Thermal barrier coating life prediction method and system based on end-state damage information enhancement

Abstract

The present application relates to the technical field of high-temperature protective material life evaluation, and particularly relates to a thermal barrier coating life prediction method and system based on terminal state damage information enhancement, the method comprising the following steps: obtaining terminal state data and constructing a terminal state damage feature vector; dividing damage degree levels; selecting a template to calculate a key node sequence; obtaining experimental data of key nodes of supplementary samples with the same or similar working conditions; training to obtain a life prediction model; and performing prediction. In the training stage, the terminal state damage information of the original sample is used to deduce the key nodes, and the experimental data of the key nodes of the supplementary samples are used to construct an enhanced training database, which overcomes the difficulty of needing to continuously monitor the intermediate damage process in the traditional method, so that after the training is completed, only the working condition parameters of the sample to be predicted need to be input, without the need to obtain any surface or cross-sectional images, thereby significantly reducing the detection cost and time in engineering applications.

Description

Technical Field

[0001] This invention relates to the field of high-temperature protective material life assessment technology, and in particular to a method and system for predicting the life of thermal barrier coatings based on enhanced final-state damage information. Background Technology

[0002] Thermal barrier coatings (TBCs) are widely used in high-temperature components such as aero-engines and gas turbines, serving as a crucial thermal protection system for improving service temperatures, reducing substrate thermal load, and enhancing thermal efficiency. In complex service environments, CaO-MgO-Al2O3-SiO2 (CMAS) deposits formed from the melting of particles such as sand, dust, or volcanic ash can wet, spread, and penetrate the TBC, leading to crack propagation, instability of columnar intergranular spaces, exacerbated interfacial damage, and ultimately, spalling failure. The combined effects of CMAS erosion and high-temperature thermal shock cycling result in a multi-factor coupled and phased degradation characteristic of TBC lifetime.

[0003] Currently, methods for assessing the lifespan of thermal barrier coatings (CMAS) mainly include physical experimental methods, numerical simulation methods, and data-driven methods. Traditional high-temperature thermal shock experiments can directly obtain lifespan results, but the testing cycle is long, the cost is high, and it is difficult to conduct full-coverage tests under different combinations of CMAS composition, viscosity, and temperature. Numerical simulation methods such as the finite element method can analyze the thermal stress field or interfacial stress distribution, but the CMAS erosion process involves complex coupled mechanisms such as melt penetration, thermochemical reactions, phase structure evolution, and crack propagation, making it difficult to establish an accurate and stable multiphysics model.

[0004] In recent years, machine learning methods have been increasingly applied to materials lifetime prediction. However, most existing data-driven methods are based on a direct mapping between static operating parameters and final lifetime labels, lacking the utilization of information on final-state damage morphology and key evolution stages. In actual experiments, complete intermediate time-series damage process data are difficult to obtain continuously, and cross-sectional cracks and interface damage often require destructive sampling. How to enhance the model's ability to learn lifetime evolution laws under limited final-state data conditions is a critical problem that urgently needs to be solved.

[0005] On the other hand, using final-state images as a necessary input for model deployment would significantly increase the barrier to engineering applications. In particular, acquiring cross-sectional images requires slicing, cold mosaicking, grinding, and microscopic observation, making them unsuitable as routine input for rapid prediction.

[0006] Therefore, there is an urgent need to propose a method that can effectively utilize final-state damage images and final failure information to enhance the model's learning ability during the training phase, while relying solely on readily available operating condition parameters to achieve high-precision life prediction during the prediction phase. Summary of the Invention

[0007] To overcome the aforementioned problems in the existing technology, this invention proposes a thermal barrier coating lifetime prediction method and system based on enhanced final-state damage information. This method enables the effective use of the final-state damage information of the sample to infer key nodes and construct an enhanced training database during the training phase. As a result, the trained multi-task neural network can output accurate lifetime prediction results by relying solely on operating parameters during the prediction phase.

[0008] Therefore, the first objective of this invention is to provide a method for predicting the lifetime of thermal barrier coatings based on enhanced final-state damage information, comprising the following steps:

[0009] The final state data of the original thermal barrier coating sample are obtained and a final state damage feature vector is constructed. The final state damage feature vector includes at least the operating condition parameters, the final failure cycle number, and the final state damage characteristics.

[0010] The damage level of the original sample is classified based on the final state damage feature vector;

[0011] Based on the damage severity level, a corresponding template is selected from multiple preset key node proportion templates to calculate the key node sequence;

[0012] Based on the key node sequence, experimental data of supplementary samples with the same or similar working conditions as the original sample are obtained at each key node, and the experimental data is integrated with the final state data to construct an enhanced training database; the experimental data includes working condition parameters and stage damage characteristics.

[0013] A multi-task neural network is trained using the enhanced training database to obtain a lifespan prediction model.

[0014] The operating parameters of the sample to be predicted are input into the lifetime prediction model, and the lifetime prediction result of the sample to be predicted is output.

[0015] By using the final damage information of the original sample during the training phase (without intermediate process data) to infer key nodes, and using supplementary samples to obtain experimental data of key nodes to build an enhanced training database, the difficulty of continuously monitoring intermediate damage processes in traditional methods is overcome. After training, only the working parameters of the sample to be predicted (such as CMAS composition, viscosity and temperature) need to be input during actual prediction, without the need to obtain any surface or cross-sectional images, which significantly reduces the detection cost and time in engineering applications.

[0016] Preferably, the step of classifying the damage level of the original sample based on the final state damage feature vector includes:

[0017] The final state damage intensity index is calculated by weighting the final state damage features in the final state damage feature vector.

[0018] The final damage intensity index is compared with a preset grading threshold to classify the original sample into different damage levels.

[0019] Preferably, the method for setting the hierarchical threshold includes:

[0020] Determine the number of levels that need to be divided;

[0021] The number of grading thresholds is determined based on the number of grades required.

[0022] The grading threshold value is determined based on the number of samples required for each grade.

[0023] Preferably, the method for obtaining the experimental data of the supplementary sample at each key node includes:

[0024] For each key node, prepare an independent parallel supplementary sample;

[0025] The supplementary sample was subjected to thermal shock testing until the number of cycles corresponding to the critical node was reached, at which point the testing was stopped.

[0026] Destructive testing was then performed on the supplementary samples after the stop to obtain the stage damage characteristics of the node.

[0027] Preferably, the preset multiple key node ratio templates correspond to different damage levels, and the key node ratios in each template are distributed at non-equal intervals, with the early intervals being larger than the later intervals. Furthermore, the more severe the damage, the more key nodes are included in the template.

[0028] Multiple pre-set key node proportion templates correspond to different damage levels and exhibit a non-uniform distribution characterized by "sparse in the early stage and dense in the later stage," with more nodes appearing in the templates for more severe damage. This differentiated template design fully conforms to the physical law of "slow in the early stage and accelerated in the later stage" in the damage evolution of thermal barrier coatings. It enables the model to focus more on key stages such as crack propagation and critical failure during training, improving the information density of training samples and the model's ability to distinguish key intervals in lifetime prediction, thereby achieving higher prediction accuracy under limited sample conditions.

[0029] Preferably, the multi-task neural network includes a shared backbone feature extraction module and three parallel output heads, and the shared backbone feature extraction module is provided with residual connections, and the three output heads include:

[0030] The lifetime regression output header is used to output the predicted lifetime value;

[0031] The stage-assisted classification output head is used to output the probability distribution of a sample belonging to a preset key damage stage;

[0032] And a lifetime range output header, used to output the predicted lifetime range or parameters representing the prediction uncertainty.

[0033] The residual connections set in the shared backbone feature extraction module effectively alleviate the gradient vanishing problem in deep fully connected networks during gradient backpropagation by directly superimposing the input signal across layers to the output. This allows the 4-layer fully connected network to converge stably even with small sample training, reducing the risk of overfitting and improving the model's generalization ability. The three output heads output the predicted lifetime value, stage probability distribution, and lifetime interval / uncertainty parameter, respectively, enabling the model to be jointly supervised by lifetime regression loss, stage classification loss, and interval constraint loss during training. The stage-assisted classification task guides the model to focus on the intermediate patterns of damage evolution, while the interval estimation task forces the model to output a reasonable confidence range. These three aspects mutually reinforce each other, resulting in a more accurate and robust final lifetime prediction result than a single regression model. The model can simultaneously provide point predictions (predicted lifetime value), probability predictions (stage distribution), and interval predictions (lifetime interval / uncertainty). Users can choose to use them according to their actual needs: for example, the stage probability can be used to determine the most likely damage stage of the coating under the current operating condition, and the lifetime interval can be used to assess the reliability of the prediction, providing a more comprehensive quantitative basis for the maintenance and replacement decision of the thermal barrier coating.

