Method for predicting failure of industrial system

Abstract

A method for predicting a fault in an industrial system (100), the method comprising the steps of: a) providing an input time series (1) comprising a plurality of data points (t1,..., n, y1,..., n), each data point comprising a timestamp (ti) and a value (y) of a variable W measured at the respective timestamp (ti); b) calculating a fitting parameter (2) of a log periodic power law model function W (t) (3), which minimizes a mean square error mse (4) of the input time series (1) or of at least a subset (1a) of data points of said input time series (1), in order to obtain a fitting function (5); c) identifying a local maximum (Nmax) and a local minimum (Nmin) of the fitting function (5); d) determining a trend (Tmax) from at least some of the identified local maxima (Nmax) and a trend (Tmin) from at least some of the identified local minimum (Nmin), the respective trend (Tmax, Tmin) being determined from a slope of a linear fit of the selected local maxima (Nmax) and the local minimum (Nmin); e) identifying whether a given data point (tn, yn) of the input time series (1) is a critical point (tc), if two trends (Tmax; if all the data points (tn, yn) are positive or negative, the given data point (tn, yn) is a critical point (tc); and, if the critical point (tc) has been identified in step e), performing step f) to output a signal (7) indicating a predicted fault of at least one component (8) in the industrial system (100).

Description

Technical Field

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

[0002] The concept of predictive maintenance, i.e., detecting and predicting future faults based on multivariate or univariate time series data collected from an industrial system, has far-reaching significance and application potential in various industrial applications because it allows for the necessary maintenance work to be planned in advance. By avoiding potential faults or machine failures, the uptime of the machine can be increased, and the costs of unplanned downtime and standard repair operations can be reduced.

[0003] The development of supervised predictive maintenance methods based on machine learning (ML) and machine operator algorithms is known. However, in practice, the reliability and accuracy of the predictive maintenance methods obtained in this way are often affected by the operator's misunderstanding and / or inaccurate description of the faults. In most cases, the cause of the fault over time cannot be accurately located based on the existing data. This poses serious problems for learning ML models based on supervised methods and detecting statistical biases in the data. This requires frequent manual intervention in the ML production pipeline.

[0004] In the prior art, the article by BANERJEE, A et al. (Imprints of log-periodicity in thermoacoustic systems close to lean burst out, ARXIV.ORG, Cornell University Library) is known, which explores critical phenomena accompanied by power laws that are singular at the critical points where the system state undergoes a sudden change. The authors of the article point out that lean blowout in a turbulent thermoacoustic system can be regarded as a critical phenomenon, and there is discrete scale invariance when the system dynamics approach lean blowout. In the pressure fluctuations before lean blowout, there is a log-periodic oscillation in the time evolution of the amplitude of the low-frequency oscillation main mode. The existence of discrete scale invariance indicates that the blowout develops recursively. The authors further point out that the amplitude of the low-frequency oscillation main mode exhibits a faster growth rate than exponential growth and becomes a singular value at the time of blowout. They proposed a model that describes the evolution of the amplitude of the low-frequency oscillation main mode based on the log-periodic correction of the power law associated with its growth. According to the authors, the blowout can be predicted a few seconds in advance.

[0005] In the prior art, US2010 / 0106458A1 is also known, which relates to computer programs and methods for detecting and predicting valve failures in complex machinery, such as reciprocating compressors. The method is based on the fact that the pressure signal has a non-stationary waveform. Wavelet packet decomposition can be used to extract the features of the signal. The extracted features and the temperature data of the reciprocating compressor are used to train a logistic regression model to classify the failures and normal operations of the valves. For a given set of inputs, the model will give the probability that the input belongs to the normal or failure signature group. In other words, the logistic regression model is used as an indicator of the system health status.

[0006] However, the above publication does not lead to the claimed invention. Summary of the Invention

[0007] The object of the present invention is to overcome these and other deficiencies of the prior art, and in particular to provide an improved method for predicting failures in industrial systems, such as reciprocating compressors, which is cost-effective, reliable and easy to implement. Another object of the present invention is to provide an industrial system, especially a reciprocating compressor system, which can predict failures in a cost-effective and reliable manner.

[0008] The above 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 for predicting failures in an industrial system disclosed herein, according to the independent claims. Preferred embodiments are defined by the dependent claims.

