Method for life prediction and monitoring

Abstract

A method for predicting and monitoring the lifespan of a device, as well as a corresponding system, are provided. The method involves calculating a probability density function over time for an aging degradation variable based on solving at least one equation from an aging degradation model having end-of-life (EOL) boundary conditions, where the boundary conditions include a first boundary condition and a second boundary condition, the first boundary condition is a no-flux boundary condition, and the second boundary condition is an absorption boundary condition or a partial absorption boundary condition; measuring an observable quantity related to the state of the device; obtaining first data representing the measured value of the observable quantity; calculating a likelihood for the aging degradation variable from the first data; updating the calculated probability density function of the aging degradation variable based on the likelihood; and generating a signal indicating the health prediction of the device based on the probability density function, the aging degradation model, and the EOL boundary conditions.

Description

Technical Field

[0001] The present disclosure relates to a method and a system for monitoring devices, and more particularly, for monitoring devices for the generation, transmission, distribution, and / or use of electrical energy.

Background Art

[0002] The failure of a device can have dramatic consequences. In many cases, the damage caused by an unexpected device failure can far exceed the cost of the device. In some cases, device failures are prevented by monitoring the device. Monitoring includes detecting and indicating deviations in device characteristics that may indicate degradation of the device's state. When a device is monitored while it is operating, it is also called online monitoring. Existing monitoring uses physical sensors to observe device characteristics. Alternatively, in other cases, statistical prediction is used to prevent device failures. For example, a device can be periodically maintained after, for example, a minimum predetermined amount of time has elapsed, or after the device has executed a predetermined number of cycles.

Summary of the Invention

Problems to be Solved by the Invention

[0003] An object of the present disclosure is to provide a more accurate method for preventing failures.

Means for Solving the Problems

[0004] This objective is addressed by a method for monitoring a device. The method includes providing or obtaining an aging degradation model, where the aging degradation model includes at least one equation having end-of-life (EOL) boundary conditions and aging degradation variables of the device; calculating a probability density function over time for the aging degradation variables based on solving at least one equation from the aging degradation model having the EOL boundary conditions; measuring observable quantities related to the operation of the device; obtaining first data representing the measured values of the observable quantities; calculating a likelihood for the aging degradation variables from the first data; updating the calculated probability density function of the aging degradation variables based on the likelihood; and generating a signal indicating the health prediction and remaining useful life (RUL) of the device based on the probability density function, the aging degradation model, the EOL boundary conditions, and the reliability calculated therefrom.

[0005] The aforementioned objective is also addressed by another method for monitoring a device. The method includes calculating a probability density function over time for the aging degradation variables based on solving at least one equation from an aging degradation model having end-of-life (EOL) boundary conditions; measuring observable quantities related to the operating state of the device; obtaining first data representing the measured values of the observable quantities; calculating a likelihood for the aging degradation variables from the first data; updating the calculated probability density function of the aging degradation variables based on the likelihood; and generating a signal indicating the health prediction of the device based on the probability density function, the aging degradation model, and the EOL boundary conditions. The aging degradation model may include the EOL boundary conditions and at least one equation having the aging degradation variables of the device. The method may further include providing or obtaining the aging degradation model.

[0006] The foregoing objective is also addressed by another method for monitoring a device. The method involves calculating a probability density function over time for aging variables based on solving at least one equation from an aging model having end-of-life (EOL) boundary conditions, where the boundary conditions include a first boundary condition and a second boundary condition, the first boundary condition being a no-flux boundary condition, and the second boundary condition being an absorption boundary condition or a partial absorption boundary condition; measuring an observable quantity related to the operating state of the device; obtaining first data representing the measured value of the observable quantity; calculating a likelihood for the aging variables from the first data; updating the calculated probability density function of the aging variables based on the likelihood; and generating a signal indicative of the device's soundness prediction based on the probability density function, the aging model, and the EOL boundary conditions. The aging model may include the EOL boundary conditions and at least one equation having the device's aging variables. The method may further include providing or obtaining the aging model.

[0007] The method described above provides a more accurate and reliable signal indicative of the device's soundness prediction (fault prediction). In this way, the device's faults may be more reliably and efficiently prevented.

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[0013] Additional boundary conditions that do not reflect the EOL boundary condition may be defined. For example, a boundary condition without flux, i.e., a boundary condition without probability decrease, may be defined. When the boundary condition includes a first boundary condition and a second boundary condition, the first boundary condition is a boundary condition without flux, and the second boundary condition is an absorption boundary condition or a partial absorption boundary condition, the aging can be accurately modeled. Therefore, the prediction can be more accurate, and the maintenance can be more efficient and effective.

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[0021] Finally, the method includes generating a signal indicative of the device's health prediction based on a probability density function, an aging degradation model, and EOL boundary conditions. The signal indicative of the health prediction may include any of a life curve, a reliability curve, a failure probability density curve, remaining life values, RUL values, reliability values, unreliability values, failure probability values, and / or similar values or curves related to the predicted device health and / or the predicted device reliability.

[0022] Various embodiments may preferably implement the following features. Preferably, the method further includes providing or obtaining a device model, the device model includes an equation having an aging degradation variable as a device parameter, the EOL boundary conditions are based on the device model, and the likelihood calculation is based on the device model.

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[0026] By providing or obtaining a device model, the EOL boundary conditions better reflect the actual failure, and the likelihood better reflects the actual information contained in the measured values. Therefore, the prediction becomes more accurate. In this way, unexpected device failures are prevented and unnecessary preventive maintenance is reduced.

[0027] Preferably, the method further includes providing or obtaining a monitoring model, the monitoring model includes an equation having observable quantities and aging degradation variables, the monitoring model is based on a device model, and calculating the likelihood is based on the monitoring model.

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[0031] By providing or obtaining a monitoring model, the actual information contained in the measured values may be extracted more completely and accurately. Therefore, the prediction becomes more accurate. In this way, unexpected device failures are prevented and unnecessary preventive maintenance is reduced.

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[0035] Preferably, the generation of the signal includes calculating a Remaining Useful Lifetime (RUL) value.

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[0037] Additional signals indicating soundness may include the lifetime PDF, the hazard function, and the mean time to failure (MTTF). The lifetime PDF indicates the progression of reliability over time and describes the net probability flow from Ω a The lifetime PDF describes the net probability flow from Ω

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[0039] MTTF is the expected, i.e., predicted, average time until device failure. It is

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[0041] Note that MTTF is not necessarily equal to t EOL In fact, the reliability at MTTF is often unacceptable, and t EOL is earlier. By calculating the RUL value, predictions obtained from the aging models of multiple devices become comparable and manageable. For example, bottlenecks in overhauls and replacements that could lead to device failures may be identified in advance, and thus their occurrence is prevented. In this way, it becomes easy to manage the device fleet without the risk of failure.

