A low thermal conductivity rare earth pyrosilicate design method based on weight automatic optimization and multi-evidence joint scoring and application thereof

Abstract

The application relates to the technical field of high-temperature protective coating material design, and discloses a low-thermal-conductivity rare earth pyrosilicate design method based on weight automatic optimization combined scoring and application thereof. By constructing a low-temperature average thermal conductivity score, a low-temperature decline trend score, a relative priority score, a target temperature thermal conductivity reference score, a physical priori score and a prediction risk score, target temperature thermal conductivity data is measured, interpolated, extrapolated and adjacent temperature alternative source marked, and the source credibility weight is given according to the data reliability; the above evidence scores are uniformly included into a comprehensive scoring function, and the candidate compositions of the rare earth pyrosilicate materials meeting the requirements of the target temperature thermal conductivity are graded and output. Through the weight assignment of multiple sources, the joint scoring of multiple evidences and the automatic optimization of the weight, the application avoids the independent dependence on the absolute thermal conductivity prediction value or the artificial fixed weight, and improves the reliability of the low-thermal-conductivity rare earth pyrosilicate candidate screening under the condition of high temperature and small sample.

Description

Technical Field

[0001] This invention relates to the field of high-temperature protective coating material design technology, specifically to a design method for low thermal conductivity rare earth pyrosilicon based on weighted automatic optimization and multi-evidence joint scoring, and its application. Background Technology

[0002] Rare earth pyrosilicon (RE)₂Si₂O₇ is considered an important candidate material for environmental barrier coatings and high-temperature thermal insulation ceramic systems due to its low thermal conductivity, good high-temperature phase stability, and thermal expansion behavior that matches SiC-based composites. As the service temperatures of aero-engines and gas turbines increase, coating materials not only need to resist high-temperature water-oxygen corrosion but also require further reductions in thermal conductivity to decrease heat transfer and extend the service life of the substrate.

[0003] Single rare-earth pyrosilicates typically struggle to simultaneously meet multiple requirements, including low thermal conductivity, high-temperature stability, thermal expansion matching, cost control, and processability. Synergistically controlling the composition of pyrosilicates using multiple rare-earth components has become an important direction for improving the overall performance of materials. However, multi-rare-earth systems involve a large number of elements, complex element combinations, and a wide range of component ratios, rapidly expanding the material design space. Traditional R&D methods relying on empirical judgment and individual experiments are costly, time-consuming, and difficult to efficiently screen candidates with low thermal conductivity.

[0004] In existing data-driven methods, a common approach is to establish an absolute value regression model for thermal conductivity and then rank candidate components from low to high based on predicted thermal conductivity. However, high-temperature thermal conductivity databases generally suffer from problems such as limited sample size, inconsistent temperature points, significant differences in testing conditions across different literatures, and the need for interpolation or extrapolation of some target temperature data. Under these conditions, the predicted median value of the absolute value regression model may be unstable, and simply ranking the experimental samples based on the candidate with the lowest predicted value can easily lead to overconfident recommendations.

[0005] On the other hand, for material systems with similar crystal structures and heat transfer mechanisms, such as rare-earth pyrosilicones, thermal conductivity often exhibits similar trends with temperature. Completely discarding extrapolated high-temperature data would further reduce the training sample size for the target temperature; conversely, treating extrapolated and measured data with equal weight would introduce unreliable labels. Therefore, a method is needed that can utilize extrapolated data under trend consistency constraints and differentiate the weights of measured, interpolated, extrapolated, and adjacent temperature surrogate data. Summary of the Invention

[0006] The purpose of this invention is to provide a weighted optimization machine learning method for designing low thermal conductivity rare earth pyrosilicates and its application, which integrates evidence of low thermal conductivity and target high temperature ranking. This method can improve the reliability of candidate screening for low thermal conductivity rare earth pyrosilicates under high temperature and small sample conditions.

[0007] To achieve the above objectives, the present invention adopts the following technical solution: A design method for low thermal conductivity rare earth pyrosilicon based on weighted automatic optimization and multi-evidence joint scoring includes: S1. Collect thermal conductivity data of various rare earth pyrosilicon materials at different temperatures, extract the corresponding material composition and temperature to form a database, wherein the temperature includes room temperature and target temperature; S2. Construct a set of physical descriptor features to characterize the local disorder, mass difference, size mismatch or chemical environment of rare earth pyrosilicon materials; normalize each physical descriptor and combine it with the ranking results of the thermal conductivity of each rare earth pyrosilicon material in the database from low to high to obtain the physical prior score of each rare earth pyrosilicon material in the database. S3. The normalized data value of the average thermal conductivity of each rare earth pyrosilicon material in the database within the range from room temperature to a given characteristic temperature is determined as the low-temperature average thermal conductivity score of the corresponding rare earth pyrosilicon material, wherein the characteristic temperature is less than the target temperature. S4. The normalized data value of the rate of decrease in thermal conductivity of each rare earth pyrosilicon material in the database during the process of increasing from room temperature to the characteristic temperature is determined as the corresponding low temperature trend score. S5. Based on the source of thermal conductivity data for each rare earth pyrosilicon material at the target temperature in the database, assign different source credibility weights to the thermal conductivity data at the target temperature. S6. Using all or part of the rare earth pyrosilicate materials in the database as the training set, compare the thermal conductivity data of the rare earth pyrosilicate materials in the training set at the target temperature pairwise to construct paired comparison samples; determine the training weight of the paired comparison samples based on the difference in thermal conductivity of the paired comparison samples and the corresponding source credibility weight; train the prediction probability model of the thermal conductivity of one rare earth pyrosilicate material in the paired comparison samples being lower than that of the other rare earth pyrosilicate material at the target temperature, and calculate the relative priority score of each rare earth pyrosilicate material having lower thermal conductivity at the target temperature relative to other rare earth pyrosilicate materials in the training set. S7. Using the material composition and physical descriptor of rare earth pyrosilicon materials in the training set as model input, and the corresponding physical prior score, low-temperature average thermal conductivity score, low-temperature trend score, relative priority score, and thermal conductivity at the target temperature as learning objectives, establish a learning model that outputs the physical prior score, low-temperature average thermal conductivity score, low-temperature trend score, relative priority score, and predicted thermal conductivity at the target temperature of rare earth pyrosilicon candidate materials. S8. Using rare earth pyrosilicon materials in the database, perform multi-round group cross-validation in the learning model, and calculate the probability that the predicted thermal conductivity of the target temperature of each rare earth pyrosilicon material is lower than the preset benchmark thermal conductivity in the multi-round validation. Then, use the normalized value of the mean of the predicted results of each rare earth pyrosilicon material in each round of validation as the reference score of the target temperature thermal conductivity of the corresponding rare earth pyrosilicon material. S9. Based on the absolute error between the mean value of each rare earth pyrosilicon material in the database and the actual thermal conductivity data value, and the probability that the predicted result of each rare earth pyrosilicon material is lower than the preset benchmark thermal conductivity in multiple rounds of verification, analyze and obtain the uncertainty risk score of the target temperature thermal conductivity of the corresponding rare earth pyrosilicon material. S10. Using the material composition and physical descriptor of rare earth pyrosilicon materials in the training set as model input, output modules for the reference score and uncertainty risk score of the target temperature thermal conductivity of rare earth pyrosilicon materials are constructed in the learning model. The learning model is used to evaluate the physical prior score, low-temperature average thermal conductivity score, low-temperature trend score, relative priority score, and target temperature thermal conductivity prediction value of the candidate materials, and the reference score and uncertainty risk score of the target temperature thermal conductivity of the candidate materials are output simultaneously. S11. Based on the relative priority score of the candidate materials, the reference score of thermal conductivity at the target temperature, the score of average thermal conductivity at low temperature, the score of low temperature trend, the score of physical prior and the score of uncertainty risk, construct a weighted comprehensive score for the candidate materials. If the weighted comprehensive score is greater than or equal to the preset score threshold, it is determined that the corresponding candidate material meets the thermal conductivity requirement at the target temperature; otherwise, it does not meet the requirement.

[0008] Furthermore, in step S2, the method for obtaining the physical prior scores of each rare earth pyrosilicon material in the database includes: From descriptors including average ionic radius, radius mismatch parameter, average atomic mass, mass mismatch parameter, mass disorder parameter, average electronegativity, electronegativity mismatch parameter, or mixing entropy, physical descriptors are selected that indicate the thermal conductivity of rare-earth pyrosilicon materials at the target temperature increases or decreases with increasing corresponding physical descriptors. The selected physical descriptors are then normalized to obtain their corresponding descriptor scores. ;

[0009] in, For the first The first rare earth pyrosilicate material Original values ​​of physical descriptors, For the training set The maximum value of a physical descriptor. For the training set The minimum value of a physical descriptor. For the first The first rare earth pyrosilicate material The descriptor score after normalization of each physical descriptor; Calculate the physical prior score based on the descriptor score. ,in, For a given first The contribution coefficients of each descriptor satisfy: , , The number of physical descriptors selected.

