Method and system for predicting life of cmas erosion coating based on physical information neural network

Abstract

The application discloses a CMAS erosion coating life prediction method and system based on a physical information neural network, and relates to the field of high-temperature material performance prediction of an aero-engine. The method comprises the following steps: collecting experimental data of a CMAS erosion thermal barrier coating and constructing a material input vector and a physical field input vector; a physical information neural network is built, which simultaneously outputs a stress field, a CMAS concentration field, a reaction-degradation state field and a displacement field of the coating in a time-depth domain; a life prediction network is built, which fuses the four physical field features and the backbone hidden features of the material input vector and then outputs a coating life prediction value; a physical constraint model of mechanical equilibrium, constitutive consistency, CMAS diffusion, chemical reaction and damage evolution as well as boundary and initial conditions is established, physical matching points are generated in the time-depth domain, the two networks are jointly trained based on a joint loss function, and a life prediction model is obtained.

Description

Technical Field

[0001] This invention relates to the field of high-temperature material performance prediction for aero-engines, specifically to a CMAS erosion coating lifetime prediction method and system based on physical information neural networks. Background Technology

[0002] Thermal barrier coatings (TBCs) are core protective materials for high-temperature hot-end components of aero-engines and gas turbines, and their service life directly affects the overall safety and reliability of the aircraft. In actual service environments, foreign deposits such as dust and volcanic ash melt at high temperatures to form CMAS (calcium magnesium aluminum silicate) melts. These melts penetrate and wet the coating pores and crack networks, undergoing complex physicochemical reactions with the ceramic layer, significantly accelerating coating degradation. Therefore, accurately predicting the service life of TBCs under CMAS erosion conditions is a key technical issue in the research and engineering application of high-temperature protective materials.

[0003] Currently, the assessment and prediction of thermal barrier coating lifetime under CMAS (Complex Component Algebraic Acid) mainly employs methods such as high-temperature thermal shock testing, empirical regression models, finite element numerical simulation, and mechanism-based evolution analysis. While high-temperature thermal shock testing can directly obtain lifetime data, it suffers from long testing cycles, high costs, and a limited range of CMAS composition systems and temperature conditions it can cover, making it difficult to meet the needs of large-scale material screening and operational condition assessment. Empirical regression models or semi-empirical prediction models offer high computational efficiency, but they struggle to accurately characterize the multi-factor coupling relationships between diffusion, penetration, thermal stress, chemical reactions, and damage evolution during CMAS erosion, significantly limiting their prediction accuracy and generalization ability under complex operating conditions. While traditional finite element simulations or mechanistic models can analyze local stress, temperature fields, or damage states from a physical perspective, these methods require the prior determination of relatively complete material parameters, boundary conditions, and evolution equations. However, key parameters in the CMAS erosion process, such as the effective diffusion amplitude parameter, effective pre-reaction factor, apparent activation energy parameter, and equivalent permeability coefficient, are usually affected by factors such as CMAS composition, temperature, material microstructure, and service history. They have strong uncertainties and conditional sensitivity, making them difficult to obtain accurately. Improper parameter selection will directly affect the reliability of the calculation results.

[0004] In recent years, data-driven models have provided a new approach for performance prediction of complex material systems, promising to directly learn lifetime response laws from inputs such as material composition, service temperature, and environmental characteristics. However, lifetime prediction of CMAS (Conditional Condition Assurance System) erosion thermal barrier coatings faces the typical problem of small sample size: on the one hand, related experiments are time-consuming and costly, resulting in very limited effective lifetime data; on the other hand, the lifetime evolution process is governed by multiple coupling mechanisms, and relying solely on data fitting can easily lead to model overfitting, insufficient extrapolation ability, and lack of physical consistency. Furthermore, traditional black-box neural networks struggle to reveal the evolution of key intermediate physical fields during degradation, and prediction results often lack interpretability, failing to meet the engineering requirements for assessing the credibility of prediction conclusions. Physical information neural networks (PINs) embed the governing equations, boundary conditions, initial conditions, and physical priors into the network training process, enabling the model to satisfy basic physical constraints while fitting observational data. This results in better physical consistency and generalization ability under data scarcity. However, currently, there is a lack of effective solutions that integrate PINs with lifetime prediction, combining simultaneous modeling of four physical fields and simultaneous inversion of key physical parameters in thermal barrier coating systems.

[0005] In summary, existing technologies have not yet solved the technical problem of performing high-precision, physically interpretable, and simultaneously lifetime prediction and key mechanism parameter inversion on CMAS-eroded thermal barrier coatings under conditions of limited experimental samples, complex physical mechanisms, and difficulty in accurately obtaining key parameters. Summary of the Invention

[0006] This disclosure provides a method and system for predicting the lifetime of CMAS-eroded thermal barrier coatings based on physical information neural networks.

[0007] In a first aspect, this disclosure provides a method for predicting the lifetime of CMAS-eroded coatings based on a physical information neural network, including:

[0008] Experimental data on CMAS erosion of thermal barrier coatings were collected. After preprocessing the experimental data, a material input vector was constructed. Based on the material input vector, time coordinates and depth coordinates were introduced to construct a physical field input vector.

[0009] A physical information neural network backbone network is constructed. The physical information neural network backbone network takes the physical field input vector as input and outputs the physical field features of the backbone hidden features, the stress field of the coating in the time-depth domain, the CMAS concentration field, the reaction-degradation state field and the displacement field.

[0010] A lifetime prediction network is constructed by fusing the physical field characteristics of the stress field, the concentration field, the reaction-degradation state field, and the displacement field with the backbone hidden features and inputting them into the lifetime prediction network, and outputting the coating lifetime prediction value.

[0011] Based on the deviation between the predicted coating lifetime and the actual lifetime, the physical information neural network backbone and the lifetime prediction network are jointly trained using physical constraint loss to obtain the trained lifetime prediction model.

[0012] The content of the CMAS component to be tested, temperature, and viscosity are input into the trained lifetime prediction model, and the coating lifetime prediction value is output.

[0013] Optionally, the joint training further includes:

[0014] A physical constraint model is established, which includes mechanical loss constraints, CMAS diffusion loss constraints, chemical loss constraints, as well as boundary conditions and initial conditions constraints.

[0015] The effective diffusion amplitude parameter, effective pre-reaction factor, apparent activation energy parameter, and equivalent permeability coefficient in the physical constraint model are set as trainable physical parameters.

[0016] Generate physical collocations in the time-depth domain;

[0017] The physical loss term is calculated based on the physical collocation points and the physical constraint model. A joint loss function is constructed by combining the data fitting loss term between the predicted coating lifetime and the actual lifetime value, and the parameter regularization loss term of the trainable physical parameters.

[0018] The physical information neural network backbone and the lifetime prediction network are jointly trained using the joint loss function, and the trainable physical parameters are simultaneously inverted and identified during the training process to obtain the trained lifetime prediction model.

[0019] Optionally, the physical constraint model includes:

[0020] Mechanical loss term: The elastic modulus is set as a function of the reaction-degradation state field, the displacement gradient is calculated from the displacement field, the constitutive stress is constructed based on the displacement gradient and the elastic modulus, and the mechanical loss term is constructed using the stress balance residual and the constitutive consistency residual, respectively.