[0042] Preferably, the aging model includes an equation having at least two aging variables of the device, calculating the probability density function includes calculating the joint probability density function of at least two aging variables, calculating the likelihood includes calculating the likelihood for at least two aging variables and the first data, and updating the probability density function includes updating the joint probability density function.

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[0044] When the aging degradation model includes an equation having at least two aging degradation variables of the device, the prediction obtained from the aging degradation model has a higher dimension and may thus be more reliable. The interdependencies between different failure scenarios can be more reliably identified. In this way, unexpected device failures are prevented.

[0045] Preferably, the aging degradation model includes an equation having at least two aging degradation variables of the device, calculating the probability density function includes calculating the joint probability density function of each aging degradation variable of the device, measuring the observable quantity includes measuring one or more observable quantities of the device, the first data represents the measured value of the observable quantity, calculating the likelihood includes calculating the likelihood for the aging degradation variables and the first data, and updating the probability density function includes updating the joint probability density function.

[0046] The method is also suitable for monitoring a fleet of at least two devices as described above. For example, in a system comprising a plurality of devices, it may be even more important to monitor the devices and predict the failure of a single device that may affect the entire system.

[0047] In this case, measuring the observable quantity includes measuring one or more observable quantities of the device. In other words, for each device monitored using this hybrid monitoring method, at least one observable quantity is measured. The observable quantities may be measured together for all devices at once, for example, at regular time intervals. For example, if different devices or different sensors provide measurements at different intervals or based on events, the observable quantities may be measured at different times. The first data represents the measured values of the observable quantities, that is, the first data can represent any measured value of any observable quantity available at a given time. If the observable quantities are measured at different times, the first data can represent only a part of a single observable quantity or only the measured value of a single observable quantity at a given time.

[0048] The hybrid monitoring method according to the present disclosure may be combined with known monitoring methods. For example, some parts of the device may be monitored as described above, while some parts of the device may be modeled using an aging degradation model that does not update the probability density function without measurements. In this way, existing devices without online monitoring capabilities may be included in the monitoring.

[0049] If the aging degradation model includes an equation having aging degradation variables of at least two devices, the method may be applied to a fleet of devices where preventive maintenance is particularly important. Furthermore, the predictions obtained from the aging degradation model may have a higher dimension and thus be more reliable. Interdependencies between different devices and bottlenecks in future maintenance may be more reliably identified. In this way, unexpected device failures are efficiently prevented.

[0050] Preferably, the device is selected from the group including a circuit breaker, a transformer, a power electronics device, and an energy storage device. For example, when using a circuit breaker as a reference, the opening and closing speed of the movable contact, the moving amount of the movable contact, the total moving amount of the movable contact, the excessive moving amount of the movable contact, the repulsive amount of the movable contact, the opening and closing time, and the opening and closing peak coil current of the circuit breaker, or at least one of its observable quantities such as the current, voltage, and further physical quantity, electrical quantity, or chemical quantity of the transformer, power electronics device, or energy storage device must be considered.

[0051] The power electronics device can be, for example, a converter, an inverter, or a cycloconverter. The energy storage device can be, for example, a battery, a capacitor, a fuel cell, or a supercapacitor.

[0052] The aging variables that enable prediction of device failures may include, for example, driving spring stiffness, friction coefficient, or coil resistance.

[0053] By applying the method to a device selected from the group including a circuit breaker, a transformer, a power electronics device, and an energy storage device, it is possible to prevent failures for some of the most important basic devices. Furthermore, accurate monitoring becomes possible for devices where it is particularly difficult to observe and display failure scenarios that are difficult to prevent.

[0054] By applying the method to a device selected from the group including a circuit breaker, a transformer, a power electronics device, and an energy storage device, it is possible to prevent failures for some of the most important basic devices. Furthermore, accurate monitoring becomes possible for devices where it is particularly difficult to observe and display failure scenarios that are difficult to prevent.

[0055] By measuring one of the opening and closing speed of the movable contact of the circuit breaker, the moving amount of the movable contact, the total moving amount of the movable contact, the excessive moving amount of the movable contact, the repulsive amount of the movable contact, the opening and closing time of the circuit breaker, and the opening and closing peak coil current of the circuit breaker, observable quantities can be easily measured, and at the same time, they are highly reliable and beneficial. In this way, the method can be easily applied to many devices, and device failures can be efficiently prevented.

[0056] Preferably, the method further includes triggering maintenance, overhaul, replacement, or load reduction of the device in response to a generated signal indicating an important soundness prediction within a predetermined amount of time.

[0057] For example, when the device operates within the device fleet, if the reliability of the device is low, the load of the device may decrease, and if the reliability of the device is high, the load of the device may increase. In this way, device failures may be delayed until the device can be maintained or replaced.

[0058] In another example, the replacement of the device may be automatically triggered. The replacement device may already be installed, and it only needs to be activated when the generated signal indicates an important soundness prediction, such as a high failure probability.

[0059] Important soundness predictions may include, for example, an RUL that is too short, an unreliability that is too high, or similar soundness indicators that exceed and / or violate important thresholds or criteria.

[0060] By triggering maintenance, overhaul, replacement, or load reduction, the prediction ability of the method is automatically and consistently utilized. In this way, human errors that may lead to unnecessary device failures are prevented.

[0061] Preferably, the method further includes indicating a warning in response to a generated signal indicating a critical health prediction within a predetermined amount of time for use in future maintenance scheduling.

[0062] For example, a warning may be indicated when the predicted reliability value of a device falls below a predetermined reliability value, for example, below 0.9 or 0.95, for a predetermined period of time, for example, one week. In response to the warning, the device may be scheduled for regular weekly maintenance, thus preventing the failure of the device without the need for emergency measures. At the same time, since the safety margin is based not on inference but on the best available knowledge of the technical state of the device, the warning enables the wearable component or device to be used to its optimal lifespan.

[0063] By providing a warning in response to a generated signal indicating a critical health prediction within a predetermined amount of time, an organized and balanced maintenance schedule is facilitated. In this way, the health status balance of the devices within the fleet may be achieved, and the failure of the devices may be efficiently prevented.