[0010] Furthermore, the contribution coefficient is determined using a finite weight combination search method, specifically as follows: 1) Arrange the rare earth pyrosilicon materials in the training set in ascending order of thermal conductivity data at the target temperature, and determine the materials with lower thermal conductivity as materials with higher priority for low thermal conductivity, thus forming a priority ranking result for low thermal conductivity based on measured thermal conductivity. 2) Under the condition that each contribution coefficient is non-negative and the sum is 1, generate multiple contribution coefficient combinations according to different step sizes for each contribution coefficient; calculate the physical prior score of each rare earth pyrosilicon material for different contribution coefficient combinations, sort them in descending order according to the size of the physical prior score, and determine the materials with larger physical prior scores as materials with higher priority for low thermal conductivity, forming a low thermal conductivity priority ranking result based on physical prior scores; 3) Calculate the degree of consistency between the low thermal conductivity priority ranking results based on physical prior scores and the low thermal conductivity priority ranking results based on measured thermal conductivity, and select the combination of contribution coefficients with the highest degree of consistency as the final contribution coefficient of each physical descriptor; the degree of consistency is the Spearman rank correlation coefficient or Kendall rank correlation coefficient between the low thermal conductivity priority ranking results based on physical prior scores and the low thermal conductivity priority ranking results based on measured thermal conductivity.

[0011] Further, in step S3, the method for obtaining the low-temperature average thermal conductivity score of rare earth pyrosilicon materials includes: Calculate the arithmetic mean of the thermal conductivity of the rare earth pyrosilicon material at at least five temperature points, including the room temperature thermal conductivity and the characteristic temperature thermal conductivity, within the range from room temperature to the characteristic temperature, and determine the arithmetic mean as the average thermal conductivity of the corresponding rare earth pyrosilicon material. The low-temperature average thermal conductivity score Lavg,i corresponding to the i-th rare earth pyrosilicon material is calculated according to the following formula: Lavg,i=(kavg,max-kavg,i) / (kavg,max-kavg,min) Where kavg,i is the average thermal conductivity of the i-th rare earth pyrosilicon material in the training set, kavg,max is the maximum value of the average thermal conductivity in the training set, and kavg,min is the minimum value of the average thermal conductivity in the training set; and when the calculated result of Lavg,i is less than 0, it is taken as 0, and when the calculated result is greater than 1, it is taken as 1. In step S4, the rate of decrease in thermal conductivity Dtrend,i = 1 - k during the process of raising the temperature of the i-th rare earth pyrosilicon material from room temperature to the characteristic temperature is... 1000,i / k RT,i k 1000,i Let k be the thermal conductivity of the i-th rare-earth pyrosilicon material at the characteristic temperature. RT,i Let be the room temperature thermal conductivity of the i-th rare earth pyrosilicon material; The low-temperature trend score of the i-th rare earth pyrosilicon material is Ltrend,i = (Dtrend,i - Dtrend,min) / (Dtrend,max - Dtrend,min), where Dtrend,max is the maximum value of the thermal conductivity decrease rate in the training set, and Dtrend,min is the minimum value of the thermal conductivity decrease rate in the training set.

[0012] Further, in step S5, the data sources include measured data, interpolated data, extrapolated data, and nearby temperature data. The source confidence weight is set to 1 when the data source is measured data, and different source confidence weights are assigned in a manner that the source confidence weights decrease sequentially for interpolated data, extrapolated data, and nearby temperature data.

[0013] Furthermore, in step S6, the process for obtaining the relative priority score corresponding to the i-th rare earth pyrosilicon material is as follows: The material composition and the selected physical descriptor of the i-th rare earth pyrosilicon material and the j-th rare earth pyrosilicon material in the paired comparison sample are respectively used to form feature vectors xi and xj, where xi is the feature vector of the i-th rare earth pyrosilicon material and xj is the feature vector of the j-th rare earth pyrosilicon material. Using Δxij = xi - xj as the input to the prediction probability model, the output label is 1 when the target temperature thermal conductivity of the i-th rare earth pyrosilicon material is lower than that of the j-th rare earth pyrosilicon material, and 0 otherwise. A supervised classification method is used to establish a probability prediction model for outputting the prediction probability that the target temperature thermal conductivity of the i-th rare earth pyrosilicon material is lower than that of the j-th rare earth pyrosilicon material. The predicted probability of the i-th rare earth pyrosilicon material relative to all other rare earth pyrosilicon materials in the training set is weighted by source confidence, and this weighted average is determined as the relative priority score Rtarget,i corresponding to the i-th rare earth pyrosilicon material; Furthermore, in step S7, the learning model includes one or more of the following: random forest regression model, gradient boosting regression model, support vector regression model, and linear regression model. In step S8, the method for obtaining the reference score of the thermal conductivity at the target temperature of rare earth pyrosilicon materials includes: The rare earth pyrosilicate materials in the database are grouped according to their material composition information. Samples with the same material composition are grouped together. Multiple rounds of cross-validation are performed in the learning model, and the average of the prediction results for the i-th rare earth pyrosilicate material in each round of validation is used as the predicted value of thermal conductivity at the target temperature. Then to After normalization, the corresponding normalized value is used as the reference score for the thermal conductivity at the target temperature of the i-th rare earth pyrosilicon material. ; In step S9, the method for obtaining the uncertainty risk score of the target temperature thermal conductivity of the corresponding rare earth pyrosilicon material includes: Calculate the i-th rare earth pyrosilicate material The absolute error E between the measured value and the actual value i Predicted thermal conductivity at target temperature Subtract the absolute error E i The lower bound of the prediction is obtained. Predicted thermal conductivity at target temperature Add the absolute error E i Obtain the upper bound of the prediction The difference between the upper and lower bounds of the prediction is used as the prediction interval width W for the thermal conductivity at the target temperature of the i-th rare earth pyrosilicon material. i ; The prediction interval width W for each rare earth pyrosilicate material in the database i And the upper bound of prediction Normalization is performed separately to obtain the normalized prediction interval width. and normalized prediction upper bound :

[0014]

[0015] in, This represents the minimum predicted interval width for rare earth pyrosilicon materials in the database. This represents the maximum predicted interval width for rare earth pyrosilicon materials in the database. This represents the maximum value of the upper bound predicted for rare earth pyrosilicon materials in the database. This is the minimum value of the predicted upper bound for rare earth pyrosilicon materials in the database; Using the 25th percentile of the target temperature thermal conductivity in the database as the benchmark thermal conductivity, the probability that the predicted target temperature thermal conductivity of the i-th rare earth pyrosilicon material is lower than the benchmark thermal conductivity in multiple rounds of verification is: ; Uncertainty risk score Calculate according to the following formula:

[0016] Wherein, β1, β2, and β3 are the weights corresponding to the prediction interval width, prediction upper bound, and probability of thermal conductivity below the baseline, respectively, and β1, β2, and β3 are all not less than 0, β1 + β2 + β3 = 1; the method for determining β1, β2, and β3 is through a finite weight combination search, that is, obtaining the uncertainty risk score of each rare earth pyrosilicon material in the database under different weight combinations. and in accordance with Arrange in ascending order and compare according to The sorting results and the predicted values ​​of thermal conductivity at the target temperature The consistency of the ranking results from smallest to largest is considered; the candidate weight combination with the highest consistency is selected as the final weight combination of β1, β2, and β3, where the consistency is determined by... The sorting results and the predicted values ​​of thermal conductivity at the target temperature Spearman correlation coefficient or Kendall correlation coefficient for sorting results from smallest to largest.

[0017] Furthermore, in step S11, the weighted comprehensive score is calculated. ,in, The relative priority score for candidate materials. This serves as a reference score for the target temperature thermal conductivity of the candidate materials. The low-temperature average thermal conductivity score of the candidate materials. Let P be the low-temperature trend score of the candidate material, P be the physical prior score of the candidate material, and U be the uncertainty risk score. , , , , and They are non-negative weight coefficients, and satisfy the following conditions: ; , , , , and The method for determining the priority of low thermal conductivity is to maximize the consistency between the weighted comprehensive score-based priority ranking result and the measured thermal conductivity-based priority ranking result. The consistency between the weighted comprehensive score-based priority ranking result and the measured thermal conductivity-based priority ranking result includes Spearman's rank correlation coefficient or Kendall's rank correlation coefficient.