[0009] The method for predicting failures in an industrial system comprises the following steps a)-f):

[0010] In step a), an input time series comprising a plurality of data points (t 1,…,n , y 1,…,n ) is provided. Each said data point comprises a timestamp (t i ) and a value (y i ) of a variable W measured at the corresponding timestamp (t i ), where the index 1 represents the first value and the index n represents a given value of the input time series. The index i represents a value between said first value and said given value. In the context of the present specification, the term "given data point" refers to the data point under consideration, i.e., determining whether it corresponds to a phase change (critical point). The given data point may specifically be the latest or last point of the input time series.

[0011] In step b), the fitting parameters of the log-periodic power-law model function W(t) are calculated for the input time series. Alternatively, the fitting can also be performed separately for different time lengths or numbers (L) of data points before a given data point in the input time series. In this alternative, the fitting parameters of the log-periodic power-law model function W(t) are calculated for at least one subset of the data points of the input time series, where each subset consists of a plurality of data points before the given data point in the input time series. In each case, the fitting is performed such that the minimum mean square error mse is obtained with respect to the input time series or for the corresponding subset of data points under consideration. In this way, the fitted log-periodic power-law function is obtained.

[0012] In step c), the local extrema (N) of the best-fitting function are identified. The local extrema (N) consist of the local maximum (N max ) and the local minimum (N min ) of the best-fitting function.

[0013] In step d), the trend (T max ) is determined based on at least some of the identified local maxima (N max ). Additionally, the trend (T min ) is determined based on at least some of the identified local minima (N min ). The corresponding trends (T max , T min ) are determined by the slopes of the linear fits of the selected local maxima (N max ) and local minima (N min ), respectively.

[0014] In step e), it is identified whether a given data point (t n , y n ) is a critical point (t c ). If the two trends (T max ; T min ) determined in step d) have the same characteristic, i.e., both positive or both negative, for the last point (t n , y n ) of the input time series before the given data point (t n-1 , y n-1 ), then the given data point (t n , y n ) is considered a critical point (t c ). In the context of identifying whether a given data point is a critical point, the term "characteristic" as used herein refers to the mathematical sign, i.e., plus sign (positive value) or minus sign (negative value). For the next point (t n+k , y n+k ) with k > 0, the trends (T max ; Tmin ) will change the trend (T n , y n ) of the input time series before a given data point (t max ; T min ) into the opposite feature or sign, respectively.

[0015] If a critical point (t c ) is determined in step e), then a signal indicating that a failure of at least one component in the industrial system is predicted is output in step f) of the method. Otherwise, if no critical point (t c ) is determined or identified in step e), the above process, i.e., at least method steps e) and f), is performed again at a later time to evaluate a new given input data point.

[0016] As outlined in the introductory part of this specification, in the case of a supervised method for developing a predictive maintenance method, poor training data quality usually results in the obtained method being unreliable or otherwise inadequate. In contrast, the method disclosed herein is particularly suitable for unsupervised prediction of faults in industrial systems and is thus more suitable for establishing a predictive maintenance process.

[0017] The inventors of the present invention unexpectedly found that an algorithm based on Log-Periodic Power Law (LPPL) matching can reliably and prematurely predict faults in reciprocating compressor systems, such as valve and piston rod packing faults. JOHANSEN, A. and SORNETTE, D. (Evaluation of the quantitative prediction of a trend reversal on the Japanese stock market in 1999, International Journal of Modern Physics C 2000, 11, no. 2, pages 359-364) and SORNETTE, D. (Critical market crashes, Physics Reports 2003, 378, no. 1, pages 1-98) proposed a similar method also based on the functional behavior of LPPL for detecting bubbles (or anti-bubbles) in economic time series. Specifically, the methods known in the prior art do not mention the application of the log-periodic power law for determining critical points in univariate time series of measurement variables related to the state of components in industrial systems, such as especially reciprocating compressor systems. The application of the log-periodic power law was not foreseeable, especially because - unlike the data situation in the financial market where the variables studied directly characterize the changes or defects of the analyzed system - the changes leading to faults in industrial systems (such as reciprocating compressors), such as material degradation, cracks, etc., cannot be measured directly, but only indirectly. For example, the opening angle of the intake or exhaust valve of a cylinder is a function of the cylinder chamber pressure, or the piston rod vibration is a function of the crankshaft rotation angle. In other words, compared with the case of direct variable measurement, the influence of the degradation (unmonitored) changes on the changes of the measurement variables is less obvious (more distorted).

