Method for estimating physical quantity of electrostatic induction device component

Abstract

The invention relates to a method for estimating a physical quantity of an electrostatic induction device assembly (10). The electrostatic induction device assembly (10) comprises a housing (14), an electrostatic induction device (12) and a liquid (18), where the housing (14) accommodates the electrostatic induction device (12) and the liquid (18) such that the electrostatic induction device (12) is at least partially, preferably completely submerged in the liquid (18). The method includes using measured temperature data obtained from the measurement assembly (20). The measured temperature data comprises: when the electrostatic induction device assembly (10) is under conditions in which at least a portion of the electrostatic induction device (12) generates heat during at least a portion of a reference time range ([Delta] Tref); a temperature (Ttrue (x, t)) at each of a plurality of different positions (x) of the electrostatic induction device assembly (10) as a function of the time (t) within the reference time range ([Delta] Tref). The method further comprises:-using a time-dependent partial differential equation characterizing a physical condition of the electrostatic induction device assembly (10) during a reference time range ([Delta] Tref) wherein the physical quantity constitutes a source term of the partial differential equation; -generating a temperature model of estimated temperature data corresponding to an estimated temperature (Test (x, t)) at each of a plurality of different positions (x) of the electrostatic induction device assembly (10) as a function of time (t), the temperature model comprising a first neural network (NN1) characterizing the estimated temperature data (Test (x, t)) and the measured temperature data (Ttrue (x, t)), and estimating the physical quantity by training a neural network system using at least the following entities: a time-dependent partial differential equation, information from the temperature model, and a second neural network (NN2) for the physical quantity.

Description

Technical Field

[0001] The present invention relates to a method for estimating a physical quantity of an electrostatic induction device component. Furthermore, the present invention relates to each of a computer program product, a non-transitory computer-readable storage medium, and a control unit. Background Art

[0002] In an electrostatic induction device assembly, such as, for example, an assembly including a transformer or a shunt reactor, it may be desirable to obtain information indicative of a physical quantity of the assembly. Purely by way of example, it may be desirable to determine information related to heat losses associated with at least a portion of the electrostatic induction device assembly.

[0003] However, obtaining such information from, for example, a numerical model of an electrostatic induction device assembly can be a challenging task. Furthermore, since the electrostatic induction device can include an electrostatic induction device surrounded by a liquid in a housing (e.g., a tank), determining the above information experimentally can also be a challenging task. Summary of the Invention

[0004] In view of the above, an object of the present invention is to provide a method for estimating a physical quantity of a component of an electrostatic induction device, which method provides reasonably reliable results.

[0005] The above objects are achieved by the method according to claim 1 .

[0006] Thus, the present invention relates to a method for estimating a physical quantity of an electrostatic induction device assembly. The electrostatic induction device assembly comprises a housing, an electrostatic induction device, and a liquid, wherein the housing houses the electrostatic induction device and the liquid such that the electrostatic induction device is at least partially, and preferably completely, immersed in the liquid. The method comprises using measured temperature data obtained from a measurement assembly. The measured temperature data comprises the temperature at each of a plurality of different locations of the electrostatic induction device assembly as a function of time within a reference time range when the electrostatic induction device assembly is subjected to conditions such that at least a portion of the electrostatic induction device generates heat during at least a portion of the reference time range.

[0007] The method further comprises:

[0008] - using a time-dependent partial differential equation, the time-dependent partial differential equation characterizing the physical condition of the electrostatic induction device component during the reference time range, wherein the physical quantity constitutes a source term of the partial differential equation;

[0009] - generating a temperature model for estimated temperature data corresponding to an estimated temperature at each of a plurality of different locations of an electrostatic induction device component as a function of time, the temperature model comprising a first neural network that characterizes the estimated temperature data and the measured temperature data, and

[0010] - estimating the physical quantity by training a neural network system using at least: a time-dependent partial differential equation, information from a temperature model, and a second neural network for the physical quantity.

[0011] The method according to the above means that the physical quantity is estimated with a suitable accuracy, since the method uses information from the temperature model to estimate the physical quantity of interest.

[0012] As used herein, the term "source term" of a partial differential equation is intended to encompass terms related to the net inflow or outflow of physical entities in a portion of an electrostatic induction device assembly.

[0013] As an example, the steady-state temperature distribution of an object can generally be established by solving the Laplace equation with appropriate boundary conditions for ΔT = 0. However, if there is a net inflow or outflow of a physical entity in a portion of the object that can be characterized by a function J, the Laplace equation can be reformulated as follows: ΔT = J. In this way, the function J is the source term in the reformulated Laplace equation.