[0018] Furthermore, after obtaining multiple rare earth pyrosilicon materials that meet the requirements, the process further includes introducing spatial applicability domain judgment, uncertainty judgment, and ranking stability judgment as risk constraints for further screening. The screening methods include: The rare earth pyrosilicon material with the smallest sum of absolute differences in the proportions of all identical elements in the training set and the candidate material is identified as the most similar material. When the difference in the proportions of all rare earth elements between the candidate material and the most similar material is not greater than a preset difference threshold, the spatial applicability domain of the candidate material is judged as passed. When the uncertainty risk score U of the candidate material is not greater than the preset risk threshold, the uncertainty judgment is passed. When the standard deviation of the low thermal conductivity priority ranking of candidate materials in multi-round group cross-validation based on weighted comprehensive score is not greater than the preset ranking position, the ranking stability is judged as passed. All candidate materials were divided into strict priority candidates and exploratory candidates based on weighted comprehensive scores and risk constraints. Strict priority candidates met the following conditions: a weighted comprehensive score of not less than 0.70 and passing all risk constraints. Exploratory candidates met the following conditions: a weighted comprehensive score of not less than 0.50, but not simultaneously passing all risk constraints, and the difference in the composition ratio of all rare earth elements was not greater than 0.20, the uncertainty risk score U was not greater than 0.50, and the ranking standard deviation was not greater than 3. From the set of candidate materials in the strict priority candidate and exploratory candidate categories, rare earth pyrosilicon materials that meet the following conditions are selected as the final design materials: all rare earth element mole fractions are non-negative and their sum is 1; the number of effective rare earth element types is within a set range; the mole fraction of a single rare earth element is within the corresponding upper and lower limits; and the rare earth pyrosilicon materials do not overlap with the rare earth pyrosilicon materials in the database.

[0019] To achieve the above-mentioned technical effects, the present invention also provides a low thermal conductivity rare earth pyrosilicate material obtained by the method described above, wherein the general formula of the rare earth pyrosilicate material is: [(Yb)] a (Sc) b (Eu) c (R) d ]2Si2O7; where R is one or more of Y, Dy, Ho, Er, Tm, Lu and Gd, and a, b, c and d are the mole fractions at rare earth sites, and satisfy a+b+c+d=1.

[0020] Compared with the prior art, the beneficial effects of this invention are: 1. More suitable for screening low thermal conductivity materials under high temperature and small sample conditions. This invention transforms the screening task of low thermal conductivity rare earth pyrosilicon materials from a single absolute thermal conductivity prediction to a multi-evidence joint scoring and priority ranking. In particular, it uses the ranking results of low thermal conductivity at the target temperature as the core decision-making basis, directly obtaining candidate components with low thermal conductivity potential at the target temperature and their priorities. Compared with methods that rely solely on high-temperature thermal conductivity regression prediction, this invention can reduce the impact of limited high-temperature sample size, large extrapolation errors, and unstable absolute value predictions on candidate screening results, making it more suitable for high-temperature, small-sample material development scenarios.

[0021] 2. Improve the objectivity of joint scoring by optimizing weighting coefficients. This invention integrates information such as low-temperature average thermal conductivity, low-temperature decreasing trend, target high-temperature ranking, target temperature absolute value reference, physical priors, and uncertainty risk into a unified scoring system. Instead of arbitrarily fixing the contribution ratio of each module, the weight coefficients of each component are optimized based on verification results. This allows for adaptive determination of the role of each evidence source in the final score based on actual prediction performance under different datasets and target temperature conditions, making the candidate ranking results more objective and stable.

[0022] 3. Able to balance basic evidence at low temperatures with judgment of target high-temperature performance. This invention considers the average thermal conductivity at low temperatures from room temperature to the characteristic temperature, the low-temperature trend score, and the paired ranking results at the target temperature simultaneously during the weight optimization process. The average thermal conductivity at low temperatures can be used to determine the baseline low thermal conductivity of candidate materials, the low-temperature decreasing trend can be used to determine whether the thermal conductivity continues to decrease after the material is heated, and the ranking at the target high temperature is used to ultimately determine the priority of candidate compositions at the target temperature. Through weight coefficient optimization, the above information can be automatically adjusted according to its verification contribution, avoiding the over-amplification or complete neglect of a certain type of evidence.

[0023] 4. It can improve the reliability of extrapolated data when used in modeling. This invention assigns source labels and credibility weights to measured, interpolated, extrapolated, and adjacent temperature surrogate data, incorporating these into the weight optimization and scoring verification process. This approach avoids both completely discarding extrapolated or adjacent temperature data, which could lead to insufficient target high-temperature samples, and treating extrapolated data as equivalent to measured data, thus preventing a decrease in label reliability. Therefore, this invention can more rationally utilize existing data resources and improve the credibility of target temperature candidate ranking when high-temperature experimental data is limited.

[0024] 5. The screening results have better robustness and interpretability. This invention utilizes weight optimization to synergistically integrate the target high-temperature ranking score, absolute value reference score, physical prior score, and uncertainty risk score, avoiding the reliance on a single model output to determine the candidate list. For selected candidates, further reasons can be provided, such as a high target high-temperature ranking, low basic thermal conductivity at low temperatures, a significant decrease in thermal conductivity after heating, or low predicted risk, thereby improving the interpretability of the screening results. Attached Figure Description

[0025] Figure 1 The graph shows the statistical results of thermal conductivity tests of the samples in Example 4 and Comparative Example 3 at 1000℃ and 1200℃. Detailed Implementation

[0026] The present invention will now be described in further detail with reference to the embodiments and accompanying drawings. However, this should not be construed as limiting the scope of the above-described subject matter of the present invention to the following embodiments; all technologies implemented based on the content of the present invention fall within the scope of the present invention.

[0027] Example 1: A design method for low thermal conductivity rare earth pyrosilicon based on weighted automatic optimization and multi-evidence joint scoring, comprising: S1. Collect thermal conductivity data of various rare earth pyrosilicon materials at different temperatures, extract the corresponding material composition and temperature to form a database, wherein the temperature includes room temperature and target temperature; In this embodiment, rare earth pyrosilicon thermal conductivity data can be collected from papers, patents, books and public databases to extract corresponding material composition, temperature (or test temperature) and other information, and to unify the thermal conductivity unit, temperature unit and composition representation to form a structured data table.

[0028] For single-point data, the thermal conductivity value at the corresponding temperature is directly extracted; for thermal conductivity data in the form of curves, a discretization method is used to extract the thermal conductivity data corresponding to multiple temperature points.

[0029] In addition, for records with incomplete composition, unclear test conditions, unreliable data sources, or that cannot be reproduced, consistency checks and deduplication are first performed on repeated data with the same material composition and at the same temperature to ensure the authenticity of thermal conductivity data.

[0030] S2. Construct a set of physical descriptor features to characterize the local disorder, mass difference, size mismatch or chemical environment of rare earth pyrosilicon materials; normalize each physical descriptor and combine it with the ranking results of the thermal conductivity of each rare earth pyrosilicon material in the database from low to high to obtain the physical prior score of each rare earth pyrosilicon material in the database. In this embodiment, physical descriptors are selected from those including average ionic radius, radius mismatch parameter, average atomic mass, mass mismatch parameter, mass disorder parameter, average electronegativity, electronegativity mismatch parameter, or mixing entropy. These descriptors indicate that the thermal conductivity of rare-earth pyrosilicon materials at the target temperature increases or decreases with the increase of the corresponding physical descriptor. The selected physical descriptors are then normalized to obtain their corresponding descriptor scores. ;

[0031] in, For the first The first rare earth pyrosilicate material Original values ​​of physical descriptors, For the training set The maximum value of a physical descriptor. For the training set The minimum value of a physical descriptor. For the first The first rare earth pyrosilicate material The descriptor score after normalization of each physical descriptor; Calculate the physical prior score based on the descriptor score. ,in, For a given first The contribution coefficients of each descriptor satisfy: , , The number of physical descriptors selected; the contribution coefficient is determined using a finite weight combination search method, specifically as follows: 1) Arrange the rare earth pyrosilicon materials in the training set in ascending order of thermal conductivity data at the target temperature, and determine the materials with lower thermal conductivity as materials with higher priority for low thermal conductivity, thus forming a priority ranking result for low thermal conductivity based on measured thermal conductivity. 2) Under the condition that each contribution coefficient is non-negative and the sum is 1, generate multiple contribution coefficient combinations according to different step sizes for each contribution coefficient; calculate the physical prior score of each rare earth pyrosilicon material for different contribution coefficient combinations, sort them in descending order according to the size of the physical prior score, and determine the materials with larger physical prior scores as materials with higher priority for low thermal conductivity, forming a low thermal conductivity priority ranking result based on physical prior scores; 3) Calculate the degree of consistency between the low thermal conductivity priority ranking results based on physical prior scores and the low thermal conductivity priority ranking results based on measured thermal conductivity, and select the combination of contribution coefficients with the highest degree of consistency as the final contribution coefficient of each physical descriptor; the degree of consistency is the Spearman rank correlation coefficient or Kendall rank correlation coefficient between the low thermal conductivity priority ranking results based on physical prior scores and the low thermal conductivity priority ranking results based on measured thermal conductivity.