[0034] Preferably, the training of the multi-task neural network adopts a multi-task joint loss function, which includes at least lifetime regression loss, stage classification loss and interval constraint loss; and physical prior constraints are introduced into the multi-task joint loss function, including temperature monotonicity constraints, that is, for samples with similar composition and viscosity but different thermal shock test temperatures, higher temperatures correspond to shorter lifetimes.

[0035] A multi-task joint loss function, comprising lifetime regression loss, stage classification loss, and interval constraint loss, is employed to simultaneously optimize all three tasks. This allows the model to fully utilize auxiliary information such as node lifetime ratios and stage labels in the enhanced training database, improving learning efficiency under small sample conditions. Furthermore, prior physical knowledge, such as temperature monotonicity constraints, is introduced to ensure that the model's lifetime predictions conform to the fundamental physical law that "higher temperatures result in shorter lifespans." This enhances the model's physical consistency and interpretability, reduces the risk of overfitting, and improves its generalization ability under unknown operating conditions.

[0036] The second objective of this invention is to provide a thermal barrier coating lifetime prediction system based on enhanced final-state damage information, comprising:

[0037] The final state data acquisition and feature extraction module is configured to acquire the final state data of the original thermal barrier coating sample and construct the final state damage feature vector, wherein the final state damage feature vector includes at least the operating condition parameters, the final failure cycle number and the final state damage features.

[0038] The damage level classification module is configured to classify the damage level of the original sample based on the final state damage feature vector;

[0039] The key node sequence generation module is configured to select a corresponding template from a plurality of preset key node proportion templates according to the damage level and calculate the key node sequence.

[0040] An enhanced database construction module is configured to acquire experimental data of supplementary samples with the same or similar working conditions as the original sample at each key node based on the key node sequence, and integrate the experimental data with the final state data to construct an enhanced training database; the experimental data includes working condition parameters and stage damage characteristics;

[0041] The model training module is configured to train a multi-task neural network using the enhanced training database to obtain a lifespan prediction model.

[0042] The lifetime prediction module is configured to input the operating parameters of the sample to be predicted into the lifetime prediction model and output the lifetime prediction result of the sample to be predicted.

[0043] A third objective of this invention is to provide a computer device, including a memory and a processor, wherein the memory stores computer instructions, and the processor executes the computer instructions to perform the method described in the first objective.

[0044] The fourth objective of this invention is to provide a computer-readable storage medium storing computer instructions that, when executed by a computer, describe the method described in the first objective.

[0045] Compared with the prior art, the present invention has the following beneficial effects:

[0046] 1. Reduced data acquisition difficulty: This invention only requires the final state data of the original sample (final failure cycle count, final state image) to infer key nodes, and constructs an enhanced training database through node experiments of a small number of parallel supplementary samples. It does not require continuous monitoring of the complete intermediate damage evolution process, thus overcoming the technical obstacle of difficult acquisition of intermediate process data in traditional methods.

[0047] 2. Significantly lowers the application threshold in the prediction stage: After training, only the operating parameters of the sample to be predicted (CMAS composition, viscosity, temperature) need to be input during actual prediction. No surface or cross-sectional images need to be obtained, avoiding complex operations such as destructive sampling and microscopic observation, greatly reducing detection costs and time, and facilitating rapid evaluation on the engineering site.

[0048] 3. Improve prediction accuracy and generalization ability under small sample conditions: By constructing an enhanced training database containing node lifetime ratios and stage labels, the model can learn the stage-specific laws of thermal barrier coating damage evolution; at the same time, by using a multi-task neural network (shared backbone, residual connections, and three output heads) and a joint loss function, the model can obtain stronger feature representation ability and generalization performance under small sample conditions, and output more accurate lifetime prediction results.

[0049] 4. Reliable predictions that conform to physical laws: By introducing physical prior knowledge such as temperature monotonicity constraints into the multi-task joint loss function, the lifetime prediction results output by the model conform to the basic physical law that "the higher the temperature, the shorter the lifetime," which enhances the physical consistency and interpretability of the model and reduces the risk of overfitting.

[0050] 5. Flexible output format to meet diverse engineering needs: The model can simultaneously output predicted lifetime values, predicted lifetime ranges, and failure probability distributions. Users can flexibly choose the output format according to actual engineering scenarios (such as maintenance plan formulation and spare parts replacement decisions), providing a more comprehensive quantitative basis for the full life cycle management of thermal barrier coatings. Attached Figure Description

[0051] Figure 1 This is a schematic diagram of the overall process of the method in Embodiment 1 of the present invention;

[0052] Figure 2 This is a schematic diagram of the lifetime prediction model structure according to Embodiment 1 of the present invention;

[0053] Figure 3 This is a schematic diagram of the reverse calculation results of the key damage stage in Embodiment 1 of the present invention;

[0054] Figure 4 This is a schematic diagram illustrating the reverse derivation of the key node sequence in Embodiment 1 of the present invention. Detailed Implementation

[0055] The present invention will be further described in detail below with reference to the accompanying drawings and specific embodiments. Obviously, the described embodiments are only some, not all, of the embodiments of the present invention. All other embodiments obtained by those skilled in the art based on the described embodiments of the present invention without inventive effort are within the scope of protection of the present invention. Unless otherwise defined, the technical or scientific terms used herein should have the ordinary meaning understood by those skilled in the art to which this invention pertains.

[0056] To further understand this invention, some terms mentioned in this invention and its embodiments are first explained:

[0057] Final state damage information enhancement: refers to the technique of using the final state damage data (images, failure counts, etc.) of the original sample to infer key nodes and build an enhanced training database.

[0058] Multi-task neural networks refer to neural networks that simultaneously learn multiple related tasks by sharing a feature extraction module. Their structure includes a shared backbone and multiple parallel task-specific output heads. In this application, the network takes operating parameters as input and simultaneously outputs predicted lifetime values, stage classification results, and predicted lifetime ranges. When residual connections are also included in the network, it can be called a multi-task residual deep network.

[0059] Multi-task residual deep network: refers to a deep learning network that includes a shared backbone feature extraction module, inter-layer residual connection structure and multiple parallel task output heads; in Example 1, the shared backbone feature extraction module is used to extract high-dimensional latent features from input working condition parameters, the residual connection is used to improve the gradient propagation and feature reuse capabilities during the training process of deep network, and the multiple parallel task output heads are used to output lifetime regression results, stage classification results and lifetime interval estimation results, respectively.

[0060] Key nodes: These refer to the predetermined number of thermal shock cycles used to collect experimental data during the lifetime evolution of the thermal barrier coating, expressed as the absolute number of cycles. The key node sequence is a queue consisting of all key nodes for a specific sample, exhibiting a non-uniformly spaced distribution characteristic of "sparse in the early stage and dense in the later stage".

[0061] Critical node ratio: refers to the proportion of critical node cycles to the final failure cycle.

[0062] To facilitate a better understanding of the present invention by those skilled in the art, the present invention will be further described in detail below with reference to the accompanying drawings and specific embodiments. The following are merely exemplary and do not limit the scope of protection of the present invention.

[0063] Example 1

[0064] This implementation proposes a method for predicting the lifetime of thermal barrier coatings under CMAS based on final-state damage enhancement training and multi-task deep learning. It involves using macroscopic surface damage information, cross-sectional crack damage information, and the number of final failure cycles at the final failure point of the thermal barrier coating sample to infer key damage stages and dynamic test nodes, constructing an enhancement training database, and further establishing a deep learning model that can predict lifetime values ​​or lifetime ranges solely based on CMAS major element composition, melt viscosity, and thermal shock test temperature. Figures 1-4 As shown in the figure. The present invention will be further described below with reference to specific embodiments, but the present invention is not limited to the following embodiments.

[0065] A method for predicting the lifetime of thermal barrier coatings based on enhanced final-state damage information, such as Figure 1 As shown, it includes the following steps:

[0066] S1: Obtain the final state data of the original samples of the failed thermal barrier coating under different operating conditions.

