Method and system for predicting bubble escape temperature under moisture dynamic migration of oil-paper insulation

Abstract

The application provides a bubble escape temperature prediction method and system under oil-paper insulation moisture dynamic migration, and belongs to the technical field of power equipment insulation state evaluation and fault mechanism analysis, and comprises the following steps: based on an initial state, solving a water dynamic migration equation in cellulose insulation paper under a given temperature rising condition, obtaining an evolution result of water content in a surface layer of the cellulose insulation paper changing with time and temperature, gradually updating a bubble radius, a bubble volume and related state parameters, and synchronously calculating a force state or evolution characteristics of the bubble at an insulation paper pore outlet, when a numerical calculation result meets a preset bubble separation judgment condition, it is judged that the bubble is separated, and a system temperature at a corresponding moment is recorded as a physical prediction result of an initial bubble escape temperature, and a nonlinear correction model of a physical prediction residual is further constructed, material non-uniformity and multi-field coupling disturbance factors which are not explicitly modeled are equivalently compensated, and a final prediction result of the initial bubble escape temperature is obtained.

Description

Technical Field

[0001] This invention belongs to the technical field of electrical equipment insulation condition assessment and fault mechanism analysis, and particularly relates to a method and system for predicting bubble escape temperature under dynamic moisture migration of oil-paper insulation. Background Technology

[0002] The statements in this section are merely background information related to the present invention and do not necessarily constitute prior art.

[0003] Oil-immersed transformers are key equipment in power systems, and their operational reliability directly affects the safety and continuity of power supply. The oil-paper insulation system, as the core structure ensuring the internal insulation performance and safe and stable operation of the transformer, is the foundation for ensuring the safe and stable operation of the equipment. Under long-term operation or short-term overload conditions, localized areas inside the transformer may experience continuous temperature rise, leading to a significant decrease in the thermal stability of the oil-paper insulation system. Existing research shows that under high temperatures, the moisture contained in the cellulose insulating paper will desorb and vaporize, forming bubbles in the pores of the insulating paper or near the oil-paper interface. The formation of bubbles not only significantly weakens the local dielectric strength but may also induce partial discharge or even arc discharge, thereby accelerating insulation aging and becoming one of the important causes of insulation degradation and even failure in oil-immersed transformers.

[0004] Under actual operating conditions, moisture inside oil-immersed transformers is mainly stored in an adsorbed state within the solid insulation of the oil-paper insulation system, especially in cellulose insulating paperboard, where the moisture content typically accounts for over 99% of the total moisture content of the entire oil-paper insulation system. Approximately 90% of the chemical composition of cellulose insulating paper consists of cellulose molecules, which are linear polymer chains formed by β-D-glucopyranose units linked by (1–4)-β-glycosidic bonds. Because the cellulose molecular chains are not completely densely packed, and the cell cavities and cell walls of the fibers themselves exhibit a layered structure, the insulating paper contains a large number of widely distributed pores. Therefore, cellulose insulating paper is structurally a typical porous medium, providing the necessary microscopic space conditions for bubble nucleation and growth.

[0005] Currently, various methods for predicting and assessing bubble escape temperatures have been proposed in research on the thermally induced bubble effect in oil-paper insulation systems. These methods typically involve establishing bubble dynamics models or using escape temperature thresholds to determine bubble risk and analyze insulation status. These methods can, to some extent, describe the bubble generation and escape process, providing a reference for transformer operation safety assessment.

[0006] However, existing technologies generally have the following shortcomings in predicting bubble escape temperature:

[0007] Firstly, most methods treat the moisture content of cellulose insulating paper as a fixed initial parameter or a uniformly distributed parameter, assuming that the moisture content of the insulating paper remains constant during heating. This fails to fully reflect the dynamic evolution characteristics of water decomposition, absorption, migration, diffusion, and phase change supply within the insulating paper under temperature rise conditions. Consequently, such methods tend to underestimate or overestimate the water vapor supply capacity within the bubbles under actual continuous heating or overload conditions, leading to deviations in the predicted initial bubble escape temperature.

[0008] Secondly, existing prediction models for the initial escape temperature of thermally induced bubbles in oil-paper insulation are typically based on idealized, uniform physical models that are numerically solved. These models struggle to adequately characterize complex real-world factors such as uneven aging distribution of the insulation paper, random evolution of pore structure, and multi-bubble coupling disturbances. Due to the existence of these un-modeled factors, the prediction results of deterministic physical models often exhibit systematic deviations from on-site monitoring or experimental measurements in actual operating environments, thus limiting engineering adaptability and prediction accuracy. Summary of the Invention

[0009] To overcome the shortcomings of existing technologies in predicting the initial bubble escape temperature, such as neglecting dynamic moisture migration and simplifying physical models that are difficult to adapt to complex actual operating conditions, this invention provides a method and system for predicting the bubble escape temperature under dynamic moisture migration in oil-paper insulation. It introduces a dynamic migration description of moisture in cellulose insulating paper with temperature changes into the bubble dynamics analysis, establishes a coupled numerical model of moisture migration-interfacial phase transition-bubble growth, and constructs a nonlinear correction model based on physical prediction residuals. This achieves hierarchical fusion prediction of the physical mechanism model and the data-driven model, more realistically reflecting the physical evolution process of the oil-paper insulation system under thermal stress, enabling a more accurate assessment of the initial bubble escape temperature, and improving the reliability and engineering applicability of thermally induced bubble risk assessment.

[0010] To achieve the above objectives, one or more embodiments of the present invention provide the following technical solutions:

[0011] The first aspect discloses a method for predicting the bubble escape temperature under dynamic moisture migration in oil-paper insulation, including:

[0012] Cellulose insulating paper is equivalent to a porous microtubule structure. Based on the migration and diffusion law of moisture in the thickness direction of cellulose insulating paper, a dynamic migration model of moisture inside cellulose insulating paper with temperature change is established.

[0013] The dynamic migration model is initialized based on the structural parameters and operating conditions of the cellulose insulating paper to determine the initial state of moisture migration and bubble growth inside the cellulose insulating paper.

[0014] Based on the initial state and given temperature rise conditions, the dynamic migration equation of moisture in cellulose insulating paper and the bubble growth kinetic model are coupled numerically solved to obtain the physical prediction value of the initial escape temperature of the bubbles.

[0015] A residual correction model is constructed based on physical predictions and actual observation data, and the residual prediction value of the initial escape temperature of the bubble is output.

[0016] The physical prediction value and the residual prediction value are fused together to obtain the final prediction result of the initial escape temperature of the bubble.

