Method for providing physically interpretable fault information of bearing by means of fault detection model

Abstract

Fault detection device and computer-implemented method for providing physically interpretable fault information of a bearing built in a machine by means of a fault detection model (11), said computer-implemented method comprising the steps of:-obtaining sensor data measured at the bearing as input data relating to an input data field, and a fault detection model (11) trained on the sensor data relating to the input data field to output a predicted fault value (12) of the bearing by processing the obtained sensor data (10),-mapping the measured sensor data (10) from the input data field to a selected data field to produce an expanded fault detection model (13), wherein the selected data field has a physical significance for a fault of the bearing,-performing a feature attribution (14) on the extended fault detection model (13) to quantify an importance of at least one individual feature for the extended fault value associated with the selected data field, and-performing a feature attribution (14) on the extended fault detection model (13) to quantify the importance of the at least one individual feature for the extended fault value associated with the selected data field. And-displaying (S4), at the user interface, the individual features (15) and the corresponding quantitative importance (16) in the selected data field.

Description

[0001] The present disclosure relates to a fault detection apparatus and a computer-implemented method for providing physically interpretable fault information of a bearing built into a machine through a fault detection model.

[0002] Sensors are ubiquitous in all kinds of heavy machinery, motors and similar equipment. One particularly important application area for sensors is the detection of bearing failures in rotating machinery such as motors, turbines and pumps. Failures in bearings are one of the most common causes of failure of rotating equipment. Such failures can be detected in vibration patterns. In order to obtain the required information, sensors such as position sensors, velocity sensors, accelerometers and spectral emission energy sensors can be mounted directly on the bearings or on these machines. This allows measurements that can be used for vibration analysis to be obtained by extracting the vibration frequency and amplitude. If the bearing is subject to different damage, geometric defects or faults, the sensor values ​​often indicate suspicious patterns and anomalies. Although there are a variety of tools and methods derived from physical theory that in principle will allow this information to be obtained from sensor measurements, this remains a very challenging task.

[0003] However, there are still a number of issues associated with detecting faults in bearings from sensor data that need to be addressed. Since the time series of sensor data is only an indirect measurement of the real physical mechanism and has a very complex data structure, the machine learning model trained to detect faults in bearings itself needs to be complex and is therefore usually not human-understandable, often referred to as a black box algorithm. This means that it is impossible to understand how the model behaves, why the model predicts the failure of the bearing, and therefore whether the results of the algorithm are consistent with physical reasoning. This creates obstacles for data scientists / model developers to build better and more robust models, and for domain experts (such as engineers or operators) to understand and trust the model results. This also leads to problems with the detection of the root causes of faults in bearings (such as bearing or crankshaft failures), and therefore leads to a lack of recognition from the user side.

[0004] Signal processing methods for detecting faults on bearings are standard in application and well-founded in theory. The faults in the identified bearings may occur at different parts of the bearing. In a bearing, the fault may occur in the outer ring of the bearing, in the inner ring, in the cage or at the balls of a ball bearing. Different methods and formulas are needed to describe the physical relationship between the measured sensor data and the type of individual faults. Since these formulas usually describe the damage frequencies of different kinds of damage types of the bearing based on the properties of the bearing and the rotational speed, different phenomena can be physically explained. In order to perform fault diagnosis on these different damages of the acceleration data, it is important to know these physical properties of the bearing and the rotational speed at which the bearing was running when the data was recorded. Since some of the fault effects are amplitude modulated in the vibration spectrum and covered by resonance effects, different pre-processing steps are applied to the recorded raw data to reveal specific fault frequencies.

[0005] However, signal processing methods often encounter some problems. For example, the generated vibration spectrum is highly dependent on the installation position of the speed sensor and the possible load of the machine. In addition, noisy sensor signals with multiple confounding factors hinder signal processing.

[0006] Furthermore, machine learning methods have been considered for performing fault detection in bearings. In order to perform the training of a machine learning algorithm, it is necessary to have access to a sufficient amount of ideally labeled training data containing real vibration signals measured during actual operation of the machine of interest with healthy and defective parts. However, such algorithms are essentially very complex black box models. This means that it is not at all clear on what logic such methods are based on to form their decisions.