[0067] Final state data refers to the data collected when the thermal barrier coating sample reaches the preset failure criterion (such as the coating peeling area reaching 20% ​​of the total coating area), including operating parameters, final failure cycle number, and final state image.

[0068] This step aims to provide a realistic and reliable training basis for model building by systematically collecting the final failure cycle number and final state images of original thermal barrier coating samples that fail under different operating conditions, thus ensuring the accuracy of subsequent backtesting and lifetime prediction.

[0069] Operating parameters refer to the test condition parameters that affect the life of thermal barrier coatings, including:

[0070] CMAS major element composition: represented by a feature vector consisting of the content of several oxides, including but not limited to... , , , , , , , , , One or more of the following. The major elements usually refer to element oxides that account for more than 1% of the mass in the CMAS composition, but for CMAS from a specific source, the specific dimensions of the feature vector can be determined based on the actual composition analysis results;

[0071] CMAS melt viscosity Numerical characteristics obtained through experiments or calculations based on composition, such as the melt viscosity at a specific temperature calculated using FactSage software based on CMAS chemical composition, or directly measured using a rotational viscometer.

[0072] Thermal shock test temperature The parameters set for the experiment are usually selected within the range of 1000℃-1300℃.

[0073] The final failure cycle count is the number of thermal shock cycles that a sample undergoes before reaching a preset failure criterion. For example, the preset failure criterion can be set to the coating peeling area reaching 20% ​​of the total coating area. That is, when the coating peeling area reaches more than 20% of the total coating area, the thermal barrier coating is judged to have failed, and its final failure cycle count is recorded as a lifetime label.

[0074] Final state images are images used to record the state of a coating surface or cross-section, including:

[0075] Final failure surface image: used to record the macroscopic peeling morphology of the coating surface. As an example, it can be acquired by a high-resolution digital camera or optical microscope when the sample reaches the preset failure criteria.

[0076] Final failure cross-sectional image: used to record the crack propagation path, columnar crystal structure changes and interface damage state inside the coating. It is collected and recorded when the sample reaches the preset failure criterion. As an example, the collection steps may include: first, placing the failed sample in a mold for cold mounting, then cutting along the direction perpendicular to the surface of the unpeeled coating, followed by sample preparation processes such as coarse grinding, fine grinding and polishing, and finally observing the cross-sectional structure and taking images by scanning electron microscope (SEM) or optical microscope.

[0077] To ensure consistency in feature extraction, the cross-sectional sampling location should be fixed at the unpeeled area 2 mm from the edge of the sample's maximum peeling region. If the sample has no macroscopic peeling, sampling should be performed at the center of the sample.

[0078] In addition, to improve data quality, the raw data collected can be preliminarily verified to remove obvious outliers, such as data points where the melt viscosity exceeds the reasonable range, or samples with blurred surface images that make it impossible to identify the peeling area.

[0079] S2: Extract final state damage features from the final state image and fuse operating parameters and the final failure cycle number to construct a final state damage feature vector.

[0080] This step aims to process the final state image to obtain the final state damage features, providing a quantitative basis for the subsequent construction of the final state damage feature vector, and enhancing the model's ability to learn the correlation between surface spalling morphology and failure mechanism.

[0081] As an example, the final state image in this embodiment includes the final failure surface image and the final failure cross section image. Correspondingly, the final state damage features include the surface macroscopic damage feature vector and the cross section crack damage feature vector, which are used to characterize the overall damage state of the sample when it finally fails.

[0082] S21: Extract the surface macroscopic damage feature vector from the final failed surface image.

[0083] Specifically, the following image processing and feature extraction operations are performed on each final failed surface image obtained in step S1:

[0084] S211: Perform image preprocessing on the final failed surface image.

[0085] The preprocessing includes one or more of the following: grayscale conversion, denoising, binarization, and morphological opening / closing operations. Grayscale conversion transforms the original color image into a grayscale image for easier subsequent processing. Denoising removes noise introduced during image acquisition; for example, median filtering or Gaussian filtering is used. Binarization separates the eroded and non-eroded areas; for example, Otsu's thresholding method or a preset thresholding method is used. Morphological opening / closing operations remove scattered noise and fill local holes. The opening operation involves erosion followed by dilation to eliminate fine noise, while the closing operation involves dilation followed by erosion to fill small holes within the eroded area.

[0086] S212: Perform region segmentation on the preprocessed image.

[0087] Region segmentation can employ threshold segmentation, region growing, contour extraction, or boundary detection-based segmentation methods to accurately identify the boundaries of the peeled-off region.

[0088] As an example, multiple methods can be combined to improve segmentation accuracy. For instance, Canny edge detection (high-low threshold ratio 2:1) can be used to extract preliminary boundaries, followed by region growing (growing threshold 15 gray levels) to fill the internal regions, and finally, an active contour model (Snake algorithm, weight parameters α=0.2, β=0.1) can be used to optimize the boundaries. Preferably, a deep learning-based semantic segmentation model (such as U-Net) is used instead of traditional image processing methods for stripped region segmentation. This model needs to be trained on no fewer than 50 manually labeled images. The segmentation result is output as a binary mask of the stripped region.

[0089] S213: Obtain the complete contour of the peeled area using a contour extraction algorithm.

[0090] As an example, the outer contour can be extracted using the findContours function in OpenCV (search mode RETR_EXTERNAL, approximation method CHAIN_APPROX_SIMPLE), and then the polygon can be approximated using the approxPolyDP function (precision parameter can be set to 0.5%) to reduce redundant points.

[0091] S214: Calculate the surface macroscopic damage feature vector based on the contour of the peeling region.

[0092] The surface macroscopic damage feature vector includes multiple surface macroscopic damage features. As an example, the surface macroscopic damage feature vector... Set as:

[0093] ;

[0094] The definitions and calculation methods for the macroscopic damage characteristics of each surface are as follows:

[0095] (1) Area of ​​the peeling region The result is obtained by counting the total number of pixels in the peeled area and converting it with the actual area represented by each pixel using an image scale. The unit is square millimeters.

[0096] (2) The proportion of the peeled area to the total sample surface area :

[0097] As an example, the proportion of the peeled area to the total sample surface area in this embodiment This represents the percentage of the peeled area to the total sample surface area. The total sample surface area can be calculated from the sample's outer contour in the image or from a pre-defined standard sample size (e.g., 10mm × 10mm).

[0098] (3) Length of the peeling boundary :

[0099] Length of peeling boundary The perimeter of the peeled-off area is calculated by summing the contour pixels and combining this with an image scale, in millimeters. As an example, the specific steps could be: calculate the sum of the Euclidean distances between contour points and multiply it by the pixel-to-actual-size conversion ratio.

[0100] (4) Irregularity of the peeling shape :

[0101] Irregularity of peeling shape The formula used to characterize the degree of deviation of the shape of the peeled area from a circle can be:

[0102] ;

[0103] When the peeled area is circular, the value is 1; the more irregular the shape, the larger the value. To reduce pixel jaggedness, the extracted contour can be Gaussian smoothed (sigma=1.5) first, and then the sum of the Euclidean distances of the smoothed contour can be calculated. To reduce the influence of noise, an upper limit can be set for the irregularity (e.g., 10), and values ​​exceeding this limit are considered outliers.

[0104] (5) Spatial distribution of the spalling area :

[0105] Spatial distribution of the exfoliation zone The positional offset of the centroid of the detached region relative to the center of the sample can be obtained by calculating the Euclidean distance between the coordinates of the centroid of the detached region and the coordinates of the center of the sample, reflecting whether the detachment is concentrated in a certain local area.

[0106] (6) Percentage of edge damage area :

[0107] Percentage of edge damage area This represents the proportion of the flaked area located at the sample edge, used to characterize the severity of edge damage. As an example, the edge region is defined as the area within 1 mm of the sample boundary. The percentage of the intersection area between the flaked region and this recessed region can be calculated by creating a 1 mm inward contour of the sample border.

[0108] It should be noted that the final failed surface image is mainly used to extract macroscopic spalling and surface instability features, and is not used to directly infer information such as microscopic crack density, stress field, or chemical reaction thickness that cannot be obtained from image stabilization. When no surface photograph is available, the surface macroscopic damage feature vector can be set to empty or not included in subsequent calculations. All extracted features can be normalized (e.g., Min-Max normalization to the [0,1] interval) to eliminate the influence of dimensions, and the software tools and versions used for feature extraction (e.g., OpenCV 4.5.1), parameter configurations, and processing timestamps should be recorded to ensure traceability of the process.