[0017] As a further technical solution, the structural parameters of the cellulose insulating paper include: insulating paper thickness, pore equivalent size and microtube geometry, used to characterize the moisture migration path and bubble nucleation and growth space; the operating parameters of the cellulose insulating paper include initial moisture content, ambient pressure and system temperature rise mode.

[0018] As a further technical solution, a dynamic migration model of moisture inside cellulose insulating paper with temperature change is established. Specifically, the cellulose insulating paper is regarded as a one-dimensional porous diffusion medium. Under continuous heating conditions, moisture in the thickness direction of the insulating paper is driven by both the concentration gradient and the temperature gradient to undergo dynamic migration. The migration and diffusion process satisfies Fick's second law. A dynamic migration equation for the evolution of the moisture mass fraction inside the insulating paper with time is established, thereby obtaining the evolution results of the surface moisture content at the oil-paper interface with time and temperature.

[0019] As a further technical solution, after coupling the dynamic migration equation of moisture in cellulose insulating paper and the bubble growth kinetic model with numerical solution, the evolution result of the surface moisture content at the oil-paper interface with time and temperature is used as the boundary condition for water vapor generation and supply at the bubble interface during bubble growth. This is then introduced into the bubble growth kinetic model to describe the driving effect of moisture phase change evaporation on bubble volume growth.

[0020] As a further technical solution, the bubble growth dynamics model is specifically as follows: based on the equation of state of water vapor and non-water vapor gas inside the bubble, combined with the pressure balance relationship inside and outside the bubble, surface tension effect and bubble escape criterion, a dynamic evolution model of the bubble radius changing with time is established to predict the whole process of the bubble from nucleation to continuous expansion until escape.

[0021] As a further technical solution, it also includes: gradually updating the bubble radius, volume and water vapor state parameters inside the bubble, and simultaneously calculating the force state or evolution characteristics of the bubble at the outlet of the insulating paper pores. When simultaneously calculating the force state or evolution characteristics of the bubble at the outlet of the insulating paper pores, the specific calculation of the molar amount of water vapor inside the bubble and the evolution of the bubble radius state parameters over time is used to describe the growth process of the bubble from nucleation to continuous expansion inside the insulating paper pores.

[0022] As a further technical solution, the physical prediction value of the initial escape temperature of the bubble is obtained by numerical solution of the above-mentioned moisture dynamic migration model and bubble growth kinetic model, which is used to characterize the initial escape temperature of the bubble under ideal or equivalent uniform assumptions.

[0023] Based on this, as a further technical solution, it also includes: constructing physical prediction residual sample data based on the difference between the physical prediction value of the initial escape temperature of the bubble and the actual escape temperature obtained by experimental measurement; establishing a nonlinear mapping relationship between the system state feature vector and the prediction residual, constructing a residual correction model, and outputting the escape temperature residual prediction value.

[0024] As a further technical solution, the residual correction model uses material structure parameters, operating condition parameters, and intermediate state variables in the bubble growth kinetics model as input features. By establishing a nonlinear mapping relationship between the input features and the physical prediction residual, the physical prediction residual is modeled and corrected to compensate for the deviation of the prediction results caused by factors not explicitly modeled in the physical model.

[0025] As a further technical solution, the physical prediction value of the initial escape temperature of the bubble is fused with the residual prediction value to calculate the final prediction result of the initial escape temperature of the bubble. The process of calculating the prediction result of the initial escape temperature of the bubble can be repeated under different insulation paper moisture content, heating rate and structural parameters, so as to realize the quantitative analysis and assessment of the risk of thermally induced bubble escape in the oil-paper insulation system.

[0026] Secondly, a system for predicting the bubble escape temperature under dynamic moisture migration in oil-paper insulation is disclosed, including:

[0027] The dynamic migration model construction module is configured to: treat cellulose insulating paper as a porous microtubule structure, and establish a dynamic migration model of moisture inside cellulose insulating paper as temperature changes based on the migration and diffusion law of moisture in the thickness direction of cellulose insulating paper.

[0028] The initialization setting module is configured to: initialize the dynamic migration model based on the structural parameters and operating conditions of the cellulose insulating paper, in order to determine the initial state of moisture migration and bubble growth inside the cellulose insulating paper;

[0029] The solver module is configured to perform coupled numerical solutions on the dynamic migration equation of moisture in cellulose insulating paper and the bubble growth kinetics model based on the initial state and a given temperature rise condition, so as to obtain the physical prediction value of the initial escape temperature of the bubbles.

[0030] The residual correction module is configured to: construct a residual correction model based on the physical prediction value and the actual observation data, and output the residual prediction value of the initial escape temperature of the bubble;

[0031] The fusion output module is configured to fuse the physical prediction value and the residual prediction value to obtain the final prediction result of the initial escape temperature of the bubble.

[0032] The above one or more technical solutions have the following beneficial effects:

[0033] This invention provides a numerical description of the entire process from the moisture content of insulating paper and temperature evolution to bubble detachment behavior. It couples the dynamic migration of moisture with the kinetics of bubble growth, avoiding the simplification of the moisture content of insulating paper as a static parameter. This approach reflects the dynamic migration characteristics of moisture during temperature rise and its impact on bubble escape conditions. Furthermore, this invention introduces a residual correction mechanism based on the physical mechanism model to effectively compensate for complex factors such as material inhomogeneity and multi-field coupling perturbations that are not explicitly modeled. While maintaining physical interpretability, this improves the accuracy and engineering applicability of the predicted initial bubble escape temperature.

[0034] Advantages of additional aspects of the invention will be set forth in part in the description which follows, and in part will be obvious from the description, or may be learned by practice of the invention. Attached Figure Description

[0035] The accompanying drawings, which form part of this invention, are used to provide a further understanding of the invention. The illustrative embodiments of the invention and their descriptions are used to explain the invention and do not constitute an improper limitation of the invention.

[0036] Figure 1 A flowchart for predicting the temperature at which thermally induced bubbles escape from oil-paper insulation.

[0037] Figure 2 This is a schematic diagram of moisture migration in oiled paper insulation.

[0038] Figure 3 This is a schematic diagram of bubble growth at the oil paper interface;

[0039] Figure 4 This is a schematic diagram of the force analysis of the bubble. Detailed Implementation

[0040] It should be noted that the following detailed descriptions are exemplary and intended to provide further illustration of the invention. Unless otherwise specified, all technical and scientific terms used herein have the same meaning as commonly understood by one of ordinary skill in the art to which this invention pertains.

[0041] It should be noted that the terminology used herein is for the purpose of describing particular implementations only and is not intended to limit the exemplary implementations of the present invention.