[0007] Therefore, the object of the present application is to provide an apparatus and method for fault detection of rolling objects by machine learning methods, which output physically interpretable information that even indicates the root cause of the detected fault. Another specific object is to improve the interpretability of bearing fault detection using a machine learning algorithm trained on vibration or current data of a rotating machine.

[0008] This object is solved by the features of the independent claim. The dependent claims contain further developments of the invention.

[0009] A first aspect relates to a computer-implemented method for providing physically interpretable fault information of a bearing built into a machine through a fault detection model, comprising the following steps:

[0010] - obtaining sensor data measured at the bearing as input data associated with an input data domain, and a fault detection model, which has been trained on the sensor data associated with the input data domain, to output a predicted fault value of the bearing by processing the obtained sensor data,

[0011] - mapping measured sensor data from an input data domain to a selected data domain and generating an augmented fault detection model, the augmented fault detection model outputting an augmented predicted fault value associated with the selected data domain instead of the input data domain, wherein the selected data domain has physical meaning for a fault of the bearing,

[0012] - performing feature attribution on the augmented fault detection model of the acquired sensor data, thereby quantifying the importance of at least one individual feature of the input data to the augmented fault value associated with the selected data domain, and

[0013] -Displaying individual features and corresponding quantitative importance in a selected data domain at the user interface.

[0014] The method is based on a "conventional" fault detection model that associates an input signal, e.g. sensor data measured over time, with a predicted fault value, e.g. whether a fault is present (value 1) or not (value 0). The feature attribution applied to the predicted fault value will provide data points in the input data domain, e.g. in the time domain. The data features include at least one but most often several adjacent sensor data points. These data features in the input domain will not provide information about the underlying specific fault. The quantitative data features in the input data domain neither provide hints for the root cause of the predicted fault value nor are they interpreted in a manner consistent with recognized physical theories. In contrast, the feature attribution performed on an augmented fault detection model associated with a selected data domain provides features in the selected data domain instead of features in the input data domain. The augmented predicted fault value generated from the augmented fault detection model is equivalent to, and in particular even identical to, the predicted fault value generated from the obtained fault detection model. The selected data domain has a physical meaning for the faults of the bearing and is therefore interpretable, e.g. comparable to the typical fault frequencies of the considered bearing.

[0015] In an embodiment of the method, the domain map consists of a plurality of concatenated domain maps.

[0016] Such cascaded domain mappings can simulate / reflect different domain transformations and thus provide greater flexibility with respect to faults that are physically explainable in another domain as the input data domain in which the fault detection model is trained.

[0017] In an embodiment of the method, at least one domain mapping is performed by applying a reversible bijective transformation function on the measured input data.

[0018] This ensures a unique and unambiguous mapping between the output of the fault detection model in the input data domain (ie, predicted fault values) and the output of the augmented fault model in the selected data domain (ie, augmented fault values). The predicted fault values ​​and augmented predicted fault values ​​are equivalent, ie, they have the same value.

[0019] In an embodiment of the method, feature attribution is performed by any model-agnostic feature attribution method suitable for the type of machine learning model used for the fault detection model.

[0020] This ensures that the data features that are most relevant to the output of the augmented fault detection model can be analyzed independently on the augmented learning model and only rely on the “original” fault detection model.

[0021] In an embodiment of the method, the fault detection model is a deep neural network, in particular an autoencoder, a convolutional neural network or a deep belief network.

[0022] Deep neural networks can learn extremely complex patterns, and they are flexible and able to cope with high-dimensional complex sensor input data.

[0023] In an embodiment of the method, the sensor data are vibration data or current data measured at or near the bearing.

[0024] The vibration data are particularly indicative of fault indications of bearings, since defects in the bearings can produce periodic interruptions due to, for example, defects in the balls. A machine with a defective bearing will generally require more current than a non-defective state.

[0025] In an embodiment of the method, sensor data measured at the bearing are measured in the time domain and a mapping into the frequency domain is performed.

[0026] Sensors primarily measure physical parameters of machines that vary over time and are therefore available in the time domain in most cases. Since a fault in a bearing results in periodically occurring disturbances in the sensor data measured over time, the frequency domain of the signal envelope is the most likely domain where a physical interpretation seems possible.

[0027] In an embodiment of the method, an alert is automatically output to a user interface if the quantified significance of the augmented fault detection model is detected with a predefined frequency, the predefined frequency being related to a root cause of the bearing.