[0018] After analyzing the data collected from reciprocating compressor fault cases, it was concluded that before rupture (the start of an irreversible (deterioration) process at the critical point), the behavior of the machine is normal and usually no fault signs appear. However, some changes indicating functional behavior can be observed, which indicate potential problems after rupture. Surprisingly, it was found that it is only necessary to determine whether a given (current) time point is the rupture moment. If the current time point corresponds to rupture, then based on the knowledge of the dynamic time characteristics of the entire compressor system, the time period during which a fault occurs can be identified, i.e., the time when the changes in operating parameters are significant enough to have the possibility of machine failure or damage.

[0019] The log-periodic power-law model applied in the method disclosed herein describes the process approaching the second-order phase transition critical point. For an industrial system (such as a machine or a process), the critical point refers to the time point at which one (or more) components of the machine or process fail.

[0020] In a preferred embodiment of the method disclosed herein, the log-periodic power-law model function W(t) is given by formula (1):

[0021] (1)

[0022] In the above formula (1), the following parameters are used: W – a vector of variables for analyzing the industrial system; t c = the critical point regarded as the detection of future failures; t = [t n-1-pmax , t n-pmax ,..., t n-2 , t n-1 – is a transverse vector from past time points (t ≤ t n-1 ), the length of which is determined by the p max parameter, achieving the minimum value of the mean squared error mse of fitting the function W(t) to the data used; A, B, m, C1, ω, Φ, p max = fitting parameters of the log-periodic power-law model function.

[0023] The inventor of the present invention has found that formula (1) can be particularly effectively used to find the time point indicating the failure of a component in an industrial system (especially in the reciprocating compressor system under consideration) in the time series of input data. However, those skilled in the art should understand that the above formula (1) can also be expressed, rearranged, or modified differently into an equivalent form.

[0024] Particularly preferably, the following constraints are imposed on the following fitting parameters in the above formula (1): A > 0 and / or 0 < m < 1 and / or 2 < ω < 8. In a 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.

[0025] The fitting parameter "A" is determined by the characteristics of the input data and is always positive in this application. The preferred range of the parameter "m" ensures the critical time (t cThe fitted value of () is greater than zero (m > 0), and near the critical point (m < 1), the rate of change of the fitted value is faster than the exponential change. This improves the sensitivity of the method described in this article. The preferred condition of the parameter "ω" avoids, on the one hand, too fast log-periodic oscillations (otherwise it will fit the random component of the input data), and on the other hand, too slow log-periodic oscillations (otherwise it will cause trend changes). The remaining fitting parameters "B" and "C1" in formula (1) can be fitted without additional constraints.

[0026] In a preferred embodiment of the method described in this article, the corresponding trends of the local maxima (T max ) and local minima (T min ) are determined as follows in step d):

[0027] In step d1), select N - 1 extrema from the local extrema (N) identified in step c) that are closest to the given data point (t n , y n ). In step e), determine whether this data point corresponds to the critical point (tc).

[0028] In step d2), use linear regression to fit the selected N - 1 extrema to obtain a regression line and determine the slope of this regression line. This slope determines the trends (T) of the local maxima (T max ) and local minima (T min ) respectively.

[0029] The process of finding the trend, that is, steps d1) and d2), is performed separately for the maximum and minimum values, and can be performed simultaneously or sequentially.

[0030] Since the number of parameters to be determined during the fitting process of the log-periodic power-law function is large and there are many local extrema (N), the entire process of obtaining the best-fitting function of the log-periodic power-law function may be difficult and the computational cost is also relatively high.

[0031] To this end, in a preferred embodiment of the method disclosed in this article, in step b), the fitting parameters of the log-periodic power-law model function W(t) are calculated for multiple subsets of the input time series provided in step a). This fitting function is obtained from the subset (p max ≥L min , p max ≤L max and t ≤ t n ) in multiple subsets that satisfies the conditions and gives the overall minimum mean square error mse. max )

[0032] In this way, the computing power and time required to execute this method can be reduced. However, it should be noted that using a small amount of past data (L min ), that is, determining whether it corresponds to a critical point (t c ) in step e), for the given data points (t n , y n ) before the data points corresponding to the critical point may result in (too) many good fits (with very small fitting errors), which may correspond to a random correlation between the input data and the form of the fitting function. The upper limit of the number of input time series (L max ) is due to the fact that as the number of data points increases, the probability of finding a good match becomes smaller and smaller.