[0014] It should be noted that, depending on the partial differential equation and the nature of the net inflow or net outflow, the function J may depend on one or more of a plurality of parameters, such as at least one of the following parameters: time t, position x, and temperature T. Thus, the source term may be formulated, for example, according to: J=J(t, x, T).

[0015] Purely by way of example, the time-dependent partial differential equation may be the heat equation with temperature T as unknown variable. This example may apply to every embodiment of the present invention.

[0016] Optionally, the method further comprises establishing a set of partial differential equation entities associated with a probability distribution of solutions to the time-dependent partial differential equation. The method further comprises generating a partial differential equation cost function comprising the partial differential equation entities, wherein training the neural network system comprises:

[0017] - determining the set of partial differential equation entities such that corresponding values ​​of the partial differential equation cost function are within a predetermined range, and / or

[0018] - varying the set of partial differential equation entities until a predetermined stopping condition is obtained.

[0019] The above characteristics mean that training the neural network system can involve an iterative process that performs multiple iterations. This, in turn, means that the likelihood of obtaining reasonably accurate results is reasonably high.

[0020] Optionally, the partial differential equation cost function includes at least one of the following:

[0021] - a set of residual entities and a residual associated with the time-dependent partial differential equation, preferably the residual entity comprises a residual functional, alternatively consists of a residual functional;

[0022] - a set of boundary condition entities and at least one boundary condition associated with the time-dependent partial differential equation, preferably the boundary condition entities comprising boundary condition functionals, alternatively consisting of boundary condition functionals, and

[0023] - a set of initial condition entities and at least one initial condition associated with the time-dependent partial differential equation, preferably the initial condition entities include initial condition functionals, alternatively consist of initial condition functionals.

[0024] As used herein, the term "functional" is intended to encompass any mapping from a space to a real or complex field. A space may include functions, where a functional may be referred to as a function that takes another function as input. As a non-limiting example, an integral may be an example of a functional, as the integral uses a function as input, and the result of the integral may be a real or complex number, depending on, for example, the properties of the function input to the integral.

[0025] Optionally, the residuals associated with the time-dependent partial differential equation are determined using at least information from a temperature model, preferably an estimated temperature at each of a plurality of different locations of the electrostatic induction device component as a function of time. In this way, information from the temperature model (e.g., estimated temperature) can be used to determine the aforementioned set of residual entities. This in turn means that measured temperature data represented by the temperature model can be used when determining the aforementioned residuals. However, the measured temperature data itself does not need to be used when determining the residuals. Instead, the measured temperature data can be represented by a first neural network, which in turn forms part of the temperature model. This means that the accuracy level of the residuals is appropriately high because the temperature model can be associated with an accuracy level that exceeds the accuracy of the measured temperature data itself. For example, the temperature model can provide temperature information for locations and / or instances where the temperature is not measured.

[0026] Optionally, the set of partial differential equation entities includes a set of temperature entities associated with a probability distribution of solutions to a temperature model, wherein the partial differential equation cost function includes a summand including the temperature entity and a temperature cost function, the summand including the temperature entity, and the temperature cost function including the estimated temperature data and the measured temperature data. Preferably, the temperature entity includes, or alternatively consists of, temperature hyperparameters.

[0027] Optionally, the method comprises training a first neural network using the measured temperature data to obtain a temperature model, wherein the temperature model is thereafter used to train the neural network system.

[0028] As shown above, using a temperature model rather than measured temperature data to train the neural network system simply means that the method has a reasonably high accuracy.

[0029] Optionally, the step of obtaining the temperature model comprises establishing a set of temperature entities associated with a probability distribution of a solution to the temperature model. Preferably, the temperature entities comprise, or alternatively consist of, temperature hyperparameters, wherein training the first neural network comprises: generating a temperature cost function comprising the set of temperature entities, the estimated temperature data, and the measured temperature data, and

[0030] - determining the set of temperature entities such that corresponding values ​​of the temperature cost function are within a predetermined temperature range, and / or

[0031] - Varying the set of temperature entities until a predetermined stop condition is obtained.

[0032] In this way, temperature entities (such as temperature hyperparameters) can be determined, for example, using an iterative process that performs a number of iterations. This in turn means that the likelihood of obtaining reasonably accurate results is reasonably high.

[0033] Optionally, the physical quantity characterizes at least one of the following of the electrostatic induction device assembly: heat losses through the housing, stray losses in metal portions of the electrostatic induction device, and a hot spot temperature associated with the electrostatic induction device.

[0034] Optionally, the electrostatic induction device includes a transformer and / or a shunt reactor.