[0042] Where there is no conflict, the embodiments and features in the embodiments of the present invention can be combined with each other.

[0043] Example 1

[0044] This embodiment discloses a method for predicting the bubble escape temperature under dynamic moisture migration in oil-paper insulation. The specific process is detailed in the appendix. Figure 1 This includes the following steps:

[0045] Step 1: Establish an equivalent microtube model based on the microstructure of insulating paper.

[0046] In this embodiment, to describe the influence of the porous structure of cellulose insulating paper on the bubble nucleation and growth process, the pores of the insulating paper are equivalent to cylindrical microtubule structures based on scanning electron microscopy observations. The microtubule model is used to characterize the geometric features of the internal pores of the insulating paper and the space for bubble nucleation.

[0047] Specifically, let the radius of the microtube be... The length of the microtube is ,in It is taken as twice the diameter of the microtubule, that is: .

[0048] The microtubule radius The thickness is selected based on the aging state of the insulating paper, typically within the range of 10–30 μm, with the thickness under new paper conditions being the most suitable. =10μm, and can be gradually increased according to experimental patterns after aging.

[0049] The nucleation site of the bubble is assumed to occur at the end of the microtube or at a local vacuole, with an initial nucleation radius... 0 represents the micrometer scale and is used as the initial condition for subsequent bubble growth kinetics models.

[0050] By modeling the equivalent microtube structure described above, the influence of the pores in the insulating paper on moisture migration and bubble growth behavior can be characterized in engineering, providing a structural basis for subsequent solutions to dynamic moisture migration and prediction of bubble escape temperature.

[0051] Step 2: Establish the basic assumptions about bubble nucleation and growth.

[0052] In this embodiment, under continuous heating conditions, the surface moisture of the cellulose insulating paper desorbs, migrates, and vaporizes into the pores of the insulating paper, thereby forming a bubble embryo near the pore outlet, which gradually grows under the continuous supply of water vapor.

[0053] To facilitate the establishment of subsequent bubble growth kinetic models and the prediction of escape temperatures, this embodiment makes the following basic assumptions about the bubble evolution process:

[0054] (1) The initial radius of the bubble is taken as the critical radius for nucleation. 0, used as the initial condition for subsequent bubble growth calculations;

[0055] (2) The bubbles maintain a spherical shape during growth, and the insulating oil medium is regarded as an incompressible fluid;

[0056] (3) The bubbles are mainly composed of water vapor and contain a small amount of residual air from the vacuum drying process of the insulating paper and non-water vapor gas generated by the aging and cracking of the insulating material. The volume fraction of the non-water vapor gas in the thermally induced bubbles formed under normal operation or overload heating conditions is less than 10%, and it is assumed that its molar number remains unchanged during the bubble growth process.

[0057] Based on the above assumptions, step three obtains the dynamic evolution result of the surface moisture content of the oil-paper interface, and inputs this evolution result as the water vapor supply boundary condition of the bubble interface into the bubble growth kinetic model in step four, thereby realizing the prediction of the initial escape temperature of thermally induced bubbles.

[0058] Step 3: Solving the one-dimensional moisture migration and diffusion dynamics of insulating paper.

[0059] During the continuous heating of local hot spots in an oil-immersed transformer, moisture in the insulating paper, currently in an adsorbed state, gradually desorbs and migrates towards the oil-paper interface under temperature-driven conditions. This provides a crucial source of material for subsequent bubble growth and directly affects the water vapor evaporation supply during bubble formation. Therefore, this step aims to establish a moisture migration and diffusion model within the insulating paper to obtain the surface moisture mass fraction at the oil-paper interface. This is used as the key input condition for the bubble growth model in step four.

[0060] Given the small spatial scale of the hotspot region and the short study timescale, the influence of the temperature gradient can be reasonably ignored, and the local temperature field can be considered approximately uniform. To uniformly characterize the thermal effects of water dynamic migration and the initial bubble formation process, a time-dependent system temperature variable is introduced. As a model input, its temperature rise process can be approximated as a linear relationship:

[0061] (1)

[0062] In the formula,T 0 = 293K, corresponding to an initial temperature of 20℃ (room temperature). k =7K / min is the average heating rate; t Let 's' be the time variable, 's'. for t The system temperature at time t, in K.

[0063] Under these heating conditions, the water solubility of the insulating oil increases with increasing temperature, while the adsorption capacity of the cellulose insulating paper for water molecules decreases, driving the gradual desorption of adsorbed moisture in the insulating paper and its migration towards the oil-paper interface. Given the small distance between the oil channels within the winding and the insulating paperboard, the migration and diffusion effect of moisture along the winding direction is relatively limited. It can be reasonably assumed that moisture near the winding mainly exhibits a unidirectional diffusion process away from the winding. Simultaneously, since the effective area of ​​the upper and lower surfaces of the insulating paperboard is much larger than its sidewall area, the influence of moisture penetration through the sidewalls can be ignored, thus approximating the insulating paperboard as a one-dimensional diffusion system along the thickness direction of the insulating paper. Under this model assumption, moisture migration and diffusion do not occur on the side of the insulating paperboard in close contact with the winding, while moisture migration and diffusion are allowed on the side in direct contact with the transformer oil.

[0064] Under the above assumptions, the moisture migration and diffusion process inside the insulating paperboard follows Fick's second diffusion law, and its governing equation is:

[0065] (2)

[0066] In the formula, for t Always along the thickness direction of the insulating paper x The moisture content (mass fraction) of the insulating paper at the location, % x Let be the coordinate value along the thickness direction of the insulating paperboard, in mm, and denote the interface between the insulating paper and the winding as . x =0; Let m be the diffusion coefficient of moisture in the insulating paper. 2 / s.

[0067] Wherein, diffusion coefficient D The diffusion coefficient is used to characterize the ability of substances to migrate and diffuse in a medium. Differences in the diffusion behavior and mechanisms of different substances can be reflected by the value of the diffusion coefficient. For moisture in insulating paperboard, the diffusion coefficient is not a fixed constant but varies with moisture concentration and ambient temperature. Scholars Guidi and Fullerton studied the diffusion characteristics of moisture in insulating paperboard and derived the diffusion coefficient through experimental fitting. D The calculation expression:

[0068] (3)

[0069] In the formula,D 0、 k D , E a , T These are undetermined coefficients determined by the material properties. Foss obtained the values ​​of each undetermined coefficient through experiments, which are as follows: D 0 = 1.34 × 10 -13 m 2 / s、 k D =0.5、 E a =8074、 T 0 = 293K.