[0028] In such a case, an alarm draws the operator's attention, indicating a high probability of bearing failure. This allows quick action to be taken at the machine, such as changing settings, stopping the machine or scheduling maintenance work.

[0029] In an embodiment of the method, the quantitative importance of the outputs is displayed in a color code with respect to the quantity.

[0030] This helps to identify, for example, critical or highly relevant values ​​in a continuous spectrum of importance values.Color codes can indicate different quantitative values ​​in different colors of a predefined color scale or in different intensities of one color.

[0031] In an embodiment of the method, a fault detection model for the bearing is trained on the signal envelope of sensor data measured in the time domain and analyzed in the frequency domain for specific fault frequencies.

[0032] The signal envelope highlights the time distance between two peaks in the sensor data measured in the time domain. Characteristic faults of bearings depend on parameters such as the diameter of the ball or the pitch diameter of the bearing and generate disturbances at different time intervals which are directly related to the frequency depending on the values ​​of the above parameters.

[0033] In an embodiment of the method, the domain mapping is performed by a Fourier transform function.

[0034] The Fourier transform or Fast Fourier Transform functions are well known and require very little processing power.

[0035] In an embodiment of the method, the machine is a rotating machine, in particular an electric motor, a turbine, a pump or a press.

[0036] A second aspect relates to a fault detection device for providing physically interpretable fault information of a bearing built into a machine through a fault detection model, the fault detection device comprising at least one processor configured to perform the following steps:

[0037] - obtaining sensor data measured at the bearing as input data associated with an input data domain, and a fault detection model, the fault detection model being trained on the sensor data associated with the input data domain to output a predicted fault value of the bearing by processing the obtained sensor data,

[0038] - mapping the measured sensor data from an input data domain to a selected data domain, thereby generating an augmented fault detection model, the augmented fault detection model outputting an augmented predicted fault value associated with the selected data domain, wherein the selected data domain has physical meaning for a fault of the bearing,

[0039] - performing feature attribution on the augmented fault detection model of the acquired sensor data, thereby quantifying the importance of at least one individual feature of the input data to the augmented fault value associated with the selected data domain, and

[0040] -Displaying individual features and corresponding quantitative importance in a selected data domain at the user interface.

[0041] A third aspect relates to a computer program product directly loadable into the internal memory of a digital computer, comprising software code portions for performing the steps as described above when said product is run on said digital computer.

[0042] The present invention will be explained in more detail by referring to the accompanying drawings. Similar objects will be marked by the same reference symbols.

[0043] Figure 1 An embodiment of a computer-implemented method of the present invention is illustrated by a flow chart.

[0044] Figure 2 The interaction of the individual process steps is schematically illustrated in more detail.

[0045] Figure 2A The domain mapping and the resulting augmented fault detection model are schematically illustrated.

[0046] Figure 2B The characteristics of the transformation function applied to domain mapping are schematically illustrated.

[0047] Figure 3A The output of the fault detection model in the input domain is schematically illustrated.

[0048] Figure 3B The output of an embodiment of an augmented fault detection model in a selected domain is schematically illustrated.

[0049] Figure 4 A comparison of the output of feature attribution of a fault detection model in an input domain and the output of feature attribution of an augmented fault detection model in a selected domain is schematically illustrated.

[0050] Figure 5 An embodiment of the fault detection device of the present invention is illustrated as a block diagram.

[0051] Note that in the detailed description of the following embodiments, the drawings are schematic only, and the illustrated elements are not necessarily shown to scale. Rather, the drawings are intended to illustrate the functions and collaboration of the components. Here, it is to be understood that any connection or coupling of functional units, devices, components or other physical or functional elements can also be realized by directly connecting or indirectly connecting coupling elements (e.g., via one or more intermediate elements). The connection or coupling of entities or components can be realized, for example, by being based on wired, wireless connections and / or based on a combination of wired and wireless connections. Functional units can be implemented by dedicated hardware (e.g., processors, firmware) or by software, and / or by a combination of dedicated hardware and firmware and software. Further note that each functional unit described for the device can perform the functional steps of the related method, and vice versa.

[0052] First, a description of standard methods for detecting bearing faults is provided, which are standard in application and well-founded in theory. However, they often suffer from a series of problems. Examples are (too) noisy raw signals of sensor data, multiple confounding factors. These standard methods lack flexibility and cannot cope with high-dimensional complex sensor data. Since the method is based on a physical derivation of the bearing behavior during fault conditions, it will be described in detail below.