[0033] Therefore, in another preferred embodiment of the method disclosed herein, the minimum number of previous data points (L min ) is 40, and the maximum number of previous data points (L max ) is 101. In this embodiment, the optimal past data length (p max ) can be specifically in days.

[0034] If a critical point (t c ) is determined in step e), a preferred embodiment of the method disclosed herein further includes step g). In step g), based on the mean square error mse obtained in step b), the period during which a predicted failure of at least one component of the industrial system is expected to occur is output.

[0035] The accuracy of determining the critical point (tc) depends on the fitting error between the log-periodic power-law model function W(t) and the input data. The smaller the mean square error mse, the higher the reliability that a given point of the input time series is indeed a critical point (or not). In addition, near the critical point, a group of points with high goodness of fit (i.e., small mean square error mse) can be observed. This group of points with similar matching errors appears at a certain time before the predicted failure is actually identified (for example, when maintenance is performed on the monitored industrial system). For a reciprocating compressor system, this group of points with similar matching errors may occur approximately 40 days before the failure identification time, as will be discussed in more detail below.

[0036] Step g) can be executed simultaneously with step f) or after step f).

[0037] Due to various reasons (economic, production, etc.), not all failures require corrective measures. Sometimes, minor failures may not be a reasonable reason to stop the industrial system or process.

[0038] In a preferred embodiment of the method disclosed herein, the output signal further indicates the severity of the detected fault. In this way, the beneficial effects of the method are enhanced because the user can easily determine, for example, whether further measures need to be taken immediately or at a future point in time, or whether the system is likely to continue operating without failure.

[0039] By comparing the faults detected by the method disclosed herein with the resulting operating behavior of the system and / or the actual fault occurrences evaluated by an expert of the monitored industrial system, it is found that the matching error, i.e., the mean square error mse, depends on the criticality (severity) of the actually identified faults in the future. Therefore, in order to control the number of detected faults and the corresponding output signals (e.g., error messages) within limits, especially to reduce them to truly relevant events, a threshold for the mean square error mse and the corresponding criticality or severity of the predicted faults can be defined.

[0040] For example, the following predicted fault classification can be applied, especially when the industrial system is a reciprocating compressor system:

[0041] 1. Critical event: mse < 6·10 -5 ; A serious fault is expected to occur, and the system needs to be inspected and prepared for repair.

[0042] 2. Monitoring event: 6·10 -5 ≤ mse < 10·10 -5 ; Problems may be expected to occur, and the system behavior needs to be monitored.

[0043] 3. Irrelevant event: 10·10 -5 ≤ mse; The prediction is not significant, and the system behavior can be optionally monitored.

[0044] Therefore, in a preferred embodiment of the method disclosed herein, the signal is output in step f) only when the mean square error mse is less than or equal to a predetermined threshold. In a more preferred embodiment of the method disclosed herein, the signal is output in step f) only when the mean square error mse is less than 10·10 -5 . In a particularly preferred embodiment of the method disclosed herein, the signal is output in step f) only when the mean square error mse is less than 6·10 -5 .

[0045] According to the method described herein, more accurate identification of expected problems can be achieved if the input data or the input time series is respectively related to a specific part of the monitored industrial system (especially a reciprocating compressor).

[0046] In a preferred embodiment of the method disclosed herein, the input time series is related to the opening angle of at least one suction valve in a reciprocating compressor cylinder. The opening angle is a function of the pressure, which is represented by or can be represented by the crankshaft rotation angle.

[0047] In another preferred embodiment of the above method, the reciprocating compressor is a double-acting reciprocating compressor, which includes a double-acting cylinder having a crank end and a head end. At least one suction valve is arranged at the crank end of the double-acting cylinder, and at least one suction valve is arranged at the head end of the double-acting cylinder.

[0048] Thus, any critical point t detected c is an indication of a potential future local failure of the cylinder. For example, in the case where the input time series is related to the suction valve arranged at the crankshaft end of the double-acting cylinder, if the predicted trend of the suction valve opening angle is decreasing, there is a possibility of a suction valve failure or a piston rod packing damage. If the trend indicates an increasing angle, the problem lies with the discharge valve. Similarly, in the case where the input time series is related to the suction valve arranged at the head end of the double-acting cylinder, if the trend of the suction valve opening angle is decreasing, it indicates a suction valve failure or a cylinder seal damage. On the other hand, an increasing trend of the opening angle indicates a discharge valve failure.

[0049] Therefore, based on the method disclosed herein, the algorithm can predict the time period when a failure will occur and the component group where a failure may occur.