[0035] Optionally, the neural network system further uses temperature-dependent material properties of at least a portion of the housing, such as thermal conductivity.

[0036] A second aspect of the present invention relates to a method for evaluating an electrostatic induction device assembly. The electrostatic induction device assembly includes an electrostatic induction device located within a housing. The assembly further includes a liquid located within the housing, the liquid surrounding the electrostatic induction device. The method comprises:

[0037] - arranging the electrostatic induction device assembly under conditions where at least a portion of the electrostatic induction device generates heat;

[0038] determining measured temperature data using the measurement assembly, the measured temperature data comprising: a temperature at each of a plurality of different locations of the electrostatic induction device assembly as a function of time within a reference time range when the electrostatic induction device assembly is under conditions such that at least a portion of the electrostatic induction device generates heat during at least a portion of the reference time range; and

[0039] - using the method according to the first aspect of the invention to estimate a physical quantity of a component of an electrostatic induction device.

[0040] Optionally, the housing has an outer surface facing away from the interior of the housing, wherein the measurement assembly comprises one or more sensing devices adapted to sense the temperature at a plurality of different locations on the outer surface of the housing.

[0041] Optionally, the measurement assembly comprises one or more thermal imaging cameras, and wherein the step of determining measured temperature data comprises capturing an image of the exterior surface using the one or more thermal imaging cameras.

[0042] Optionally, the step of determining measured temperature data comprises transforming images captured by one or more thermal imaging cameras onto the exterior surface.

[0043] A third aspect of the invention relates to a computer program product comprising program code for performing the method of the first aspect of the invention when executed by a processor device.

[0044] A fourth aspect of the present invention relates to a non-transitory computer-readable storage medium comprising instructions which, when executed by a processor device, cause the processor device to perform the method of the first aspect of the present invention.

[0045] A fifth aspect of the invention relates to a control unit arranged to perform the method of the first aspect of the invention. BRIEF DESCRIPTION OF THE DRAWINGS

[0046] With reference to the accompanying drawings, the following is a more detailed description of embodiments of the present disclosure cited as examples.

[0047] In the attached figure:

[0048] Figure 1 is a schematic diagram of components of an electrostatic induction device;

[0049] Figure 2 is a schematic diagram of an embodiment of the method of the present invention, and

[0050] Figure 3is a schematic diagram of another method embodiment of the present invention. DETAILED DESCRIPTION

[0051] Hereinafter, preferred embodiments of the present disclosure will be discussed with reference to the accompanying drawings.

[0052] Figure 1 An embodiment of an electrostatic induction device assembly 10 is schematically illustrated. The electrostatic induction device assembly comprises a housing 14, an electrostatic induction device 12, and a liquid 18, wherein the housing 14 contains the electrostatic induction device 12 and the liquid 18 such that the electrostatic induction device 12 is at least partially, preferably completely, immersed in the liquid 18. Figure 1 In the embodiment of the present invention, the electrostatic induction device 12 is completely immersed in the liquid 18. As a non-limiting example, the electrostatic induction device 12 may include a transformer and / or a shunt reactor, or even be composed of a transformer and / or a shunt reactor. Figure 1 As shown, the housing 14 may be defined by a housing wall 16 .

[0053] Purely by way of example, the housing wall 16 may comprise, or even consist of, a metallic material such as steel.

[0054] Furthermore, as a non-limiting example, housing 14 may be referred to as a canister.

[0055] Further, purely by way of example, the liquid 18 may comprise, or even consist of, a dielectric liquid such as mineral oil.

[0056] The electrostatic induction device assembly 10 may be adapted to have conditions where at least a portion of the electrostatic induction device 12 generates heat. Purely by way of example and as Figure 1 As indicated, when the electrostatic induction device 12 operates, the electrostatic induction device may generate internal heat loss q int As a non-limiting example, if the electrostatic induction device 12 comprises or even consists of a transformer and / or a shunt reactor, the internal heat loss q int This internal heat loss q int It can propagate via the liquid 18 towards the housing wall 16 .

[0057] Additionally, heat can propagate through the housing wall 16, resulting in a housing wall heat loss q 壁 Purely by way of example, the magnitude of the heat loss from the housing wall, q 壁The temperature difference across the housing wall 16 (i.e., the difference between the temperature of the liquid 18 inside the housing wall and the temperature of the fluid surrounding the housing wall 16 (e.g., air)) and housing heat transfer parameters (e.g., the wall diffusion coefficient k that indicates the diffusion across the housing wall 16) may be dependent on the temperature difference across the housing wall 16 (i.e., the difference between the temperature of the liquid 18 inside the housing wall and the temperature of the fluid surrounding the housing wall 16 (e.g., air)). 壁 ).