[0032] S3. The normalized data value of the average thermal conductivity of each rare earth pyrosilicon material in the database within the range from room temperature to a given characteristic temperature is determined as the low-temperature average thermal conductivity score of the corresponding rare earth pyrosilicon material, wherein the characteristic temperature is less than the target temperature. In this embodiment, taking a target temperature of 1200℃ as an example, 1000℃ is selected as the characteristic temperature. The arithmetic mean of the thermal conductivity of the rare earth pyrosilicon material is calculated at at least 5 temperature points in the range from room temperature (20℃) to the characteristic temperature (1000℃), including the room temperature thermal conductivity and the characteristic temperature thermal conductivity. The arithmetic mean is determined as the average thermal conductivity of the corresponding rare earth pyrosilicon material. The low-temperature average thermal conductivity score Lavg,i corresponding to the i-th rare earth pyrosilicon material is calculated according to the following formula: Lavg,i=(kavg,max-kavg,i) / (kavg,max-kavg,min) Where kavg,i is the average thermal conductivity of the i-th rare earth pyrosilicon material in the training set, kavg,max is the maximum value of the average thermal conductivity in the training set, and kavg,min is the minimum value of the average thermal conductivity in the training set; and when the calculated result of Lavg,i is less than 0, it is taken as 0, and when the calculated result is greater than 1, it is taken as 1.

[0033] S4. The normalized data value of the rate of decrease in thermal conductivity of each rare earth pyrosilicon material in the database during the process of increasing from room temperature to the characteristic temperature is determined as the corresponding low temperature trend score. In this embodiment, the rate of decrease in thermal conductivity Dtrend,i = 1 - k during the process of raising the temperature of the i-th rare earth pyrosilicon material from room temperature to the characteristic temperature is defined. 1000,i / k RT,i k 1000,i Let k be the thermal conductivity of the i-th rare-earth pyrosilicon material at the characteristic temperature. RT,i Let be the room temperature thermal conductivity of the i-th rare earth pyrosilicon material; The low-temperature trend score of the i-th rare earth pyrosilicon material is Ltrend,i = (Dtrend,i - Dtrend,min) / (Dtrend,max - Dtrend,min), where Dtrend,max is the maximum value of the thermal conductivity decrease rate in the training set, and Dtrend,min is the minimum value of the thermal conductivity decrease rate in the training set.

[0034] S5. Based on the source of thermal conductivity data for each rare earth pyrosilicon material at the target temperature in the database, assign different source credibility weights to the thermal conductivity data at the target temperature. The data sources include measured data, interpolated data, extrapolated data, and data from nearby temperature sources. The source reliability weight is set to 1 when the data source is measured data, and different source reliability weights are assigned in descending order of weight for interpolated data, extrapolated data, and data from nearby temperature sources. For example, in this embodiment, when the target temperature is between two existing temperatures of the corresponding rare earth pyrosilicon material in the database, the thermal conductivity of the target temperature is obtained through interpolation and marked as interpolated data, with a source reliability weight of 0.60–0.85. When the target temperature is outside the existing temperature range of the corresponding rare earth pyrosilicon material in the database, the thermal conductivity of the target temperature is obtained through extrapolation and marked as extrapolated data, with a source reliability weight of 0.50–0.60. When only nearby temperature data exists, the thermal conductivity of the nearby temperature is used as a substitute and marked as nearby temperature substitute data, with a source reliability weight of 0.40–0.50.

[0035] S6. Using all or part of the rare earth pyrosilicate materials in the database as the training set, compare the thermal conductivity data of the rare earth pyrosilicate materials in the training set at the target temperature pairwise to construct paired comparison samples; determine the training weight of the paired comparison samples based on the difference in thermal conductivity of the paired comparison samples and the corresponding source credibility weight; train the prediction probability model of the thermal conductivity of one rare earth pyrosilicate material in the paired comparison samples being lower than that of the other rare earth pyrosilicate material at the target temperature, and calculate the relative priority score of each rare earth pyrosilicate material having lower thermal conductivity at the target temperature relative to other rare earth pyrosilicate materials in the training set. In this embodiment, the material composition and the selected physical descriptor of the i-th rare earth pyrosilicon material and the j-th rare earth pyrosilicon material in the paired comparison sample are respectively used to form feature vectors xi and xj, where xi is the feature vector of the i-th rare earth pyrosilicon material and xj is the feature vector of the j-th rare earth pyrosilicon material. Using Δxij = xi - xj as the input to the prediction probability model, the output label is 1 when the target temperature thermal conductivity of the i-th rare earth pyrosilicon material is lower than that of the j-th rare earth pyrosilicon material, and 0 otherwise. A supervised classification method is used to establish a probability prediction model for outputting the prediction probability that the target temperature thermal conductivity of the i-th rare earth pyrosilicon material is lower than that of the j-th rare earth pyrosilicon material. The predicted probability of the i-th rare earth pyrosilicon material relative to all other rare earth pyrosilicon materials in the training set is weighted by source confidence, and this weighted average is determined as the relative priority score Rtarget,i corresponding to the i-th rare earth pyrosilicon material.

[0036] S7. Using the material composition (e.g., mole fraction of rare earth elements) and physical descriptor of rare earth pyrosilicate materials in the training set as model inputs, and the corresponding physical prior scores, low-temperature average thermal conductivity scores, low-temperature trend scores, relative priority scores, and thermal conductivity at the target temperature as learning objectives, establish a learning model that outputs the physical prior scores, low-temperature average thermal conductivity scores, low-temperature trend scores, relative priority scores, and predicted thermal conductivity at the target temperature of rare earth pyrosilicate candidate materials. The learning model described in this embodiment includes one or more of the following: random forest regression model, gradient boosting regression model, support vector regression model, and linear regression model.

[0037] S8. Using rare earth pyrosilicon materials in the database, perform multi-round group cross-validation in the learning model, and calculate the probability that the predicted thermal conductivity of the target temperature of each rare earth pyrosilicon material is lower than the preset benchmark thermal conductivity in the multi-round validation. Then, use the normalized value of the mean of the predicted results of each rare earth pyrosilicon material in each round of validation as the reference score of the target temperature thermal conductivity of the corresponding rare earth pyrosilicon material. In this embodiment, rare earth pyrosilicate materials in the database are grouped according to their material composition information. Samples with the same material composition are grouped together. Multiple rounds of cross-validation are performed in the learning model, and the average of the prediction results of the i-th rare earth pyrosilicate material in each round of validation is used as the predicted value of the thermal conductivity at the target temperature. Then to After normalization, the corresponding normalized value is used as the reference score for the thermal conductivity at the target temperature of the i-th rare earth pyrosilicon material. .

[0038] Then calculate the i-th rare earth pyrosilicon material. The absolute error E between the measured value and the actual value i Predicted thermal conductivity at target temperature Subtract the absolute error E i The lower bound of the prediction is obtained. Predicted thermal conductivity at target temperature Add the absolute error E i Obtain the upper bound of the prediction The difference between the upper and lower bounds of the prediction is used as the prediction interval width W for the thermal conductivity at the target temperature of the i-th rare earth pyrosilicon material. i ; The prediction interval width W for each rare earth pyrosilicate material in the database i and the upper bound of prediction Normalization is performed separately to obtain the normalized prediction interval width. and normalized prediction upper bound :

[0039]

[0040] in, This represents the minimum predicted interval width for rare earth pyrosilicon materials in the database. This represents the maximum predicted interval width for rare earth pyrosilicon materials in the database. This represents the maximum value of the upper bound predicted for rare earth pyrosilicon materials in the database. This is the minimum value of the predicted upper bound for rare earth pyrosilicon materials in the database; Using the 25th percentile of the target temperature thermal conductivity in the database as the benchmark thermal conductivity, the probability that the predicted target temperature thermal conductivity of the i-th rare earth pyrosilicon material is lower than the benchmark thermal conductivity in multiple rounds of verification is: ; Uncertainty risk score Calculate according to the following formula:

[0041] Wherein, β1, β2, and β3 are the weights corresponding to the prediction interval width, prediction upper bound, and probability of thermal conductivity below the baseline, respectively, and β1, β2, and β3 are all not less than 0, β1 + β2 + β3 = 1; the method for determining β1, β2, and β3 is through a finite weight combination search, that is, obtaining the uncertainty risk score of each rare earth pyrosilicon material in the database under different weight combinations. and in accordance with Arrange in ascending order and compare according to The sorting results and the predicted values ​​of thermal conductivity at the target temperature The consistency of the ranking results from smallest to largest is considered; the candidate weight combination with the highest consistency is selected as the final weight combination of β1, β2, and β3, where the consistency is determined by... The sorting results and the predicted values ​​of thermal conductivity at the target temperature Spearman correlation coefficient or Kendall correlation coefficient for sorting results from smallest to largest.