[0050] This object is also achieved by an industrial system, which includes at least one component for which future failures are to be predicted, at least one sensor, a condition monitoring unit, and means for outputting a signal indicating a predicted failure of the component. The at least one sensor is configured to provide an input time series containing a plurality of data points to the condition monitoring unit. Each data point contains a time stamp and the value of the variable W measured at the corresponding time stamp. The condition monitoring unit is configured to perform the steps of any of the methods disclosed herein.

[0051] The beneficial effects of such an industrial system are basically the same as those of the method described herein. Specifically, such an industrial system is characterized by high reliability of being ready for operation and generally having a longer service life, because the predictive maintenance method described herein can also prevent or at least reduce a series of errors or failures with consequent damages.

[0052] In a preferred embodiment of the industrial system disclosed above, the industrial system is a reciprocating compressor, including a crankshaft and a cylinder having at least one suction valve. The at least one sensor is configured to measure an opening angle of at least one of the suction valves as a function of a pressure represented by or capable of being represented by a crankshaft rotation angle.

[0053] In another preferred embodiment of the reciprocating compressor system disclosed above, the reciprocating compressor is a double-acting reciprocating compressor, which includes a double-acting cylinder having a crank end and a head end. At least one suction valve is arranged at the crank end of the double-acting cylinder, and at least one suction valve is arranged at the head end of the double-acting cylinder.

[0054] This object is also solved by a computer program including instructions, which, when executed by a computer, cause the computer to perform the steps of the method disclosed herein.

[0055] This object is also achieved by a computer-readable storage medium, which contains a computer program including instructions that, when executed by a computer, cause the computer to perform the steps of the method as disclosed herein.

[0056] In the context of the present invention, the term "storage medium" specifically includes cloud storage, flash memory, and embedded storage.

[0057] The present invention further achieves the above object by using the method for predicting faults in an industrial system disclosed herein. Specifically, the industrial system includes or consists of a reciprocating compressor system. Description of the Drawings

[0058] The present invention will be better understood with reference to the following preferred embodiments and descriptions of the drawings, in which the same reference numerals are used to represent the same or equivalent features in different embodiments and examples:

[0059] Figure 1 is a flowchart showing the order of steps of an embodiment of the method disclosed herein;

[0060] Figure 2a is an example of a fitted LPPL function for which the selected data points show a positive trend;

[0061] Figure 2b is an example of a fitted LPPL function for which the selected data points show a negative trend;

[0062] Figure 3 is an example of detecting a time point corresponding to a critical point in an input time series;

[0063] Figure 4 is at Figure 3An example of the predicted time period of the occurrence of a fault at the critical point determined in the example of Detailed Description of the Invention

[0064] Figure 1 shows the order of steps of an embodiment of the method described herein for determining whether a given data point (t n , y n ) (not shown separately in Figure 1 ) in the time series of input data 1 is a critical point t c of that time series. The detection of the critical point t c is regarded as the detection of a future fault of at least one component 8 in the industrial system 100. The algorithm is executed by the state monitoring unit 10, which is part of the industrial system 100 but can be physically separated therefrom. For clarity, Figure 1 the corresponding maximum and minimum values of the regression line 6, its slope s, and the local extremum N of the trend T in Figure 1 are not shown separately with subscripts max or min (not shown in

[0065] ). However, it will be clear from the present specification that the above elements refer to the corresponding maximum and minimum values.