[0064] The objective is further addressed by a system or device for monitoring a device. The system comprises at least one sensor configured to measure an observable quantity related to the operating state of the device, a memory configured to store an aging degradation model, wherein the aging degradation model includes at least one equation having end-of-life (EOL) boundary conditions and aging degradation variables of the device, a controller or another device having appropriate computing capabilities configured to calculate a time-dependent probability density function for the aging degradation variables based on solving at least one equation from the aging degradation model having EOL boundary conditions, obtain first data representing the measured value of the observable quantity, calculate a likelihood for the aging degradation variables from the first data, update the calculated probability density function of the aging degradation variables based on the likelihood, and generate a signal indicating the health prediction of the device based on the probability density function, the aging degradation model, and the EOL boundary conditions.

[0065] The objective is further addressed by a system or device for monitoring a device. The system comprises at least one sensor configured to measure an observable quantity related to the operating state of the device, a controller or another device having appropriate computing capabilities configured to calculate a time-dependent probability density function for the aging degradation variables based on solving at least one equation from the aging degradation model having EOL boundary conditions, obtain first data representing the measured value of the observable quantity, calculate a likelihood for the aging degradation variables from the first data, update the calculated probability density function of the aging degradation variables based on the likelihood, and generate a signal indicating the health prediction of the device based on the probability density function, the aging degradation model, and the EOL boundary conditions. The aging degradation model may include EOL boundary conditions and at least one equation having aging degradation variables of the device. The system or device may further comprise a memory configured to store the aging degradation model.

[0066] The objective is further addressed by a system or device for monitoring a device. The system is configured to measure at least one observable quantity related to the operating state of the device, and to calculate a probability density function over time for an aging degradation variable based on solving at least one equation from an aging degradation model having end-of-life (EOL) boundary conditions, where the boundary conditions include a first boundary condition and a second boundary condition, the first boundary condition being a no-flux boundary condition, and the second boundary condition being an absorption boundary condition or a partial absorption boundary condition; to obtain first data representing a measured value of the observable quantity; to calculate a likelihood for the aging degradation variable from the first data; to update the calculated probability density function of the aging degradation variable based on the likelihood; and to generate a signal indicating a health prediction of the device based on the probability density function, the aging degradation model, and the EOL boundary conditions, and includes a controller or another device having appropriate computing capabilities. The aging degradation model may include an EOL boundary condition and at least one equation having an aging degradation variable of the device. The system or device may further include a memory configured to store the aging degradation model.

[0067] The controller may comprise at least one integrated circuit. Alternatively or additionally, the controller may comprise a memory.

[0068] Various embodiments can preferably implement features corresponding to those described above with reference to the method, along with corresponding technical effects and advantages.

[0069] The following items refer to preferred embodiments. 1. A method for monitoring a device, comprising: providing or obtaining an aging degradation model, the aging degradation model including an end-of-life (EOL) boundary condition and at least one equation having an aging degradation variable of the device; Calculating a time-dependent probability density function for an aging variable based on solving at least one equation from an aging model having an EOL boundary condition; Measuring an observable quantity related to the operating state of the device; Obtaining first data representing a measured value of the observable quantity; Calculating a likelihood for the aging variable from the first data; Updating the calculated probability density function of the aging variable based on the likelihood; Generating a signal indicating a health prediction of the device based on the probability density function, the aging model, and the EOL boundary condition A method comprising.

[0070] 2. A method for monitoring a device, comprising: Calculating a time-dependent probability density function for an aging variable based on solving at least one equation from an aging model having an end-of-life (EOL) boundary condition; Measuring an observable quantity related to the operating state of the device; Obtaining first data representing a measured value of the observable quantity; Calculating a likelihood for the aging variable from the first data; Updating the calculated probability density function of the aging variable based on the likelihood; Generating a signal indicating a health prediction of the device based on the probability density function, the aging model, and the EOL boundary condition A method comprising.

[0071] 3. The method according to item 2, wherein the aging model includes an EOL boundary condition and at least one equation having an aging variable of the device; 4. Further comprising providing or obtaining a device model, the device model including an equation having an aging variable as a device parameter, the EOL boundary condition is based on the device model, the calculation of the likelihood is based on the device model, The method according to any one of items 1 to 3.

[0072] 5. Further including providing or obtaining a monitoring model, the monitoring model including an equation having observable quantities and aging degradation variables, the monitoring model being based on a device model, calculating a likelihood being based on the monitoring model, The method according to any one of items 1 to 4.

[0073] 6. Generating a signal includes calculating an expression of time-dependent unreliability based on a probability density function, an aging degradation model, and EOL boundary conditions, the method according to any one of items 1 to 5.

[0074] 7. Generating a signal includes calculating a remaining useful life (RUL) value, the method according to any one of items 1 to 6.

[0075] 8. The aging degradation model includes an equation having at least two aging degradation variables of the device, calculating a probability density function includes calculating a joint probability density function of at least two aging degradation variables, calculating a likelihood includes calculating a likelihood for at least two aging degradation variables and first data, updating a probability density function includes updating a joint probability density function, The method according to any one of items 1 to 7.

[0076] 9. The aging degradation model includes an equation having aging degradation variables of at least two devices, calculating a probability density function includes calculating a joint probability density function of the aging degradation variables of each of the devices, measuring an observable quantity includes measuring one or more observable quantities of the device, the first data representing measured values of the observable quantities, Calculating the likelihood includes calculating the likelihood for the aging degradation variable and the first data, Updating the probability density function includes updating the joint probability density function, The method according to any one of items 1 to 8.

[0077] 10. The device is selected from the group including a circuit breaker, a transformer, a power electronics device, and an energy storage device, The observable quantity is one of the opening / closing speed of the moving contact of the circuit breaker, the moving amount of the moving contact, the total moving amount of the moving contact, the excessive moving amount of the moving contact, the repulsive amount of the moving contact, the opening / closing time of the circuit breaker, and the opening / closing peak coil current of the circuit breaker, The method according to any one of items 1 to 9.

[0078] 11. Triggering maintenance, overhaul, replacement, or load reduction of the device in response to a generated signal indicating an important soundness prediction within a predetermined amount of time The method according to any one of items 1 to 10, further including.

[0079] 12. Indicating a warning in response to a generated signal indicating an important soundness prediction within a predetermined amount of time, which is used for future maintenance scheduling The method according to any one of items 1 to 11, further including.

[0080] 13. A system or device for monitoring a device, At least one sensor configured to measure an observable quantity related to the operating state of the device, A memory configured to store an aging degradation model, the aging degradation model including at least one equation having end-of-life (EOL) boundary conditions and aging degradation variables of the device, the memory, Calculating a time-dependent probability density function for the aging degradation variable based on solving at least one equation from the aging degradation model having EOL boundary conditions, Obtain first data representing a measured value of an observable quantity, calculate the likelihood for the aging degradation variable from the first data, update the calculated probability density function of the aging degradation variable based on the likelihood, generate a signal indicating the health prediction of the device based on the probability density function, the aging degradation model, and the EOL boundary condition A controller configured as follows A system or device comprising.