[0070] Furthermore, related studies have shown that the moisture exchange rate at the interface between insulating paper and transformer oil is significantly higher than the diffusion rate of moisture within solid insulating materials. Based on this characteristic, it can be reasonably assumed that moisture can quickly reach a dynamic equilibrium state at the oil-paper interface, and the corresponding equilibrium moisture concentration can be used as the boundary condition of the model. The dynamic equilibrium moisture concentration can be determined by various empirical relationship curves, including the Fabre–Pichon curve, the Oommen curve, and the Griffin curve. Through experimental data comparison and verification, the Oommen curve has high applicability in characterizing the moisture balance relationship in actual oil-paper insulating media. Researchers such as Fessler et al., based on the experimental results of many scholars, further proposed an empirical formula for calculating the moisture balance concentration in insulating paper, as shown in equation (4):

[0071] (4)

[0072] In the formula, W paper_eq Indicates the equilibrium concentration of moisture in the insulating paper, %; T Let K be the system temperature. p v It can be based on the relative humidity of the oil. RH The calculated water partial pressure values ​​are shown in equations (5)-(6):

[0073] (5)

[0074] In the formula, ppm This indicates the water concentration in the oil, expressed in mg / kg. ppm sat This indicates the concentration of water under saturated conditions, expressed in mg / kg. P sat This represents the saturated vapor pressure of water, expressed in Pa. P sat The water concentration under saturated conditions was calculated using the Antoni equation mentioned in step four. ppm sat It can then be calculated using the following formula:

[0075] (6)

[0076] In the formula, the values ​​of parameters A and B are related to the type of insulating oil used and its aging state. For mineral insulating oil, based on existing research and experimental data, typical values ​​A=7.09 and B=1567 are selected.

[0077] Under the constraints of the above governing equations and boundary conditions, the moisture distribution inside the insulating paper can be obtained by solving equations (2)–(6). The dynamic evolution of this moisture content over time was studied, and the surface moisture content at the oil-paper interface was obtained. This interfacial moisture content serves as a key input to the bubble interface evaporation model in step four, characterizing the water vapor supply capacity during bubble formation.

[0078] Step 4: Numerical solution of bubble growth kinetics and acquisition of escape temperature.

[0079] In step three, the surface moisture content of the oil paper interface is obtained. Based on this, this step further establishes a bubble growth kinetic model and, combined with the bubble detachment criterion, finally determines the initial escape temperature of thermally induced bubbles.

[0080] The driving force for bubble growth mainly comes from the internal pressure of the bubble, while the hindering factors include the viscous resistance of the oil phase medium and the external environmental pressure. In the modeling process, it is assumed that the bubble expansion behavior occurs under quasi-static equilibrium conditions. Based on this assumption, and combined with the Navier-Stokes equations in spherical coordinates, while comprehensively considering the surface tension at the gas-liquid interface, the influence of viscous stress in the normal direction, and the force balance relationship formed by the pressure difference between the inside and outside of the bubble, a formula for describing the bubble radius can be derived. r The time-varying Rayleigh–Plesset differential equation is shown in equation (7):

[0081] (7)

[0082] In the formula, Density of insulating oil, kg / m³ 3 ; μ Pa is the kinematic viscosity of the oil. s; σ The surface tension coefficient of oil; t For time; P B This represents the gas pressure inside the bubble, specifically the partial pressure of water vapor within the bubble. P wTotal partial pressure of other gases within the bubble P g The sum of, Pa; P out The external pressure of the bubble is determined by atmospheric pressure. P atm and static oil pressure of insulating oil P oil Composition, Pa. As shown in equation (8):

[0083] (8)

[0084] In the formula, P atm =10 5 Pa; P oil = This refers to the static pressure of the insulating oil. g =9.81m / s 2 It is the acceleration due to gravity. h The oil depth is expressed in meters (m). Given that the operating temperature of the oil-paper insulation system is significantly lower than the critical temperature (647K) and the system pressure is relatively low, the water vapor and other mixed gases within the bubbles can be considered ideal gases, and their partial pressures satisfy the ideal gas law, as shown in equations (9)-(10):

[0085] (9)

[0086] (10)

[0087] In the formula, for t The number of moles of water vapor in the bubble at any given time, in mol; =4 / 3π r ( t ) 3 Let m be the volume of the bubble. 3 ; r Let R be the bubble radius, in meters; R be the molar gas constant, with a value of 8.31 J / (mol). K); n g denoted as the number of moles of other gases inside the bubble, in mol.

[0088] As shown in equation (7), the dynamic evolution of the bubble radius is driven by the pressure difference between the inside and outside of the bubble, while the pressure change inside the bubble is caused by the increase in the molar amount of water vapor due to the phase change and evaporation of moisture at the interface of the oil-paper insulation and its entry into the bubble. Moisture in the pores of the insulation paper absorbs heat and vaporizes to form water vapor, which diffuses and migrates into the bubble, increasing the molar number of gas inside the bubble and thus driving bubble growth. This phase change process is constrained by the saturated vapor pressure of water at the corresponding temperature. The saturated vapor pressure is the gas phase pressure when the gas and liquid phases are in phase equilibrium, described by the Clausius-Clapeyron equation. For ease of engineering calculation, it is integrated and simplified, resulting in the Antoni equation as follows:

[0089] (11)

[0090] In the formula, For temperature T The saturated vapor pressure of wastewater, in Pa.

[0091] The saturated vapor pressure gives the thermodynamic limit of interfacial phase change evaporation. When the partial pressure of water vapor at the interface is lower than the saturated vapor pressure at the corresponding temperature, a net evaporation process occurs at the interface. However, the actual phase change process is not instantaneous but is limited by the molecular migration rate at the interface. Macroscopically, this is manifested as the net evaporation flux of water vapor per unit area of ​​the gas-liquid interface. This net evaporation flux of interfacial water vapor is the direct source of the increase in the molar amount of water vapor within the bubble, and is calculated using the Hertz-Knudsen equation, expressed as:

[0092] (12)

[0093] In the formula, J This represents the water vapor mass flux per unit area at the bubble interface, expressed in kg / (m²). 2 s); M =0.018 kg / mol is the molar mass of water; R = 8.314 J / (mol) K) is the universal gas constant; P w This represents the actual partial pressure of water vapor inside the bubble; β The interfacial phase transition coefficient characterizes the probability of water vapor molecules colliding with the bubble interface and entering the bubble. β Mass fraction of moisture on the surface of insulating paper Closely related, difficult to β Precise theoretical calculations are performed. Referring to existing research findings, this embodiment uses an approximate exponential function form to... β To characterize, that is β = k e Ws(t) ,ink =4.04×10 10 It is an empirical constant. This represents the mass fraction of moisture in the surface layer of the insulating paper.