[0065] The method includes steps a) to f): In step a), an input time series 1 related to the state of at least one component 8 in the industrial system 100 for which a future fault is to be predicted is provided. The input time series 1 contains a plurality of data points (t 1,…,n , y 1,…,n ), where each data point contains a time stamp t i and the value y i of a variable W measured at the corresponding time stamp t i . The input time series 1 can 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 for determining whether it is a critical point). Figure 1 The dashed arrow in max indicates an alternative using the subset 1a of the input time series 1. In step b), the best fit 5 of the function W(t)3 is determined by calculating the fitting parameters 2 of the logarithmic periodic power law model function W(t)3. The best fit 5 is characterized in that its mean square error mse 4 is the smallest with respect to the input time series 1 or the subset 1a of the input data (specifically, the time length p max subset that gives the overall minimum mean square error mse (not shown)). Next, in step c), the local extremum N of the fitting function 5 is identified. The local extremum N consists of the local maximum N max and the local minimum N min of the fitting function 5. In step d) (in Figure 1In the illustrated embodiment, which includes steps d1) and d2), the trend T of the identified local extremum N is identified. More specifically, based on at least some of the identified local maxima N max a first trend T is determined max , and based on at least some of the identified local minima N min a second trend T is determined min . In this example, the trend of the local maxima T max is determined by selecting, in step d1), the N - 1 local maxima from the local maxima N max identified in step c) that are closest to a given data point (t n , y n ), where it is determined in step e) whether the data point corresponds to a critical point t c . In step d2), the selected N - 1 local maxima are fitted using linear regression to obtain a regression line δ max , and the slope s max of the regression line δ max is determined. The slope s max determines the trend of the local maxima T max . The trend of the local minima T min is determined in a similar manner, i.e., based on the selected N - 1 local minima and the slope s min of the corresponding regression line δ min . In step e), it is identified whether a given data point (t n , y n ) of the input time series 1 is a critical point t c , where, if the two trends (i.e., the trend T max determined based on at least some of the identified local maxima N max and the trend T min determined based on at least some of the identified local minima N min ) have the same characteristic for the last point (t n , y n ) of the input data before the given data point (t n-1 , y n-1 ) (i.e., both slopes are positive or both slopes are negative), then the given data point (t n , y n ) is a critical point t c . If it is determined in step e) that the given data point (t n , y n ) under study is a critical point t c , then a signal 7 indicating a failure of at least one component 8 in the predicted industrial system 100 is output.

[0066] Figure 2a and 2b shows an example of a log-periodic power law function 5 that fits a subset of the input time series with a time length p max of the input time series, subset p max has a positive trend ( Figure 2a ) and a negative trend ( Figure 2b ) for the given data points, respectively. From the corresponding Figure 2a and 2b it can be seen that the given data point (t n , y n ) is the critical point t c because the determined trend T max and the determined trend T min have the same characteristics, that is, for the last point of the input time series before the given data point, the regression lines δ max and δ min have a positive slope ( Figure 2a ) or a negative slope ( Figure 2b ). Figure 2a and 2b The examples in are respectively derived from the backtesting of the historical data of the 1-year and 2-year time periods by the prediction method disclosed in this article, and the critical points are calculated for these time periods. Starting from the starting time t start , for each next timestamp of the input time series, the best-fit LPPL function 5 is calculated, which is characterized by having the minimum mean square error mse of the input time series 1. Figure 2a and Figure 2b The resulting graph 5 shown in shows the results over time in days.

[0067] Figure 3 shows an example of a predicted future failure corresponding to the critical point t c of the given input time series 1. Figure 3 The input time series in is a solid line, and its measurement points are marked with reference number 1. Each vertical line marked with t c represents the critical point t c determined by the algorithm disclosed in this article. For each critical point t c , moving from left to right in Figure 3 , the average value of the LPPL function fitting error (mean square error mse) is marked. Figure 3 The four vertical lines in are marked with thick arrows indicating the compressor repair dates (diagnostic breakpoints), and these repairs usually occur within a few days to a few weeks after the failure is predicted by the state monitoring system using the method disclosed in this article. Except for the detected critical point marked with t c * and the prediction determined by the maximum error (mse = 0.000249), the detected critical point t cThe correlation with the diagnostic breakpoint is clearly visible. In other words, the determined critical point t c * can be classified as an irrelevant event because its mean squared error mse is greater than or equal to the corresponding mse threshold of 10·10 for irrelevant events -5 .

[0068] Figure 4 shows the predicted time period 11 for the occurrence of the fault at the critical point t Figure 3 determined in the example of c . Figure 4 Each of the three diagrams a), b) and c) in c shows the same input time series marked with reference numeral 1 and the critical point t c determined for the input time series 1, where, moving forward in chronological order from left to right in the respective diagram, the critical point t c is additionally marked as A to F respectively. For each critical point t Figure 4 , the corresponding time period 11 (the area enclosed by the vertical dashed line) is provided, which indicates when the monitored component is expected to fail. It is worth noting that in c , the criticality classification of the predicted fault is represented by dividing into three separate diagrams, where a) shows that the critical points t c A - C and t -5 E - F and the corresponding time periods 11A - C and 11E - F belong to the "critical event" category. In this example, the "critical event" category is characterized by a mean squared error mse < 6·10 -5 . Diagram b) shows the "monitoring event" category, which in this example is characterized by a mean squared error mse of 6·10 -5 ≤ mse < 10·10 c . In this example, the "monitoring event" category does not have any marked vertical lines because the algorithm determines that no critical point t -5 satisfies this requirement for the mean squared error mse. Finally, diagram c) shows the "irrelevant event" category, which in this example is characterized by a mean squared error mse equal to or greater than 10·10 Figure 4 . As can be seen from diagram c) of c , the algorithm only determines one critical point t Figure 4 D that satisfies the mean squared error mse requirement, but no actual fault occurred within the corresponding predicted time period 11D. It can be seen that the compressor was not repaired. The repair (maintenance) time is indicated by the black arrow in Figure 4It can be seen that for the "critical event" and "monitoring event" categories, the correlation between the predicted failure occurrence time period 11 and the actual repair date, as well as the time period when the expert detected abnormal behavior of the compressor, is very good. The predictions in the "irrelevant event" category are not followed or confirmed by any repair and diagnostic records, which further proves the effectiveness of the method disclosed in this article.