[0109] Through the above operations, the final failed surface image of each sample is transformed into a surface macroscopic damage feature vector composed of several numerical features. This feature vector will be used as a component of the final state damage feature vector in step S23, providing surface macroscopic damage information for subsequent key stages.

[0110] S22: Extract cross-sectional crack damage features from the final failure cross-sectional image.

[0111] This step aims to perform structural identification, crack annotation, and quantitative measurement on the final failure cross-sectional image acquired in step S1, extract structured numerical features that can characterize the damage state inside the coating, and form a final cross-sectional crack damage feature vector. This provides a quantitative basis at the microscopic mechanism level for the subsequent construction of the final damage feature vector, and enhances the model's ability to learn the correlation between internal crack evolution and failure mechanism.

[0112] As an example, we can define the final-state cross-sectional crack damage characteristic vector. for:

[0113] ;

[0114] in, This represents the total length of the transverse crack. This represents the number of transverse cracks. This represents the number of longitudinal cracks. This represents the total length of the longitudinal crack. The degree of intersection of transverse and longitudinal cracks. The damage level is determined by the intergranular structure. For TGO continuity level.

[0115] Specifically, the final failure cross-sectional image is processed as follows:

[0116] S221: Label the crack, columnar intergranular space, and TGO (thermally grown oxide) regions in the cross-sectional image.

[0117] As an example, annotation methods include manual annotation or semi-automatic assisted annotation.

[0118] Manual annotation can be performed by materials experts using image annotation software (such as ImageJ's Freehand Selection tool). As an example, the annotation criteria for cracks can be: clearly separated gaps (width ≥ 0.5 μm); the annotation criteria for columnar intergranular damage can be: widened grain boundaries (> 2 μm) or foreign matter filling; the annotation criteria for TGO can be: a continuous dark oxide layer located between the ceramic layer and the binder layer.

[0119] Semi-automatic assisted annotation can use deep learning segmentation models (e.g., U-Net architecture, input size 512×512, training data ≥ 50 labeled images). The model first generates initial annotations, which are then corrected by experts, thus improving annotation efficiency.

[0120] S222: Calculate the total length of the transverse crack Number of transverse cracks Number of longitudinal cracks and total length of longitudinal crack .

[0121] As an example, the calculation can be performed using image measurement software. The specific steps could be: in ImageJ or MATLAB, use the Skeletonize tool to extract the crack centerline, calculate the pixel length, and then multiply it by a scale conversion factor (e.g., 1 μm / pixel). Transverse cracks are defined as cracks with an angle <30° to the direction parallel to the coating surface, and longitudinal cracks are defined as cracks with an angle <30° to the direction perpendicular to the coating surface. When counting cracks, microcracks <2 μm in length are not included to avoid noise interference.

[0122] S223: Count the number or degree of intersection of transverse and longitudinal cracks. .

[0123] As an example, the detection method for intersection points can be: refine the crack centerline and calculate the number of pixels with a node degree (number of connecting branches) ≥ 3; the degree of intersection can be defined as the ratio of the number of intersection points to the total number of cracks, or the connection density of the crack network (number of intersection points per unit area) can be calculated.

[0124] S224: Classification of the degree of damage to columnar intergranular spaces and TGO continuity.

[0125] Preferably, the damage level of the columnar intergranular spaces can be determined. Defined as a three-level discrete variable:

[0126] Grade 0 (minor damage): normal gap (1-2μm), no foreign matter filling;

[0127] Grade 1 (moderate damage): Localized widening of the space (2-5 μm) or small amount of foreign body filling;

[0128] Grade 2 (Severe Damage): Widening of large-area gaps (>5μm) or complete filling with CMAS material.

[0129] Similarly, the TGO continuity level can be... Defined as:

[0130] Level 0 (Continuous): The TGO layer is continuous and complete, with uniform thickness;

[0131] Level 1 (local discontinuity): 3-5 fractures appear in the TGO layer, with a fracture width of <5μm;

[0132] Level 2 (significant instability): Multiple fractures (>5) in the TGO layer, with fracture width >5μm or large-area peeling.

[0133] Through the above operations, the final failure cross-sectional image corresponding to each sample is transformed into a cross-sectional crack damage feature vector composed of several numerical features. This feature vector will serve as a key component in constructing the final state damage feature vector in step S23, providing internal microscopic damage information for subsequent key stages.

[0134] S23: Integrate operating parameters, final failure cycle count, and final state damage characteristics to construct a final state damage feature vector.

[0135] This sub-step aims to organically integrate the operating condition parameters and final failure cycle count from step S1, as well as the final-state damage features extracted from steps S21 and S22, to construct a unified final-state damage feature vector. This results in a high-dimensional feature representation that can comprehensively reflect the failure state of thermal barrier coatings, providing structured data input for the subsequent inference of key damage stages and key node sequences, and enhancing the model's ability to characterize multi-factor coupled failure mechanisms.

[0136] As an example, the operating parameters, the final failure cycle count, and the final state damage characteristics are integrated into a unified vector:

[0137] ;

[0138] in, The CMAS principal element composition vector is usually represented as a vector of the mass percentage of each oxide. Before integration, it can be normalized (e.g., divided by the total amount to make the sum equal to 1) or standardized (e.g., Z-score standardization) to eliminate dimensional differences.

[0139] This refers to the melt viscosity. If the viscosity values ​​vary widely (10...), -3 -10 3 If Pa·s), then a logarithmic transformation is performed before use to improve the distribution characteristics;

[0140] The thermal shock test temperature. This represents the final failure cycle count.

[0141] At this point, the final state damage feature vector Build complete.

[0142] S3: Classify the damage level of the original thermal barrier coating sample based on the final state damage feature vector.

[0143] This step aims to calculate the final state damage intensity index and classify the damage level based on the final state damage feature vector constructed in step S2, so as to provide a basis for selecting the corresponding template from the preset key node proportion template in the future.

[0144] Specifically, it includes the following steps:

[0145] S31: Calculate the final state damage intensity index based on the final state damage feature vector.

[0146] This sub-step aims to, for each original sample, use the final-state damage feature vector of that sample output from step S2. (Including at least the total length of transverse cracks, the number of longitudinal cracks, the degree of intersection of transverse and longitudinal cracks, the proportion of spalling area, and the TGO continuity level, etc.), the final damage intensity index D is calculated by weighted fusion to provide an objective and quantifiable basis for subsequent damage degree classification.

[0147] Specifically, constructing a final-state damage intensity index The calculation formula can be:

[0148] ;

[0149] in, , , , and These are the normalized transverse crack length, longitudinal crack number, crack intersection degree, spalling area ratio, and TGO continuity index, respectively. ~ These are weighting coefficients, which can be set to 0.30, 0.20, 0.15, 0.20, and 0.15 respectively.

[0150] As an example, the normalization method can be linear normalization. Taking the transverse crack length as an example, the normalization formula can be:

[0151] ;

[0152] in, and The global extreme value of the transverse crack length is taken (i.e., the minimum and maximum values ​​of this feature among all samples). When the feature distribution is significantly skewed (e.g., the proportion of the spalling area is concentrated in 0-30%), quantile normalization (using the 5% and 95% quantiles as cutoff points) can be used to improve robustness and avoid interference from extreme values.

[0153] Weighting coefficients can be determined in two ways:

[0154] (1) Based on past expert experience;

[0155] (2) Based on a portion of the calibrated samples (≥15 groups, including intermediate process observation data) from step S1, the final damage characteristics and the final failure cycle number were fitted by linear regression. The relationship is such that the regression coefficients are normalized and used as weights, so that the final damage intensity index D is more in line with the actual damage evolution law.

[0156] As an example, the weighting coefficient can be set as follows:

[0157] , , , , ;

[0158] S32: Classify the damage level of the original sample according to the final damage intensity index.

[0159] This sub-step aims to compare the final damage intensity index D of each original sample calculated in S31 with the preset grading threshold for classifying damage levels, thereby classifying the original samples into different damage levels, achieving quantitative and standardized classification of damage levels, and laying the foundation for differentiated generation of key node sequences.