[0081] 14. The memory is to store a device model, the device model including an equation having an aging degradation variable as a device parameter, the EOL boundary condition being based on the device model, and / or to store a monitoring model, the monitoring model including an equation having an observable quantity and an aging degradation variable, the monitoring model being based on the device model is further configured to perform The controller is further configured to calculate the likelihood based on the device model and / or the monitoring model The system or device according to item 13.

[0082] 15. The controller is further configured to generate a signal using to calculate an expression of the failure probability over time based on the probability density function, the aging degradation model, and the EOL boundary condition and / or using to calculate a remaining useful life (RUL) value, the system or device according to item 13 or 14 16. The memory, the controller, and at least one sensor are configured to implement and / or execute the method according to any one of items 1 to 10 The system or device according to any one of items 13 to 15.

[0083] 17. The memory is further configured to store an aging degradation model including an equation having at least two aging degradation variables of the device, The controller, Calculates the probability density using the calculation of the joint probability density function of at least two aging degradation variables, Calculates the likelihood using the calculation of the likelihood for at least two aging degradation variables and the first data, Updates the probability density function using the update of the joint probability density function And is further configured to The system or device according to any one of items 13 to 16.

[0084] 18. The memory is further configured to store an aging degradation model including an equation having aging degradation variables of at least two devices, The controller, Calculates the probability density using the calculation of the joint probability density function of the aging degradation variables of each of at least two devices, Calculates the likelihood using the calculation of the likelihood for the aging degradation variables and the first data, Updates the probability density function using the update of the joint probability density function And is further configured to The sensor is further configured to measure one or more observable quantities of at least two devices, and the first data represents a measured value of the observable quantity, The system or device according to any one of items 13 to 17.

[0085] 19. The device is selected from the group including a circuit breaker, a transformer, a power electronics device, and an energy storage device, The sensor is further configured to measure an observable quantity including one of the opening and closing speed of the movable contact of the circuit breaker, the moving amount of the movable contact, the total moving amount of the movable contact, the excessive moving amount of the movable contact, the repulsive amount of the movable contact, the opening and closing time of the circuit breaker, and the opening and closing peak coil current of the circuit breaker, or the current, voltage, and further physical quantity, electrical quantity, or chemical quantity of a transformer, a power electronics device, or an energy storage device. The system or device according to any one of items 13 to 18.

[0086] 20. The controller is further configured to trigger maintenance, overhaul, replacement, or load reduction of the device in response to a generated signal indicating an important soundness prediction within a predetermined amount of time. The system or device according to any one of items 13 to 18.

[0087] 21. The controller is further configured to show a warning in response to a generated signal indicating an important soundness prediction within a predetermined amount of time, which is used for future maintenance scheduling. The system or device according to any one of items 13 to 20.

[0088] 22. A system or device for monitoring a device, at least one sensor configured to measure an observable quantity related to the operating state of the device, calculate a probability density function over time for an aging degradation variable based on solving at least one equation from an aging degradation model having end-of-life (EOL) boundary conditions, acquire first data representing a measured value of the observable quantity, calculate a likelihood for the aging degradation variable from the first data, update the calculated probability density function of the aging degradation variable based on the likelihood, generate a signal indicating the soundness prediction of the device based on the probability density function, the aging degradation model, and the EOL boundary conditions a controller configured as such, and A system or device comprising

[0089] 23. A memory configured to store an aging degradation model The system or device according to item 22, further comprising

[0090] 24. The system or device according to item 22 or 24, wherein the aging degradation model includes an EOL boundary condition and at least one equation having an aging degradation variable of the device

[0091] 25. The memory is Storing a device model, the device model including an equation having an aging degradation variable as a device parameter, and the EOL boundary condition being based on the device model, and / or Storing a monitoring model, the monitoring model including an equation having an observable quantity and an aging degradation variable, and the monitoring model being based on the device model Further configured to perform The controller is further configured to calculate a likelihood based on the device model and / or the monitoring model The system or device according to any one of items 22 to 24

[0092] 26. The controller is further configured to generate a signal by using to calculate an expression of the failure probability over time based on a probability density function, an aging degradation model, and an EOL boundary condition, and / or by using to calculate a remaining useful life (RUL) value. The system or device according to any one of items 22 to 25 27. The memory, the controller, and at least one sensor are configured to implement and / or execute the method according to any one of items 1 to 10 The system or device according to any one of items 22 to 26

[0093] 28. The memory is further configured to store an aging degradation model including an equation having at least two aging degradation variables of the device, The controller, using to calculate a probability density by calculating a joint probability density function of at least two aging degradation variables, using to calculate a likelihood by calculating a likelihood for at least two aging degradation variables and first data, using to update the probability density function by updating the joint probability density function is further configured as follows, The system or apparatus according to any one of items 22 to 27.

[0094] 29. The memory is further configured to store an aging degradation model including an equation having aging degradation variables of at least two devices, The controller, using to calculate a probability density by calculating a joint probability density function of the aging degradation variables of each of at least two devices, using to calculate a likelihood by calculating a likelihood for the aging degradation variables and first data, using to update the probability density function by updating the joint probability density function is further configured as follows, The sensor is further configured to measure one or more observable quantities of at least two devices, and the first data represents a measured value of the observable quantity, The system or apparatus according to any one of items 22 to 28.

[0095] 30. The device is selected from the group including a circuit breaker, a transformer, a power electronics device, and an energy storage device, The sensor is further configured to measure an observable quantity including one of the opening and closing speed of the movable contact of the circuit breaker, the moving amount of the movable contact, the total moving amount of the movable contact, the excessive moving amount of the movable contact, the repulsive amount of the movable contact, the opening and closing time of the circuit breaker, and the opening and closing peak coil current of the circuit breaker, or the current, voltage, and further physical quantity, electrical quantity, or chemical quantity of a transformer, a power electronics device, or an energy storage device. The system or device according to any one of items 22 to 29.

[0096] 32. The controller is further configured to trigger maintenance, overhaul, replacement, or load reduction of the device in response to a generated signal indicating an important soundness prediction within a predetermined amount of time. The system or device according to any one of items 22 to 31.

[0097] 33. The controller is further configured to indicate a warning in response to a generated signal indicating an important soundness prediction within a predetermined amount of time, which is used for future maintenance scheduling. The system or device according to any one of items 22 to 32.