[0053] Local faults in bearings, especially rolling element bearings, can occur at different parts of the bearing, either in the bearing outer ring, in the inner ring, in the cage or at the rolling elements. Depending on the fault, different methods are required. For the following formulas, we will use the following symbols: d is the bearing ball diameter, D is the pitch diameter, f is the diameter of the bearing ball, and f is the diameter of the bearing ball. r is the shaft speed, n is the number of rolling elements, and Φ is the bearing contact angle.

[0054] The inner race damage is caused by an irregularity on the inner race of the bearing. When the rolling element hits the fault, an impact is introduced, which emits a high-frequency resonance. The envelope spectrum shows this fault at the BFPI frequency:

[0055]

[0056] The outer race damage is caused by an irregularity on the outer race of the bearing. The envelope spectrum shows this fault at the BFPI frequency:

[0057]

[0058] Wear or deformation will cause the cage to move from its central position. Unbalanced forces occur, which cause shock pulses.

[0059]

[0060] The damaged rolling element periodically contacts the bearing inner and outer rings and generates impact signals. Since the rolling element rotates around itself and simultaneously experiences relative movement through the cage, sidebands are expected. The envelope spectrum shows peaks at the following locations:

[0061]

[0062] Since these formulas describe the damage frequencies of different kinds of bearing damage types based on the bearing physical properties and the rotational speed, the different phenomena can be physically explained. In order to perform troubleshooting on these different bearing damages from acceleration data, it is important to know these physical properties of the bearing and the rotational speed at which the bearing was running when the data was recorded.

[0063] Since some of the fault effects are amplitude modulated in the vibration spectrum and covered by resonance effects, different pre-processing steps are applied to the recorded raw data in order to reveal specific fault frequencies. It should be noted that the resulting vibration spectrum is highly dependent on the mounting position of the speed sensor and the possible load of the machine.

[0064] The signal processing based approach applies a bandpass filter to the acceleration signal containing the operating noise of the bearing. The envelope signal of the pre-filtered signal is then calculated and transferred to the frequency domain.

[0065] By calculating the envelope, the amplitude modulated damage fault signal can be demodulated and the resulting envelope spectrum shows different bearing faults in the form of peaks at the characteristic frequencies BPFI, BPFO, FTF and BSF as defined above.

[0066] The common way to obtain the envelope spectrum is to calculate the analytical signal and then transfer it to the frequency domain. Since strong background noise (such as pulsed electromagnetic noise and periodic harmonic noise generated by shaft rotation, etc.) has a large influence on the selection of the resonance frequency band, it is important to correctly select the upper and lower limits of the bandpass filter and the appropriate cutoff frequency of the center frequency.

[0067] To achieve this, the frequency band with the highest signal-to-noise ratio is determined by calculating the kurtogram. The kurtogram shows the spectral peaks for different window widths and center frequencies. Kurtosis is a measure of the "tail" of the probability distribution of a real-valued random variable.

[0068]

[0069] Due to the fourth power, the pulses deviate from the mean resulting in large kurtosis values.

[0070] Selecting the center frequency and bandwidth from the kurtosis plot with the highest kurtosis value is a promising choice for the applied bandpass filter. As mentioned above, this approach requires detailed knowledge about the mounted bearings and a lot of manual work by domain experts.

[0071] In the following about Figure 1 Describes embodiments of the method of the present invention and relates to Figure 2 and Figure 3A / B explains an embodiment of the method of the present invention in more detail.

[0072] The first step S1 (see Figure 1 ) is used to provide physically interpretable fault information of a bearing built into a machine, i.e., to obtain sensor data 10 measured at the bearing (see Figure 2 ), as input data associated with the input data domain, and a fault detection model 11, the fault detection model 11 being trained on sensor data associated with the input data domain. Preferably, the sensor data 10 is vibration data or current data measured at or near the bearing. The sensor data 10 measured at the bearing is measured in the time domain. The output of the fault detection model 11 is a predicted fault value 12 of the bearing obtained by processing the obtained sensor data 10.