[0160] Specifically, based on the final state damage intensity index Methods for classifying the degree of damage to the original sample can be:

[0161] S321: Determine the number of levels to be divided.

[0162] As an example, the damage severity is divided into three levels: mild terminal damage, moderate terminal damage, and severe terminal damage.

[0163] S322: Determine the grading threshold for classifying the final state damage intensity index.

[0164] First, determine the number of grading thresholds based on the required number of levels. For example, to divide the injury into three levels, two grading thresholds need to be set. and .

[0165] Then, the grading threshold is determined based on the number of samples required for each grade. For example, the 33% and 66% quantiles of the final damage intensity index D in the dataset can be used as grading thresholds to ensure that the number of samples in the three classes is roughly balanced (the ratio is close to 1:1:1), and to avoid the failure of the key node proportion template due to too few samples in one class.

[0166] S323: Compare the final damage intensity index of the original sample with the grading threshold to obtain the damage level of the original sample.

[0167] The final damage intensity index of the original sample With two graded thresholds and ,For example:

[0168] when At that time, it was classified as mild terminal damage;

[0169] when At that time, it was classified as moderate terminal damage;

[0170] when At that time, it was classified as severe terminal damage.

[0171] The classification results can be stored in a structured manner: generate classification labels ("Light" / "Medium" / "Severe") and associate them with the sample ID and the final damage intensity index. Final state damage feature vector association and archiving; for those at the threshold boundary (such as...) For samples, add manual verification marks to improve classification reliability.

[0172] S4: Select the corresponding template from the preset key node ratio template according to the damage level, and calculate the key node sequence according to the ratio of each key node in the template.

[0173] This step aims to determine the damage level and the final failure cycle number for each original sample, based on S32. Following the pre-defined non-uniform interval distribution rules of the selected critical node proportion template, a unique critical node sequence (i.e., the specific number of cycles to be observed in supplementary experiments) and its corresponding critical damage stages (e.g., stabilization stage, damage initiation stage, crack propagation stage, and pre-critical failure stage) are generated for each sample. This ensures that the node distribution strictly follows the physical law of "slow in the early stage and accelerated in the later stage" in the damage evolution of thermal barrier coatings. The definition of critical damage stages can be set empirically.

[0174] As an example, the specific steps could be:

[0175] S41: Preset the corresponding key node proportion template according to the number of damage severity levels.

[0176] Taking step S32 as an example of dividing damage into three levels, the corresponding preset templates for the proportions of the three key nodes are as follows:

[0177] A key node proportion template is generated based on the damage level of the sample. The key node proportion template includes several non-equidistant key node proportions, namely:

[0178] (1) For samples with a minor damage level, the key node proportion template is set as follows:

[0179] ;

[0180] (2) For samples with moderate damage, the key node proportion template is set as follows:

[0181] ;

[0182] (3) For samples with severe damage, the key node proportion template is set as follows:

[0183] ;

[0184] The number of nodes can be flexibly adjusted according to project requirements, such as... Figure 4 As shown. As a further example, mild final-state damage can be reduced to 2 nodes (keeping 0.80 and 0.90), while severe final-state damage can be expanded to 6 nodes (increasing by 0.98).

[0185] The label for the critical damage stage is used to record the state of the sample at the current loop number.

[0186] As a preferred option, the labels for key damage stages can also be named according to the key node proportion template.

[0187] For example, for samples with moderate damage, the key damage stages are divided into four stages, such as... Figure 3 As shown, the labels for the corresponding key damage stages are as follows:

[0188] Stable phase: ≤0.3;

[0189] Damage initiation stage: 0.3≤ ≤0.6;

[0190] Crack propagation stage: 0.6≤ ≤0.9;

[0191] Pre-critical failure stage: >0.9.

[0192] S42: Correct the key node proportion template using a pre-trained shallow learning model.

[0193] To further adapt the density of key nodes to different CMAS operating conditions and damage levels, a shallow learning model that is friendly to small samples can be used to correct the key node ratio template obtained in step S41. The shallow learning model can be a decision tree model, a random forest model, a gradient boosting tree model, or an XGBoost model. As an example, an XGBoost model is used for correction, with the main parameters set as follows: number of trees: 100, maximum depth: 3, learning rate: 0.05.

[0194] The operating parameters and final damage characteristics are transformed into structured numerical inputs, which are then fed into a pre-trained shallow learning model to output node lifetime proportional density levels, node lifetime proportional template categories, or node correction coefficients. Based on these outputs, the node lifetime proportions of the key node proportional templates in step S4 are adjusted to obtain key node proportional templates that better reflect the actual damage evolution of the samples.

[0195] As an example, historical samples with existing phased thermal shock test data can be selected as training samples. The CMAS major element composition, melt viscosity, thermal shock test temperature, and final damage characteristics are used as inputs, and the node lifetime proportional template category or node correction coefficient is used as a supervision label to pre-train the shallow learning model. For the sample to be analyzed, the key node proportional template generated in step S41 is first used as a basis, and then corrected using the shallow learning model to improve the accuracy of key node back-calculation.

[0196] S43: Select the corresponding critical node proportion template according to the damage level and calculate the critical node sequence.

[0197] For each original sample, a template corresponding to the damage level determined in S32 is selected from the key node proportion template preset in S41.

[0198] Then based on the final failure cycle count Calculate the sequence of key nodes.

[0199] As an example:

[0200] (1) For the original sample with mild final state damage, the key node sequence is set as follows:

[0201] ;

[0202] (2) For the original sample with moderate terminal damage, the key node sequence is set as follows:

[0203] ;

[0204] (3) For the original sample with severe final state damage, the key node sequence is set as follows:

[0205] .

[0206] Steps S3 and S4 aim to infer the key damage stages (such as damage initiation, crack propagation, and critical failure) and their corresponding key nodes (i.e. a series of specific cycle numbers) in the life evolution process of thermal barrier coatings through a physical mechanism-guided inversion method, so as to provide a quantitative basis for the selection of key nodes in the supplementary test in step S5.

[0207] S5: Based on the key node sequence, obtain experimental data of supplementary samples with the same or similar working conditions as the original samples at each key node, and integrate them with the original time-state data to construct an enhanced training database.

[0208] This step aims to obtain experimental data at key nodes of supplementary samples with the same or similar working conditions based on the key node sequence obtained in step S3, and integrate it with the original time-state data to form an enhanced training database, providing high-quality training samples containing complete damage evolution time-series information for the multi-task neural network model.

[0209] The experimental data includes:

[0210] Operating parameters, i.e., CMAS principal component vectors Melt viscosity and thermal shock temperature ;

[0211] The stage damage characteristics include the number of cycles at the critical nodes (i.e., the number of cycles at the critical nodes), the node lifetime ratio, and stage labels of the supplementary sample; it also includes observable characteristics that characterize the degree of coating damage when the supplementary sample reaches the critical nodes, such as: macroscopic surface damage characteristics (peeling area, peeling area ratio, etc.) and / or cross-sectional crack damage characteristics (transverse crack length, longitudinal crack number, crack intersection degree, etc.). Specific methods for extracting observable characteristics of coating damage degree can be found in steps S2 and S3.

[0212] The experimental data can be obtained through methods such as: conducting phased thermal shock tests independently (pausing the test at each critical point and collecting sample status), extracting from existing test databases, collecting from public literature or technical reports, or generating through numerical simulation.

[0213] It must be noted that in this step, the final failure cycle number of the supplementary sample is... The final failure cycle count of the original sample (already recorded in step S1) is directly used, without testing the supplementary sample to failure. The supplementary test is only performed up to each node in the critical node sequence, pausing at each node and collecting stage damage characteristics.

[0214] The following explanation uses the method of obtaining experimental data through staged thermal shock tests as an example.

[0215] S51: Determine the required number of supplementary samples based on the key node sequence of the original sample.

[0216] At least one independent parallel supplementary sample is required for each critical node. The number of supplementary samples is determined based on the critical node sequence output in step S3. This step does not require experimentation and is directly calculated from the output of step S3.

[0217] S52: Determine the node lifetime ratio and the label of the critical damage stage based on the critical node ratio template.

[0218] Based on the key node ratio template output in step S41, output the node lifetime ratio and stage label corresponding to the key node.