[0021] Diffusion loss term: Establish an effective diffusion coefficient coupled with temperature and viscosity, construct the diffusion equation residual based on the effective diffusion coefficient and the concentration field, and apply focusing weights in the shallow region and the early time region to construct the diffusion loss term using the weighted diffusion residual;

[0022] Chemical loss term: Construct an Arrhenius-type reaction rate expression, use a Washburn-type penetration depth relationship to determine the position of the penetration front, construct a smoothing switching function based on the position of the penetration front to distinguish between the penetrated and non-penetrated areas, and construct the damage evolution residual from the reaction rate, the concentration field, and the reaction-degradation state field. Apply weights to the penetration front zone and the active reaction zone, and construct the chemical loss term from the weighted damage evolution residual.

[0023] Boundary loss term and initial loss term: The surface concentration boundary is set to an exponentially approaching saturation value over time, and the bottom concentration gradient and damage gradient are set to zero; the displacement field, reaction-degradation state field and stress field at the initial moment are set to zero, and the initial concentration value in the region outside the preset thickness of the surface is set to zero.

[0024] Optionally, the trainable physical parameters are bounded reparameterized using a Sigmoid function mapping or a logarithmic space mapping, so that the trainable physical parameters remain within a preset physical feasible region during the training process.

[0025] Optionally, generating physical collocation points in the time-depth domain includes: generating collocation points using Latin hypercube sampling in a two-dimensional domain consisting of normalized time and normalized depth, and performing hotspot-intensive sampling in the early time region, shallow depth region, and penetration front region.

[0026] Optionally, the joint loss function is composed of a weighted sum of the data fitting loss term, multiple physical loss sub-terms, and the parameter regularization loss term. During training, the weights of each physical loss sub-term are dynamically adjusted, and the dynamic weights are calculated using the Softmax function based on the ratio of each sub-term loss to the initial loss.

[0027] Optionally, the preprocessing includes:

[0028] The experimental data were checked for missing values, outliers, and units were standardized. The input variables and lifetime labels were Z-score standardized and the training and validation sets were divided according to a preset ratio.

[0029] The material input vector is composed of the CMAS principal oxide composition content, the CMAS melt viscosity, and the thermal shock test temperature.

[0030] The physical field input vector incorporates normalized time coordinates and normalized depth coordinates based on the material input vector.

[0031] Optionally, the physical information neural network is a fully connected network with residual connections between adjacent equal-dimensional hidden layers, and layer normalization and Dropout are introduced; the stress field, the concentration field, the reaction-degradation state field, and the displacement field are output as four independent output heads from the shared hidden features; wherein, the stress field is multiplied by a stress scaling factor before output, the reaction-degradation state field is constrained to the 0-1 interval by a Sigmoid function, and the displacement field is set to zero at the bottom depth position.

[0032] Optionally, the physical information neural network backbone takes the physical field input vector as input and outputs the physical field features of the backbone hidden features, the stress field, CMAS concentration field, reaction-degradation state field, and displacement field of the coating in the time depth domain. It then fuses the physical field features of the stress field, the concentration field, the damage variable field, and the displacement field with the material input vector, including:

[0033] The hidden features of the backbone are extracted from the terminal hidden layer of the physical information neural network, and the stress field, concentration field, reaction-degradation state field and displacement field are constructed based on the hidden features of the backbone.

[0034] Secondly, the present invention discloses a CMAS erosion coating lifetime prediction system based on a physical information neural network, characterized in that it includes:

[0035] The data acquisition module is used to collect experimental data of CMAS erosion thermal barrier coating. After preprocessing the experimental data, a material input vector is constructed, and time coordinates and depth coordinates are introduced on the basis of the material input vector to construct a physical field input vector.

[0036] The physical information neural network module is used to build the backbone network of the physical information neural network. The physical information neural network takes the physical field input vector as input and outputs the physical field features of the backbone hidden features, the stress field of the coating in the time-depth domain, the CMAS concentration field, the reaction-degradation state field and the displacement field.

[0037] The lifetime prediction network module is used to build a lifetime prediction network. It integrates the physical field characteristics of the stress field, the concentration field, the reaction-degradation state field and the displacement field with the backbone hidden features and inputs them into the lifetime prediction network to output the coating lifetime prediction value.

[0038] The joint training module is used to jointly train the physical information neural network backbone network and the lifetime prediction network based on the deviation between the coating lifetime prediction value and the actual lifetime value, combined with physical constraint loss, to obtain the trained lifetime prediction model.

[0039] The lifetime prediction module is used to input the content of the CMAS component to be tested, temperature and viscosity into the trained lifetime prediction model, and output the coating lifetime prediction value.

[0040] The beneficial effects of this disclosure are that, compared with the prior art, this disclosure has the following advantages:

[0041] 1) This invention breaks through the dependence of existing thermal barrier coating lifetime prediction methods on a large number of experimental samples. By embedding the physical constraint model into the joint training process of the neural network, the stress field, concentration field, reaction-degradation state field and displacement field in the CMAS erosion process are modeled simultaneously. This enables the coating lifetime prediction results with strong physical consistency and high prediction accuracy to be obtained even under the condition of limited experimental data and small sample size, which significantly improves the applicability and reliability of the model in the material lifetime assessment scenario.

[0042] 2) This invention innovatively sets key physical parameters such as effective diffusion amplitude parameter, effective pre-reaction factor, apparent activation energy parameter and equivalent permeability coefficient as trainable variables, and incorporates these parameters into the physical constraint model of CMAS erosion for joint optimization and synchronous inversion identification. This enables the lifetime prediction model after training to output the coating lifetime prediction value and simultaneously provide the corresponding key mechanism parameter identification results. This effectively solves the technical problem of the difficulty in accurately obtaining key physical parameters in traditional methods, and enhances the interpretability and engineering analysis value of the prediction results.

[0043] 3) This invention constructs a complete physical constraint system covering mechanical equilibrium, constitutive consistency, CMAS diffusion, chemical reaction and damage evolution, as well as boundary and initial conditions. It explicitly embeds the multi-physics coupling mechanism of coating degradation into the network training process, overcoming the shortcomings of existing pure data-driven models in lack of physical consistency and insufficient extrapolation ability. At the same time, it adopts training strategies such as collocation hotspot encryption, bounded reparameterization of trainable parameters, and dynamic weight adjustment of loss function to improve the convergence efficiency and prediction accuracy of the model in key local areas such as penetration front, early time and shallow region. Attached Figure Description

[0044] The accompanying drawings, which are incorporated in and form a part of this specification, illustrate embodiments consistent with this disclosure and, together with the description, serve to explain the principles of this disclosure.

[0045] Figure 1 This is a flowchart illustrating the overall process of the CMAS erosion coating lifetime prediction method based on physical information neural networks of the present invention.

[0046] Figure 2 This is a flowchart of the lifespan prediction model obtained through joint training in this invention;

[0047] Figure 3This is a schematic diagram of the structure of the physical information neural network backbone network and the lifetime prediction network outputting the average lifetime in this invention;

[0048] Figure 4 This is a schematic diagram of the training architecture of the physical information neural network-lifetime prediction joint model in this invention.