[0073] The measured sensor data 10 are mapped from the input data domain to the selected data domain, thereby generating an augmented fault detection model which outputs an augmented predicted fault value associated with the selected data domain, see step S2. The selected data domain has a physical meaning for the fault of the bearing and is therefore a semantic representation of the sensor data. For monitoring the bearing, a mapping is preferably performed from time as the input data domain to frequency as the selected data domain. In Figure 2 In FIG. 1 , the mapping and the resulting augmented fault detection model are depicted by reference symbol 13 .

[0074] A feature attribution 14 is performed on the augmented fault detection model 13, thereby quantifying the importance of at least one individual feature of the input data in the selected data domain to an augmented fault value, wherein the augmented fault value is equal to or even identical to the fault value of the obtained fault detection model, see step S3. The feature attribution is performed by any model-independent feature attribution method suitable for the fault detection model.

[0075] In a final step S4, the individual features of the input data and the corresponding quantitative importance in the selected data fields are displayed at a user interface. Figure 2An example of a display output is shown as graph 15. The color of the vertical line 16 indicates the value of the importance of that frequency feature to the predicted fault value output by the fault detection model. A frequency feature is a dedicated frequency or a frequency band consisting of several subsequent frequencies that together contribute to the indicated importance. Based on a predefined critical value in a selected data domain related to the root cause of the bearing, an alert is automatically output to the user interface if the quantitative importance of the augmented fault detection model is detected at the predefined critical value. Preferably, the output quantitative importance is displayed in a color code with respect to the quantity.

[0076] Figure 2A and Figure 2B The domain mapping and resulting augmented fault detection model 13 are shown in more detail. is applied to the measured sensor data 10 and by taking the inverse form of the transformation function is applied to the fault detection model 11 to perform domain mapping. Thus, the acquired sensor data 10 associated with the input data domain t is transferred to sensor data 101 in the selected data domain f. The inverse form of the transformation function applied to the fault detection model 11 is An augmented fault detection function 13 is generated. Therefore, the obtained sensor data 10 mapped into the selected data domain is input into the augmented fault detection model 13, which outputs an augmented fault value 12. The input data in the selected data domain, the augmented fault detection model 13, and the augmented fault value 12 are input into a feature attribution 14. The feature attribution 14 outputs a quantification of the importance of features in the obtained sensor data 101 in the selected data domain.

[0077] Figure 2B The transformation function is shown in more detail Transformation function is a reversible bijective transformation function. This means that the transformation function applied to the sensor data 100 obtained in the input data domain x The sensor data 101 in the selected data domain z is output. On the other hand, the inverse form of the transformation function applied to the sensor data 101 in the selected data domain z is Output sensor data 100 in input data domain x. Input data domain x can be any parameter, for example Figure 2A The selected data domain z can be any parameter, for example, Figure 2A The frequencies shown in .

[0078] In many operating situations, sensor data is measured over time. Typically, one or several sensors detect vibrations of the bearing based on accelerations of the entire bearing or a portion of the bearing. Another parameter measured in order to derive bearing defects is the current data of the machine. The sensor is usually located at a portion of the machine close to the bearing. Figure 2 The acquired sensor data 10 shown in FIG. 1 provides acceleration values ​​a measured over time t. Time is an input data field.

[0079] The machine learning model for fault detection, i.e., the fault detection model 11, can be viewed as a function f that maps the input sensor data 10 to an output that provides a predicted fault value (e.g., a decision whether a fault is present (value 1) or not (value 0)). θ : R N →{0, 1}. The fault detection model is trained by a sufficient amount of ideally labeled training data containing actual sensor data, such as vibration signals measured in the input data domain over time during actual operation of the machine of interest with healthy and defective parts.

[0080] The fault detection model 11 is preferably a deep neural network, in particular an autoencoder, a convolutional neural network or a deep belief network capable of learning extremely complex patterns. Most methods using deep neural networks show good performance on test data, are flexible and capable of dealing with high-dimensional complex sensor data, and their predictions are reliable. However, such models are essentially very complex black box models. This means that it is not clear at all what logic such models are based on to form their decisions.