[0058] The method of the present invention includes using the measured temperature data obtained from the measuring assembly 20. The measured temperature data includes: when the electrostatic induction device assembly 10 is in at least a portion of the electrostatic induction device 12 within the reference time range ΔT ref When heat is generated during at least a portion of the time, the reference time range ΔT ref The temperature T at each of the multiple different positions of the electrostatic induction device assembly 10 as a function of time t 真实 (x, t). For the sake of completeness, it should be noted that herein position is generally denoted by x in order to clarify that the position may be represented in one, two or three dimensions, eg depending on the characteristics of the measured temperature data.

[0059] like Figure 1 As indicated, measurement component 20 may include one or more measurement entities.

[0060] exist Figure 1 In the embodiment of FIG. 1 , the housing 14 has an outer surface 22 facing away from the interior of the housing 14. Purely by way of example and as shown Figure 1 As indicated, outer surface 22 may be the exterior surface of housing wall 16. Furthermore, measurement assembly 20 may include one or more sensing devices adapted to sense temperature at a plurality of different locations on outer surface 22 of housing 14.

[0061] Purely by way of example, the measurement assembly 20 may include one or more thermal imaging cameras 24 ( Figure 1 Only one camera is indicated in the figure), and the step of determining measured temperature data may comprise capturing images of the exterior surface using one or more thermal imaging cameras.

[0062] However, embodiments of the measurement assembly 20 may include other types of sensors. Figure 1 , wherein an array 26 of temperature sensors is located within the interior of the housing 14 , wherein each temperature sensor in the array 26 can, for example, measure the temperature of the liquid 18 located within the interior of the housing 14 .

[0063] For the sake of completeness, it should be noted that an embodiment of the measurement assembly 20 may include a plurality of different sensors of different types.

[0064] Regardless of how the reference time range ΔT is determined refThe temperature T at each of the multiple different positions of the electrostatic induction device assembly 10 as a function of time t 真实 (x, t), the method of the present invention includes:

[0065] - Using a time-dependent partial differential equation, the time-dependent partial differential equation characterizes the electrostatic induction device component in a reference time range ΔT 参考 The physical conditions during the period, wherein the physical quantity constitutes the source term of the partial differential equation;

[0066] - Generate estimated temperature data T est (x, t) temperature model, which estimates the temperature data T est (x, t) corresponds to the estimated temperature at each of the plurality of different locations of the electrostatic induction device assembly 10 as a function of time t, the temperature model including the temperature data T representing the estimated temperature est (x, t) and measured temperature data T 真实 The first neural network NN1 of (x, t), and

[0067] - estimating the physical quantity by training a neural network system using at least the following entities: a time-dependent partial differential equation, information from a temperature model, and a second neural network NN2 for the physical quantity.

[0068] As non-limiting examples, the physical quantity may characterize at least one of the following of the electrostatic induction device assembly 10 : heat losses through the housing 14 , stray losses in metal portions of the electrostatic induction device 12 , and a hot spot temperature associated with the electrostatic induction device 12 .

[0069] Purely by way of example, a neural network system may be referred to as a physical information neural network.

[0070] also, Figure 1 The control unit 28 is indicated. Purely by way of example, the control unit 28 may be arranged to perform the method of the first aspect of the invention. To this end, although purely by way of example, the control unit 28 may be adapted to receive information from relevant entities, such as the measurement assembly 20 and the electrostatic induction device 12.

[0071] Purely by way of example, the method further comprises establishing a set of partial differential equation entities β associated with the probability distribution of solutions to the time-dependent partial differential equation PDE , β IC , β BC The method further comprises generating a partial differential equation entity β PDE , β IC , β BC The partial differential equation cost function L 总, wherein training the neural network system comprises:

[0072] -Determine the entity β of the set of partial differential equations PDE , β IC , β BC , so that the partial differential equation cost function L 总 The corresponding value of is within a predetermined range, and / or

[0073] - varying the set of partial differential equation entities until a predetermined stopping condition is obtained.

[0074] As non-limiting examples, the partial differential equation cost function may include at least one of the following:

[0075] - a set of residual entities associated with time-dependent partial differential equations and a residual e PDE , preferably, the residual entity comprising, alternatively consisting of, residual functionals;

[0076] - a set of boundary condition entities associated with the time-dependent partial differential equations and at least one boundary condition L BC , preferably, the boundary condition entity comprises a boundary condition functional, alternatively consists of a boundary condition functional, and

[0077] - a set of initial condition entities associated with the time-dependent partial differential equation and at least one initial condition L IC Preferably, the initial condition entity includes an initial condition functional, or alternatively consists of an initial condition functional.