[0049] The accompanying drawings have illustrated specific embodiments of this disclosure, which will be described in more detail below. These drawings and descriptions are not intended to limit the scope of the concept in any way, but rather to illustrate the concepts of this disclosure to those skilled in the art through reference to particular embodiments. Detailed Implementation

[0050] The present disclosure will be further described below with reference to the accompanying drawings. The following embodiments are only used to illustrate the technical solutions of the present disclosure more clearly, and should not be used to limit the scope of protection of the present disclosure.

[0051] Figure 1 This is a flowchart illustrating the overall process of the CMAS erosion coating lifetime prediction method based on a physical information neural network according to the present invention. See also... Figure 1 The following is a detailed discussion of each step in conjunction with this embodiment.

[0052] S100. Collect experimental data of CMAS erosion thermal barrier coating. After preprocessing the experimental data, construct a material input vector and introduce time coordinates and depth coordinates on the basis of the material input vector to construct a physical field input vector.

[0053] This step is the data preparation stage of the entire method, aiming to transform the raw experimental records into structured inputs that can be directly processed by the backbone network of the subsequent Physics-Informed Neural Network (PINN). Specifically, high-temperature thermal shock experimental data of CMAS erosion of thermal barrier coatings are first collected. After data cleaning and standardization, temperature, viscosity, and the content of CMAS principal oxide components are organized into a material input vector to describe the service conditions of the coating and the intrinsic properties of the material. Based on this, normalized time coordinates and normalized depth coordinates are further introduced to form a physical field input vector, providing the necessary spatiotemporal annotations for the subsequent network to simultaneously output stress field, concentration field, reaction-degradation state field, and displacement field in the time-depth domain. The specific implementation method of this step is described in detail below:

[0054] S110. Perform missing value checks, outlier checks, and unit unification processing on the experimental data. Perform Z-Score standardization on the input variables and lifetime labels respectively, and divide the training set and validation set according to a preset ratio.

[0055] In this embodiment, the collected experimental data on CMAS erosion thermal barrier coatings include the content of CMAS major oxide components, CMAS melt viscosity, thermal shock test temperature, and corresponding coating lifetime. Specifically, sample failure is defined as the number of thermal cycles recorded at this point when the area of ​​coating peeling exceeds 20% of the total coating area.

[0056] The collected raw experimental data were first checked for missing values ​​and outliers, and units were standardized. To eliminate the influence of different units on model training, the input variables and lifetime labels were Z-score standardized, with the expression:

[0057]

[0058]

[0059] in, Represents any component in the input variable. and These represent the mean and standard deviation of the component on the training set, respectively. For lifespan, and These represent the mean and standard deviation of lifetimes on the training set, respectively. The preprocessed data is divided into a training set and a validation set according to a preset ratio.

[0060] S120. Construct a material input vector, which is composed of the CMAS principal oxide composition content, the CMAS melt viscosity, and the thermal shock test temperature.

[0061] The standardized temperature, viscosity, and content of ten CMAS principal oxide components were used to construct the material input vector:

[0062]

[0063] in For temperature, It represents viscosity. The content of 10 oxide components.

[0064] S130. Based on the material input vector, normalized time coordinates and normalized depth coordinates are introduced to construct the physical field input vector.

[0065] Further, time and depth coordinates are introduced to construct the physics input vector:

[0066]

[0067] in, For normalized time coordinates, Normalized depth coordinates are defined as follows:

[0068]

[0069] in, For physical time, For physical depth, For time scale, This refers to the coating thickness.

[0070] S200. Construct a physical information neural network backbone network. The physical information neural network backbone network takes the physical field input vector as input and outputs the backbone hidden features, the stress field of the coating in the time-depth domain, the CMAS concentration field, the reaction-degradation state field, and the displacement field.

[0071] This step is the core modeling stage of physical field reconstruction, aiming to construct a neural network capable of directly mapping service conditions and spatiotemporal coordinates to the multi-physics distribution within the coating. Unlike traditional surrogate models that only output a single scalar, the PINN backbone network here takes the physical field input vector constructed in S130 as input and outputs four physical fields: the backbone hidden features, the stress field of the coating in the time-depth domain, the CMAS concentration field, the reaction-degradation state field, and the displacement field. This achieves an integrated characterization of the coupled states of multiple physical fields, such as diffusion, thermal stress, chemical reactions, and damage evolution during CMAS erosion. The joint output of these four physical fields not only provides physically meaningful intermediate features for the subsequent lifetime prediction network in S300 but also provides directly verifiable field quantity objects for applying the physical constraint model in S400.

[0072] In this embodiment, the PINN backbone network is a fully connected network with residual connections between adjacent equal-dimensional hidden layers, and layer normalization and Dropout are introduced. The stress field, concentration field, reaction-degradation state field, and displacement field are output separately from the shared hidden features as four independent output heads. The stress field is multiplied by a stress scaling factor before output, the reaction-degradation state field is constrained to the 0-1 interval by the Sigmoid function, and the displacement field is set to zero at the bottom depth position.

[0073] The specific implementation method of this step will be explained in detail below.

[0074] A PINN backbone network is established, using the physical field input vector as input, to learn the multiphysics distribution of the thermal barrier coating in the time-depth domain under CMAS erosion conditions. The hidden layer structure of the PINN backbone network is set to 128, 128, 64, 64, 32, and the activation function is Tanh. Let the PINN backbone network be represented as... Its output backbone hidden features are:

[0075]

[0076] Based on the hidden feature h of the backbone, stress field, concentration field, reaction-degradation state field, and displacement field are constructed and output respectively:

[0077]

[0078] in, For stress field, For CMAS concentration field, For the reaction-degenerate state field, For displacement field, This is the stress scaling factor.

[0079] The stress scaling factor is determined by the elastic modulus, coefficient of thermal expansion, coefficient of phase transformation expansion, and temperature fluctuation range, and can be expressed as:

[0080]

[0081] in, The elastic modulus after densification. The coefficient of thermal expansion is... The phase transition expansion coefficient is... To prevent extremely small positive numbers with a denominator of zero, and

[0082]

[0083] By introducing in the damage item Introduced in the displacement term This allows the model to possess prior structural features such as initial damage and displacement approaching zero and bottom displacement being restricted.

[0084] S300. Construct a lifetime prediction network by fusing the physical field characteristics of the stress field, the concentration field, the reaction-degradation state field, and the displacement field with the backbone hidden features, and then inputting the network into the lifetime prediction network to output the coating lifetime prediction value.

[0085] This step is the conversion from physical field to lifetime. It aims to fuse the degradation state information contained in the four physical fields output by the S200 with the hidden features of the backbone, and output a coating lifetime prediction value through an independent lifetime prediction network. Unlike black-box models that directly map from raw data to lifetime, this lifetime prediction network is built upon physically meaningful intermediate field quantities output by the PINN backbone network. This ensures that the lifetime prediction value not only relies on the statistical regularities of experimental data but also uses the internal stress distribution of the coating, the degree of CMAS penetration, the damage accumulation state, and deformation characteristics as inference bases, thereby enhancing the physical interpretability of the prediction results.