[0098] According to a preferred embodiment according to any one of items 1 to 33, the boundary conditions include a first boundary condition and a second boundary condition. The first boundary condition is a zero-flux boundary condition, and the second boundary condition is an absorption boundary condition or a partial absorption boundary condition. When the boundary conditions are thus distinguished into the first zero-flux boundary condition and the second absorption boundary condition or partial absorption boundary condition, the aging degradation may be accurately modeled. Therefore, the prediction can be more accurate, and the maintenance can be more efficient and effective.

[0099] The exemplary embodiments disclosed herein are directed to providing features that will be readily apparent by reference to the following description when used in conjunction with the accompanying drawings. According to various embodiments, exemplary systems, methods, devices, and computer program products are disclosed herein. However, it is understood that these embodiments are presented by way of example and not limitation, and it will be apparent to those skilled in the art reading this disclosure that various modifications to the disclosed embodiments can be made within the scope of this disclosure.

[0100] Accordingly, this disclosure is not limited to the exemplary embodiments and applications described and illustrated herein. Additionally, the particular order and / or hierarchy of steps in the methods disclosed herein are merely exemplary approaches. Based on design preferences, the particular order or hierarchy of steps in the disclosed methods or processes can be rearranged while remaining within the scope of this disclosure. Thus, those skilled in the art will understand that the methods and techniques disclosed herein present various steps or operations in a sample order, and this disclosure is not limited to the particular order or hierarchy presented, unless otherwise specified.

[0101] The above and other aspects and their implementations are described in more detail in the drawings, description, and claims.

Brief Description of the Drawings

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[0103] FIG. 1 shows a diagram of a method according to an embodiment of the present disclosure.

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[0106] According to one embodiment, the first step 101 includes providing or obtaining a device model, the device model includes an equation having an aging variable as a device parameter, the EOL boundary condition is based on the device model, and the likelihood calculation is based on the device model.

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[0110] By providing or obtaining a device model in Project 101, the EOL boundary conditions better reflect the actual failure risk, and the likelihood better reflects the actual information contained in the measurement values. Therefore, the prediction becomes more localized and accurate. In this way, unexpected device failures are prevented and unnecessary preventive maintenance is reduced.

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[0113] According to one embodiment, the aging model includes an equation having at least two aging variables of the device. Calculating the probability density function includes calculating the joint probability density function of at least two aging variables. Calculating the likelihood includes calculating the likelihood for at least two aging variables and the first data. Updating the probability density function includes updating the joint probability density function.

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[0115] When the aging model includes an equation having at least two aging variables of the device, the prediction obtained from the aging model has a higher dimension and may therefore be more reliable. The interdependencies between different failure scenarios can be more reliably identified. In this way, unexpected device failures are prevented.

[0116] According to one embodiment, the aging model includes an equation having aging variables of at least two devices, calculating a probability density function includes calculating a joint probability density function of the aging variables of each of the devices, measuring an observable quantity includes measuring one or more observable quantities of the device, the first data represents a measured value of the observable quantity, calculating a likelihood includes calculating a likelihood for the aging variables and the first data, and updating the probability density function includes updating the joint probability density function.

[0117] The method is also suitable for monitoring a fleet of at least two devices, as described above. For example, in a system comprising a plurality of devices, it may be even more important to monitor the devices and predict the failure of a single device that may affect the entire system.

[0118] In this case, measuring an observable quantity includes measuring one or more observable quantities of the device. In other words, for each of the devices monitored using this hybrid monitoring approach, at least one observable quantity is measured. The observable quantities may be measured together for all devices at once, for example, at regular time intervals. For example, if different devices or different sensors provide measurements at different intervals or based on events, the observable quantities may be measured at different times. The first data represents a measured value of the observable quantity, i.e., the first data can represent any measured value of any observable quantity available at a given time. If the observable quantities are measured at different times, the first data can represent only a part of a single observable quantity or only the measured value of a single observable quantity at a given time.

[0119] The hybrid monitoring method according to the present disclosure may be combined with known monitoring techniques. For example, some parts of the device may be monitored as described above, while some parts of the device may be modeled using an aging degradation model that does not have measurement values and does not update the probability density function. In this way, existing devices without online monitoring capabilities may be included in the method.

[0120] When the aging degradation model includes an equation having aging degradation variables of at least two devices, the method may be applied to a fleet of devices where preventive maintenance is particularly important. Furthermore, the predictions obtained from the aging degradation model may have a higher dimension and thus may be more reliable. The interdependencies between different devices and the bottlenecks of future maintenance may be more reliably identified. In this way, unexpected device failures are efficiently prevented.

[0121]

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[0122] According to one embodiment, the fourth step 104 includes providing or obtaining a monitoring model, the monitoring model includes an equation having observable quantities and aging degradation variables, the monitoring model is based on a device model, and the calculation of the likelihood is based on the monitoring model.

[0123]

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[0125] By providing or obtaining a monitoring model, the actual information contained in the measured values may be extracted more completely and accurately. Therefore, the prediction becomes more localized and accurate. In this way, unexpected device failures are prevented and unnecessary preventive maintenance is reduced.

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[0131] In the ninth step 109, using the corrected state, restart from the time t in the sixth step 106 m and restart.

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[0133] At any point in the method, a signal indicating the health prediction of the device may be generated. The health prediction of the device is based on a probability density function, an aging degradation model, and EOL boundary conditions. For example, a signal indicating the health prediction of the device may be generated after the sixth step 106 or after the eighth step 108.

[0134] According to one embodiment, the generation of the signal includes calculating an expression of future time-dependent unreliability based on a probability density function, an aging degradation model, and EOL boundary conditions.

[0135]

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[0137] By calculating the expression of time-dependent unreliability, the prediction obtained from the aging degradation model becomes understandable and executable. The time-dependent failure probability prediction enables further analysis and allows for a flexible response adjusted for both technical requirements and the remaining operating time of the device. In this way, it becomes easier to manage the optimal lifespan of the device without the risk of failure.

[0138] According to one embodiment, the generation of the signal includes calculating a Remaining Useful Life (RUL) value.

[0139] The RUL value reflects the predicted remaining amount of time until the device can no longer be considered useful according to the operating requirements. The RUL is obtained by calculating the time-dependent failure probability. A predetermined threshold of the failure probability defines the acceptable unreliability of the device. When the failure probability exceeds the threshold P EOL , that is, 1 - R(t EOL ) ≧ P EOL at the time point t EOL , it is the predicted time point when the device can no longer be considered useful. Then, the RUL can be obtained as the amount of time from t EOL - t, that is, the amount of time until t EOL .

