Empirical trend-based fitting correction method for corrosion morphology parameters with small sample size and constraint fusion

Abstract

The application relates to a fitting correction method for corrosion morphology parameters based on experience trend fusion constraint small sample, and relates to the technical field of metal corrosion morphology parameter prediction and data extrapolation, and comprises the following steps: S1, obtaining self corrosion test data and public literature corrosion data; S2, normalizing the mass loss rates obtained from different batches of corrosion tests according to sample sizes, establishing correlation fitting models of various corrosion morphology parameters, and fusing multiple model parameters to obtain an experience trend fusion model; S3, taking the maximum normalized mass loss rate in the self corrosion test data as a boundary to divide an inner region and an extrapolation region, the inner region guarantees fitting precision, and the extrapolation region takes the slope of the experience trend fusion model as a trend constraint; and S4, constructing a joint objective function, and obtaining an optimal correction fitting model through screening. The application can improve the stability and extrapolation rationality of the fitting curve of corrosion morphology parameters under small sample conditions, and avoids unreasonable deviation of the model in a high mass loss rate interval.

Description

Technical Field

[0001] This invention relates to the field of metal corrosion morphology parameter prediction and data extrapolation technology, specifically to a method for fitting and correcting small-sample corrosion morphology parameters based on empirical trend fusion constraints. Background Technology

[0002] Metallic materials are susceptible to corrosion in service environments such as the atmosphere, salt spray, and ocean. Corrosion causes material loss and forms surface morphology damage such as corrosion pits and non-uniform corrosion. The mass loss rate is a commonly used indicator for evaluating the degree of metal corrosion, but it mainly reflects the overall material loss and is difficult to fully describe local characteristics such as the depth of corrosion pits, the degree of corrosion non-uniformity, and changes in the morphology of corrosion pits.

[0003] To further evaluate the impact of corrosion damage on the performance of metal components, it is usually necessary to establish a quantitative relationship between the mass loss rate and corrosion morphology characterization parameters. However, in actual corrosion tests, the sample size of the corrosion test data is often small due to limitations such as the number of specimens, test cycle, and testing cost. If only small sample data is used for fitting, the resulting model is easily affected by local data fluctuations, especially when extrapolating within the mass loss rate range, which may lead to trend deviations or unreasonable prediction results.

[0004] Numerous corrosion test data are available in the published literature, providing a reference for the variation trends of corrosion morphology parameters. However, differences exist between different literature data in terms of specimen thickness, test conditions, and data processing methods. Directly mixing and fitting literature data with one's own experimental data may weaken the representativeness of the experimental data. Therefore, there is an urgent need for a corrosion morphology parameter fitting and correction method that can incorporate the trend constraints of literature data while maintaining the fitting accuracy of one's own data. Summary of the Invention

[0005] The technical problem to be solved by this invention is to address the issue that the fitting of small sample corrosion test data in proprietary experiments is easily affected by local data fluctuations and the extrapolation stability in the high-quality loss rate range is insufficient. This invention provides a method for correcting the fitting of small sample corrosion morphology parameters based on empirical trend fusion constraints, so as to improve the stability and extrapolation rationality of the corrosion morphology parameter fitting curve.

[0006] The technical solution adopted by this invention to solve its technical problem is: a method for fitting and correcting corrosion morphology parameters of small samples based on empirical trend fusion constraints, comprising the following steps: S1: Obtain proprietary corrosion test data and corrosion data from several sets of publicly available literature or materials. Both proprietary corrosion test data and publicly available literature corrosion data include mass loss rate and corrosion morphology characterization parameters corresponding to the mass loss rate. S2: Normalize the mass loss rate obtained from different batches of corrosion tests according to the sample size; establish a correlation fitting model between various corrosion morphology characterization parameters and normalized mass loss rate; fuse the model parameters of the correlation fitting model of corrosion morphology characterization parameters in multiple sets of literature data to obtain an empirical trend fusion model. S3: Using the maximum normalized mass loss rate in the proprietary corrosion test data as the boundary, the fitting interval is divided into an inner region and an extrapolation region. Within the inner region, the optimal fit is performed using an association fitting model that is compatible with the proprietary corrosion test data. In the extrapolation region, the slope of the empirical trend fusion model is used as the trend constraint. S4: Based on the fitting error of the inner zone fitting model using proprietary corrosion test data, construct the basic weights of the inner zone. Based on the difference between the slope of the inner zone fitting model and the slope of the empirical trend fusion model, construct the basic weights of the extrapolation zone. Introduce an extrapolation weight amplification coefficient to adjust the basic weights of the extrapolation zone, construct a joint objective function that includes the fitting error of the inner zone and the slope error of the extrapolation zone, and obtain a corrected fitting model of the relationship between corrosion morphology parameters and normalized mass loss rate by traversing the extrapolation weight amplification coefficient, limiting the inner zone error, and screening the comprehensive evaluation index.