[0086] In this embodiment, fusing the physical field features of the stress field, the concentration field, the reaction-degradation state field, and the displacement field with the backbone hidden features includes: extracting backbone hidden features from the terminal hidden layer of the PINN backbone network, extracting field features from the stress field, the concentration field, the reaction-degradation state field, and the displacement field respectively, and inputting the backbone hidden features and each of the field features into the lifetime prediction network.

[0087] The specific implementation method of this step will be explained in detail below.

[0088] An independent lifetime prediction network is set up after the PINN backbone network, and the backbone hidden features are fused with the physical field output for lifetime prediction. The backbone hidden features extracted from the terminal hidden layer of the PINN backbone network are concatenated with stress features, concentration features, damage features, and displacement features to construct the input of the lifetime prediction network:

[0089]

[0090] in, These are the hidden features of the PINN backbone network output. , , and These represent the stress field, concentration field, reaction-degradation state field, and displacement field, respectively, with LayerNorm being the layer normalization operation.

[0091] The lifetime prediction network outputs lifetime values:

[0092]

[0093] in, For the hidden layer mapping of the lifetime prediction network, the hidden layer structure of the lifetime prediction network is set to 64 and 32. and These are the weights and biases for the output layer.

[0094] S400. Based on the deviation between the predicted coating lifetime and the actual lifetime, the physical information neural network backbone and the lifetime prediction network are jointly trained using physical constraint loss to obtain the trained lifetime prediction model.

[0095] This step is the core training stage for physical constraint embedding and parameter inversion. It aims to explicitly embed the multi-physics coupling mechanism of CMAS erosion of thermal barrier coatings into the network training process, ensuring that the final lifetime prediction model not only fits experimental data but also follows physical laws such as mechanical equilibrium, diffusion, chemical reaction, and damage evolution. Unlike traditional pure data-driven training methods that only optimize data fitting loss, this joint training mechanism introduces physical loss terms in addition to data fitting loss. These terms encompass mechanical equilibrium constraints, constitutive consistency constraints, CMAS diffusion constraints, chemical reaction and damage evolution constraints, as well as boundary and initial condition constraints. Furthermore, key physical parameters such as the effective diffusion amplitude parameter, effective pre-reaction factor, apparent activation energy parameter, and equivalent permeability coefficient from each physical loss term are set as trainable variables and inverted simultaneously during training. By generating physical collocations in the time-depth domain, calculating physical loss terms based on the physical collocations and the physical constraint model, and combining the data fitting loss term between the predicted coating lifetime and the actual lifetime value with the parameter regularization loss term of the trainable physical parameters, a joint loss function is constructed. This allows the network to be driven by experimental data and constrained by physical laws during training, while adaptively identifying key mechanism parameters that are difficult to obtain accurately in traditional methods.

[0096] S500: Input the content of the CMAS component to be tested, temperature and viscosity into the trained lifetime prediction model, and output the coating lifetime prediction value.

[0097] This step is the model usage phase. After the S400 completes joint training and obtains the trained lifetime prediction model, this model is used to predict lifetime and retrieve mechanistic parameters for new CMAS erosion conditions. In use, only the CMAS principal oxide content, CMAS melt viscosity, and thermal shock test temperature of the sample to be tested need to be input into the trained lifetime prediction model. The model first generates the stress field, CMAS concentration field, reaction-degradation state field, and displacement field of the coating in the time-depth domain through the PINN backbone network. Then, the lifetime prediction network outputs the coating lifetime prediction value based on the physical field characteristics and the hidden features of the backbone.

[0098] Figure 2 This is a flowchart illustrating the lifespan prediction model obtained through joint training in this invention. Now, combined with... Figure 2 The specific embodiments of this application are further described below.

[0099] S410. Establish a physical constraint model, which includes mechanical loss constraints, CMAS diffusion loss constraints, chemical loss constraints, and boundary conditions and initial conditions constraints.

[0100] This step is the implementation stage of embedding physical laws in joint training. It aims to explicitly embed the multi-physics coupling mechanism followed by CMAS during the erosion of thermal barrier coatings into the network training process in the form of quantifiable mathematical constraints. Unlike traditional training methods that rely solely on data fitting loss, the physical constraint model established in this step ensures that the stress and displacement fields satisfy the fundamental laws of solid mechanics through mechanical equilibrium equations, guarantees thermodynamic consistency between stress output and displacement gradient through constitutive consistency constraints, ensures that the spatiotemporal evolution of the concentration field conforms to mass transfer laws through CMAS diffusion equation constraints, and ensures that the coupling relationship between damage accumulation and reaction kinetics and penetration front advancement is followed through chemical reaction and damage evolution equation constraints. Furthermore, boundary condition constraints and initial condition constraints define the definite states of each physical field at the coating surface, bottom interface, and initial time. These physical constraints collectively constitute the source of the physical loss term in network training, ensuring that the model, while fitting limited experimental data, must adhere to the fundamental physical laws of coating degradation, thereby obtaining prediction results with strong physical consistency and reliable extrapolation ability under small sample conditions.

[0101] In this embodiment, the physical constraint model specifically includes a mechanical loss term, a diffusion loss term, a chemical loss term, a boundary loss term, and an initial loss term.

[0102] The following provides a detailed explanation of the specific implementation methods for each physical constraint.

[0103] Mechanical loss term: The mechanical loss term is used to constrain the mechanical consistency between the internal stress field, displacement field, and reaction-degradation state field of the coating. In this embodiment, the reaction-degradation state field is denoted as q, and is used to characterize the combined effects of CMAS penetration, reactive densification, and localized degradation on the coating state.

[0104] Since the depth variable in the network input uses normalized coordinates ξ, the physical depth z and the normalized depth ξ satisfy:

[0105]

[0106] Where H is the coating thickness. Therefore, the physical depth derivative satisfies:

[0107]

[0108] Considering the effects of CMAS erosion, reactive densification, and localized degradation on the mechanical properties of the coating, the elastic modulus is set as a function of the reactive-degradation state variables:

[0109]

[0110] in, The initial elastic modulus, It represents the elastic modulus after densification.

[0111] Constitutive stress is constructed based on displacement gradient, response-dependent strain, and thermal expansion strain:

[0112]

[0113] in, For displacement field, The strain coefficient is related to the reaction or phase transformation. Let be the coefficient of thermal expansion, where The thermodynamic temperature is obtained by denormalizing the input temperature from the network and then converting it, and the unit is K. This is the reference temperature for thermal strain. All temperatures in the physical constraint terms are based on... The temperature is not standardized using Z-Score.

[0114] Further construct the stress equilibrium residual and constitutive consistency residual:

[0115]

[0116]

[0117] in, The stress field output by the PINN backbone network. The constitutive stress is constructed based on the displacement field and the response-degradation state field.

[0118] The corresponding mechanical loss function can be expressed as:

[0119]

[0120] in, and These are the weighting coefficients for the stress balance term and the constitutive consistency term, respectively.

[0121] Diffusion loss term: The diffusion loss term is used to constrain the transport process of the CMAS concentration field in the time-depth domain. Since the penetration and diffusion behavior of the CMAS melt is affected by both temperature and viscosity, this embodiment establishes an effective diffusion coefficient coupled with temperature and viscosity:

[0122]

[0123] in, For effective diffusion amplitude parameters, The effective diffusion coefficient.