[0140] Additional signals indicating soundness may include the lifetime PDF, the hazard function, and the mean time to failure (MTTF). The lifetime PDF indicates the progression of reliability over time and describes the net probability current flow from Ω a The hazard function is the failure rate at time t, conditional on survival after time t. It is

[0141] [Number]

[0142] The MTTF is the expected, i.e., predicted, amount of time until device failure. It is

[0143] [Number]

[0144] By calculating the RUL value, predictions obtained from the aging degradation models of multiple devices become comparable and manageable. For example, bottlenecks in overhauls and replacements that may lead to device failures may be identified in advance, thus preventing device failures. In this way, it becomes easier to manage the device fleet without the risk of failure.

[0145] [Number]

[0146] According to one embodiment, the method further includes triggering maintenance, overhaul, replacement, or load reduction of the device in response to a generated signal indicating a critical soundness prediction within a predetermined amount of time.

[0147]

[0148] ​For example, when a device operates within a fleet of devices, if the reliability of the device is low, the load on the device may decrease, and if the reliability of the device is high, the load on the device may increase. In this way, a device failure may be delayed until the device can be maintained or replaced.

[0149] In another example, the replacement of a device may be automatically triggered. The replacement device may already be installed and only needs to be activated when the generated signal indicates an important health prediction, such as a high probability of failure.

[0150] By triggering maintenance, overhaul, replacement, or load reduction, the predictive capabilities of the method are automatically and consistently utilized. In this way, human errors that could lead to unnecessary device failures are prevented.

[0151] According to one embodiment, the method further includes indicating a warning in response to a generated signal that indicates an important health prediction within a predetermined amount of time for use in future maintenance scheduling.

[0152] For example, a warning may be indicated when it is predicted that a device will fall below a predetermined reliability value, such as below 0.9, within a predetermined time period, such as within one week or one month. In response to the warning, the device may be scheduled for regular weekly or monthly maintenance, thus preventing device failure without the need for emergency measures. At the same time, since the safety margin is based not on inference but on the best available knowledge of the technical state of the device, the warning enables the wearable parts or the device to be used to the optimal extent of their lifespan.

[0153] By indicating a warning in response to a generated signal indicating important health predictions within a specified amount of time, an organized and balanced maintenance schedule is facilitated. In this way, the balance of the health states of the devices in the fleet may be achieved, and device failures may be efficiently prevented.

[0154] According to one embodiment, the device is selected from the group including a circuit breaker, a transformer, a power electronics device, and an energy storage device, and at least one observable quantity is one of the opening / closing speed of the movable contact of the circuit breaker, the moving amount of the movable contact, the total moving amount of the movable contact, the excessive moving amount of the movable contact, the repulsive amount of the movable contact, the opening / closing time of the circuit breaker, and the opening / closing peak coil current of the circuit breaker. Additionally or alternatively, the observable quantity may include a current value, a voltage value, and / or a state of charge value.

[0155] The power electronics device can be, for example, one of a converter, an inverter, or a cycloconverter. The energy storage device can be, for example, a battery, a capacitor, a fuel cell, or a supercapacitor.

[0156] The aging degradation variables of the circuit breaker that enable prediction of device failures may include, for example, driving spring stiffness, friction constant, or pull-out coil resistance.

[0157] By applying the method to a device selected from the group including a circuit breaker, a transformer, a power electronics device, and an energy storage device, failures can be prevented for some of the most important base devices. Furthermore, accurate monitoring becomes possible for devices where it is particularly difficult to observe and display failure scenarios that are difficult to prevent.

[0158] By applying the method to a device selected from a group including a circuit breaker, a transformer, a power electronics device, and an energy storage device, it is possible to prevent failures in some of the most important basic devices. Furthermore, accurate monitoring becomes possible for devices where it is particularly difficult to observe and display failure scenarios that are difficult to prevent.

[0159] By measuring one of the opening and closing speed of the movable contact of the circuit breaker, the moving amount of the movable contact, the total moving amount of the movable contact, the excessive moving amount of the movable contact, the repulsive amount of the movable contact, the opening and closing time of the circuit breaker, and the opening and closing peak coil current of the circuit breaker, the observable quantity can be easily measured, and at the same time, it is highly reliable and beneficial. In this way, the method can be easily applied to many devices, and failures of the devices are efficiently prevented.

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[0163] Figure 3 shows a diagram of an exemplary predicted output according to a further embodiment of the present disclosure.

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[0165] Figure 4 shows a diagram of an exemplary predicted output according to a further embodiment of the present disclosure.

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[0167] In Sub - figure b), three reliability curves are plotted for the same different aging degradation rates as in Sub - figure a). The figure shows the reliability as a value from 0 to 1 on the vertical axis and the lifetime in years on the horizontal axis. Each curve represents the reliability as a function of time for a specific aging degradation rate of the second aging degradation variable. For example, when the aging degradation rate f2 = 0 V / y, the predicted reliability after a 40 - year lifetime is 0.3, which corresponds to a 70% failure rate. In other words, after 40 years, the reliability of the device is expected to be below 0.3. As seen in Sub - figure b), the predicted reliability drops particularly rapidly within a short critical time frame that depends on the aging degradation rate. For example, for an aging degradation rate of f2=-0.8 V / y, the reliability drops from 0.9 to 0.2 within 5 years after the 22nd year. Similar rapid drops in reliability can be observed after the 25th year and after the 35th year for aging degradation rates of f2=-0.4 V / y and f2 = 0 V / y, respectively.

[0168] Therefore, the predicted reliability curve makes it possible to identify the time after which the reliability deteriorates rapidly, and thus it is particularly effective to consider maintenance or replacement after this time.

[0169] In Sub - figure c), three failure probability density curves are plotted for the same different aging degradation rates as in Sub - figure a). The figure shows the failure probability density on the vertical axis and the time in years on the horizontal axis. Each curve represents the failure probability density as a Gaussian function of time for a specific aging degradation rate. For example, for an aging degradation rate of f2=-0.8 V / y, the failure probability density has a peak at time t = 24 y. In other words, the time when the likelihood of a failure is highest is around 24 years. This corresponds to the drop in reliability around that time, as observed in Sub - figure b). The peak of the failure probability density curve corresponds to the time frame of the steep drop in the observable quantity observed in Sub - figure b).

[0170] Generally speaking, the failure probability density can be obtained as the derivative of the failure probability with respect to time. In other words, the failure probability density can be obtained as the derivative of 1 minus the reliability with respect to time. Conversely, the reliability can be obtained as the integral of 1 minus the failure probability density with respect to time.