[0081] A method for interpreting black-box machine learning models is presented through feature attribution methods. Such methods quantify the extent to which individual input data features contribute to the model’s final predicted fault value. Input data features include one or several neighboring data points of the input data. The decision of the machine learning model, i.e. the predicted fault value, can be viewed as attributing the d-dimensional sensor data x∈R d A function f that maps to a real number f(x) representing the decision of the prediction model: R d →R. In the case of fault detection of bearings, f(x) may, for example, indicate a logical value or a corresponding probability of the presence of a defect estimated by a fault detection model. The goal of feature attribution is to identify an importance vector φ∈R d , so that Φ i Quantize each input feature x i The importance of the model’s prediction f(x) for a fixed input x.

[0082] So far, any such feature attribution method will retrieve feature attributions in units of sensor data features x, i.e., in units of the input data domain of sensor data 10. So, for example, if the fault detection model 11 is trained to classify sensor data in the time domain, then Φ will specify the importance of sensor data features in the time domain, such as Figure 3A . Sensor data features with high importance for predicting the fault value of the bearing are marked by dashed lines 21, and sensor data features with low importance for predicting the fault value of the bearing are marked by dotted lines 22. Importance can also be indicated by color, where the value of the importance score is encoded by the color scale and / or intensity of the lines 21, 22. In cases where the fault detection model is primarily concerned with frequency information, but feature importance is displayed in the time domain, this will lead to uninterpretable results and may not make sense at all to a domain expert.

[0083] If you can Figure 3A As seen in the previous section, it is difficult to infer any specific pattern or find specific reasons to explain the decisions of the fault detection model. On the other hand, see Figure 3B If the value of the feature importance is calculated in the frequency domain, which provides a frequency representation of the measured sensor data, it is immediately clear that the presence of a single frequency peak (see line 31) has a significant impact on the predicted fault value. Figure 3A In , the importance values ​​in the selected data domain (here the frequency domain) are encoded by different structures or lines of different colors at the corresponding frequencies, see Figure 3B .

[0084] To implement feature attribution in a selected domain different from the input data domain of the measured sensor data 10, the feature attribution is transformed into the selected domain by applying a bijective mapping that captures a reversible one-to-one correspondence between the input data domain of the fault detection model 11 and the selected domain. For example, the Fourier transform can be viewed as such a mapping from the time domain into a frequency representation, which is also reversible.

[0085] Mathematically, the mapping to a domain in D is given by the reversible function specifies, which means there is another function Make A domain mapping can also consist of multiple cascaded mappings, all of which are reversible. The goal is to transform the sensor data features in the input domain into a more meaningful domain of choice. is called an interpretable or semantic representation of x. If an appropriate domain mapping function is specified It can then be combined with feature attribution methods to compute feature importance values ​​based on the selected domain (i.e., semantic representation z) rather than based on sensor data features x. More specifically, Can be used to create extended models

[0086] in

[0087] Any model-independent feature attribution method can now be used in Instead of evaluating on f, it produces important values ​​in the chosen domain. This is correct because model-agnostic methods are designed to work with any machine learning model. If a model-specific attribution method is to be applied, then it is necessary to check Are the necessary assumptions of the method still met (e.g. differentiability) or does the method need further adaptation to such a model (e.g. a new LRP-rule).

[0088] Semantic interpretation for bearing fault detection

[0089] A defect in a bearing causes a fault signal, i.e., the measured sensor data, which has an amplitude modulation effect on a specific carrier signal. Domain experts can detect such an effect by analyzing the envelope spectrum and checking whether a specific fault frequency exists. This logic is strictly based on the physical understanding of bearing fault defects. If a machine learning model is trained to identify bearing faults from raw or pre-processed signals (i.e., sensor data in the input data domain), the connection to existing domain knowledge about the physics of the problem may be ignored or at least unknown. This is especially true for machine learning models, especially deep neural networks, which have been proven to be successful in the task of bearing fault detection.

[0090] Such a model may exploit any potential characteristics of the sensor data to make decisions based on it, and some of them may be spurious. This may lead to overfitting and may cause the model to perform poorly in deployment. In order to prevent this from happening and ensure a credible model with high predictive quality, it is necessary to verify to what extent the model follows the physical basis routines of the domain experts. More precisely, in the case of fault detection of bearings installed in machines, if one wants to check which features are important for the fault detection model 11 via feature attribution methods, it would be ideal to obtain values ​​for feature importance based on the frequency components of the envelope spectrum of the sensor data measuring the vibration of the machine close to the bearing. This information will be immediately accessible to the domain expert and will make it easy to check whether the fault detection model conforms to the physical understanding of bearing faults.