[0042] S9. Based on the absolute error between the mean value and the actual thermal conductivity data value of each rare earth pyrosilicon material in the database, and the probability that the predicted result of each rare earth pyrosilicon material is lower than the preset benchmark thermal conductivity in multiple rounds of verification, analyze and obtain the uncertainty risk score of the target temperature thermal conductivity of the corresponding rare earth pyrosilicon material.

[0043] S10. Using the material composition and physical descriptor of rare earth pyrosilicon materials in the training set as model input, output modules for the target temperature thermal conductivity reference value and uncertainty risk value of rare earth pyrosilicon materials are constructed in the learning model respectively. The learning model is used to evaluate the physical prior value, low temperature average thermal conductivity value, low temperature trend value, relative priority value and target temperature thermal conductivity prediction value of candidate materials, and the target temperature thermal conductivity reference value and uncertainty risk value of candidate materials are output simultaneously.

[0044] S11. Based on the relative priority score of the candidate materials, the reference score of thermal conductivity at the target temperature, the score of average thermal conductivity at low temperature, the score of low temperature trend, the score of physical prior and the score of uncertainty risk, construct a weighted comprehensive score for the candidate materials. If the weighted comprehensive score is greater than or equal to the preset score threshold, it is determined that the corresponding candidate material meets the thermal conductivity requirement at the target temperature; otherwise, it does not meet the requirement. In this embodiment, the weighted comprehensive score is used. ,in, The relative priority score for candidate materials. This serves as a reference score for the target temperature thermal conductivity of the candidate materials. The low-temperature average thermal conductivity score of the candidate materials. Let P be the low-temperature trend score of the candidate material, P be the physical prior score of the candidate material, and U be the uncertainty risk score. , , , , and They are non-negative weight coefficients, and satisfy the following conditions: ; , , , , and The method for determining the priority of low thermal conductivity is to maximize the consistency between the weighted comprehensive score-based priority ranking result and the measured thermal conductivity-based priority ranking result. The consistency between the weighted comprehensive score-based priority ranking result and the measured thermal conductivity-based priority ranking result includes Spearman's rank correlation coefficient or Kendall's rank correlation coefficient.

[0045] The core of this embodiment lies in the fact that the weights are not fixed arbitrarily, but rather determined through optimization based on verification results. Therefore, the low-temperature average thermal conductivity, low-temperature trend, target high-temperature ranking, absolute value reference, physical prior, and uncertainty risk are not simply concatenated, but adaptively fused according to their actual contribution to the candidate selection effect, thus forming reproducible and interpretable screening rules for low thermal conductivity candidate components. Compared with methods that only rank based on the predicted absolute thermal conductivity value of the target temperature, this embodiment, through weighting based on the credibility of the target temperature data source, pairwise ranking of target temperatures, joint scoring of multiple evidences, and risk constraint hierarchical output, can reduce the impact of high-temperature small samples, interpolation extrapolation errors, and prediction uncertainties on the candidate recommendation results, making it more suitable for discovering candidate components of low thermal conductivity rare earth pyrosilicate materials.

[0046] After obtaining multiple rare earth pyrosilicon materials that meet the requirements, this embodiment can further introduce spatial applicability domain judgment, uncertainty judgment, and ranking stability judgment as risk constraints for further screening. The screening methods include: S12. The rare earth pyrosilicon material with the smallest sum of absolute differences in the proportions of all identical elements in the training set and the candidate material is determined as the most similar material. When the difference in the proportions of all rare earth elements between the candidate material and the most similar material is not greater than a preset difference threshold, the spatial applicability domain of the candidate material is judged as passed. The preset difference threshold ranges from 0.10 to 0.20, and is exemplarily taken as 0.2 in some embodiments. When the uncertainty risk score U of the candidate material is not greater than the preset risk threshold, the uncertainty judgment is passed; the preset risk threshold ranges from 0.30 to 0.50, and in some embodiments it is exemplarily taken as 0.4; When the candidate material is ranked in a preset ranking position with a weighted comprehensive score based on low thermal conductivity in multi-round group cross-validation, and the standard deviation of the ranking position is no greater than 1 to 3, preferably no greater than 2, the ranking stability is judged as passing. S13. All candidate materials are divided into strict priority candidates and exploratory candidates based on weighted comprehensive scores and risk constraints. Strict priority candidates must meet the following conditions: weighted comprehensive score not lower than 0.70 and all risk constraints are passed. Exploratory candidates must meet the following conditions: weighted comprehensive score not lower than 0.50, but not all risk constraints are passed at the same time, and the difference in the composition ratio of all rare earth elements is not greater than 0.20, the uncertainty risk score U is not greater than 0.50, and the ranking standard deviation is not greater than 3. S14. From the set of candidate materials in the strict priority candidate and exploration candidate, select rare earth pyrosilicon materials that meet the following conditions: the mole fraction of rare earth elements is non-negative and their sum is 1; the number of effective rare earth element types is within the set range; the mole fraction of a single rare earth element is within the corresponding upper and lower limits; and the rare earth pyrosilicon materials do not overlap with the rare earth pyrosilicon materials in the database. These materials will be used as the final design materials.

[0047] Example 2 This embodiment, based on Embodiment 1, adjusts the weighting coefficients in the Score formula. , , , , and Optimization is needed. The parameters to be optimized include relative priority scores and weights. Target temperature thermal conductivity reference score weight Weighting of Low Temperature Average Thermal Conductivity Score Weight of low temperature trend score Physical prior score weights And the penalty weight wU for uncertainty risk score.

[0048] In a preferred embodiment, weight optimization is performed using cross-validation grouped by composition. The inner cross-validation layer selects a weight combination among relative priority scores, target temperature thermal conductivity reference scores, low-temperature average thermal conductivity scores, low-temperature trend scores, physical prior scores, and uncertainty risk scores. The outer cross-validation layer evaluates the candidate ranking effect of the selected weight combination on data not involved in weight adjustment. Grouping by composition means that the same material composition belongs to only one of the training or test sets in the same round of partitioning, to avoid different temperature points of the same composition appearing simultaneously in both the training and test sets, thereby improving the realism of cross-composition generalization evaluation.

[0049] In a preferred embodiment, the ranking of low thermal conductivity based on a weighted composite score and the ranking of low thermal conductivity based on measured thermal conductivity are determined by maximizing the degree of consistency. The degree of consistency between the weighted composite score-based ranking and the measured thermal conductivity-based ranking includes Spearman's rank correlation coefficient or Kendall's rank correlation coefficient. In some other embodiments, the degree of consistency (ranking accuracy) can also be achieved using pairwise ranking AUC.

[0050] Within a parameter search range: The value is 0.35 to 0.75. The value is 0.05 to 0.25. The value is 0.05 to 0.30. The value is 0.05 to 0.25. The value is 0.05 to 0.25. The weight is set to 0.05–0.30; and the sum of all non-negative weights is equal to 1. Preferably, the relative priority score weight is... The weight of the target temperature relative priority score Rtarget is higher than that of any single piece of auxiliary evidence, so that the target temperature remains dominant in the final screening of low thermal conductivity candidates.

[0051] On a representative dataset, after optimization through cross-validation, the following weight combination was obtained: =0.52; =0.12; =0.14; =0.08; =0.08; =0.06, with a weight sum of 1. In this optimized weight combination, the target temperature ranking weight wH has the highest proportion, indicating that the relative ranking of low thermal conductivity at the target temperature is the dominant factor in the final candidate selection; the low-temperature average thermal conductivity score Lavg and the low-temperature trend score Ltrend serve as auxiliary evidence to determine whether the candidate composition has a low thermal conductivity basis and whether the thermal conductivity continues to decrease after heating; the target temperature thermal conductivity reference score Atarget provides a numerical scale reference for the target temperature thermal conductivity; the physical prior score P is used to constrain the physical rationality of the candidate composition; and the uncertainty risk score U is used to penalize candidate compositions with high prediction risk or unstable ranking.

[0052] On the same representative dataset, the above adaptive weight combination yielded the following validation results: The target temperature pairwise AUC (Area Under the Pairwise Ordination Curve) was 0.82; the Spearman correlation coefficient was 0.71; the Kendall correlation coefficient was 0.56; the Top-5 low thermal conductivity candidate hit rate was 80%; the prediction interval coverage was 91%; and the average prediction interval width was 0.38 W·m. -1 ·K -1 .