[0219] The labels for critical damage stages are used to record the state of the sample at the current cycle number, and have already been defined in step S3. Taking a sample with moderate damage as an example, the critical damage stages are divided into four phases, and the corresponding labels for the critical damage stages are as follows:

[0220] Stable phase: ≤0.3;

[0221] Damage initiation stage: 0.3≤ ≤0.6;

[0222] Crack propagation stage: 0.6≤ ≤0.9;

[0223] Pre-critical failure stage: >0.9.

[0224] This step requires no experimentation; it is determined directly by calculation and rules.

[0225] S53: Conduct staged thermal shock tests on the supplementary samples and record the staged damage characteristics of the supplementary samples at each critical node.

[0226] As an example, the specific steps of the staged thermal shock test include:

[0227] S531: Obtain multiple sets of supplementary samples with the same or similar operating conditions as the original sample and specify the key nodes corresponding to the supplementary samples.

[0228] Select several parallel supplementary samples with the same or similar operating conditions as the original sample, the specific number being equal to the number of critical nodes requiring supplementary testing. "Same or similar operating conditions" means that the CMAS major element composition, melt viscosity, and thermal shock test temperature are similar to the original sample (e.g., compositional differences are within acceptable range, viscosity is on the same order of magnitude, and temperature is the same). The coating preparation process, substrate material, and dimensions of the supplementary samples should be consistent with the original sample to ensure the comparability of damage evolution patterns.

[0229] Since destructive testing of samples is required when acquiring stage damage characteristics, the number of supplementary samples should be no less than the number of critical nodes. For each critical node, a dedicated supplementary sample should be assigned, and it is recommended to prepare 1-2 extra spare samples.

[0230] Since the data from the original sample has already been obtained, there is no need to set up the sample for the entire test until final failure, thus reducing the workload of supplementary testing.

[0231] S532: Set the temperature for the thermal shock test.

[0232] The supplementary sample is placed in a high-temperature thermal shock test equipment, and the thermal shock test temperature is set (the same as the test temperature of the original sample). Each thermal shock cycle includes stages such as heating, holding, and cooling, and the cycle period is the same as the test conditions of the original sample.

[0233] S533: The test shall be stopped after each supplementary sample has been tested to the specified critical point.

[0234] For each critical node: place the corresponding parallel sample into the test equipment and start the thermal shock test; when the number of cycles precisely reaches the critical node, immediately stop the test and remove the sample from the equipment; the sample will not be subjected to further cycles.

[0235] S534: Stage damage characteristics of supplementary samples after the collection test has been stopped.

[0236] For each sample after stopping, obtain the stage damage characteristics according to the method in step S2, for example:

[0237] Macroscopic surface damage characteristics: If necessary, surface images can be taken first using a digital camera or optical microscope, and then features such as the area of ​​the peeled region, the proportion of the peeled area, the length of the peeled boundary, the irregularity of the peeled shape, the spatial distribution of the peeled area, and the proportion of the edge damage area can be extracted according to S2.

[0238] Cross-sectional crack damage characteristics: Due to the need for destructive testing, the sample was cold-mounted, cut, ground, and polished according to the S3 method. Then, cross-sectional images were captured using a scanning electron microscope (SEM) or an optical microscope to extract features such as total transverse crack length, number of transverse cracks, number of longitudinal cracks, total longitudinal crack length, degree of intersection of transverse and longitudinal cracks, damage level of columnar intergranular spaces, and TGO continuity level.

[0239] Since each sample is used for only one node, thorough destructive testing can be performed without worrying about sample continuity.

[0240] S54: Integrate the experimental data of the supplementary samples with the original time-state data to form an enhanced training database.

[0241] The final state data of the original samples are integrated with the node data of the supplementary samples for each key node to form an augmented training database. Each sample record in the database corresponds to a stage damage feature under a specific key node, as shown in Table 1 as one example:

[0242] Table 1. Examples of a single data entry in the augmented training database

[0243]

[0244] S6: Use the enhanced training database to train a multi-task neural network to obtain a lifespan prediction model.

[0245] This step aims to construct a deep learning model that relies solely on readily available operating condition parameters during the prediction phase, while fully utilizing augmented training database information during the training phase. A high-performance prediction model is obtained through a specialized training strategy. A schematic diagram of the lifespan prediction model is shown below. Figure 2 As shown.

[0246] Specifically, the steps include the following:

[0247] S61: Construct a multi-task neural network.

[0248] Construct a multi-task neural network whose input consists of readily available operating parameters, for example, which can be represented as: That is, the principal component vector of CMAS Melt viscosity and thermal shock temperature .

[0249] As an example, the multi-task neural network used in this embodiment is a multi-task residual deep network structure. Introducing residual connections between adjacent layers can alleviate gradient vanishing, enhance feature reuse and cross-layer information flow, thereby improving training stability, reducing overfitting risk and improving prediction accuracy under small sample multi-task learning conditions.

[0250] The network architecture includes a shared backbone feature extraction module, which consists of multiple fully connected layers. Each layer is followed by a ReLU activation function, LayerNorm, and Dropout, and residual connections are introduced to adjacent layers. As an example, the shared backbone network is configured with four fully connected layers, with the following neuron counts: 128, 128, 64, and 32. The activation function is ReLU, the normalization is LayerNorm, and Dropout is set to 0.2.

[0251] The formula for residual connection can be:

[0252] ;

[0253] in For the first Hidden features of layers and For parameters, This is the activation function.

[0254] After sharing the backbone network, the network branches into three parallel output heads:

[0255] (1) Lifetime regression output head, used to output the predicted final lifetime value. .

[0256] (2) Stage-assisted classification output head, used to output the probability distribution of a sample belonging to a preset key damage stage (stable stage, damage initiation stage, crack propagation stage, and pre-critical failure stage), which can be expressed by the formula:

[0257] .

[0258] (3) Lifetime range output header, used to output the upper and lower boundaries of the predicted lifetime. Or a parameter representing the uncertainty of prediction .

[0259] S62: Design a joint loss function for multiple tasks as the total loss function.

[0260] During training, a multi-task joint loss function is introduced as the overall loss function. This allows the model to simultaneously learn final lifetime, stage evolution, and uncertainty information. As an example, the formula can be expressed as:

[0261] ;

[0262] In this embodiment, the weights can be exemplified as follows: , , ;

[0263] in, For lifetime regression loss (such as mean squared error), as an example, using mean squared error, the formula can be expressed as:

[0264] ,in, It is the true lifetime value of the i-th sample. It is the lifetime value predicted by the model for the i-th sample;

[0265] For stage classification loss, as an example, we use cross-entropy loss, which can be expressed as:

[0266] ;in One-hot encoding for stage labels. It is the probability predicted by the model that the i-th sample belongs to stage k;

[0267] This is the interval constraint loss, used to penalize cases where the predicted interval fails to cover the true value. As an example, when the model outputs the upper and lower boundaries, the formula can be expressed as:

[0268] ;in, and These are the lower and upper bounds of the lifetime interval predicted by the model for the i-th sample. This represents the positive part of the function.

[0269] Through joint optimization, the model learns final lifetime, stage evolution, and uncertainty information simultaneously under limited sample conditions. The output of this step is a fully trained deep learning model with multi-task prediction capabilities.

[0270] S63: Add physical prior constraints consistent with the failure law of thermal barrier coatings to the total loss function.

[0271] To make the model output more consistent with the basic physical laws of thermal barrier coating failure, this step aims to add a physical constraint term to the total loss function as a preferred implementation method. By introducing physical laws, the generalization ability and interpretability of the model can be improved, and the physical consistency of the model can be enhanced.

[0272] For example, in the total loss function By incorporating a temperature monotonicity constraint, for samples a and b with similar composition and viscosity but different thermal shock test temperatures, a higher temperature typically corresponds to a shorter lifespan, i.e.:

[0273] ;

[0274] Therefore, the corresponding temperature monotonic constraint term It can be represented as:

[0275] ;

[0276] Therefore, the total loss function It can be represented as:

[0277] ;

[0278] in The prior constraint weight, for example, can be set to 0.2. By introducing this constraint, the model can still maintain a reasonable lifetime change trend under small sample sizes.

[0279] S64: Use a few-sample training strategy for model training.