[0094] Based on the analysis of the dynamic migration of moisture in the insulating paper in step three, since the moisture exchange rate at the paper-oil interface is much faster than the moisture diffusion process inside the solid insulator, it can be assumed that the moisture at the interface instantaneously reaches a dynamic equilibrium state, that is, it is considered that... .

[0095] Furthermore, the growth rate of the number of water vapor moles within the bubble can be determined jointly by the interfacial evaporation flux and the bubble surface area:

[0096] (13)

[0097] In the formula, dn w / dt This represents the rate of change of the number of moles of water vapor inside the bubble over time. Let m be the surface area of ​​the bubble. 2 .

[0098] Therefore, by substituting the interfacial moisture content obtained in step three into equations (12)–(13) and solving them simultaneously with equations (7)–(10), the bubble radius can be obtained. The dynamic evolution of internal pressure.

[0099] During bubble growth, the stress state changes as the bubble volume increases. After reaching a certain size, the bubble loses stability under the combined action of various forces, detaches from the cardboard surface, and enters the insulating oil as a free bubble. The corresponding bubble size at this point is defined as the bubble detachment diameter, and the system temperature at the moment of bubble detachment is the initial bubble escape temperature.

[0100] This embodiment uses a force balance analysis method to establish a bubble detachment criterion. During the growth of bubbles attached to the oil-paper interface, they are mainly subjected to buoyancy in the vertical direction. F b Viscous resistance F d Surface tension F s and inertial force F i The role of buoyancy and inertial force is the positive force that causes the bubble to detach from the interface, while viscous drag and surface tension are the negative forces that inhibit bubble detachment. The resultant force on the bubble in the vertical direction can be expressed as:

[0101] (14)

[0102] In the formula, ∑ F y This represents the net force (N) acting on the bubble in the vertical direction. F b Represents buoyancy, in N; F iy , F dy , F sy Let N represent the components of inertial force, viscous drag, and surface tension in the vertical direction, respectively.

[0103] As the temperature continues to rise, water vapor is continuously generated inside the bubble, causing the bubble volume to grow rapidly. The positive force gradually increases, while the negative force's constraint on the bubble's stability gradually weakens. When the positive force exceeds the negative force, the stable adhesion of the bubble to the cardboard surface is disrupted, and the bubble detaches. That is, when the bubble growth process satisfies the following conditions:

[0104] (15)

[0105] This means that the bubble escaping condition is met, the bubble escapes, and the system temperature corresponding to the escaping moment is recorded. T The initial escape temperature of the bubble is determined and used for subsequent temperature prediction and operational risk assessment.

[0106] In the specific implementation of the numerical calculation model for predicting the initial escape temperature of thermally induced bubbles in an oil-paper insulation system, the model is first initialized based on the structural parameters and operating condition parameters of the insulation paper. The initialization parameters include the insulation paper thickness. cellulose pore equivalent radius Structural characteristic parameters, and initial moisture content of the insulating paper External pressure P atm In-depth analysis of hot topics System initial temperature T 0 and heating rate k Operating parameters, such as those mentioned above, are used as model inputs to determine the initial and boundary conditions for the moisture migration equation and the bubble dynamics equation.

[0107] In the model solution process, firstly, given the heating function... Under the given conditions, based on the one-dimensional moisture diffusion control equation (2) of the insulating paper established in step three, and combined with the empirical expression of the diffusion coefficient (3) and the dynamic equilibrium boundary condition equations (4)-(6) of the oil-paper interface, the moisture distribution in the thickness direction of the insulating paper is analyzed. Numerical solutions were performed to obtain the surface moisture mass fraction at the oil-paper interface. The dynamic evolution law of this interface is observed. The moisture content at this interface serves as the material supply condition for phase change evaporation at the bubble interface, providing a key input for subsequent bubble growth calculations.

[0108] Furthermore, the obtained In the interfacial evaporation model introduced in step four, the net evaporation flux of water vapor at the bubble interface is determined by the Hertz–Knudsen equation (12). The growth rate of the number of water vapor moles inside the bubble is calculated using equation (13). dn w / dt As the molar amount of gas inside the bubble increases, the internal pressure of the bubble also increases. The bubble radius is updated in real time by the ideal gas law (9)–(10) and further substituted into the Rayleigh–Plesset equation (7). The dynamic control equations are obtained, thereby realizing the step-by-step iterative solution of the bubble growth process and obtaining the evolution results of bubble radius, volume and internal pressure with time and temperature.

[0109] During the continuous expansion of the bubble, the model simultaneously calculates the force state of the bubble at the outlet of the insulating paper pores and judges the stability of the bubble according to the detachment criterion (15) established in step four. When the calculation result meets the preset detachment condition, that is, when the resultant force of the bubble in the vertical direction is greater than zero, the model determines that the bubble detaches from the paperboard surface and enters the oil phase, and records the system temperature corresponding to the detachment moment. The physical model prediction of the initial escape temperature of the thermally induced bubble is denoted as... .

[0110] Step 5: Constructing a nonlinear correction model for escape temperature based on a physical residual learning mechanism.

[0111] In step four, the physical prediction of the initial escape temperature of the bubbles is obtained by numerically solving the coupled moisture dynamic migration model and the bubble growth kinetics model. This predicted value, based on the equivalent simplification assumptions described in step two, can characterize the bubble generation and detachment mechanism of the oil-paper insulation system under ideal or near-uniform conditions. However, in actual operation, complex factors such as the non-uniformity of the aging distribution of the insulation paper, the random evolution of the pore structure, and the multi-bubble coupling effect are difficult to fully characterize through explicit governing equations. These unmodeled factors can lead to systematic deviations between the physical prediction results and the actual observed escape temperature.

[0112] To improve the adaptability and accuracy of the prediction results under actual engineering conditions, this step introduces a residual correction model while keeping the physical model calculation framework unchanged. This model is then applied to the physical prediction results obtained in step four. Provide equivalent compensation.

[0113] Let the actual initial bubble escape temperature under given material conditions and operating conditions be... The physical prediction residual is defined as:

[0114] (16)

[0115] In the formula, The physical prediction value obtained in step four; This represents the actual residual caused by factors such as material inhomogeneity and multi-field coupling perturbations. Among them, It can be directly calculated using deterministic physical governing equations, while It reflects the comprehensive impact of complex microstructures and multi-physics interactions under actual operating conditions, which is difficult to accurately characterize through analytical formulas or explicit control equations.