[0078] As a non-limiting example, the residual e associated with the time-dependent partial differential equation PDE The estimated temperature T at each of a plurality of different locations x of the electrostatic induction device assembly 10 as a function of time t may be determined using at least information from the temperature model, preferably using an estimated temperature T at each of a plurality of different locations x of the electrostatic induction device assembly 10. est Thus, although by way of example only, the estimated temperature data T est at least a portion of (x, t) to determine the residual e PDE .

[0079] Purely by way of example, the set of partial differential equation entities includes a set of temperature entities associated with the probability distribution of solutions to the temperature model Among them, the partial differential equation cost function includes the addend and the temperature cost function L T , the addend includes the temperature entity The temperature cost function includes the estimated temperature data T est (x, t) and measured temperature data T 真实 (x, t). Preferably, the temperature entity Comprising, or alternatively consisting of, a temperature hyperparameter.

[0080] Thus, in an embodiment of the present invention, the first neural network NN1 and the neural network system can be trained simultaneously. Figure 2 Such an embodiment is schematically illustrated in .

[0081] Optionally, the method may include using measured temperature data T 真实 (x, t) is used to train the first neural network NN1 to obtain a temperature model, wherein the temperature model is subsequently used to train the neural network system.

[0082] In this way, Figure 3 As illustrated in FIG, in an embodiment of the present invention, a first neural network NN1 may be trained in a first step S10, and the result of the first step S10 will thereafter be used to train a neural network system, see Figure 3 Step S12 in .

[0083] In addition, if Figure 3 As indicated, the step S10 of obtaining the temperature model comprises establishing a set of temperature entities associated with a probability distribution of solutions to the temperature model. Preferably, the temperature entity includes a temperature hyperparameter, or alternatively consists of a temperature hyperparameter, wherein training the first neural network NN1 comprises: generating a temperature cost function L 总 , the temperature cost function includes the set of temperature entities Estimated temperature data T est (x, t) and measured temperature data T 真实 (x,t), and

[0084] - Determine the temperature of the group So that the temperature cost function L 总 is within a predetermined temperature range, and / or

[0085] -Change the temperature of this group of entities Until the predetermined stopping condition is obtained.

[0086] Thus, the temperature entity (For example, the temperature hyperparameter ) can be determined, for example, using an iterative process that performs a number of iterations. Thereafter, the temperature entity In order to determine the estimated temperature data T est (x,t).

[0087] It should be noted that the process of training the first neural network NN1 can be performed in the manner presented in US10,963,540B2. It should be noted that any of the training processes presented in US10,963,540B2 can be applied to the training processes described above with reference to Figure 2 and Figure 3 Each of the embodiments presented.

[0088] Optionally, the neural network system further uses the following items: temperature-dependent material properties D(T) of at least a portion of the housing 14, such as thermal conductivity. Figure 2 and Figure 3 This possibility is indicated in each of .

[0089] It should be noted that although Figure 2 The embodiment simultaneously trains the first neural network NN1 and the neural network system and Figure 3 The embodiment of the invention trains the first neural network NN1 simultaneously before the neural network system, but other embodiments of the method of the invention are also envisaged.

[0090] Purely by way of example, it is contemplated that embodiments of the method of the present invention may employ an iterative process in which the first neural network NN1 is only partially trained, and the temperature model obtained from such partial training is thereafter used to train the neural network system. Thereafter, the first neural network NN1 may be further trained, and the resulting temperature model may be used to further train the neural network system.

[0091] Purely by way of example, the first neural network NN1 may be trained only in part by selecting a first predetermined temperature range and determining, for example, the temperature entity Let the temperature cost function L 总 The corresponding value of is within the first predetermined temperature range. Thereafter, in further training of the first neural network NN1, a second predetermined temperature range narrower than the first predetermined temperature range may be used, so that the temperature entity Let the temperature cost function L 总 The corresponding value of is within the second predetermined temperature range.

[0092] A second aspect of the present invention relates to a method for evaluating an electrostatic induction device assembly 10. The electrostatic induction device assembly 10 includes an electrostatic induction device 12 located within a housing 14. The assembly 10 further includes a liquid 18 located within the housing 14, the liquid 18 at least partially surrounding the electrostatic induction device 12. The method includes:

[0093] - arranging the electrostatic induction device assembly 10 under conditions where at least a portion of the electrostatic induction device 12 generates heat;

[0094] - Determine the measured temperature data T using the measuring assembly 20 真实 (x, t), measured temperature data T 真 The value (x, t) includes: when the electrostatic induction device assembly 10 is in at least a portion of the electrostatic induction device 12 within the reference time range ΔT ref When heat is generated during at least a portion of the time, the reference time range ΔT ref the temperature at each of a plurality of different locations of the electrostatic induction device assembly as a function of time, and

[0095] - using the method according to the first aspect of the invention to estimate a physical quantity of a component of an electrostatic induction device.