[0007] Further, in step S1, the corrosion morphology characterization parameters include uneven corrosion depth, corrosion pit depth statistical parameters, and corrosion pit diameter-to-depth ratio statistical parameters. The corrosion pit depth statistical parameters and corrosion pit diameter-to-depth ratio statistical parameters are represented by logarithmic distribution mean or logarithmic distribution characteristic values. The specific definitions and calculation methods of each parameter are as follows: Obtain three-dimensional morphological data of the corrosion specimen surface, and discretize the corrosion test area into... Let the nth measuring point be the th measurement point. The corrosion depth at each measuring point is The corrosion depth corresponding to the location with the lightest corrosion in the test area is Then the first The relative corrosion depth at each measuring point is: ; Uneven corrosion depth Represented as: ; Corrosion pits on the surface of the corrosion test specimen are identified. Let the number of identified corrosion pits be... , No. The depth of the corrosion pits is The pit diameter is The mean of the logarithmic distribution of corrosion pit depth is... Represented as: ; Logarithmic distribution mean of corrosion pit diameter-to-depth ratio Represented as: ; in, Used to characterize the non-uniformity of a corroded surface. The statistical level used to characterize the depth of corrosion pits It is used to characterize the relative relationship between the lateral expansion and vertical development of corrosion pits.

[0008] Further, in step S1, the mass loss rate is calculated as follows: The mass of the specimen before corrosion is obtained. and the quality after removing corrosion products Original mass loss rate Represented as: .

[0009] Furthermore, in step S2, the original mass loss rates obtained from different batches of corrosion tests are normalized, that is, the original mass loss rates are converted according to the thickness ratio of the specimens in each batch. The conversion relationship is as follows: ; in, Let be the normalized mass loss rate in the corrosion data of the i-th group of literature. Let be the original mass loss rate in the corrosion data of the i-th group of literature. Let be the specimen thickness corresponding to the corrosion data in the i-th group of literature. The thickness is the specimen thickness.

[0010] Furthermore, in step S2, the literature reference model uses a normalized quality loss rate. The parameters are characterized by corrosion morphology as the independent variable. The dependent variable is denoted by ; the corresponding correlation fitting model is determined according to the type of corrosion morphology characterization parameter. Specifically, the statistical parameter of corrosion pit depth is described using a power function model, while the statistical parameters of uneven corrosion depth and corrosion pit diameter-to-depth ratio are described using an exponential saturation model. Power function model: ; Exponential saturation model: ; in, For corrosion morphology characterization parameters, To normalize the quality loss rate, , , These are the parameters to be fitted.

[0011] Furthermore, in step S2, when fusing the model parameters of the correlation fitting models of corrosion morphology characterization parameters in each group of literature data, the fusion object is the relevant parameters affecting the change of trend slope in the obtained multiple correlation fitting models, and the purpose of fusion is to provide the empirical trend slope of the extrapolation region: (1) When the correlation fitting model of the corrosion morphology characterization parameters in the literature is a power function model, its expression is: ; The corresponding slope is: ; Let the parameters of the power function model corresponding to the corrosion data of the j-th group of documents be... If the number of literature corrosion datasets participating in the fusion is M, then only the slope-related parameters are considered. By fusing the data, we obtain the slope-related parameters of the empirical trend fusion model in the form of a power function: ; ; in, Let be the fusion weights of the association fitting model for the j-th group of literature data, and satisfy: ; When using an equal-weight fusion method: ; The trend slope of the empirical trend fusion model in the extrapolation region, in the form of a power function, is expressed as: ; Among them, parameters It does not participate in the fusion of slope-related parameters; (2) When the correlation fitting model of the corrosion morphology characterization parameters in the literature is an exponential saturation model, its expression is: ; The corresponding slope is: ; Let the parameters of the exponential saturation model corresponding to the corrosion data of the j-th group of documents be... If the number of literature corrosion datasets participating in the fusion is M, then only the slope-related parameters are considered. By performing fusion, the slope-related parameters of the empirical trend fusion model in the form of exponential saturation are obtained: ; ; in, Let be the fusion weights of the association fitting model for the j-th group of literature data, and satisfy: ; When using an equal-weight fusion method: ; The reference slope of the exponentially saturated empirical trend fusion model in the extrapolation region is expressed as: ; Among them, parameters It does not participate in the fusion of slope-related parameters.