[0116] This embodiment establishes a nonlinear correction model to... An approximate estimate is performed to achieve equivalent compensation for the influence not explicitly represented in the physical model. Specifically, the nonlinear correction model is achieved by establishing a system state characteristic vector. X With actual residual Based on the mapping relationship between them, a residual prediction model is constructed to obtain the residual prediction values:

[0117] (17)

[0118] In the formula, M (·) represents the nonlinear correction model. θ For the set of model parameters, These are the predicted residual values ​​output by the model.

[0119] To ensure that the modified model remains consistent with the physical evolution process, the feature vectors X It consists of multi-source information, including material structural characteristics, operating condition characteristics, and intermediate variables of the physical model. Among these, the material structural characteristics include the degree of polymerization (DP) of the insulating paper and its initial moisture content. Equivalent pore radius and insulation paper thickness Operating characteristics include the system temperature rise rate. k Load rate and hotspot duration; intermediate variables in the physical model include peak surface moisture content. W s,max Maximum radius of the bubble r max Peak bubble growth rate ( dr / dt ) max and physical prediction of escape temperature .

[0120] In one embodiment, the nonlinear correction model employs L A layered feedforward neural network structure is implemented. This network consists of an input layer, two hidden layers, and an output layer. Each hidden layer employs a non-linear activation function to enhance the coupling and expressive power between features, and the output layer uses a linear mapping to output the residual prediction value. Its computational structure can be represented as follows:

[0121] (18)

[0122] In the formula, and The first l Layer weight matrix and bias vector; It is a nonlinear activation function. By cascading multiple linear transformations and nonlinear activation functions, a continuous approximation of the residual function is achieved, thereby improving the ability to characterize complex nonlinear disturbances.

[0123] The training samples for the model are derived from transformer field operation monitoring data and laboratory accelerated heating-induced bubble escape test data. For each set of samples, the physical prediction escape temperature is first calculated according to step four. Secondly, the corresponding actual escape temperature was obtained through experimental measurement. Then calculate the actual residual. And construct training sample pairs The model training objective is to minimize the mean squared error between the predicted and actual residuals, and its loss function is defined as:

[0124] (19)

[0125] In the formula, L loss The loss function; N This represents the number of training samples; and The first i The predicted correction and the actual correction for each training sample.

[0126] Model parameters were analyzed using the gradient descent algorithm. θ The loss function is iteratively updated to gradually converge to the minimum value, thereby obtaining the optimal residual correction model.

[0127] Step Six: Escape Temperature Layered Fusion Calculation and Final Prediction Output.

[0128] After completing the residual correction model training in step five, for new material states and operating conditions, physical model calculations are first performed according to steps one through four to obtain the physical prediction value of the initial bubble escape temperature. Then construct the corresponding feature vectors. X Inputting it into the residual correction model yields the predicted residual value. Finally, the corrected predicted escape temperature value was obtained through hierarchical fusion calculation. :

[0129] (20)

[0130] Through the aforementioned hierarchical computational mechanism, the physical mechanism model and the data-driven correction model are synergistically integrated. The physical model characterizes deterministic processes such as moisture migration and diffusion, interfacial phase change evaporation, and bubble dynamics evolution, while the residual correction model characterizes the combined effects of un-modeled factors such as material microstructure perturbations and multi-field coupling. Both are structurally independent but sequentially connected in their computational flow, thus forming an escape temperature prediction system with both physical interpretability and engineering adaptability.

[0131] Escape temperature prediction results after layered fusion This method can be used to characterize the critical temperature level at which thermally induced bubbles escape from oil-paper insulation systems under current operating conditions, providing a quantitative basis for subsequent operational status analysis and safety margin assessment. Essentially, the method proposed in this invention constructs a predictive model for the initial escape temperature of thermally induced bubbles in oil-paper insulation systems, taking into account dynamic moisture migration. This model can be used for numerical analysis and risk assessment under different moisture contents, heating rates, and structural conditions, providing a quantitative predictive means for the safe operation of oil-immersed transformer insulation systems.

[0132] The above process can be summarized as the following prediction flow:

[0133] 1. Model initialization and parameter setting: Based on the structure and operating conditions of the oil-paper insulation system to be analyzed, the moisture dynamic migration model and the bubble growth kinetics model are initialized and set.

[0134] 2. Solution of dynamic migration of moisture in insulating paper: Under given heating conditions, the dynamic migration process of moisture in the thickness direction of insulating paper is numerically solved based on a one-dimensional moisture diffusion model, and the evolution of moisture content at the oil-paper interface with time and temperature is obtained.

[0135] 3. Bubble growth kinetics calculation: Combining the water phase change evaporation mechanism and bubble kinetics theory, a kinetic model of bubble growth is constructed and numerically solved to calculate the evolution of state parameters such as the molar amount of water vapor inside the bubble and the bubble radius over time, so as to describe the growth process of bubbles from nucleation to continuous expansion in the pores of insulating paper.

[0136] 4. Bubble detachment determination and acquisition of physical prediction value of escape temperature: During the bubble growth process, the stability of the bubble is evaluated according to the preset bubble detachment determination criteria. When the detachment condition is met, the bubble is determined to have detached, and the corresponding system temperature is recorded as the physical prediction value of the initial escape temperature of the bubble.

[0137] 5. Calculation of residual correction: Construct a system state feature vector based on the physical prediction value and input it into the pre-trained residual correction model to obtain the residual prediction value of the initial escape temperature of the bubble, which is used to characterize the prediction deviation caused by unexplicitly modeled factors.

[0138] 6. Results Output and Operating Condition Analysis: The physical prediction value and the residual prediction value are fused together to calculate the final prediction result of the initial bubble escape temperature. The above prediction process can be repeated under different insulation paper moisture content, heating rate and structural parameters to realize the quantitative analysis and assessment of the risk of thermally induced bubble escape in the oil-paper insulation system.