[0124] Since time and depth use normalized coordinates, let:

[0125]

[0126] Then we have:

[0127]

[0128]

[0129] The diffusion residual of the concentration field can be expressed as:

[0130]

[0131] in, For CMAS concentration field.

[0132] The corresponding diffusion loss can be expressed as:

[0133]

[0134] in, The number of physical collocation points used for diffusion residual calculation; Number the physical points; For the first Diffusion residuals at each physical collocation point; For the first The diffusion residual weights at each physical coordinate point are used to enhance the constraint strength in the shallow and early time regions. Normalized CMAS concentration field; The effective diffusion coefficient is the result of temperature and viscosity coupling. and These are normalized time coordinates and normalized depth coordinates, respectively; For time normalization scale; This refers to the coating thickness.

[0135] Chemical loss term: The chemical loss term is used to constrain the reaction, penetration, and localized degradation processes induced by CMAS erosion. First, the effective reaction rate is described using an Arrhenius-type expression centered at the reference temperature:

[0136]

[0137] in, As an effective pre-reaction factor, For apparent activation energy parameters, The gas constant is... This is the Arrheius reference temperature.

[0138] Considering the evolution of the penetration front of CMAS in the coating, a Washburn-type penetration depth relationship is introduced:

[0139]

[0140] in, This is the equivalent permeability coefficient.

[0141] Based on the penetration front, a smooth switching function is further defined:

[0142]

[0143] in, Used to distinguish between permeable and non-permeable areas. The steepness parameter is the front edge.

[0144] Further construct the evolutionary residuals of the reaction-degeneration state variables:

[0145]

[0146] in, For the reaction-degenerate state field, Saturation effect used to characterize local reactions or degenerative states.

[0147] Accordingly, the weighted chemical loss is:

[0148]

[0149] in, The number of physical collocation points used for calculating residuals of chemical reactions and degradation evolution; Number the physical points; For the first Chemical reaction and degradation evolution residuals at each physical coordinate point; For the first The residual weights at each physical coordinate point are used to enhance the constraint strength of the permeation front and active reaction zone. It is determined by the reaction rate, CMAS concentration field, reaction-degradation state field, and smooth permeation front switching function.

[0150] Boundary loss term and initial loss term: The surface concentration boundary is set to an exponentially approaching saturation value over time, and the bottom concentration gradient and damage gradient are set to zero; the displacement field, reaction-degradation state field and stress field at the initial moment are set to zero, and the initial concentration value in the region outside the preset thickness of the surface is set to zero.

[0151] Specifically, regarding boundary conditions, the surface location satisfies the surface source term boundary conditions:

[0152]

[0153] in, The surface boundary start time is slightly greater than zero to avoid conflict with the initial corner point. The bottom location satisfies the zero-flux condition for bottom concentration and the zero-gradient condition for bottom reaction-degenerate state variables.

[0154]

[0155]

[0156] Therefore, the boundary condition loss can be expressed as:

[0157]

[0158] The surface concentration boundary loss is:

[0159]

[0160] The bottom concentration with no flux loss is:

[0161]

[0162] The bottom reaction-degenerate state field zero gradient loss is:

[0163]

[0164] in, , and These are the surface concentration boundary loss, bottom concentration flux-free loss, and bottom reaction-degradation state field zero gradient loss, respectively. , and These are the corresponding weighting coefficients; , and These represent the number of coordinate points at the surface concentration boundary, the number of coordinate points at the bottom concentration boundary, and the number of coordinate points at the bottom reaction-degradation state field boundary, respectively. This is the surface concentration boundary function.

[0165] Regarding the initial conditions, at t=0, the following conditions are satisfied:

[0166]

[0167]

[0168]

[0169] For the initial concentration value, it is desirable to satisfy the following in principle:

[0170]

[0171] However, due to the simultaneous requirements of the surface boundary... ,exist There is a natural conflict at this location. To avoid this corner conflict causing instability in training, in this embodiment, a certain thickness is applied at a distance from the surface. Apply an initial concentration of zero to the region outside of this area, i.e.:

[0172]

[0173] in, To exclude the surface thickness, a thickness of 0.02H is preferred.

[0174] The corresponding initial conditional loss can be expressed as:

[0175]

[0176] in, , , and These are the initial reaction-degradation state field loss, initial displacement loss, initial stress uniformity loss, and initial concentration loss, respectively. These are the initial displacement term weights. Each initial condition loss term can be expressed as:

[0177]

[0178]

[0179]

[0180]

[0181] in, , , and These represent the number of initial collocation points used for the initial reaction-degenerate state field, initial displacement, initial stress consistency, and initial concentration constraint, respectively. For the first The physical depth corresponding to each initial collocation point; Exclude thickness from the surface; For indicator functions, when The value is 1 if the concentration is high, and 0 otherwise. This is because the surface concentration boundary is... The concentration is established over time, to avoid the surface boundary from the initial zero concentration condition. A corner collision occurs at the point where the initial concentration loss is only at the distance from the surface excluding the thickness. Calculations for areas outside of this region.

[0182] S420. Set the effective diffusion amplitude parameter, effective pre-reaction factor, apparent activation energy parameter, and equivalent permeability coefficient in the physical constraint model as trainable physical parameters.

[0183] This step involves the inversion and identification of key physical parameters, aiming to transform physical parameters, which are difficult to accurately obtain in traditional methods, from fixed constants into trainable variables that can be adaptively optimized during training. In the problem of CMAS erosion of thermal barrier coatings, key parameters such as effective diffusion amplitude, effective pre-reaction factor, apparent activation energy, and equivalent permeability coefficient are usually affected by factors such as CMAS composition, temperature conditions, material microstructure, and service history, exhibiting strong uncertainty and condition sensitivity. Using empirical values ​​or literature references often fails to guarantee prediction accuracy. By setting these parameters as trainable physical parameters and optimizing them synchronously with the network weights, the model can adaptively invert parameter values ​​that match the current CMAS composition system and service conditions based on experimental data, guided by physical constraints. This effectively overcomes the limitation of parameter selection on the reliability of prediction results in traditional methods.

[0184] In this embodiment, the trainable physical parameters are bounded reparameterized using a Sigmoid function mapping or a logarithmic space mapping, so that the trainable physical parameters remain within a preset physical feasible region during the training process.

[0185] The specific implementation method of this step will be explained in detail below.

[0186] For any inversion parameter p, we have:

[0187]

[0188] in, This represents any trainable physical parameter to be inverted, which can be the effective diffusion amplitude parameter. Effective pre-reaction factors Apparent activation energy parameters Or equivalent Washburn permeability coefficient ; For parameters The corresponding unconstrained original training variables; For the reason The intermediate variable obtained by mapping via the Sigmoid function satisfies ; and Parameters The preset physical lower and upper bounds. Through the above logarithmic space mapping, the parameters can be made... Always in position during training Within the physically feasible range.

[0189] To avoid raw parameters If the boundary is too close, a soft regularization term can be introduced:

[0190]

[0191] in, This is the threshold constant.

[0192] S430, Generate physical collocations in the time-depth domain.