[0012] Further, in step S3, the fitting interval is divided into an inner region and an extrapolation region, using the largest normalized mass loss rate in the proprietary corrosion test data as the boundary, and the sampling points in the extrapolation region are determined. This specifically includes the following steps: (1) Determine the interval division boundary, and set the maximum value of the normalized mass loss rate in the proprietary corrosion test data as . ,Will As the boundary between the inner and outer regions; (2) Divide the area into an inner zone and an extrapolation zone, which are represented as follows: ; ; in, For the inner area, The extrapolation region is used to maintain the consistency between the correlation fitting model and the proprietary corrosion test data, ensuring that the modified fitting model has fitting accuracy within the coverage of the proprietary test data. The extrapolation region is used to constrain the trend slope of the modified fitting model, so that the modified fitting model is constrained by the trend slope of the empirical trend fusion model within the high-quality loss rate range that exceeds the range of the proprietary test data. (3) Determine the range of values ​​for the extrapolation region, wherein the range of values ​​for the extrapolation region is: ; in, This is the extrapolation range coefficient, used to control the extrapolation range of the modified fitted model for trend constraints; (4) Set up extrapolation sampling points. Set up a number of extrapolation sampling points in the extrapolation area. The sampling points are used to calculate the slope error between the correction fitting model and the empirical trend fusion model.

[0013] Further, in step S4, the basic weight of the inner zone is determined based on the error of the inner zone fitting model of the proprietary corrosion test data; firstly, an adapted correlation fitting model is used to fit the proprietary corrosion test data to obtain the inner zone fitting model. And calculate the fitting error of the inner region fitting model: ; in, The fitting error of the inner region fitting model is represented by [missing information]. The number of proprietary corrosion test data. For the first i Normalized mass loss rate corresponding to proprietary corrosion test data These are the true values ​​of the corresponding corrosion morphology characterization parameters. For the inner region fitting model in The predicted value at that location; The basic weights of the extrapolation region are determined based on the slope difference between the inner region fitting model and the empirical trend fusion model within the extrapolation region; q sampling points are set within the extrapolation region, and the slope error of the extrapolation region is calculated. ; in, The slope error of the extrapolation region is given by q, where q is the number of sampling points in the extrapolation region. For the extrapolation zone, the first Normalized quality loss rate corresponding to k sampling points For the inner region fitting model in The slope at that point For the experience trend fusion model in The trend slope at that point.