[0139] To address the challenges of accurately determining the initial escape temperature of thermally induced bubbles in oil-paper insulation systems under continuous heating conditions, and the biased prediction results caused by existing methods neglecting the dynamic migration characteristics of moisture in the insulation paper and failing to accurately characterize complex actual operating conditions, this invention proposes a method for predicting the formation and initial escape temperature of thermally induced bubbles that considers the dynamic migration behavior of moisture in the insulation paper and incorporates a residual correction mechanism. This method first treats cellulose insulation paper as an equivalent porous microtubule structure. Based on the migration and diffusion law of moisture along the thickness direction of the insulation paper, a dynamic migration model of moisture inside the insulation paper with temperature changes is established. Combined with the transient equilibrium relationship of moisture at the oil-paper interface, a time-varying characterization of the surface moisture content of the insulation paper is achieved. Subsequently, based on classical bubble dynamics theory, a moisture phase change evaporation mechanism is introduced. Combining the ideal gas law and the Rayleigh–Plesset equation, a dynamic model describing the continuous entry of water vapor into bubbles and driving bubble growth is constructed to characterize the nucleation and expansion process of bubbles within the pores of the insulation paper. Furthermore, by establishing a force balance criterion for the growth of bubbles on the insulating paper surface, the critical conditions for bubble instability and detachment from the insulating paper surface are determined, thereby obtaining a physical prediction result of the initial escape temperature of thermally induced bubbles. Based on this, to address prediction biases that may be caused by un-modeled factors such as material aging non-uniformity, random evolution of pore structure, and multi-bubble coupling disturbances, a nonlinear correction model based on the physical prediction residual is constructed to equivalently compensate for the physical prediction results. The final predicted value of the initial escape temperature of the bubbles is obtained through hierarchical fusion calculation. This method improves the adaptability and accuracy stability of the prediction results in complex engineering operating environments while maintaining the interpretability of the physical mechanism.

[0140] The technical solution of this embodiment constructs a prediction model for the initial escape temperature of thermally induced bubbles, which takes into account the dynamic migration behavior of moisture in insulating paper and the correction mechanism of physical prediction residuals. This model has important research significance and practical value for revealing the formation mechanism of thermally induced bubbles in oil-paper insulation systems and improving the rationality and engineering applicability of the prediction of the initial escape temperature of bubbles.

[0141] Example 2

[0142] The purpose of this embodiment is to provide a computer device, including a memory, a processor, and a computer program stored in the memory and executable on the processor, wherein the processor executes the program to implement the steps of the above-described method.

[0143] Example 3

[0144] The purpose of this embodiment is to provide a computer-readable storage medium.

[0145] A computer-readable storage medium having a computer program stored thereon, which, when executed by a processor, performs the steps of the above method.

[0146] Example 4

[0147] The purpose of this embodiment is to provide a system for predicting the bubble escape temperature under dynamic moisture migration in oil-paper insulation, including:

[0148] The dynamic migration model construction module is configured to: treat cellulose insulating paper as a porous microtubule structure, and establish a dynamic migration model of moisture inside cellulose insulating paper as temperature changes based on the migration and diffusion law of moisture in the thickness direction of cellulose insulating paper.

[0149] The initialization setting module is configured to: initialize the dynamic migration model based on the structural parameters and operating conditions of the cellulose insulating paper, in order to determine the initial state of moisture migration and bubble growth inside the cellulose insulating paper;

[0150] The solver module is configured to: based on the initial state and under given temperature rise conditions, numerically couple the equation for the dynamic migration of moisture in cellulose insulating paper and the model for bubble growth kinetics to obtain the physical prediction of the initial escape temperature of the bubbles.

[0151] The residual correction module is configured to: construct a residual correction model based on the physical prediction value and the actual observation data, and output the residual prediction value of the initial escape temperature of the bubble;

[0152] The fusion output module is configured to fuse the physical prediction value and the residual prediction value to obtain the final prediction result of the initial escape temperature of the bubble.

[0153] This embodiment introduces a dynamic moisture migration model for oil-paper insulation systems, extending the moisture content of the insulation paper from a static constant to a dynamic variable that evolves over time. This model is then coupled with the bubble growth kinetics calculation to obtain a physical prediction of the initial bubble escape temperature. Furthermore, a nonlinear correction model for the physical prediction residual is constructed to effectively compensate for factors such as material inhomogeneity not explicitly modeled, multi-field coupling disturbances, and stochastic structural evolution. This achieves a more accurate prediction of the initial bubble escape temperature that reflects actual operating conditions. This solves the problem of insufficient accuracy in bubble escape temperature prediction in existing technologies due to neglecting dynamic moisture migration and complex engineering disturbances, thus improving the reliability and engineering applicability of bubble risk assessment.

[0154] Example 5

[0155] The purpose of this embodiment is to provide a computer program product containing instructions that, when run on a computer, cause the computer to perform the methods and functions involved in any of the above embodiments.

[0156] The steps and methods involved in the apparatus of the above embodiments correspond to those in Embodiment 1. For specific implementation details, please refer to the relevant description section of Embodiment 1. The term "computer-readable storage medium" should be understood as a single medium or multiple media including one or more instruction sets; it should also be understood as including any medium capable of storing, encoding, or carrying an instruction set for execution by a processor and enabling the processor to perform any of the methods in this invention.

[0157] Those skilled in the art will understand that the modules or steps of the present invention described above can be implemented using general-purpose computer devices. Optionally, they can be implemented using computer-executable program code, thereby allowing them to be stored in a storage device for execution by a computer device, or they can be fabricated as separate integrated circuit modules, or multiple modules or steps can be fabricated as a single integrated circuit module. The present invention is not limited to any particular combination of hardware and software.

[0158] While the specific embodiments of the present invention have been described above in conjunction with the accompanying drawings, this is not intended to limit the scope of protection of the present invention. Those skilled in the art should understand that various modifications or variations that can be made by those skilled in the art without creative effort based on the technical solutions of the present invention are still within the scope of protection of the present invention.