[0096] Reference again Figure 1 The housing 14 may have an outer surface 22 facing away from the interior of the housing 14 , wherein the measurement assembly includes one or more sensing devices adapted to sense the temperature at a plurality of different locations on the outer surface 22 of the housing 14 .

[0097] As a non-limiting example, the step of determining measured temperature data may include transforming an image captured by one or more thermal imaging cameras 24 onto the exterior surface.

[0098] The method according to the invention will now be illustrated by the following time-dependent partial differential equation:

[0099]

[0100] in:

[0101] T = T(x, t) represents the temperature at each of a plurality of different locations (x) as a function of time (t);

[0102] D(T) characterizes a temperature-dependent material property (such as thermal conductivity) of at least a portion of housing 14, and

[0103] q 壁 (I(t), T) characterizes the housing wall heat loss, where such heat loss may depend on any of: the current I(t) fed to the electrostatic induction device 12 and the temperature T (such as the temperature of the inside of the housing wall 16).

[0104] As can be appreciated from the above, the physical quantities constituting the source term of the partial differential equation presented in Equation 1 above are given by the heat loss q through the housing wall. 壁 (I(t), T) is used as an example.

[0105] Furthermore, as already indicated in the above description, the method of the present invention comprises a temperature model for generating estimated temperature data corresponding to an estimated temperature T at each of a plurality of different positions x of the electrostatic induction device assembly 10 as a function of time t. est (x, t). The temperature model includes characterizing the estimated temperature data T est (x, t) and measured temperature data T 真实 The first neural network NN1 (see Figure 2 and Figure 3 each of them).

[0106] refer to Figure 3 , estimated temperature data T est (x, t) can be calculated in a separate step S10 by using the measured temperature data T 真实 (x, t) is determined by training the first neural network NN1. Figure 3 The result of step S10 in the embodiment may be the estimated temperature data T est (x,t).

[0107] For this reason and as Figure 3 As indicated, the step of obtaining the temperature model comprises establishing a set of temperature entities associated with a probability distribution of solutions to the temperature model.

[0108] Preferably, although not necessarily, the temperature entity comprising, alternatively consisting of, a temperature hyperparameter, and training the first neural network NN1 comprises generating a temperature cost function L 总 , the temperature cost function includes the set of temperature entities Estimated temperature data T est (x, t) and measured temperature data T 真实 (x, t). As a non-limiting example, the estimated temperature data T est (x, t) and measured temperature data T 真实 (x,t) can be included in the cost function L T (T est (x,t),T 真实 (x,t)), and the total cost function can be defined as follows:

[0109] Furthermore, although purely by way of example, the process of obtaining a temperature model may include

[0110] - Determine the temperature of the group So that the temperature cost function L 总 is within a predetermined temperature range, and / or

[0111] -Change the temperature of this group of entities Until the predetermined stopping condition is obtained.

[0112] Regardless of how the estimated temperature data T is determined, est The temperature model of (x, t), the estimated temperature data T obtained from this est (x, t) can then be entered into Equation 1 above according to the following:

[0113]

[0114] As can be appreciated from the above, using the estimated temperature data T in Equation 2 above est (x, t) and assuming for example that the current I(t) is known, then the unknown entity in equation 2 above is related to the heat loss q 壁 (I(t),T) is related.

[0115] Heat loss from the shell wall q 壁 (I(t), T) can be estimated by training a neural network system using at least the following entities: a time-dependent partial differential equation (see, for example, Equation 2), information from a temperature model (see, for example, Equation 2), and a second neural network NN2 for this physical quantity. Purely by way of example, the above training can be performed in a system such as Figure 3 The process is performed in the indicated separate step S12.

[0116] Thus, we can construct a set of PDE entities β associated with the probability distribution of solutions to the time-dependent PDEs. PDE , β IC , β BC To determine an estimate of the heat loss from the enclosure wall, q est (I(t),T).

[0117] The method may further comprise generating a partial differential equation entity β PDE , β IC , β BC The partial differential equation cost function L 总 , and training the neural network system may include:

[0118] -Determine the entity β of the set of partial differential equations PDE , β IC , β BC , so that the partial differential equation cost function L 总 The corresponding value of is within a predetermined range, and / or

[0119] -Change the entity β of the set of partial differential equations PDE , β IC , βBC , until the predetermined stopping condition is obtained.