[0091] Below, domain mappings are provided for three common scenarios of a bearing fault detection model (FD model) based on the type of sensor data measured in the input domain used to train the obtained fault detection model 11 and used as the input data 10 of the obtained fault detection model 11, see also Table 1 below.

[0092] First, the fault detection model 11 is trained on the signal envelope in the time domain, which is given by the amplitude of the analysis signal (e.g., measured sensor data). In that case, the domain mapping applied is the Fourier transform, so

[0093]

[0094] Secondly, the fault detection model 11 is trained on the sensor data in the time domain. In order to derive the signal envelope of the sensor data from the time domain signal x, the signal envelope is calculated via the amplitude of the analyzed signal. This means that the signal envelope x env Mathematically, x env =|x+iHT(x)|, where HT is similar to the Hilbert transform. Now we can use FT(x env ) to compute the desired envelope spectrum. The goal is to find a domain mapping that derives the envelope spectrum from the time domain signal while being reversible. However, the absolute value will violate the requirement. To avoid this problem, it is also necessary to preserve the phase information of the analysis signal by computing its argument arg(x+iHT(x)). This yields the following domain mapping

[0095] in

[0096] Its reverse This ultimately allows us to obtain an effective semantic representation of time-domain signals based on their envelope spectra.

[0097] Finally, the fault detection model is trained on the sensor data in the frequency domain. In this case, the sensor data is first transformed to the time domain using an inverse Fourier transform, and then the above specified Applied to mapping from time domain to frequency domain.

[0098] Different domain mappings of different input data domains to the frequency domain as a selected data domain and their inverse transforms are summarized in the table below.

[0099]

[0100] Table 1

[0101] In this way, the proposed method provides tools to assess the extent to which a machine learning model trained to detect bearing faults is consistent with existing prior knowledge about the underlying physics. The domain map φ can be combined with existing feature attribution methods to estimate to what extent the model has exploited the presence of characteristic fault frequencies. Such information is immediately accessible to domain experts, in contrast to uninterpretable importance values ​​on the input domain (i.e., also known as raw data, which are produced solely by feature attribution methods). This is particularly useful in Figure 4 Visualization.

[0102] This is Figure 4 The fault detection model was trained on sensor data signals measured in the time domain and a bearing fault has been detected in the presented signals. On the left, the importance values ​​of the feature attributions evaluated in the time domain are depicted41,42. Again, it is difficult to infer any useful information about the potential causes of predicted bearing faults. In particular, it is not clear whether the fault detection model is consistent with the existing domain knowledge, i.e., that in case of a fault, a specific peak in the envelope spectrum should be present. However, if the feature attributions are computed based on a semantic representation, i.e., a selected data domain that is relevant to the physical interpretation, see Figure 4 On the right hand side of FIG. 4 , it can be verified that the fault detection model places great emphasis on the relevant fault frequency indicated by the vertical line 46. At least one importance value 45 indicating high importance coincides with the relevant fault frequency 46, with the importance values ​​44 indicating low importance clearly separated. This information is extremely useful to the domain expert and can be used to verify or improve the fault detection model accordingly.

[0103] Figure 5 An embodiment of a fault detection device 50 is shown in FIG. The fault detection device 50 comprises a data interface 51, which is configured to obtain sensor data measured at a bearing mounted at the machine 40 as input data. The input data is associated with an input data domain. In addition, a fault detection model is obtained via the data interface 51. The fault detection model is trained on sensor data associated with the input data domain to output a predicted fault value of the bearing by processing the obtained sensor data. The machine 10 is a rotating machine, in particular a motor, a turbine, a pump and a press.

[0104] The fault detection device 50 includes a data mapping unit 52, which is configured to map the measured sensor data from the input data domain to the selected data domain, thereby generating an extended fault detection model, which outputs an extended predicted fault value associated with the selected data domain. The selected data domain is configured so that it has physical meaning for the fault of the bearing.

[0105] The fault detection apparatus 50 comprises a feature attribution unit 53 configured to perform feature attribution on the augmented fault detection model, thereby quantifying the importance of at least one individual feature of the input data to the augmented fault value associated with the selected data domain.

[0106] The fault detection apparatus 50 includes a user interface 54 configured to display individual features of the input data and the corresponding quantitative importance in selected data fields.