Claims

1. A method for predicting bubble escape temperature under dynamic moisture migration in oil-paper insulation, characterized by: include: Cellulose insulating paper is equivalent to a porous microtubule structure. Based on the migration and diffusion law of moisture in the thickness direction of cellulose insulating paper, a dynamic migration model of moisture inside cellulose insulating paper with temperature change is established. The moisture migration and diffusion process inside the insulating cardboard follows Fick's second diffusion law, and its governing equation is: In the formula, Let be the mass fraction of moisture in the insulating paper at point x along the thickness direction of the insulating paper at time t, %; x is the coordinate value of the insulating paperboard along the thickness direction, mm; and let x=0 be the interface between the insulating paper and the winding. Let m be the diffusion coefficient of moisture in the insulating paper. 2 / s; The distribution of moisture inside the insulating paper and its dynamic evolution over time were obtained, and the surface moisture mass fraction at the oil-paper interface was obtained. The interface moisture content was used as a key input to the bubble interface evaporation model to characterize the water vapor supply capacity during the bubble generation process. Based on the obtained moisture content of the surface layer at the oil-paper interface, a bubble growth kinetic model was further established. The dynamic migration model is initialized based on the structural parameters and operating conditions of the cellulose insulating paper to determine the initial state of moisture migration and bubble growth inside the cellulose insulating paper. Based on the initial state and given temperature rise conditions, the dynamic migration equation of moisture in cellulose insulating paper and the bubble growth kinetic model are coupled numerically solved to obtain the physical prediction value of the initial escape temperature of the bubbles. A residual correction model is constructed based on physical predictions and actual observation data, and the residual prediction value of the initial escape temperature of the bubble is output. The physical prediction value and the residual prediction value are fused together to obtain the final prediction result of the initial escape temperature of the bubble. It also includes: constructing physical prediction residual sample data based on the difference between the physical prediction value of the initial escape temperature of the bubble and the actual escape temperature obtained by experimental measurement; establishing a nonlinear mapping relationship between the system state feature vector and the prediction residual, constructing a residual correction model, and outputting the escape temperature residual prediction value; The residual correction model uses material structure parameters, operating condition parameters, and intermediate state variables in the bubble growth kinetics model as input features. By establishing a nonlinear mapping relationship between the input features and the physical prediction residual, the physical prediction residual is modeled and corrected to compensate for the deviation of the prediction results caused by factors not explicitly modeled in the physical model. The physical prediction value of the initial bubble escape temperature is fused with the residual prediction value to calculate the final prediction result of the initial bubble escape temperature. The process of calculating the prediction result of the initial bubble escape temperature can be repeated under different insulation paper moisture content, heating rate and structural parameters, so as to realize the quantitative analysis and assessment of the risk of thermal bubble escape in the oil paper insulation system. Let the actual initial bubble escape temperature under given material conditions and operating conditions be... The physical prediction residual is defined as: In the formula, The physical prediction value obtained in step four; This refers to the actual residual caused by factors such as material inhomogeneity and multi-field coupling perturbations; among which, It can be directly calculated using deterministic physical governing equations, while It reflects the comprehensive impact of complex microstructures and multi-physics interactions under actual operating conditions; By establishing a nonlinear correction model... An approximate estimate is performed to achieve equivalent compensation for the influence not explicitly represented by the physical model. Specifically, the nonlinear correction model is established by creating a system state feature vector. X With actual residual Based on the mapping relationship between them, a residual prediction model is constructed to obtain the residual prediction values: In the formula, M (·) represents the nonlinear correction model. θ For the set of model parameters, These are the predicted residual values ​​output by the model; The feature vector X It consists of multi-source information, including material structural characteristics, operating condition characteristics, and intermediate variables of the physical model. Among them, the material structural characteristics include the degree of polymerization (DP) of the insulating paper and the initial moisture content. Equivalent pore radius and insulation paper thickness Operating characteristics include the system temperature rise rate. k Load rate and hotspot duration; intermediate variables in the physical model include peak surface moisture content. W s,max Maximum radius of the bubble r max Peak bubble growth rate ( dr / dt ) max and physical prediction of escape temperature ; The nonlinear correction model adopts L A layered feedforward neural network structure is implemented; the network includes an input layer, two hidden layers and an output layer. Each hidden layer uses a non-linear activation function to enhance the coupling and expressive ability between features, and the output layer uses a linear mapping to output the residual prediction value. By cascading multiple linear transformations and nonlinear activation functions, a continuous approximation of the residual function is achieved, thereby improving the ability to characterize complex nonlinear disturbances. The training samples for the model are derived from transformer field operation monitoring data and laboratory accelerated heating induced bubble escape test data. For each set of samples, the physical prediction escape temperature is first calculated according to step four. Secondly, the corresponding actual escape temperature was obtained through experimental measurement. Then calculate the actual residual. And construct training sample pairs The model training objective is to minimize the mean squared error between the predicted and actual residuals, and its loss function is defined as: In the formula, L loss The loss function; N This represents the number of training samples; and The first i The predicted correction and the actual correction for each training sample; The model parameters θ are iteratively updated using the gradient descent algorithm, causing the loss function to gradually converge to its minimum value, thereby obtaining the optimal residual correction model.

2. The method for predicting bubble escape temperature under dynamic moisture migration in oil-paper insulation as described in claim 1, characterized in that, The structural parameters of the cellulose insulating paper include: insulating paper thickness, equivalent pore size, and microtube geometry, which are used to characterize the moisture migration path and the space for bubble nucleation and growth; the operating parameters of the cellulose insulating paper include initial moisture content, ambient pressure, and system temperature rise method.

3. The method for predicting bubble escape temperature under dynamic moisture migration in oil-paper insulation as described in claim 1, characterized in that it further... include: The bubble radius, volume, and water vapor state parameters inside the bubble are updated step by step, and the stress state or evolution characteristics of the bubble at the outlet of the insulating paper pores are calculated simultaneously. When calculating the stress state or evolution characteristics of the bubble at the outlet of the insulating paper pores, the specific calculation of the molar amount of water vapor inside the bubble and the evolution of the bubble radius state parameters over time is used to describe the growth process of the bubble from nucleation to continuous expansion in the insulating paper pores.

4. A system for predicting the bubble escape temperature under dynamic moisture migration in oil-paper insulation using the method described in claim 1, characterized in that, include: The dynamic migration model construction module is configured to: treat cellulose insulating paper as a porous microtubule structure, and establish a dynamic migration model of moisture inside cellulose insulating paper as temperature changes based on the migration and diffusion law of moisture in the thickness direction of cellulose insulating paper. The initialization setting module is configured to initialize the dynamic migration model based on the structural parameters and operating conditions of the cellulose insulating paper, in order to determine the initial state of moisture migration and bubble growth inside the cellulose insulating paper. The solver module is configured to perform coupled numerical solutions on the dynamic migration equation of moisture in cellulose insulating paper and the bubble growth kinetic model based on the initial state and a given temperature rise condition, so as to obtain the physical prediction value of the initial escape temperature of the bubbles. The residual correction module is configured to: construct a residual correction model based on the physical prediction value and the actual observation data, and output the residual prediction value of the initial escape temperature of the bubble; The fusion output module is configured to fuse the physical prediction value and the residual prediction value to obtain the final prediction result of the initial escape temperature of the bubble.

5. A computer program product, comprising a computer program, characterized in that, When the computer program is executed by a processor, it implements the method of any one of claims 1 to 3.

6. A computer device comprising a memory, a processor, and a computer program stored in the memory and executable on the processor, characterized in that, When the processor executes the program, it implements the steps of the method described in any one of claims 1-3.

7. A computer-readable storage medium having a computer program stored thereon, characterized in that, When the program is executed by the processor, it performs the steps of the method described in any one of claims 1-3 above.

Images