[0120] In addition, as e.g. Figure 3 As indicated, the partial differential equation cost function L 总 May include at least one of the following:

[0121] - a set of residual entities associated with time-dependent partial differential equations and a residual e PDE , preferably, the residual entity e PDE comprising, alternatively consisting of, residual functionals;

[0122] - a set of boundary condition entities associated with the time-dependent partial differential equations and at least one boundary condition L BC , preferably, the boundary condition entity includes boundary condition functionals, alternatively consists of boundary condition functionals, and

[0123] - a set of initial condition entities associated with the time-dependent partial differential equation and at least one initial condition L IC , preferably, the initial condition entity Comprising, or alternatively consisting of, an initial condition functional.

[0124] exist Figure 3 In the example, the partial differential equation cost function L 总 includes each of the entities listed in the three above, but also contemplates the partial differential equation cost function L 总 Other embodiments may include only one or two of the entities listed in the above three items.

[0125] In addition, in the partial differential equation cost function L of the method of the present invention 总 Includes a set of residual entities In an embodiment, at least information from the temperature model may be used to determine the residual e associated with the time-dependent partial differential equation PDE .

[0126] To this end, although purely by way of example, the method may include: the neural network system testing various residual entities For example, various residual functionals. For each residual entity evaluated The residual entity thus evaluated can be used and estimated temperature data T est (x, t) to determine the residual e PDE Purely by way of example, the residual e PDE This can be determined based on the following:

[0127]

[0128] Or alternatively:

[0129]

[0130] By determining the appropriate entity (such as the appropriate residual entity ), an estimate of the heat loss from the enclosure wall q can be determined est (I(t),T) is the physical quantity of interest in the above example.

[0131] It should be noted that although the above examples use heat loss from the housing wall as an example, the method of the present invention can also be applied to other examples of this physical quantity. As non-limiting examples, the physical entity can be related to stray losses in the metal portion of the electrostatic induction device 12 and / or the hot spot temperature associated with the electrostatic induction device 12.

[0132] In such an example, the procedure presented above, starting with Equation 1, can be employed, but can be modified, for example, by replacing the enclosure wall heat loss q with another source term 壁 (I(t),T) source term, or heat loss q to the shell wall 壁 The source term composed of (I(t), T) adds another source term to update the source term of the partial differential equation in Equation 1.

[0133] Furthermore, although the example presented above starting with Equation 1 includes two separate steps S10 and S12 , other examples of the method of the present invention may also be performed in a single step.

[0134] Finally, it should be understood that the described characteristics of the method for estimating a physical quantity of a component of an electrostatic induction device apply to all embodiments of such a method that fall within the scope of the appended claims.

Claims

1. A method for estimating a physical quantity of an electrostatic induction device assembly (10), the electrostatic induction device assembly (10) comprising a housing (14), an electrostatic induction device (12) and a liquid (18), wherein: The housing (14) houses the electrostatic induction device (12) and the liquid (18) so that the electrostatic induction device (12) is at least partially, preferably completely, immersed in the liquid (18). The method includes using measured temperature data obtained from a measurement assembly (20), the measured temperature data including: when the electrostatic induction device assembly (10) is in at least a portion of the electrostatic induction device (12) within a reference time range (ΔT ref ) is under the condition that heat is generated during at least a portion of the time, as the reference time range (ΔT ref ) as a function of time (t) at each of a plurality of different positions (x) of the electrostatic induction device assembly (10) 真实 (x,t)), The method further comprises: - using a time-dependent partial differential equation, wherein the time-dependent partial differential equation characterizes the electrostatic induction device component (10) in the reference time range (ΔT ref ), wherein the physical quantity constitutes the source term of the partial differential equation; - a temperature model for generating estimated temperature data corresponding to an estimated temperature (T) at each of the plurality of different locations (x) of the electrostatic induction device assembly (10) as a function of time (t) est (x, t)), the temperature model includes characterizing the estimated temperature data (T est (x, t)) and the measured temperature data (T 真实 (x, t)), and - estimating the physical quantity by training a neural network system using at least: the time-dependent partial differential equation, information from the temperature model, and a second neural network (NN2) for the physical quantity.

2. The method according to claim 1, wherein The method further comprises establishing a set of partial differential equation entities (β PDE , β IC , β BC ), the method further comprising generating a partial differential equation cost function (L 总 ), wherein training the neural network system comprises: - Determine the set of partial differential equation entities (β PDE , β IC , β BC ), so that the partial differential equation cost function (L 总 ) is within a predetermined range, and / or - changing the set of partial differential equation entities (β PDE , β IC , β BC ) until a predetermined stopping condition is obtained.