[0069] The following embodiments can be envisioned:

[0070] A method for predicting faults in an industrial system (100), particularly a reciprocating compressor (100), the method comprising the following steps:

[0071] a) Providing an input time series (1) comprising a plurality of data points (t 1,…,n , y 1,…,n ), each data point comprising a timestamp (t i ) and a value (y i ) of a variable W measured at the corresponding timestamp (t i ), wherein the index 1 represents the first value, the index n represents a given value, and the index i represents a value located between the first value and the given value of the input time series (1);

[0072] b) Calculating fitting parameters (2) of a log-periodic power-law model function W(t)(3) that minimizes the mean square error mse(4) of the input time series (1) or at least one subset (1a) of the data points of the input time series (1), wherein each subset (1a) consists of L data points (t n , y n ) preceding a given data point (t i,…,n-1 , y i,…,n-1 ) of the input time series (1) to obtain a fitting function (5);

[0073] c) Identifying local extrema (N) of the fitting function (5), wherein the local extrema (N) consist of local maxima (N max ) and local minima (N min ) of the fitting function (5);

[0074] d) Determining trends (T max ) respectively based on at least some of the identified local maxima (N max ), and determining trends (T min ) based on at least some of the identified local minima (N min );

[0075] e) Identifying whether a given data point (t n , y n ) is a critical point (t c), wherein, if the two trends (T max ; T min ) for the last point (t n , y n ) of the input time series before the given data point (t n-1 , y n-1 ) have the same characteristics, then the given data point (t n , y n ) is regarded as a critical point (t c ); and

[0076] f) If a critical point (t c ) has been identified in step e), then output a signal (7) indicating that a failure of at least one component (8) in the industrial system (100) is predicted.

[0077] This embodiment can be combined with any of the embodiments disclosed above.

Claims

1. A method for predicting faults in an industrial system (100), in particular a reciprocating compressor (100), the method comprising the following steps: a) Provide an input time series (1) including a plurality of data points (t 1,…,n , y 1,…,n ), each data point containing a timestamp (t i ) and a value (y i ) of a variable W measured at the corresponding timestamp (t i ), where index 1 represents the first value, index n represents the given value, and index i represents a value between the first value and the given value of the input time series (1); b) Calculate the fitting parameters (2) of the log-periodic power law model function W(t) (3), which minimizes the mean square error mse (4) of the input time series (1) or at least one subset (1a) of the data points of the input time series (1), where each subset (1a) consists of the number L of data points (t n , y n ) prior to the given data point (t i,…,n-1 , y i , … ,n-1 ) of the input time series (1) to obtain the fitting function (5); characterized in that the method further comprises the following steps: c) Identify the local extrema (N) of the fitting function (5), where the local extrema (N) consist of the local maximum (N max ), and the local minimum (N min ); d) Determine trends (T max ) respectively based on at least some of the identified local maxima (N max ), and determine trends (T min ) based on at least some of the identified local minima (N min ), wherein the corresponding trends (T max , T min ) are respectively determined by the slopes of the linear fits of the selected local maxima (N max ) and local minima (N min ); e) Identify whether a given data point (t n , y n ) is a critical point (t c ), where, if both of the two trends (T max ; T min ) determined in step d) are positive or negative for the last point (t n , y n ) of the input time series before the given data point (t n-1 , y n-1 ), then the given data point (t n , y n ) is considered a critical point (t c ); and f) If a critical point (t c ) has been identified in step e), then output a signal (7) indicating that a failure of at least one component (8) in the industrial system (100) is predicted.