[0193] This step is the discretization sampling stage of physical constraints, which aims to provide a set of collocation points for calculating physical residuals in the physical constraint model established in S410. By generating discrete collocation points in the time-depth domain, continuous physical constraints such as mechanical equilibrium equations, diffusion equations, and chemical reaction and degradation evolution equations can be transformed into residual calculations at each collocation point, and further summarized into physical loss terms.

[0194] In this embodiment, generating physical collocation points in the time-depth domain includes: generating collocation points using Latin hypercube sampling in a two-dimensional domain consisting of normalized time and normalized depth, and performing hotspot encryption sampling on the early time region, shallow depth region and penetration front region.

[0195] Specifically, collocation points for physical constraint calculations are generated within the time-depth domain. Preferably, Latin hypercube sampling is used only for normalized time τ and normalized depth ξ, while the material parameters are partially taken from real material combinations existing in the training set to avoid constructing unrealistic virtual material samples. For each training sample's material input vector, it can be combined with multiple time-depth collocation points to form a physical field input vector for physical constraint calculations.

[0196] To enhance the model's ability to characterize the initial penetration, shallow diffusion, and penetration front regions of CMAS, hotspot density sampling can be further implemented. This hotspot density sampling includes increasing the point density in the early time region, increasing the point density in the shallow region near the coating surface, and increasing the point density near the penetration front based on the estimated location of the Washburn-type penetration front. This point-selection strategy improves the guidance effect of physical constraints on training in key degradation regions.

[0197] S440. Calculate the physical loss term based on the physical collocation points and the physical constraint model, combine the data fitting loss term between the predicted coating lifetime and the actual lifetime value, and the parameter regularization loss term of the trainable physical parameters, to construct a joint loss function.

[0198] This step is the unified construction phase of the training objective. It aims to discretize and evaluate the physical constraint model established in S410 on the physical collocations generated in S430, thereby transforming the physical constraints in the continuous domain into quantifiable physical loss terms. These terms, together with the data fitting loss term for lifetime prediction and the parameter regularization loss term for trainable physical parameters, constitute a joint loss function. This joint loss function is used to establish a unified optimization objective among data fitting accuracy, physical consistency, and parameter rationality.

[0199] In this embodiment, the joint loss function is composed of a weighted sum of the data fitting loss term, multiple physical loss sub-terms, and the parameter regularization loss term.

[0200] Specifically, the physical loss term can be expressed as:

[0201]

[0202] in, , These are mechanical losses, diffusion losses, chemical losses, boundary condition losses, and initial condition losses, respectively. These are the weighting coefficients for the corresponding physical loss sub-items.

[0203] The joint loss function can be expressed as:

[0204]

[0205] in, The data fitting loss is the difference between the predicted lifespan and the actual lifespan. For the regularized loss of trainable physical parameters, These are the corresponding weighting coefficients.

[0206] S450. The physical information neural network backbone network and the lifetime prediction network are jointly trained using the joint loss function, and the trainable physical parameters are simultaneously inverted and identified during the training process to obtain the trained lifetime prediction model.

[0207] This step is the optimization execution phase of the joint training, aiming to perform end-to-end joint training of the PINN backbone network and the lifetime prediction network using the joint loss function constructed by S440 as the optimization objective. Simultaneously, the trainable physical parameters are inverted and identified during the training process. Unlike the traditional two-stage approach of fixing the network first and then extracting parameters, this step places network weight updates and physical parameter inversion within a unified gradient backpropagation framework. This allows the physical parameters to be continuously adjusted based on the physical field and physical constraint residuals output by the current network, while the network weights are also influenced by the constraints brought about by the physical parameter updates. The two evolve together, ultimately resulting in a lifetime prediction model that is both physically self-consistent and accurate in prediction.

[0208] In this embodiment, the weights of each physical loss sub-item are dynamically adjusted during training—the dynamic weights are calculated using the Softmax function based on the ratio of each sub-item loss to the initial loss.

[0209] The specific implementation method of this step will be explained in detail below.

[0210] For physical sub-loss weights The weights can be fixed or dynamically adjusted based on the changes in each loss relative to the initial loss during training. If a dynamic weighting strategy is used, an exponential moving average of each physical sub-loss can be defined:

[0211]

[0212] Redefine the ratio relative to the initial loss:

[0213]

[0214] Finally, the dynamic weights are calculated using the Softmax function:

[0215]

[0216] in, The number of physical tasks participating in the dynamic weighting, The moving average coefficient, For temperature coefficient, To prevent extremely small positive numbers with a denominator of zero.

[0217] in, This is the current training round; Number the current physical loss sub-item; Number the physical loss sub-item in the Softmax normalized summation; The number of physical loss sub-items participating in the dynamic weighting; For the first The physical loss sub-item is in the first Loss value during training rounds; For the first The exponential moving average of each physical loss sub-item; For the first The initial loss value of each physical loss item; For the first The ratio of the change of each physical loss item relative to the initial loss; For the first The physical loss sub-item is in the first Dynamic weights during rounds of training; The coefficient of the exponential moving average; The temperature coefficient is used for Softmax dynamic weighting to adjust the smoothness of the differences in weights between different physical loss sub-items; To prevent extremely small positive numbers with a denominator of zero.

[0218] Through the above joint training, the weight parameters of the PINN backbone network and the lifetime prediction network are determined after training is completed. At the same time, the trainable physical parameters converge to values ​​that match the current CMAS component system and service conditions, which is the trained lifetime prediction model.

[0219] Further optionally, S500 also includes: synchronously outputting the globally effective physical parameters obtained during training.

[0220] In this embodiment, the trained lifetime prediction model simultaneously outputs the coating lifetime prediction value and the effective diffusion amplitude parameter obtained from the inversion identification. Effective pre-reaction factors Apparent activation energy parameters and equivalent permeability coefficient It is used to analyze the differences in diffusion, reaction, and penetration mechanisms under different CMAS compositions and service conditions.

[0221] Through the above steps, this invention realizes a CMAS-based method for predicting the lifetime of thermal barrier coatings that unifies experimental data, physical mechanisms, and trainable parameters into a single model framework. This method not only outputs lifetime prediction results for thermal barrier coatings but also simultaneously provides the evolution of key physical fields and the identification of physical parameters, thus possessing high prediction accuracy, strong physical consistency, and good engineering interpretability.

[0222] The present invention will be further described below with reference to specific embodiments. It should be noted that the following embodiments are only used to illustrate the technical solution and feasibility of the present invention, and should not be construed as limiting the scope of protection of the present invention; any equivalent substitutions, improvements or modifications made to the form of input variables, network structure, physical constraint formulas, parameter value ranges, sampling methods, training strategies or deployment forms based on the concept of the present invention should fall within the scope of protection of the present invention.

[0223] (1) In this embodiment, experimental data from CMAS erosion of thermal barrier coatings were used to verify the method of the present invention. A total of 60 experimental samples were used, and the test temperatures included three temperature groups: 1200℃, 1250℃, and 1300℃. The input variables included temperature, CMAS viscosity, and the content of 10 major oxide components, namely CaO, MgO, Al2O3, SiO2, Na2O, K2O, P2O5, TiO2, TFe2O3, and MnO. The output variable was the thermal barrier coating lifetime. The samples were divided into training and validation sets in an 8:2 ratio, and the input data and lifetime labels were standardized.