[0053] The above results show that, after optimizing the weighting coefficients, this invention can reasonably extract the absolute value reference of the target temperature, the basis of low-temperature thermal conductivity, the low-temperature trend, physical priors and uncertainty risk information while maintaining the dominant role of the target temperature ranking, thereby improving the stability and interpretability of screening low thermal conductivity candidate components.

[0054] Comparative Example 1: Candidate Screening Method with Fixed Weights To illustrate the technical effectiveness of the weight coefficient optimization module of this invention, this comparative example uses a method of manually fixing weights for candidate screening. Specifically, this comparative example does not use cross-validation for weight optimization, but instead sets the following weight combination based on experience: wH=0.30; wA=0.20; wL1=0.20; wL2=0.10; wP=0.10; wU=0.10.

[0055] The sum of the above weights is 1.

[0056] Although this fixed-weight method considers target temperature ranking, absolute value reference of target temperature, average thermal conductivity at low temperature, low temperature trend, physical prior and uncertainty risk, the weights of each item are determined by human experience and have not been verified or optimized. Therefore, it is prone to problems such as insufficient dominance of target temperature ranking, overemphasis on low temperature evidence, or unreasonable penalty for uncertainty.

[0057] Using the same dataset and evaluation method as Example 2, this comparative example yielded the following results: The target temperature pairwise ranking AUC was 0.64; the Spearman correlation coefficient was 0.52; the Kendall ranking correlation coefficient was 0.39; the Top-5 low thermal conductivity candidate hit rate was 40%; the prediction interval coverage was 78%; and the average prediction interval width was 0.43 W·m. -1 ·K -1 .

[0058] Compared to Example 2, the AUC, Spearman correlation coefficient, Kendall correlation coefficient, and Top-K low thermal conductivity candidate hit rate of this comparative example are all reduced. This indicates that manually fixing weights is difficult to adapt to the problem of inconsistent reliability of different evidence sources under high-temperature, small-sample data conditions, and easily leads to unstable candidate ranking results.

[0059] In contrast, this invention, through weight coefficient optimization, can adaptively determine the contribution ratio of Rtarget, Atarget, Lavg, Ltrend, P, and U in the joint score based on the verification results, thereby improving the objectivity and reliability of the low thermal conductivity candidate screening results.

[0060] Example 3: Candidate Compositions of Low Thermal Conductivity Rare Earth Pyrosilicates Determined Based on Optimized Weights Based on the optimized weight combination obtained in Example 2, this embodiment performs joint scoring and local optimization on the candidate compositions of multi-rare earth pyrosilicates, and finally obtains candidate compositions with low thermal conductivity potential.

[0061] In this embodiment, the candidate material preferably converges to a multi-rare earth pyrosilicon system with Yb-Sc as the dual-core framework of rare earth sites and Eu as the main component regulating element, and its general chemical formula is: [(Yb...] a (Sc) b (Eu) c (R) d ]2Si2O7. Wherein, R is one or more selected from Y, Dy, Ho, Er, Tm, Lu and Gd; a, b, c and d are the mole fractions at rare earth sites, and satisfy: a+b+c+d=1.

[0062] Preferably, R includes one or more of Y, Dy, Ho, Er, Tm, and Lu; further, R may also include Gd. Gd serves as an exploratory regulatory component to expand the candidate composition space and regulate the rare earth site size distribution. Preferably, when R includes Gd, the molar fraction of Gd in the rare earth sites does not exceed 0.15, more preferably not exceeding 0.10.

[0063] After joint scoring using the optimized weight combination in Example 2, the following two high-scoring candidate compositions are preferably obtained: Sample 1: (Yb 0.28 Sc 0.32 Eu 0.18 Dy 0.12 Lu 0.10 )2Si2O7; Sample 2: (Yb 0.26 Sc 0.34 Eu 0.18 Ho 0.17 Gd 0.05 )2Si2O7.

[0064] Sample 1 is a preferred low thermal conductivity candidate composition without Gd, while Sample 2 is an exploratory low thermal conductivity candidate composition containing a small amount of Gd. Both candidate compositions conform to [(Yb]]. a (Sc)b (Eu) c (R) d They are all of the general formula 2Si2O7, and all are non-equimolar rare earth pyrosilicate materials.

[0065] In the specific scoring example of this embodiment, after uniform scaling, the score for sample 1 is: Rtarget=0.92; Atarget=0.87; Lavg=0.84; Ltrend=0.79; P=0.82; U=0.21.

[0066] According to the Score formula: And adopt the optimized weight combination in Example 2: =0.52; =0.12; =0.14; =0.08; =0.08; =0.06; the calculated score for sample 1 is 0.817.

[0067] The score corresponding to sample 2 is: Rtarget=0.89; Atarget=0.84; Lavg=0.82; Ltrend=0.77; P=0.80; U=0.24.

[0068] The score of sample 2 was calculated to be 0.790 according to the above score formula.

[0069] The above results indicate that using Yb-Sc as the dual-core framework, Eu as the main regulating component, and introducing Dy, Ho, Er, Tm, Lu and a small amount of Gd as candidate components for R-site regulating components, exhibits superior comprehensive performance in terms of relative priority of target temperature, absolute reference of target temperature, average thermal conductivity at low temperature, low temperature trend, physical prior, and uncertainty risk.

[0070] Comparative Example 2: Candidate Compositions of Rare Earth Pyrosilicates with Low Co-scoring To further illustrate the effectiveness of the screening method of this invention, this comparative example selects a multi-element rare earth pyrosilicon combination that does not belong to the preferred candidate family of Yb-Sc-Eu-R described in Example 3 and has a low joint score as a control sample. Its composition is as follows: (Y 0.30 Er 0.25 Ho 0.15 Gd 0.10 Tb 0.20 )2Si2O7 The comparative sample did not employ a Yb-Sc dual-core framework, nor did it use Eu as a major component regulating element; therefore, it is not a preferred [(Yb]] component of this invention. a (Sc) b (Eu) c (R) d ]2Si2O7 candidate system.

[0071] Under the same scoring rules in Example 3, the score corresponding to this comparison sample is: Rtarget=0.47; Atarget=0.51; Lavg=0.55; Ltrend=0.42; P=0.49; U=0.41.

[0072] The Score of the comparison sample was calculated to be 0.431 according to the Score formula.

[0073] Compared to Samples 1 and 2 in Example 3, the comparative sample in this study had lower Rtarget, Atarget, and Ltrend scores, and a higher uncertainty risk score U, resulting in a significantly lower overall score. This demonstrates that the Score formula of this invention can not only identify candidate components with high potential for low thermal conductivity at the target temperature, but also penalize candidate components with high prediction risk, insufficient evidence of low-temperature trends, or unfavorable physical priors, thereby improving the stability of candidate screening.

[0074] Example 4: Preparation and thermal conductivity evaluation of low thermal conductivity candidate samples Samples 1 and 2 were prepared using a solid-state reaction method combined with pressureless sintering. The specific steps were as follows: High-purity oxides (Yb₂O₃, Sc₂O₃, Eu₂O₃, Dy₂O₃, Lu₂O₃, Ho₂O₃, Gd₂O₃, and SiO₂) were weighed stoichiometrically, ball-milled for 12 hours using ethanol as the medium, dried, sieved, pre-calcined at 1500℃ for 4 hours, then pulverized, bound with a binder, pressed into tablets, and subjected to cold isostatic pressing (180 MPa) before sintering at 1550℃ for 10 hours to obtain a dense bulk. The thermal diffusivity of the samples at different temperatures was tested using a laser scintillation method, and the thermal conductivity was calculated based on the sample density and specific heat capacity. The test temperature range was preferably from room temperature to 1200℃. Ideally, at least three parallel samples were prepared for each composition, and the average value was used as the final result.

[0075] Comparative Example 3: Preparation and Thermal Conductivity Evaluation of Low-Joint-Score Rare Earth Pyrosilicates This comparative example uses the low-scoring component from Comparative Example 2 as the comparison sample, and its composition is as follows: (Y 0.30 Er 0.25 Ho 0.15 Gd 0.10 Tb 0.20)2Si2O7. This comparative sample was prepared using the same preparation process as in Example 4.

[0076] Under the same test conditions, the thermal conductivity of Sample 1, Sample 2, and this comparative sample from Example 3 was evaluated. The test results are as follows: The thermal conductivity of sample 1 at 1000℃ is 1.72 W·m. -1 ·K -1 The thermal conductivity at 1200℃ is 1.63 W·m. -1 ·K -1 ; The thermal conductivity of sample 2 at 1000℃ is 1.78 W·m. -1 ·K -1 The thermal conductivity at 1200℃ is 1.66 W·m. -1 ·K -1 ; The thermal conductivity of the comparative sample at 1000℃ is 2.78 W·m. -1 ·K -1 The thermal conductivity at 1200℃ is 2.21 W·m. -1 ·K -1 .