[0280] This step aims to address the typically limited availability of CMAS (Conditional Condition Assay) erosion thermal barrier coating lifetime data by employing a specialized small-sample training strategy to prevent overfitting and improve model robustness. Specific training strategies include:

[0281] (1) The optimizer uses Adam, and the initial learning rate is set to ;

[0282] (2) Set the batch size to 8;

[0283] (3) The maximum number of training epochs is set to 300, and an early stop strategy is adopted. The number of early stop epochs is set to 30, that is, training is stopped when the verification loss does not decrease for 30 consecutive epochs.

[0284] (4) K-fold cross-validation was used to evaluate the stability of the model, with the number of folds set to 5;

[0285] (5) Use an early stopping strategy to prevent overfitting;

[0286] (6) L2 regularization is used to reduce model complexity, and the L2 regularization coefficient is set to 1. ;

[0287] A Dropout layer is used for random deactivation regularization, with the Dropout ratio set to 0.2;

[0288] (7) Standardize the input features;

[0289] (8) Assign higher training weights to samples near key nodes in the later stages. Specifically, let the weight of the node samples be... :

[0290] ;

[0291] in This represents the percentage of node lifetimes. The weighting adjustment coefficient can be set to 1.0 in this embodiment. This approach makes the model focus more on the crack propagation stage and the pre-critical failure stage, thereby improving the critical interval resolution capability of lifetime prediction.

[0292] Using the above training strategy, the multi-task residual deep network can be stably trained and effectively generalized under limited sample conditions. The output of this step is a robustly trained, high-performance multi-task residual deep network model.

[0293] S7: Input the operating parameters of the sample to be predicted into the trained lifetime prediction model and output its lifetime prediction results.

[0294] This step aims to demonstrate the simplicity and efficiency of the method of the present invention in engineering applications. In the actual prediction stage, only the CMAS major elemental composition, melt viscosity, and thermal shock test temperature of the sample to be predicted need to be obtained and input into the lifetime prediction model trained in steps S1 to S6. The lifetime prediction model will directly output the prediction results for the sample under test, including the predicted lifetime value, the predicted lifetime range (i.e., the critical loss stage), and / or the failure probability distribution. The entire prediction process does not require inputting any surface or cross-sectional photographs, significantly lowering the barrier to engineering applications.

[0295] The above is merely one specific embodiment of the present invention. For those skilled in the art, any equivalent substitutions or adjustments made to the stage division threshold, node template, number of model layers, number of neurons, loss weights, and training parameters, without departing from the core idea of ​​the present invention, should fall within the protection scope of the present invention.

[0296] Example 2

[0297] This embodiment provides a thermal barrier coating lifetime prediction system based on enhanced final-state damage information. This system is used to execute the method described in Embodiment 1. The system includes the following modules: a final-state data acquisition and feature extraction module, a damage feature extraction module, a damage level classification module, a key node sequence generation module, an enhanced database construction module, a model training module, and a lifetime prediction module. Each module is described in detail below.

[0298] Final state data acquisition and feature extraction module:

[0299] This module is configured to acquire the final-state data of the original thermal barrier coating sample and construct the final-state damage feature vector, including:

[0300] The final-state data acquisition unit is configured to acquire final-state data of raw samples of failed thermal barrier coatings under different operating conditions. Specifically, the final-state data acquisition unit is connected to high-temperature thermal shock testing equipment, a microscope, or a scanning electron microscope, or receives existing experimental data via a data interface. The acquired final-state data includes: operating conditions (CMAS principal element composition vector). Melt viscosity Thermal shock test temperature ), final failure cycle count The images include the final failed surface image and the final failed cross-sectional image. The acquisition method is exactly the same as step S1 in Example 1, and will not be repeated here.

[0301] Damage feature extraction unit:

[0302] This unit is used to extract final-state damage features from the final-state image and fuse operating parameters and the final failure cycle number to construct a final-state damage feature vector. It contains three sub-units:

[0303] 1. Surface Feature Extraction Subunit: Performs image preprocessing, region segmentation, contour extraction, and geometric calculation on the final failed surface image to generate a macroscopic surface damage feature vector. The specific processing procedure is the same as step S21 in Example 1.

[0304] 2. Section Feature Extraction Subunit: Performs structural identification, crack annotation, and quantitative measurement on the final failed section image to generate a section crack damage feature vector. The specific processing procedure is the same as step S22 in Example 1.

[0305] 3. Vector Fusion Subunit: This unit integrates operating parameters... Final failure cycle count and eigenvectors and Concatenate them into a unified final-state damage feature vector As described in step S23 of Embodiment 1.

[0306] Damage severity classification module:

[0307] This module calculates the final-state damage intensity index based on the final-state damage feature vector. The original samples are then classified into three damage levels—mild, moderate, and severe—based on a preset grading threshold. The specific calculation method is the same as steps S31 and S32 in Example 1, including the weighted fusion formula. And threshold comparison rules.

[0308] Key node proportion template storage module:

[0309] The system is configured to pre-store multiple key node ratio templates corresponding to different damage levels. Each template consists of several non-equally spaced key node ratio values, where the key node ratio represents the proportion of node cycles to the final failure cycle. The templates exhibit a "sparse in the early stage, dense in the later stage" distribution characteristic, meaning the ratio intervals at the beginning of the template are larger than those at the end, enhancing the characterization of the crack propagation stage and the pre-critical failure stage. For example, the templates include: {0.30, 0.60, 0.85} for mild damage, {0.20, 0.50, 0.75, 0.90} for moderate damage, and {0.15, 0.35, 0.55, 0.75, 0.88, 0.95} for severe damage. The number of nodes and ratio values ​​in the templates can be flexibly adjusted according to engineering needs; the more severe the damage, the more key nodes are included in the template. When the critical node sequence generation module is executed, it first selects the corresponding template from the critical node ratio template storage module according to the damage level output by the damage level classification module, and then multiplies the ratio of each critical node in the template by the final failure cycle number to calculate the absolute cycle number sequence of the critical nodes, which is used as the critical node sequence.

[0310] Key node sequence generation module:

[0311] This module selects a corresponding template from a preset critical node proportion template based on the damage severity level, and calculates the critical node sequence based on the proportion of each critical node in the template and the final failure cycle count. This module may further include a correction unit, which uses a shallow learning model (such as XGBoost) to fine-tune the proportion values ​​of the selected template to adapt to different CMAS operating conditions and damage modes. The specific implementation method is consistent with step S4 (i.e., S41, S42, S43) in Example 1. The final output critical node sequence is a list of absolute cycle counts, for example, the output for a lightly damaged sample. .

[0312] Enhanced database building modules:

[0313] This module acquires experimental data from supplementary samples with the same or similar operating conditions as the original sample at each key node based on the key node sequence, and integrates this data with the original final-state data to construct an enhanced training database. This module supports multiple data acquisition methods: conducting phased thermal shock tests independently (calling the test equipment interface), extracting data from existing test databases, collecting data from publicly available literature or technical reports, or generating data through numerical simulation. When using phased thermal shock tests, this module controls the test equipment to conduct tests on parallel supplementary samples according to the key node sequence. At each node, it stops and calls the damage feature extraction module to obtain phased damage features. Then, all supplementary data and the final-state data of the original sample are merged into a structured database. The specific steps are the same as steps S5 (S51-S54) in Example 1.

[0314] Model training module:

[0315] This module uses an enhanced training database to train a multi-task neural network to obtain a lifespan prediction model. The model training module includes the following sub-functions:

[0316] 1. Network Building Unit: Constructs a multi-task neural network, whose input is operating condition parameters. The output includes predicted lifetime values, stage classification results, and predicted lifetime intervals. In this embodiment, a multi-task residual deep network is preferably used, with a shared backbone of four fully connected layers (128-128-64-32), each followed by ReLU, LayerNorm, and Dropout, and residual connections are introduced. The network branches into three parallel output heads: a lifetime regression output head, a stage-assisted classification output head, and a lifetime interval output head. The technical effects of residual connections are as described above: mitigating gradient vanishing, enhancing feature reuse, and reducing the risk of overfitting.

[0317] 2. Loss Function Design Unit: Employing a multi-task joint loss function. ,in, Mean square error, For cross-entropy, This is the interval constraint loss. Preferably, physical prior terms such as temperature monotonic constraints can also be added.

[0318] 3. Training Policy Unit: Employs a few-shot training strategy, including the Adam optimizer (learning rate...). Batch size 8, early stopping (patience=30), K-fold cross-validation (K=5), L2 regularization (coefficient) Dropout (0.2) and subsequent node sample weighting (weights) , (Version 1.0). All training processes are performed on an augmented training database, ultimately outputting a fully trained lifespan prediction model.