[0224] (2) In this embodiment, the material input dimension is 12-dimensional, and the physical field input dimension is 14-dimensional, with the two added dimensions being the normalized time coordinate and the normalized depth coordinate, respectively; the time range is 0 hours to 500 hours, and the coating thickness is 200 μm. The hidden layer structure of the PINN backbone network is set to 128, 128, 64, 64, 32, the activation function is Tanh, residual connections and layer normalization are enabled in the network, and the dropout rate is set to 0.2. The PINN network outputs the stress field, concentration field, reaction-degradation state field, and displacement field. The hidden layers of the lifetime prediction network are set to 64 and 32, and the lifetime average is output.

[0225] (3) During training, the batch size was set to 16, and the learning rate of the PINN network was set to... The lifespan prediction network learning rate is set to The physical parameter learning rate is set to The maximum number of training epochs is set to 3000, and the weight decay is set to... The number of physical collocation points is set to 5000, the number of boundary collocation points is set to 500, and the number of initial condition collocation points is set to 500. The weights for mechanical loss, diffusion loss, and chemical loss are all set to 1.0, the weights for boundary loss and initial loss are both set to 0.5, and the weight for lifetime data loss is set to 1.0. With these parameter configurations, joint prediction of the lifetime of CMAS-eroded thermal barrier coatings can be achieved, while simultaneously obtaining the lifetime-related internal physical field distribution results.

[0226] (4) Furthermore, a trainable physical parameter inversion mechanism is enabled to enhance the model's mechanistic explanatory power. The trainable physical parameters set include the effective diffusion amplitude parameter. Effective pre-reaction factors Apparent activation energy parameters and equivalent permeability coefficient .in, The initial value is set to The value range is set to ; The initial value is set to 100, and the range of values ​​is set to... ; The initial value is set to The value range is set to ; The initial value is set to The value range is set to .

[0227] (5) In this embodiment, the initial elastic modulus of the thermal barrier coating is set to 40 GPa, the elastic modulus after densification is set to 200 GPa, and the coefficient of thermal expansion is set to The phase transition expansion coefficient was set to 0.135, and the reference temperature was set to 298.15 K. To improve the stability of the physical parameters during training, the physical parameters were frozen for 20 rounds at the beginning of training, and then gradually unfrozen for joint optimization.

[0228] (6) In addition, this embodiment adopts a hotspot region encryption sampling strategy, with the hotspot sampling ratio set to 0.4, the early time hotspot upper limit set to 0.2, the shallow depth hotspot upper limit set to 0.4, the leading edge sampling ratio set to 0.5, and the leading edge bandwidth set to 0.05. In the boundary loss, the surface concentration boundary weight is set to 1.35, the bottom concentration boundary weight is set to 1.15, and the bottom reaction-degradation state field gradient boundary weight is set to 0.75; the input gradient smoothing regularization weight is set to... Through the above settings, not only can the predicted value of the thermal barrier coating lifetime be output, but also the key physical parameters related to diffusion, reaction and penetration can be simultaneously inverted, thereby verifying that the present invention has good predictive ability, physical consistency and engineering interpretation ability under small sample conditions.

[0229] This disclosure also provides a CMAS erosion coating lifetime prediction system based on physical information neural networks, used to run the above-mentioned CMAS erosion coating lifetime prediction method based on physical information neural networks, including:

[0230] The data acquisition module is used to collect experimental data of CMAS erosion thermal barrier coating. After preprocessing the experimental data, a material input vector is constructed, and time coordinates and depth coordinates are introduced on the basis of the material input vector to construct a physical field input vector.

[0231] The physical information neural network module is used to build the physical information neural network backbone network. The physical information neural network backbone network takes the physical field input vector as input and outputs the physical field features of the backbone hidden features, the stress field of the coating in the time-depth domain, the CMAS concentration field, the reaction-degradation state field and the displacement field.

[0232] The lifetime prediction network module is used to build a lifetime prediction network. It integrates the physical field characteristics of the stress field, the concentration field, the reaction-degradation state field and the displacement field with the backbone hidden features and inputs them into the lifetime prediction network to output the coating lifetime prediction value.

[0233] The joint training module is used to jointly train the physical information neural network backbone network and the lifetime prediction network based on the deviation between the coating lifetime prediction value and the actual lifetime value, combined with physical constraint loss, to obtain the trained lifetime prediction model.

[0234] The lifetime prediction module is used to input the content of the CMAS component to be tested, temperature and viscosity into the trained lifetime prediction model, and output the coating lifetime prediction value.

[0235] According to embodiments of this disclosure, an electronic device is also provided, which may include a processor, a communications interface, a memory, and a communication bus, wherein the processor, communications interface, and memory communicate with each other via the communication bus. The processor can invoke logical instructions in the memory to execute a configuration software-based software licensing implementation method.

[0236] Furthermore, the logical instructions in the aforementioned memory can be implemented as software functional units and sold or used as independent products, and can be stored in a computer-readable storage medium. Based on this understanding, the technical solution of this disclosure, in essence, or the part that contributes to the prior art, or a part of the technical solution, can be embodied in the form of a software product. This computer software product is stored in a storage medium and includes several instructions to cause a computer device (which may be a personal computer, server, or network device, etc.) to execute all or part of the steps of the methods described in the various embodiments of this disclosure. The aforementioned storage medium includes various media capable of storing program code, such as USB flash drives, portable hard drives, read-only memory (ROM), random access memory (RAM), magnetic disks, or optical disks.

[0237] On the other hand, this disclosure also provides a non-transitory computer-readable storage medium having a computer program stored thereon, which, when executed by a processor, is implemented to perform the configuration software-based software licensing implementation methods provided by the above methods.

[0238] The device embodiments described above are merely illustrative. The units described as separate components may or may not be physically separate. The components shown as units may or may not be physical units; that is, they may be located in one place or distributed across multiple network units. Some or all of the modules can be selected to achieve the purpose of this embodiment according to actual needs. Those skilled in the art can understand and implement this without any creative effort.

[0239] Through the above description of the embodiments, those skilled in the art can clearly understand that each embodiment can be implemented by means of software plus necessary general-purpose hardware platforms, and of course, it can also be implemented by hardware. Based on this understanding, the above technical solutions, in essence or the part that contributes to the prior art, can be embodied in the form of a software product. This computer software product can be stored in a computer-readable storage medium, such as ROM / RAM, magnetic disk, optical disk, etc., and includes several instructions to cause a computer device (which may be a personal computer, server, or network device, etc.) to execute the methods described in the various embodiments or some parts of the embodiments.

[0240] It should be understood that the above embodiments are only used to illustrate the technical solutions of this disclosure, and not to limit them; although this disclosure has been described in detail with reference to the foregoing embodiments, those skilled in the art should understand that they can still modify the technical solutions described in the foregoing embodiments, or make equivalent substitutions for some of the technical features; and these modifications or substitutions do not cause the essence of the corresponding technical solutions to deviate from the spirit and scope of the technical solutions of the embodiments of this disclosure.