[0077] The statistical results of thermal conductivity tests of the samples in Example 4 and Comparative Example 3 at 1000℃ and 1200℃ are shown in the following graphs. Figure 1 As shown in the figure, the results indicate that the thermal conductivity at the target temperature of samples 1 and 2, obtained by the automatic weight optimization method of this invention, is lower than that of the comparative sample. Specifically, sample 1 exhibits even lower thermal conductivity at 1200℃, demonstrating that the present invention can improve the screening hit rate of low thermal conductivity candidate components through the optimization of the scoring formula and its weight coefficients.

[0078] Compared to the manually fixed weighting method in Comparative Example 1, the automatic weight optimization method of this invention can determine the contribution ratios among Rtarget, Atarget, Lavg, Ltrend, P, and U based on the verification results, avoiding the instability in candidate ranking caused by manually setting weights. Compared to the low-scoring components in Comparative Example 3, the high-scoring candidate components obtained by this invention have lower thermal conductivity at the target temperature, indicating that this invention can effectively identify candidate components with low thermal conductivity potential at the target temperature.

[0079] The above are merely preferred embodiments of the present invention and are not intended to limit the present invention. Any modifications, equivalent substitutions, and improvements made within the spirit and principles of the present invention should be included within the protection scope of the present invention.

Claims

1. A design method for low thermal conductivity rare earth pyrosilicon based on weighted automatic optimization and multi-evidence joint scoring, characterized in that, include: S1. Collect thermal conductivity data of various rare earth pyrosilicon materials at different temperatures, extract the corresponding material composition and temperature to form a database, wherein the temperature includes room temperature and target temperature; S2. Construct a set of physical descriptor features to characterize the local disorder, mass difference, size mismatch or chemical environment of rare earth pyrosilicon materials; Each physical descriptor is normalized, and combined with the ranking of the thermal conductivity of each rare earth pyrosilicon material in the database from low to high, the physical prior scores of each rare earth pyrosilicon material in the database are analyzed and obtained. S3. The normalized data value of the average thermal conductivity of each rare earth pyrosilicon material in the database within the range from room temperature to a given characteristic temperature is determined as the low-temperature average thermal conductivity score of the corresponding rare earth pyrosilicon material, wherein the characteristic temperature is less than the target temperature. S4. The normalized data value of the rate of decrease in thermal conductivity of each rare earth pyrosilicon material in the database during the process of increasing from room temperature to the characteristic temperature is determined as the corresponding low temperature trend score. S5. Based on the source of thermal conductivity data for each rare earth pyrosilicon material at the target temperature in the database, assign different source credibility weights to the thermal conductivity data at the target temperature. S6. Using all or part of the rare earth pyrosilicon materials in the database as the training set, compare the thermal conductivity data of the rare earth pyrosilicon materials at the target temperature in the training set in pairs to construct a pair of comparison samples. The training weights of the paired comparison samples are determined based on the difference in thermal conductivity of the paired comparison samples and the corresponding source credibility weights. The prediction probability model of the thermal conductivity of one rare earth pyrosilicon material in the paired comparison samples being lower than that of the other rare earth pyrosilicon material at the target temperature is trained, and the relative priority score of each rare earth pyrosilicon material having lower thermal conductivity at the target temperature relative to other rare earth pyrosilicon materials in the training set is calculated. S7. Using the material composition and physical descriptor of rare earth pyrosilicon materials in the training set as model input, and the corresponding physical prior score, low-temperature average thermal conductivity score, low-temperature trend score, relative priority score, and thermal conductivity at the target temperature as learning objectives, establish a learning model that outputs the physical prior score, low-temperature average thermal conductivity score, low-temperature trend score, relative priority score, and predicted thermal conductivity at the target temperature of rare earth pyrosilicon candidate materials. S8. Using rare earth pyrosilicon materials in the database, perform multi-round group cross-validation in the learning model, and calculate the probability that the predicted thermal conductivity of the target temperature of each rare earth pyrosilicon material is lower than the preset benchmark thermal conductivity in the multi-round validation. Then, use the normalized value of the mean of the predicted results of each rare earth pyrosilicon material in each round of validation as the reference score of the target temperature thermal conductivity of the corresponding rare earth pyrosilicon material. S9. Based on the absolute error between the mean value of each rare earth pyrosilicon material in the database and the actual thermal conductivity data value, and the probability that the predicted result of each rare earth pyrosilicon material is lower than the preset benchmark thermal conductivity in multiple rounds of verification, analyze and obtain the uncertainty risk score of the target temperature thermal conductivity of the corresponding rare earth pyrosilicon material. S10. Using the material composition and physical descriptor of rare earth pyrosilicon materials in the training set as model input, output modules are constructed in the learning model to respectively construct the reference score of thermal conductivity at target temperature and the uncertainty risk score of rare earth pyrosilicon materials. The learning model is used to evaluate the physical prior score, low-temperature average thermal conductivity score, low-temperature trend score, relative priority score, and target temperature thermal conductivity prediction value of candidate materials, and simultaneously outputs the target temperature thermal conductivity reference score and uncertainty risk score of candidate materials. S11. Based on the relative priority score of the candidate materials, the reference score of thermal conductivity at the target temperature, the score of average thermal conductivity at low temperature, the score of low temperature trend, the score of physical prior and the score of uncertainty risk, construct a weighted comprehensive score for the candidate materials. If the weighted comprehensive score is greater than or equal to the preset score threshold, it is determined that the corresponding candidate material meets the thermal conductivity requirement at the target temperature; otherwise, it does not meet the requirement.

2. The method according to claim 1, characterized in that, In step S2, the method for obtaining the physical prior scores of each rare earth pyrosilicate material in the database includes: From descriptors including average ionic radius, radius mismatch parameter, average atomic mass, mass mismatch parameter, mass disorder parameter, average electronegativity, electronegativity mismatch parameter, or mixing entropy, physical descriptors are selected that indicate the thermal conductivity of rare-earth pyrosilicon materials at the target temperature increases or decreases with increasing corresponding physical descriptors. The selected physical descriptors are then normalized to obtain their corresponding descriptor scores. ; in, For the first The first rare earth pyrosilicate material Original values ​​of physical descriptors, For the training set The maximum value of a physical descriptor. For the training set The minimum value of a physical descriptor. For the first The first rare earth pyrosilicate material The descriptor score after normalization of each physical descriptor; Calculate the physical prior score based on the descriptor score. ,in, For a given first The contribution coefficients of each descriptor satisfy: , , The number of physical descriptors selected.

3. The method according to claim 2, characterized in that, The contribution coefficient is determined using a finite weight combination search method, specifically as follows: 1) Arrange the rare earth pyrosilicon materials in the training set in ascending order of thermal conductivity data at the target temperature, and determine the materials with lower thermal conductivity as materials with higher priority for low thermal conductivity, thus forming a priority ranking result for low thermal conductivity based on measured thermal conductivity. 2) Under the condition that each contribution coefficient is non-negative and the sum is 1, generate multiple contribution coefficient combinations according to different step sizes for each contribution coefficient; calculate the physical prior score of each rare earth pyrosilicon material for different contribution coefficient combinations, sort them in descending order according to the size of the physical prior score, and determine the materials with larger physical prior scores as materials with higher priority for low thermal conductivity, forming a low thermal conductivity priority ranking result based on physical prior scores; 3) Calculate the degree of consistency between the low thermal conductivity priority ranking results based on physical prior scores and the low thermal conductivity priority ranking results based on measured thermal conductivity, and select the combination of contribution coefficients with the highest degree of consistency as the final contribution coefficient of each physical descriptor; the degree of consistency is the Spearman rank correlation coefficient or Kendall rank correlation coefficient between the low thermal conductivity priority ranking results based on physical prior scores and the low thermal conductivity priority ranking results based on measured thermal conductivity.