[0319] Lifetime prediction module:

[0320] This module takes the operating parameters of the sample to be predicted (only CMAS major element composition, melt viscosity, and thermal shock test temperature are required) and inputs them into the trained lifetime prediction model. It then directly outputs the predicted lifetime value, the predicted lifetime range, and / or the failure probability distribution. The entire prediction process does not require any surface or cross-sectional images, making it suitable for rapid on-site assessments.

[0321] The various modules communicate with each other via data streams, jointly realizing the complete function from the acquisition of final state data of the original sample to the prediction of the lifetime of the new sample. The system in this embodiment can be implemented in software on a computer device, or some functions (such as test control and image acquisition) can be completed in combination with hardware devices.

[0322] Example 3

[0323] This embodiment provides a computer device including a memory and a processor. The memory stores computer instructions, and the processor executes these instructions to perform the thermal barrier coating lifetime prediction method based on enhanced final-state damage information as described in Embodiment 1.

[0324] Specifically, the processor can be a central processing unit (CPU), graphics processing unit (GPU), digital signal processor (DSP), application-specific integrated circuit (ASIC), or other programmable logic device. The memory can be read-only memory (ROM), random access memory (RAM), flash memory, hard disk, or any other form of non-volatile storage medium. The computer instructions stored in the memory are organized into one or more software modules. When these modules are loaded and executed by the processor, they implement all the operations described in steps S1 to S6 of Embodiment 1, including: acquiring the final state data of the original sample, extracting the final state damage features and constructing the final state damage feature vector, classifying the damage severity level, generating a key node sequence, constructing an enhanced training database, training a multi-task neural network, and outputting lifetime prediction results for the sample to be predicted.

[0325] This computer device can be a standalone workstation, server, or embedded industrial computer, or it can be integrated into thermal barrier coating testing equipment or a gas turbine / aero-engine health monitoring system. After inputting the operating parameters of the sample to be predicted (CMAS major element composition, melt viscosity, thermal shock test temperature), the device can directly output the predicted lifetime value, predicted lifetime range, or failure probability distribution for engineers' reference.

[0326] Example 4

[0327] This embodiment provides a computer-readable storage medium storing computer instructions, which are executed by a computer to perform the thermal barrier coating lifetime prediction method based on final state damage information enhancement as described in Embodiment 1.

[0328] Computer-readable storage media include, but are not limited to, optical discs (CDs, DVDs), hard disk drives (HDDs), solid-state drives (SSDs), USB flash drives, floppy disks, magnetic tapes, read-only memory (ROM), random access memory (RAM), flash memory, and any other medium capable of storing program code. The storage medium can be installed within a computer device (such as an internal hard drive) or can be an external removable medium (such as a USB flash drive). When computer instructions in the storage medium are loaded into the memory of the computer device and executed by the processor, the computer device can perform the steps described in Embodiment 1, including all processes such as data acquisition, feature extraction, model training, and lifetime prediction.

[0329] Furthermore, the computer instructions in the computer-readable storage medium can be transmitted and distributed via wired or wireless networks, enabling multiple computer devices to share the same set of program code, facilitating the mass deployment of the method of the present invention in laboratory or industrial production environments.

[0330] The preferred embodiments of the present invention have been described in detail above with reference to the accompanying drawings. However, the present invention is not limited to the specific details of the above embodiments. Within the scope of the technical concept of the present invention, various simple modifications can be made to the technical solution of the present invention, and these simple modifications all fall within the protection scope of the present invention.

Claims

1. A method for predicting the lifetime of a thermal barrier coating based on enhanced final-state damage information, characterized in that, Includes the following steps: The final state data of the original thermal barrier coating sample are obtained and a final state damage feature vector is constructed. The final state damage feature vector includes at least the operating condition parameters, the final failure cycle number, and the final state damage characteristics. The damage level of the original sample is classified based on the final state damage feature vector; Based on the damage severity level, a corresponding template is selected from multiple preset key node proportion templates to calculate the key node sequence; Based on the key node sequence, experimental data of supplementary samples with the same or similar working conditions as the original sample are obtained at each key node, and the experimental data is integrated with the final state data to construct an enhanced training database; the experimental data includes working condition parameters and stage damage characteristics. A multi-task neural network is trained using the enhanced training database to obtain a lifespan prediction model. The operating parameters of the sample to be predicted are input into the lifetime prediction model, and the lifetime prediction result of the sample to be predicted is output.

2. The thermal barrier coating lifetime prediction method based on final-state damage information enhancement according to claim 1, characterized in that, The method of classifying the damage level of the original sample based on the final state damage feature vector includes: The final state damage intensity index is calculated by weighting the final state damage features in the final state damage feature vector. The final damage intensity index is compared with a preset grading threshold to classify the original sample into different damage levels.

3. The thermal barrier coating lifetime prediction method based on final-state damage information enhancement according to claim 2, characterized in that, The method for setting the hierarchical threshold includes: Determine the number of levels that need to be divided; The number of grading thresholds is determined based on the number of grades required. The grading threshold value is determined based on the number of samples required for each grade.

4. The thermal barrier coating lifetime prediction method based on final-state damage information enhancement according to claim 1, characterized in that, The method for obtaining experimental data of the supplementary sample at each key node includes: preparing an independent parallel supplementary sample for each key node; The supplementary samples will be subjected to thermal shock tests until the number of cycles corresponding to the critical node is reached, after which the test will be stopped. Destructive testing was performed on the supplementary samples after the stop to obtain the stage damage characteristics of the node.

5. The thermal barrier coating lifetime prediction method based on final-state damage information enhancement according to claim 1, characterized in that, The preset multiple key node ratio templates correspond to different damage levels, and the key node ratios in each template are distributed at non-equal intervals, with the early intervals being larger than the later intervals. Furthermore, the more severe the damage, the more key nodes are included in the template.

6. The thermal barrier coating lifetime prediction method based on final-state damage information enhancement according to any one of claims 1-5, characterized in that, The multi-task neural network includes a shared backbone feature extraction module and three parallel output heads. The shared backbone feature extraction module includes residual connections, and the three output heads include: The lifetime regression output header is used to output the predicted lifetime value; The stage-assisted classification output head is used to output the probability distribution of a sample belonging to a preset key damage stage; And a lifetime range output header, used to output the predicted lifetime range or parameters representing the prediction uncertainty.

7. The thermal barrier coating lifetime prediction method based on final-state damage information enhancement according to any one of claims 1-5, characterized in that, The training of the multi-task neural network adopts a multi-task joint loss function, which includes at least lifetime regression loss, stage classification loss, and interval constraint loss; and physical prior constraints are introduced into the multi-task joint loss function, including temperature monotonicity constraints, that is, for samples with similar composition and viscosity but different thermal shock test temperatures, higher temperatures correspond to shorter lifetimes.

8. A thermal barrier coating lifetime prediction system based on enhanced final-state damage information, characterized in that, include: The final state data acquisition and feature extraction module is configured to acquire the final state data of the original thermal barrier coating sample and construct the final state damage feature vector, wherein the final state damage feature vector includes at least the operating condition parameters, the final failure cycle number and the final state damage features. The damage level classification module is configured to classify the damage level of the original sample based on the final state damage feature vector; The key node sequence generation module is configured to select a corresponding template from a plurality of preset key node proportion templates according to the damage level and calculate the key node sequence. An enhanced database construction module is configured to acquire experimental data of supplementary samples with the same or similar working conditions as the original sample at each key node based on the key node sequence, and integrate the experimental data with the final state data to construct an enhanced training database; the experimental data includes working condition parameters and stage damage characteristics; The model training module is configured to train a multi-task neural network using the enhanced training database to obtain a lifespan prediction model. The lifetime prediction module is configured to input the operating parameters of the sample to be predicted into the lifetime prediction model and output the lifetime prediction result of the sample to be predicted.

9. A computer device, characterized in that, It includes a memory and a processor, wherein the memory stores computer instructions, and the processor executes the computer instructions to perform the method as described in any one of claims 1-7.

10. A computer-readable storage medium, characterized in that, The computer-readable storage medium stores computer instructions that, when executed by a computer, perform the method as described in any one of claims 1-7.

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