3. The method according to claim 2, wherein: The partial differential equation cost function (L 总 ) includes at least one of the following: - a set of residual entities associated with the time-dependent partial differential equation and a residual (e PDE ), preferably, the residual entity (e PDE ) comprises a residual functional, or alternatively consists of said residual functional; - a set of boundary condition entities associated with the time-dependent partial differential equation and at least one boundary condition (L BC ), preferably, the boundary condition entity comprising, alternatively consisting of, a boundary condition functional, and - a set of initial condition entities associated with the time-dependent partial differential equation and at least one initial condition (L IC ), preferably, the initial condition entity comprising an initial condition functional, or alternatively consisting of said initial condition functional.

4. The method according to claim 3, wherein: The residual (e PDE ) is determined using at least information from the temperature model, preferably using the estimated temperature (T ) at each of the plurality of different locations (x) of the electrostatic induction device assembly (10) as a function of time (t) est (x,t)) to determine.

5. The method according to any one of claims 2 to 4, wherein The set of partial differential equation entities includes a set of temperature entities associated with probability distributions of solutions to the temperature model Wherein, the partial differential equation cost function includes the addend and temperature cost function (L T ), the addend includes the temperature entity The temperature cost function includes the estimated temperature data (T est (x, t)) and the measured temperature data (T 真实 (x, t)), preferably, the temperature entity Comprising, or alternatively consisting of, a temperature hyperparameter.

6. The method according to any one of claims 1 to 4, wherein: The method includes using the measured temperature data (T 真实 (x, t)) to train the first neural network (NN1) to obtain the temperature model, wherein the temperature model is then used to train the neural network system.

7. The method according to claim 6, wherein: The step of obtaining the temperature model comprises: establishing a set of temperature entities associated with the probability distribution of the solution of the temperature model Preferably, the temperature entity comprises a temperature hyperparameter, alternatively consists of the temperature hyperparameter, wherein training the first neural network comprises generating a temperature cost function (L 总 ), the temperature cost function includes the set of temperature entities The estimated temperature data (T est (x, t)) and the measured temperature data (T 真实 (x,t)), and - determining the set of temperature entities So that the temperature cost function (L 总 ) is within a predetermined temperature range, and / or -Change the set of temperature entities Until the predetermined stopping condition is obtained.

8. A method according to any one of the preceding claims, wherein The physical quantity characterizes at least one of the following of the electrostatic induction device assembly (10): heat loss through the housing (14), stray losses in metal portions of the electrostatic induction device (12), and a hot spot temperature associated with the electrostatic induction device (12).

9. A method according to any one of the preceding claims, wherein The neural network system further uses temperature-dependent material properties (D(T)) of at least a portion of the housing (14), such as thermal conductivity.

10. A method for evaluating an electrostatic induction device assembly (10), the electrostatic induction device assembly (10) comprising an electrostatic induction device (12) located within a housing (14), the assembly further comprising a liquid (18) located within the housing (14), the liquid (18) surrounding the electrostatic induction device (12), the method comprising: - arranging the electrostatic induction device assembly (10) under conditions where at least a portion of the electrostatic induction device (12) generates heat; - Using the measuring assembly (20) to determine the measured temperature data (T 真实 (x, t)), the measured temperature data (T 真实 (x, t)) includes: when the electrostatic induction device component (10) is in at least a portion of the electrostatic induction device (12) within a reference time range (ΔT ref ) is under the condition that heat is generated during at least a portion of the time, as the reference time range (ΔT ref ), and - Using a method according to any one of the preceding claims for estimating a physical quantity of an electrostatic induction device component (10).

11. The method according to claim 10, wherein: The housing (14) has an outer surface (22) facing away from the interior of the housing (14), wherein the measurement assembly (20) includes one or more sensing devices adapted to sense the temperature at a plurality of different locations on the outer surface (22) of the housing (14).

12. The method according to claim 11, wherein The measurement assembly (20) comprises one or more thermal imaging cameras (24), and wherein the step of determining the measured temperature data comprises capturing an image of the outer surface (22) using the one or more thermal imaging cameras (24), preferably, the step of determining the measured temperature data comprises transforming the image captured by the one or more thermal imaging cameras onto the outer surface (22).

13. A computer program product comprising program code for performing the method of any one of claims 1 to 9 when executed by a processor device.

14. A non-transitory computer-readable storage medium comprising instructions that, when executed by a processor device, cause the processor device to perform the method of any one of claims 1 to 9.

15. A control unit (28) arranged to perform the method according to any one of claims 1 to 9.

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