim 2, wherein 2<ω<8.

4. In step d), the local maximum (T ｍａｘ ) and the local minimum (T ｍｉｎ ) each of the trends is d1) In step e), the critical point (t ｃ ) is determined to correspond to the given data point (t ｎ , y ｎ selecting the N-1 local extrema (N) identified in step c) that are closest to d2) fitting the selected N-1 extreme values ​​using linear regression to obtain a regression line (6) and determining the slope (s) of the regression line (6), wherein the slope (s) is determined by the local maximum (T ｍａｘ ) and the local minimum (T ｍｉｎ 4. The method according to claim 1, wherein the trend (T) is determined by the steps of:

5. In step b), the fitting parameters (2) of the log-periodic power-law model function W(t) (3) are calculated for each of a plurality of subsets (1a), and the fitted function (5) is calculated for the subset (p) of the plurality of subsets (1a) that gave the overall smallest mean square error mse (4a). ｍａｘ 5. The method according to claim 1, wherein the hydroxybenzoate is obtained from

6. The number of data points (L) is the minimum number (L ｍｉｎ ) 40 and the maximum number (L ｍａｘ 6. The method according to claim 1, wherein the ratio of the number of saturations to the number of saturations is between 101 and 101.

7. In step e), the critical point (t ｃ ) is determined, 7. The method according to claim 1, further comprising the step of: g) outputting a time period during which the predicted failure of the one or more components is expected to occur based on the mean square error mse(4) obtained in step b), wherein step g) is performed simultaneously with or after step f).

8. The signal (7) is detected when the mean square error mse(4) is equal to or less than a predetermined threshold, in particular when the mean square error mse(4) is equal to or less than 10.10 －５ Less than 6.10 －５ The method of any one of claims 1 to 7, wherein the output is only when the value is less than

9. 9. The method according to claim 1, wherein the input time series (1) relates to, in particular to, the change in opening angle of one or more intake valves in a cylinder of a reciprocating compressor (100) as a function of pressure, the pressure being expressed or representable by a crankshaft rotation angle.

10. 10. The method of claim 9, wherein the reciprocating compressor (100) is a double-acting reciprocating compressor comprising a double-acting cylinder having a crank end (CE) and a head end (HE), one or more intake valves located at the crank end (CE) and one or more intake valves located at the head end (HE) of the double-acting cylinder.

11. An industrial system (100) comprising one or more components (8) for which future failure is predicted, one or more sensors (9), a condition monitoring unit (10), and means for outputting a signal (7) indicating that a failure of said component (8) is predicted, said one or more sensors (9) monitoring a plurality of data points (t ｎ , y ｎ ), each data point is provided with a timestamp (t ｉ ) and each of the timestamps (t ｉ ) the value of the variable W (y ｉ ) and wherein the condition monitoring unit (10) is configured to perform the steps of the method according to any one of claims 1 to 10.

12. 12. The method of claim 11, wherein the industrial system (100) is a reciprocating compressor (100) comprising a crankshaft and a cylinder having one or more intake valves, and the one or more sensors (9) are configured to measure an opening angle of one or more of the intake valves as a function of pressure, the pressure being expressed or expressible in terms of crankshaft rotation angle.

13. 13. The industrial system of claim 12, wherein the reciprocating compressor is a double-acting reciprocating compressor comprising a double-acting cylinder having a crank end (CE) and a head end (HE), wherein one or more intake valves are disposed at the crank end (CE) and one or more intake valves are disposed at the head end (HE) of the double-acting cylinder.

14. A computer program comprising instructions which, when the program is executed by a computer, cause the computer to perform the steps of the method of any one of claims 1 to 10.

15. A computer readable storage medium embodying a computer program comprising instructions which, when executed by a computer, cause the computer to perform the steps of the method of any one of claims 1 to 10.

16. Use of the method according to any one of claims 1 to 10 for predicting faults in an industrial system (100), in particular in a reciprocating compressor.

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