4. The method according to claim 1, characterized in that, In step S3, the method for obtaining the low-temperature average thermal conductivity score of rare earth pyrosilicon materials includes: Calculate the arithmetic mean of the thermal conductivity of the rare earth pyrosilicon material at at least five temperature points, including the room temperature thermal conductivity and the characteristic temperature thermal conductivity, within the range from room temperature to the characteristic temperature, and determine the arithmetic mean as the average thermal conductivity of the corresponding rare earth pyrosilicon material. The low-temperature average thermal conductivity score Lavg,i corresponding to the i-th rare earth pyrosilicon material is calculated according to the following formula: Lavg,i=(kavg,max-kavg,i) / (kavg,max-kavg,min) Where kavg,i is the average thermal conductivity of the i-th rare earth pyrosilicon material in the training set, kavg,max is the maximum value of the average thermal conductivity in the training set, and kavg,min is the minimum value of the average thermal conductivity in the training set; and when the calculated result of Lavg,i is less than 0, it is taken as 0, and when the calculated result is greater than 1, it is taken as 1. In step S4, the rate of decrease in thermal conductivity Dtrend,i = 1 - k during the process of raising the temperature of the i-th rare earth pyrosilicon material from room temperature to the characteristic temperature is... 1000,i / k RT,i k 1000,i Let k be the thermal conductivity of the i-th rare-earth pyrosilicon material at the characteristic temperature. RT,i Let be the room temperature thermal conductivity of the i-th rare earth pyrosilicon material; The low-temperature trend score of the i-th rare earth pyrosilicon material is Ltrend,i = (Dtrend,i - Dtrend,min) / (Dtrend,max - Dtrend,min), where Dtrend,max is the maximum value of the thermal conductivity decrease rate in the training set, and Dtrend,min is the minimum value of the thermal conductivity decrease rate in the training set.

5. The method according to claim 1, characterized in that, In step S5, the data sources include measured data, interpolated data, extrapolated data, and nearby temperature data. The source confidence weight is set to 1 when the data source is measured data, and different source confidence weights are assigned in order of decreasing source confidence weight for interpolated data, extrapolated data, and nearby temperature data.

6. The method according to claim 1, characterized in that, In step S6, the process for obtaining the relative priority score corresponding to the i-th rare earth pyrosilicon material is as follows: The material composition and the selected physical descriptor of the i-th rare earth pyrosilicon material and the j-th rare earth pyrosilicon material in the paired comparison sample are respectively used to form feature vectors xi and xj, where xi is the feature vector of the i-th rare earth pyrosilicon material and xj is the feature vector of the j-th rare earth pyrosilicon material. Using Δxij = xi - xj as the input to the prediction probability model, the output label is 1 when the target temperature thermal conductivity of the i-th rare earth pyrosilicon material is lower than that of the j-th rare earth pyrosilicon material, and 0 otherwise. A supervised classification method is used to establish a probability prediction model for outputting the prediction probability that the target temperature thermal conductivity of the i-th rare earth pyrosilicon material is lower than that of the j-th rare earth pyrosilicon material. The predicted probability of the i-th rare earth pyrosilicon material relative to all other rare earth pyrosilicon materials in the training set is weighted by source confidence, and this weighted average is determined as the relative priority score Rtarget,i corresponding to the i-th rare earth pyrosilicon material.

7. The method according to claim 1, characterized in that, In step S7, the learning model includes one or more of the following: random forest regression model, gradient boosting regression model, support vector regression model, and linear regression model. In step S8, the method for obtaining the reference score of the thermal conductivity at the target temperature of rare earth pyrosilicon materials includes: The rare earth pyrosilicate materials in the database are grouped according to their material composition information. Samples with the same material composition are grouped together. Multiple rounds of cross-validation are performed in the learning model, and the average of the prediction results for the i-th rare earth pyrosilicate material in each round of validation is used as the predicted value of thermal conductivity at the target temperature. Then to After normalization, the corresponding normalized value is used as the reference score for the thermal conductivity at the target temperature of the i-th rare earth pyrosilicon material. ; In step S9, the method for obtaining the uncertainty risk score of the target temperature thermal conductivity of the corresponding rare earth pyrosilicon material includes: Calculate the i-th rare earth pyrosilicate material The absolute error E between the measured value and the actual value i Predicted thermal conductivity at target temperature Subtract the absolute error E i The lower bound of the prediction is obtained. Predicted thermal conductivity at target temperature Add the absolute error E i Obtain the upper bound of the prediction The difference between the upper and lower bounds of the prediction is used as the prediction interval width W for the thermal conductivity at the target temperature of the i-th rare earth pyrosilicon material. i ; The prediction interval width W for each rare earth pyrosilicate material in the database i And the upper bound of prediction Normalization is performed separately to obtain the normalized prediction interval width. and normalized prediction upper bound : in, This represents the minimum predicted interval width for rare earth pyrosilicon materials in the database. This represents the maximum predicted interval width for rare earth pyrosilicon materials in the database. This represents the maximum value of the upper bound predicted for rare earth pyrosilicon materials in the database. This is the minimum value of the predicted upper bound for rare earth pyrosilicon materials in the database; Using the 25th percentile of the target temperature thermal conductivity in the database as the benchmark thermal conductivity, the probability that the predicted target temperature thermal conductivity of the i-th rare earth pyrosilicon material is lower than the benchmark thermal conductivity in multiple rounds of verification is: ; Uncertainty risk score Calculate according to the following formula: Wherein, β1, β2, and β3 are the weights corresponding to the prediction interval width, prediction upper bound, and probability of thermal conductivity below the baseline, respectively, and β1, β2, and β3 are all not less than 0, β1 + β2 + β3 = 1; the method for determining β1, β2, and β3 is determined by a finite weight combination search, that is, obtaining the uncertainty risk score of each rare earth pyrosilicon material in the database under different weight combinations. and in accordance with Arrange in ascending order and compare according to The sorting results and the predicted values ​​of thermal conductivity at the target temperature The consistency of the ranking results from smallest to largest is considered; the candidate weight combination with the highest consistency is selected as the final weight combination of β1, β2, and β3, where the consistency is determined by... The sorting results and the predicted values ​​of thermal conductivity at the target temperature Spearman correlation coefficient or Kendall correlation coefficient for sorting results from smallest to largest.

8. The method according to claim 1, characterized in that, In step S11, the weighted comprehensive score is calculated. ,in, The relative priority score for candidate materials. This serves as a reference score for the target temperature thermal conductivity of the candidate materials. The low-temperature average thermal conductivity score of the candidate materials. Let P be the low-temperature trend score of the candidate material, P be the physical prior score of the candidate material, and U be the uncertainty risk score. , , , , and They are non-negative weight coefficients, and satisfy the following conditions: ; , , , , and The method for determining the priority of low thermal conductivity is to maximize the consistency between the weighted comprehensive score-based priority ranking result and the measured thermal conductivity-based priority ranking result. The consistency between the weighted comprehensive score-based priority ranking result and the measured thermal conductivity-based priority ranking result includes Spearman's rank correlation coefficient or Kendall's rank correlation coefficient.

9. The method according to claim 1, characterized in that, After obtaining multiple rare earth pyrosilicon materials that meet the requirements, further screening is conducted by introducing spatial applicability domain judgment, uncertainty judgment, and ranking stability judgment as risk constraints. The screening methods include: The rare earth pyrosilicon material with the smallest sum of absolute differences in the proportions of all identical elements in the training set and the candidate material is identified as the most similar material. When the difference in the proportions of all rare earth elements between the candidate material and the most similar material is not greater than a preset difference threshold, the spatial applicability domain of the candidate material is judged as passed. When the uncertainty risk score U of the candidate material is not greater than the preset risk threshold, the uncertainty judgment is passed. When the standard deviation of the low thermal conductivity priority ranking of candidate materials in multi-round group cross-validation based on weighted comprehensive score is not greater than the preset ranking position, the ranking stability is judged as passed. All candidate materials were divided into strict priority candidates and exploratory candidates based on weighted comprehensive scores and risk constraints. Strict priority candidates met the following conditions: a weighted comprehensive score of not less than 0.70 and passing all risk constraints. Exploratory candidates met the following conditions: a weighted comprehensive score of not less than 0.50, but not simultaneously passing all risk constraints, and the difference in the composition ratio of all rare earth elements was not greater than 0.20, the uncertainty risk score U was not greater than 0.50, and the ranking standard deviation was not greater than 3. From the set of candidate materials in the strict priority candidate and exploratory candidate categories, rare earth pyrosilicon materials that meet the following conditions are selected as the final design materials: all rare earth element mole fractions are non-negative and their sum is 1; the number of effective rare earth element types is within a set range; the mole fraction of a single rare earth element is within the corresponding upper and lower limits; and the rare earth pyrosilicon materials do not overlap with the rare earth pyrosilicon materials in the database.

10. A low thermal conductivity rare earth pyrosilicate material obtained by applying the method according to any one of claims 1 to 9, characterized in that, The general formula for the rare earth pyrosilicate material is: [(Yb)] a (Sc) b (Eu) c (R) d ]2Si2O7; where R is one or more of Y, Dy, Ho, Er, Tm, Lu and Gd, and a, b, c and d are the mole fractions at rare earth sites, and satisfy a+b+c+d=1.

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