Claims

1. A method for predicting the lifetime of CMAS erosion coatings based on physical information neural networks, characterized in that, include: Experimental data on CMAS erosion of thermal barrier coatings were collected. After preprocessing the experimental data, a material input vector was constructed. Based on the material input vector, time coordinates and depth coordinates were introduced to construct a physical field input vector. A physical information neural network backbone network is constructed. The physical field input vector is used as input, and the physical field features of the backbone hidden features, the stress field of the coating in the time-depth domain, the CMAS concentration field, the reaction-degradation state field and the displacement field are used as output. A lifetime prediction network is constructed by fusing the physical field characteristics of the stress field, the concentration field, the reaction-degradation state field, and the displacement field with the backbone hidden features and inputting them into the lifetime prediction network, and outputting the coating lifetime prediction value. Based on the deviation between the predicted coating lifetime and the actual lifetime, the physical information neural network backbone and the lifetime prediction network are jointly trained using physical constraint loss to obtain the trained lifetime prediction model. The content of the CMAS component to be tested, temperature, and viscosity are input into the trained lifetime prediction model, and the coating lifetime prediction value is output.

2. The CMAS erosion coating lifetime prediction method based on physical information neural network according to claim 1, characterized in that, The joint training also includes: A physical constraint model is established, which includes mechanical loss constraints, CMAS diffusion loss constraints, chemical loss constraints, as well as boundary conditions and initial conditions constraints. The effective diffusion amplitude parameter, effective pre-reaction factor, apparent activation energy parameter, and equivalent permeability coefficient in the physical constraint model are set as trainable physical parameters. Generate physical collocations in the time-depth domain; The physical loss term is calculated based on the physical collocation points and the physical constraint model. A joint loss function is constructed by combining the data fitting loss term between the predicted coating lifetime and the actual lifetime value, and the parameter regularization loss term of the trainable physical parameters. The physical information neural network backbone and the lifetime prediction network are jointly trained using the joint loss function, and the trainable physical parameters are simultaneously inverted and identified during the training process to obtain the trained lifetime prediction model.

3. The CMAS erosion coating lifetime prediction method based on physical information neural network according to claim 2, characterized in that, The physical constraint model includes: Mechanical loss term: The elastic modulus is set as a function of the reaction-degradation state field, the displacement gradient is calculated from the displacement field, the constitutive stress is constructed based on the displacement gradient and the elastic modulus, and the mechanical loss term is constructed using the stress balance residual and the constitutive consistency residual, respectively. Diffusion loss term: Establish an effective diffusion coefficient coupled with temperature and viscosity, construct the diffusion equation residual based on the effective diffusion coefficient and the concentration field, and apply focusing weights in the shallow region and the early time region to construct the diffusion loss term using the weighted diffusion residual; Chemical loss term: Construct an Arrhenius-type reaction rate expression, use a Washburn-type penetration depth relationship to determine the position of the penetration front, construct a smoothing switching function based on the position of the penetration front to distinguish between the penetrated and non-penetrated areas, and construct the damage evolution residual from the reaction rate, the concentration field, and the reaction-degradation state field. Apply weights to the penetration front zone and the active reaction zone, and construct the chemical loss term from the weighted damage evolution residual. Boundary loss term and initial loss term: The surface concentration boundary is set to an exponentially approaching saturation value over time, and the bottom concentration gradient and damage gradient are set to zero; the displacement field, reaction-degradation state field and stress field at the initial moment are set to zero, and the initial concentration value in the region outside the preset thickness of the surface is set to zero.

4. The CMAS erosion coating lifetime prediction method based on physical information neural network according to claim 2, characterized in that, The trainable physical parameters are bounded reparameterized using a Sigmoid function mapping or a logarithmic space mapping, so that the trainable physical parameters remain within a preset physical feasible region during the training process.

5. The CMAS erosion coating lifetime prediction method based on physical information neural network according to claim 2, characterized in that, The generation of physical collocation points in the time-depth domain includes: generating collocation points using Latin hypercube sampling in a two-dimensional domain consisting of normalized time and normalized depth, and performing hotspot encryption sampling in the early time region, shallow depth region and penetration front region.

6. The CMAS erosion coating lifetime prediction method based on physical information neural network according to claim 2, characterized in that, The joint loss function is composed of a weighted sum of the data fitting loss term, multiple physical loss sub-terms, and the parameter regularization loss term. During training, the weights of each physical loss sub-term are dynamically adjusted, and the dynamic weights are calculated using the Softmax function based on the ratio of each sub-term loss to the initial loss.

7. The CMAS erosion coating lifetime prediction method based on physical information neural network according to claim 1, characterized in that, The preprocessing includes: The experimental data were checked for missing values, outliers, and units were standardized. The input variables and lifetime labels were Z-score standardized and the training and validation sets were divided according to a preset ratio. The material input vector is composed of the CMAS main oxide composition content, the CMAS melt viscosity, and the thermal shock test temperature; The physical field input vector incorporates normalized time coordinates and normalized depth coordinates based on the material input vector.

8. The CMAS erosion coating lifetime prediction method based on physical information neural network according to claim 1, characterized in that, The physical information neural network backbone is a fully connected network with residual connections between adjacent equal-dimensional hidden layers, and layer normalization and Dropout are introduced. The stress field, concentration field, reaction-degradation state field, and displacement field are output separately from the shared hidden features as four independent output heads. The stress field is multiplied by a stress scaling factor before output, the reaction-degradation state field is constrained to the 0-1 interval by the Sigmoid function, and the displacement field is set to zero at the bottom depth position.

9. The CMAS erosion coating lifetime prediction method based on physical information neural network according to claim 1, characterized in that, The physical information neural network backbone takes the physical field input vector as input and outputs the physical field features of the backbone hidden features, the stress field, CMAS concentration field, reaction-degradation state field, and displacement field of the coating in the time-depth domain, including: The hidden features of the backbone are extracted from the terminal hidden layer of the physical information neural network, and the stress field, concentration field, reaction-degradation state field and displacement field are constructed based on the hidden features of the backbone.

10. A CMAS erosion coating lifetime prediction system based on physical information neural network, characterized in that, include: The data acquisition module is used to collect experimental data of CMAS erosion thermal barrier coating. After preprocessing the experimental data, a material input vector is constructed, and time coordinates and depth coordinates are introduced on the basis of the material input vector to construct a physical field input vector. The physical information neural network module is used to build the backbone network of the physical information neural network. The physical information neural network takes the physical field input vector as input and outputs the physical field features of the backbone hidden features, the stress field of the coating in the time-depth domain, the CMAS concentration field, the reaction-degradation state field and the displacement field. The lifetime prediction network module is used to build a lifetime prediction network. It integrates the physical field characteristics of the stress field, the concentration field, the reaction-degradation state field and the displacement field with the backbone hidden features and inputs them into the lifetime prediction network to output the coating lifetime prediction value. The joint training module is used to jointly train the physical information neural network backbone network and the lifetime prediction network based on the deviation between the coating lifetime prediction value and the actual lifetime value, combined with physical constraint loss, to obtain the trained lifetime prediction model. The lifetime prediction module is used to input the content of the CMAS component to be tested, temperature and viscosity into the trained lifetime prediction model, and output the coating lifetime prediction value.

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