2. The method according to claim 1, wherein, the log-periodic power-law model function W(t) (3) is given by formula (1): （1） where W = vector of variables for analyzing the industrial system (100), t c = is regarded as the critical point for future fault event detection, t = [t n-1-pmax , t n-pmax ,..., t n-2 , t n-1 – The horizontal vector of time points has a length p with time units max , A,B,m,C 1 ,ω,Φ,p max are fitting parameters (2).

3. The method according to claim 2, wherein, the following constraints are imposed on the fitting parameters (2) described below: — A > 0; and / or — 0 < m < 1; and / or — 2 < ω < 8; Preferably, the following constraints are imposed on the fitting parameters (2) described below: — A > 0; and — 0 < m < 1; and — 2 < ω < 8.

4. The method according to any one of claims 1 to 3, wherein, The local maximum (T max ) and the local minimum (T min ) in step d) are determined as follows, respectively: d1) Select N - 1 extreme values from the local extreme values (N) identified in step c) that are closest to the given data point (t n , y n ), and determine in step e) whether this data point corresponds to a critical point (t c ); d2) Fit the selected N - 1 extreme values using linear regression to obtain a regression line (6), and determine the slope (s) of the regression line (6), where the slope (s) determines the trends (T) of the local maximum (T max ) and the local minimum (T min ), respectively.

5. The method according to any one of claims 1 to 4, wherein, In step b), the fitting parameters (2) of the log-periodic power law model function W(t) (3) are calculated for a plurality of subsets (1a) respectively, and wherein the fitting function (5) is obtained from the subset (p max ) that gives the overall minimum mean square error mse (4a) among the plurality of subsets (1a).

6. The method according to any one of claims 1 to 5, wherein, The number L of data points lies between a minimum number (L min ) 40 and a maximum number (L max ) 101.

7. The method according to any one of claims 1 to 6, wherein, If a critical point (t c ) is determined in step e), then the method further comprises the following steps: g) Based on the mean square error mse(4) obtained in step b), output a time period (11) in which it is predicted that the at least one component (8) will have a predicted fault, wherein step g) is performed simultaneously with or after step f).

8. The method according to any one of claims 1 to 7, wherein, The signal (7) is output only when the mean square error mse(4) is less than or equal to a predetermined threshold, especially when the mean square error mse(4) is less than 10·10 -5 , preferably less than 6·10 -5 .

9. The method according to any one of claims 1 to 8, wherein, the input time series (1) relates to the variation of the opening angle of at least one suction valve as a function of pressure in the cylinder of a reciprocating compressor (100), in particular the variation of the opening angle, wherein the pressure is represented or can be represented by the crankshaft rotation angle.

10. The method according to 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), wherein at least one suction valve is arranged at the crank end (CE) of the double-acting cylinder and at least one suction valve is arranged at the head end (HE) of the double-acting cylinder.

11. An industrial system (100) comprising at least one component (8) for which future faults are to be predicted, at least one sensor (9), a condition monitoring unit (10) and means for outputting a signal (7) indicating a predicted fault of the component (8), wherein, The at least one sensor (9) is configured to provide an input time series (1) comprising a plurality of data points (t n , y n ) to the status monitoring unit (10), each data point comprising a timestamp (t i ) and a value (y i ) of a variable W measured at the corresponding timestamp (t i ), and wherein the status monitoring unit (10) is configured to perform the steps of the method according to any one of claims 1 to 10.

12. The industrial system (100) according to claim 11, wherein, the industrial system (100) is a reciprocating compressor (100) comprising a crankshaft and a cylinder having at least one suction valve, and wherein the at least one sensor (9) is configured to measure the opening angle of at least one of the suction valves as a function of pressure, wherein the pressure is represented or can be represented by the crankshaft rotation angle.

13. The industrial system (100) according to claim 12, wherein, The reciprocating compressor (100) is a double-acting reciprocating compressor, including a double-acting cylinder having a crank end (CE) and a head end (HE), wherein at least one suction valve is arranged at the crank end (CE) of the double-acting cylinder, and at least one suction valve is arranged at the head end (HE) of the double-acting cylinder.

14. A computer program including instructions, which, when executed by a computer, causes the computer to perform the steps of the method according to any one of claims 1 to 10.

15. A computer-readable storage medium containing a computer program including instructions, which, when executed by a computer, causes the computer to perform the steps of the method according to 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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