[0171] The three curves according to subfigure c) show different degrees of localization. The more localized the curve is, the more accurately the failure time can be predicted. Since the solution of the FPE results in a spread of the probability density, the update of the calculated probability density function of the age degradation variable based on the likelihood according to the embodiment enables a more localized failure probability density curve.

[0172] Each of the above-described life curve, reliability curve, and failure probability density curve is a signal indicating the health prediction. Therefore, the signal may include any of the above curves, any value according to any of the curves, and / or remaining life values, RUL values, reliability values, non - reliability values, failure probability values, or similar values or curves related to the predicted device health and / or predicted device reliability.

[0173] FIG. 5 shows a comparison of an exemplary prediction according to a known method with an exemplary prediction output according to a further embodiment of the present disclosure.

[0174] In the figure shown in FIG. 5, the RUL is plotted on the vertical axis with respect to the time on the horizontal axis. The dashed - dotted line 501 shows the deterministic remaining useful lifetime (RUL) prediction. This RUL corresponds to the difference between the predicted useful lifetime and the elapsed time. In the example shown in FIG. 5, the predicted deterministic useful lifetime is 37 years. Therefore, for example, at time t = 10y, the RUL is RUL = 37y - 10y = 27y. The deterministic RUL prediction is only a linear continuation of the initial prediction of the useful lifetime.

[0175] The solid curve 502 shows an updated remaining useful lifetime (RUL) prediction according to one embodiment. The RUL can be calculated as the difference between the updated RUL, i.e., the updated prediction of the remaining useful lifetime, and the time elapsed since the update. For example, at time t5 = 5y, the updated useful lifetime is 25.5 years. Thus, for example, at time t6 = 6y = t5 + 1y, one year after the update, the RUL can be calculated as RUL = 25.5y - 1y = 24.5y. However, at time t6 = 6y, the updated useful lifetime is 23.7 years. Thus, the figure in FIG. 5 shows a discontinuity at time t6 = 6y. The updated RUL prediction does not correspond to a direct continuation of the previous prediction of the useful lifetime.

[0176] [Number]

[0177] FIG. 6 shows a diagram of a system according to a further embodiment of the present disclosure. The system 600 includes at least one sensor 601. The sensor is configured to measure an observable quantity related to the operating state of the device.

[0178] The system 600 further includes a memory 610. The memory 610 is configured to store an aging model 611, and the aging model 611 includes end-of-life (EOL) boundary conditions and at least one equation having aging variables of the device.

[0179] Furthermore, the memory is configured to store a device model 612. The device model 612 includes an equation having aging variables as device parameters. In this case, the EOL boundary conditions are based on the device model 612. The calculation of the likelihood is based on the device model 612. According to other embodiments, the memory may not store the device model 612.

[0180] Further, the memory is configured to store the monitoring model 613. The monitoring model 613 includes equations having observable quantities and aging degradation variables. The monitoring model 613 is based on the device model 612. The calculation of the likelihood is based on the monitoring model 613. According to other embodiments, the memory may not store the monitoring model 613.

[0181] The memory 610 may store any computer program and / or model according to any of the methods disclosed herein.

[0182] The system 600 further includes a controller 620. The controller is configured to calculate a probability density function over time for the aging degradation variables based on solving at least one equation from the aging degradation model 611 having EOL boundary conditions. The controller is further configured to obtain first data representing measured values of observable quantities from the sensor 601. The controller is further configured to calculate a likelihood for the aging degradation variables from the first data. The controller is further configured to update the calculated probability density function of the aging degradation variables based on the likelihood. The controller is further configured to generate a signal indicating the health prediction of the device based on the probability density function, the aging degradation model 611, and the EOL boundary conditions.

[0183] The controller 620 may be configured to execute any of the methods disclosed herein. The controller 620 can access the data stored in the memory 610 and / or write data to the memory 610. The controller 620 can obtain data from the sensor 601 and / or trigger the measurement value of the sensor 601. The controller 620 may include at least one integrated circuit. Alternatively or additionally, the controller 620 may include the memory 610.

[0184] Although various embodiments of the present disclosure have been described above, it should be understood that they are presented by way of example only and not by way of limitation. Similarly, the various figures can depict an exemplary architecture or configuration provided to enable those skilled in the art to understand the exemplary features and functions of the present disclosure. However, such persons will understand that the present disclosure is not limited to the illustrated exemplary architecture or configuration and can be implemented using various alternative architectures and configurations. Further, as will be understood by those skilled in the art, one or more features of one embodiment can be combined with one or more features of another embodiment described herein. Accordingly, the breadth and scope of the present disclosure should not be limited by any of the above-described exemplary embodiments.

[0185] It should also be understood that any reference in this specification to an element using designations such as "first," "second," etc. generally does not limit the quantity or order of those elements. Rather, these designations can be used herein as a convenient means of distinguishing between two or more elements or instances of an element. Thus, a reference to first and second elements does not mean that only two elements can be used or that the first element must precede the second element in any way.

[0186] Furthermore, those skilled in the art will understand that information and signals can be represented using any one of a variety of different technologies and techniques. For example, the data, instructions, commands, information, signals, bits, and symbols that can be referenced in the above description can be represented by voltage, current, electromagnetic waves, magnetic fields or magnetic particles, optical fields or optical particles, or any combination thereof.

[0187] Those skilled in the art will further understand that any one of the various exemplary logical blocks, units, processors, means, circuits, methods, and functions described in connection with the aspects disclosed herein can be implemented by electronic hardware (e.g., digital implementation, analog implementation, or a combination of the two), firmware, various forms of programs or design codes that incorporate instructions (which can be referred to herein, for convenience, as "software" or "software units"), or any combination of these techniques.

[0188] To clearly illustrate this interchangeability of hardware, firmware, and software, various exemplary components, blocks, units, circuits, and processes have been generally described in terms of their functions. Whether such functions are implemented as hardware, as firmware, or as software, or as a combination of these techniques, depends on the particular application and design constraints imposed on the overall system. Those skilled in the art can implement the described functions in various ways for each particular application, but such implementation decisions do not depart from the scope of the present disclosure. According to various embodiments, a processor, device, component, circuit, structure, machine, unit, etc. can be configured to perform one or more of the functions described herein. The terms "configured to" or "configured for" as used herein with respect to a specified operation or function refer to a processor, device, component, circuit, structure, machine, unit, etc. that is physically constructed, programmed, and / or arranged to perform the specified operation or function.