[0107] It is to be understood that the description of the above examples is intended to be illustrative, and the components illustrated are susceptible to various modifications. For example, the illustrated concepts can be applied to different technical systems, and in particular to different subtypes of the corresponding technical systems with only minor adjustments.

Claims

1. A computer-implemented method for providing physically interpretable fault information of a bearing built into a machine by means of a fault detection model (11), the computer-implemented method comprising the following steps: - obtaining (S1) sensor data (10) measured at the bearing as input data associated with an input data domain, and a fault detection model (11) trained on the sensor data associated with the input data domain to output a predicted fault value (12) of the bearing by processing the obtained sensor data (10), - mapping (S2) the measured sensor data (10) from the input data domain (t) to the selected data domain (f) and generating an augmented fault detection model (13), said augmented fault detection model (13) outputting an augmented predicted fault value associated with the selected data domain, wherein the selected data domain has a physical meaning for the fault of the bearing, - performing (S3) feature attribution (14) on the augmented fault detection model (13) of the obtained sensor data (10), thereby quantifying the importance of at least one individual feature of the input data to the augmented fault value associated with the selected data domain, and - Displaying (S4) individual features in the selected data domain and the corresponding quantitative importance at a user interface.

2. The computer-implemented method of claim 1, wherein the domain map is composed of a plurality of cascaded domain maps.

3. A computer-implemented method according to claim 1 or 2, wherein at least one domain mapping is performed by applying a reversible bijective transformation function to the measured input data.

4. A computer-implemented method according to any one of the preceding claims, wherein the feature Attribution (14) is performed by any model-independent feature attribution method applicable to the fault detection model (11).

5. A computer-implemented method according to any of the preceding claims, wherein the fault detection model (11) is a deep neural network, in particular an autoencoder, a convolutional neural network or a deep belief network.

6. A computer-implemented method according to any one of the preceding claims, wherein the sensor data (10) is vibration data or current data measured at or near a bearing.

7. A computer-implemented method according to any of the preceding claims, wherein the sensor data (10) measured at the bearing is measured in the time domain and a mapping into the frequency domain is performed.

8. A computer-implemented method according to any one of the preceding claims, wherein an alert is automatically output to a user interface if the quantified significance of the augmented fault detection model is detected at a predefined frequency, the predefined frequency being related to the root cause of the bearing.

9. A computer-implemented method according to any one of the preceding claims, wherein the quantitative importance (16) of the output is displayed in a color code with respect to the quantity.

10. A computer-implemented method according to any of the preceding claims, wherein the fault detection model (11) is trained on the signal envelope of the sensor data (10) measured in the time domain and analyzed in the frequency domain for specific fault frequencies.

11. The computer implemented method of claim 10, wherein domain mapping is performed by a Fourier transform function.

12. The computer-implemented method according to any of the preceding claims, wherein the machine is a rotating machine, in particular an electric motor, a turbine, a pump and a press.

13. The computer-implemented method of claim 3, wherein the method comprises applying a transformation function (φ, 631) to the measured sensor data (10) and applying an inverse transformation function (φ, 631) to the measured sensor data (10). 632) is applied to the fault detection model (11) to perform domain mapping.

14. A fault detection device (50) for providing physically interpretable fault information of a bearing built into a machine (40) through a fault detection model (11), the fault detection device (50) comprising at least one processor, the at least one processor being configured to perform the following steps: - obtaining sensor data (10) measured at the bearing as input data associated with an input data domain, and a fault detection model (11) trained on the sensor data associated with the input data domain to output a predicted fault value (12) of the bearing by processing the obtained sensor data (10), - mapping the measured sensor data (10) from the input data domain (t) to a selected data domain (f) and generating an augmented fault detection model, the augmented fault detection model outputting an augmented predicted fault value associated with the selected data domain, wherein the selected data domain has physical meaning for the fault of the bearing, - performing feature attribution (14) on an augmented fault detection model (13) of the acquired sensor data, thereby quantifying the importance of at least one individual feature of the input data to an augmented fault value associated with a selected data domain, and -Displaying individual features and corresponding quantitative importance in a selected data domain at the user interface.

15. A computer program product directly loadable into the internal memory of a digital computer, comprising software code portions for performing the steps of claims 1 to 13 when said product is run on said digital computer.

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