[0189] Furthermore, those skilled in the art will understand that the various exemplary logical blocks, units, devices, components, and circuits described herein can be implemented in or executed by an integrated circuit (IC) that includes a general-purpose processor, a digital signal processor (DSP), an application specific integrated circuit (ASIC), a field programmable gate array (FPGA) or other programmable logic device, or any combination thereof. The logical blocks, units, and circuits can further include antennas and / or transceivers for communicating with various components within a network or device. The general-purpose processor can be a microprocessor, but in the alternative, the processor can be any conventional processor, controller, or state machine. The processor can also be implemented as a combination of computing devices, such as a combination of a DSP and a microprocessor, a plurality of microprocessors, one or more microprocessors in conjunction with a DSP core, or any other suitable configuration for performing the functions described herein. When implemented in software, the functions can be stored as one or more instructions or code on a computer-readable medium. Accordingly, the steps of the methods or algorithms disclosed herein can be implemented as software stored on a computer-readable medium.

[0190] As used herein, the term "unit" refers to software, firmware, hardware, and any combination of these elements for performing the associated functions described herein. Further, for purposes of explanation, the various units are described as individual units, but as will be apparent to those skilled in the art, two or more units can be combined to form a single unit for performing the associated functions according to embodiments of the present disclosure.

[0191] Furthermore, memory or other storage, as well as communication components, may be used in embodiments of the present disclosure. For clarity, it will be understood that the above description has described embodiments of the present disclosure with reference to different functional units and processors. However, it will be apparent that any suitable distribution of functions between different functional units, processing logic elements, or domains may be used without detracting from the present disclosure. For example, functions shown to be performed by an individual processing logic element or controller may be performed by the same processing logic element or controller. Thus, references to specific functional units are not intended to denote a strict logical or physical structure or organization, but rather are merely references to suitable means for providing the described functions.

[0192] Various modifications to the implementations described in this disclosure will be readily apparent to those skilled in the art, and the general principles defined herein may be applied to other implementations without departing from the scope of the claims. Accordingly, this disclosure is not intended to be limited to the implementations shown herein, but rather should be accorded the widest scope consistent with the novel features and principles disclosed herein, as recited in the following claims.

Claims

1. A method for monitoring a device, comprising: calculating a probability density function over time for an aging degradation variable based on solving at least one equation from an aging degradation model having end-of-life (EOL) boundary conditions, wherein the boundary conditions include a first boundary condition and a second boundary condition, the first boundary condition is a no-flux boundary condition, and the second boundary condition is an absorption boundary condition or a partial absorption boundary condition; measuring an observable quantity related to the operating state of the device; obtaining first data representing the measured value of the observable quantity; calculating a likelihood for the aging degradation variable from the first data; updating the calculated probability density function of the aging degradation variable based on the likelihood; generating a signal indicating a health prediction of the device based on the probability density function, the aging degradation model, and the EOL boundary conditions A method comprising the above steps.

2. further comprising providing a device model, the device model including an equation having the aging degradation variable as a device parameter, the EOL boundary conditions being based on the device model, the calculation of the likelihood being based on the device model, The method according to claim 1.

3. further comprising providing a monitoring model, the monitoring model including an equation having the observable quantity and the aging degradation variable, the monitoring model being based on the device model, the calculation of the likelihood being based on the monitoring model, The method according to claim 1 or claim 2.

4. The method according to any one of claims 1 to 3, wherein generating the signal includes calculating an expression of time-dependent unreliability based on the probability density function, the aging degradation model, and the EOL boundary conditions.

5. The method according to any one of claims 1 to 4, wherein generating the signal includes calculating a remaining useful life (RUL) value.

6. the aging degradation model includes an equation having at least two aging degradation variables of the device, calculating the probability density function includes calculating a joint probability density function of the at least two aging degradation variables, Calculating the likelihood includes calculating the likelihood for the at least two aging variables and the first data. Updating the probability density function includes updating the joint probability density function. The method according to any one of claims 1 to 5.

7. The aging model includes an equation having aging variables of at least two devices. Calculating the probability density function includes calculating the joint probability density function of the aging variables of each of the devices. Measuring the observable quantity includes measuring one or more observable quantities of the device, and the first data represents the measured values of the observable quantities. Calculating the likelihood includes calculating the likelihood for the aging variables and the first data. Updating the probability density function includes updating the joint probability density function. The method according to any one of claims 1 to 6.

8. The device is selected from the group including a circuit breaker, a transformer, a power electronics device, and an energy storage device. The observable quantity is one of the opening and closing speed of the movable contact of the circuit breaker, the moving amount of the movable contact, the total moving amount of the movable contact, the excessive moving amount of the movable contact, the rebound amount of the movable contact, the opening and closing time of the circuit breaker, and the opening and closing peak coil current of the circuit breaker. The method according to any one of claims 1 to 7.

9. Further comprising triggering maintenance, overhaul, replacement, or load reduction of the device in response to the generated signal indicating an important soundness prediction within a predetermined amount of time. The method according to any one of claims 1 to 8.

10. Further comprising indicating a warning in response to the generated signal indicating an important soundness prediction within a predetermined amount of time, which is used for future maintenance scheduling. The method according to any one of claims 1 to 9.

11. A system for monitoring a device, At least one sensor configured to measure an observable quantity related to the operating state of the device, A memory configured to store an aging degradation model, wherein the aging degradation model includes at least one equation having end-of-life (EOL) boundary conditions and aging degradation variables of the device, the boundary conditions include a first boundary condition and a second boundary condition, the first boundary condition is a flux-free boundary condition, and the second boundary condition is an absorption boundary condition or a partial absorption boundary condition, a memory, Calculating a probability density function over time for the aging degradation variable based on solving the at least one equation from the aging degradation model having the EOL boundary conditions, Obtaining first data representing a measured value of the observable quantity, Calculating a likelihood for the aging degradation variable from the first data, Updating the calculated probability density function of the aging degradation variable based on the likelihood, Generating a signal indicating a health prediction of the device based on the probability density function, the aging degradation model, and the EOL boundary conditions A controller configured as A system comprising.

12. The memory is Storing a device model, wherein the device model includes an equation having the aging degradation variable as a device parameter, and the EOL boundary conditions are based on the device model, storing, and / or Storing a monitoring model, wherein the monitoring model includes an equation having the observable quantity and the aging degradation variable, and the monitoring model is based on the device model, storing Further configured to perform, The controller is further configured to calculate the likelihood based on the device model and / or the monitoring model, The system according to claim 11.

13. The controller is further configured to generate the signal using calculating a representation of a failure probability over time based on the probability density function, the aging degradation model, and the EOL boundary conditions and / or using calculating a remaining useful life (RUL) value, the system according to claim 11 or 12

14. The memory, the controller, and the at least one sensor are configured to implement and / or execute the method according to any one of claims 1 to 10, The system according to any one of claims 11 to 13.

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