[0014] Furthermore, in step S4, a joint objective function is constructed based on the fitting error in the inner region and the slope error in the extrapolation region. The optimal corrected fitting model is then selected through extrapolation weight amplification coefficient traversal, inner region error limitation, and comprehensive evaluation index. This specifically includes the following steps: (1) Calculate the basic weights of the inner zone and the basic weights of the extrapolated zone. The basic weights of the inner zone are expressed as follows: ; The basic weights of the extrapolation region are represented as follows: ; in, As the basic weight of the inner area, As the basic weight for the extrapolation region, To prevent positive numbers with a denominator of zero, the value is taken as... ; (2) Introduce an extrapolation weight amplification factor, and use the extrapolation weight amplification factor λ to adjust the basic weight of the extrapolation zone. The adjusted extrapolation zone weight is expressed as: ; in, The adjusted extrapolation weights are denoted by λ, where λ is the extrapolation weight amplification factor. (3) Construct a joint objective function. Based on the inner region basic weights and the adjusted extrapolation region weights, construct a joint objective function, and solve for the corrected model parameters under the given extrapolation weight amplification coefficient λ. The joint objective function is expressed as: ; in, For the joint objective function, The corrected model parameters are to be solved. As the basic weight of the inner area, The adjusted extrapolation region weights, This represents the fitting error in the inner region. This refers to the slope error in the extrapolation region; The corresponding corrected model parameters are expressed as follows: ; in, The parameters of the corrected fitting model are given when the extrapolation weight amplification factor is λ. (4) Traverse the extrapolation weight amplification coefficient, set multiple candidate values ​​for the extrapolation weight amplification coefficient, and traverse the extrapolation weight amplification coefficient; for each candidate value for the extrapolation weight amplification coefficient, resolve the corresponding modified fitting model parameters, and calculate the inner region fitting error and the extrapolation region slope error of the corresponding modified fitting model. (5) Candidate modified fitting models are selected based on the inner region error constraint conditions, which are expressed as follows: ; in, To correct the in-zone fitting error of the candidate fitted model. β represents the inner region fitting error of the original unconstrained fitting model. This is the allowable coefficient for inner region error amplification; when a candidate corrected fitting model does not meet the inner region error limitation condition, the corrected fitting model is removed from the candidate corrected fitting models; (6) Calculate the comprehensive evaluation index and determine the optimal corrected fitting model. Calculate the comprehensive evaluation index for candidate corrected fitting models that meet the inner-region error constraint conditions. The comprehensive evaluation index is expressed as: ; Where IC is the comprehensive evaluation index, n is the number of proprietary corrosion test data, and p is the number of parameters in the corrected fitting model. To correct the in-region fitting error of the candidate fitted model, To correct the slope error of the extrapolation region corresponding to the candidate fitted model; In the set C of candidate corrected fitting models that meet the inner region error constraint, the candidate corrected fitting model with the smallest comprehensive evaluation index is determined as the optimal corrected fitting model. The parameters of the optimal corrected fitting model are expressed as follows: ; in, Let C be the parameters of the optimal corrected fitting model, and let C be the set of candidate corrected fitting models that satisfy the inner region error constraint.

[0015] Compared with the prior art, the beneficial effects of the present invention are as follows: This invention transforms corrosion data from publicly available literature and data into trend slope constraints for the extrapolation region. This allows the modified fitting model to maintain good fitting accuracy within the inner region covered by proprietary corrosion test data, while maintaining a reasonable trend in the extrapolation region where proprietary test data is lacking. This invention avoids directly mixing and fitting publicly available corrosion data with proprietary corrosion test data, thus reducing the impact of absolute numerical deviations caused by differences in specimen thickness, test conditions, or data processing methods between different data sources. This invention achieves a balance between the fitting accuracy of the inner region and the extrapolation trend constraints through the basic weights of the inner region, the basic weights of the extrapolation region, and the extrapolation weight amplification coefficient. Furthermore, it selects the optimal modified fitting model through inner region error limits and comprehensive evaluation indicators. This improves the stability and extrapolation rationality of the corrosion morphology parameter fitting curve under small sample conditions, avoiding unreasonable deviations in the high-quality loss rate range. This invention is suitable for correcting the fitting relationship between the quality loss rate and corrosion morphology characterization parameters when the number of proprietary corrosion test samples is small, and for improving the extrapolation stability and rationality of the model in the high-quality loss rate range. Attached Figure Description

[0016] Figure 1 is a schematic diagram of the overall process of the method of the present invention; Figure 2 shows the corrected fitting results for uneven corrosion depth; Figure 3 shows the evaluation results of the extrapolation weight magnification factor for uneven corrosion depth. Figure 4 shows the fitting and correction results of the statistical parameters for corrosion pit depth; Figure 5 shows the evaluation results of extrapolating the statistical parameters of corrosion pit depth using the weight amplification factor. Figure 6 shows the fitting correction results of the statistical parameters for the corrosion pit diameter-to-depth ratio; Figure 7 shows the evaluation results of the extrapolation weighting amplification coefficient of the statistical parameter for the corrosion pit diameter-to-depth ratio. Detailed Implementation

[0017] The present invention will be further described below with reference to the accompanying drawings and embodiments.

[0018] Referring to Figure 1, this embodiment provides a method for fitting and correcting small-sample corrosion morphology parameters based on empirical trend fusion constraints. This method uses proprietary corrosion test data as a foundation, introduces corrosion data from publicly available literature or materials to establish an empirical trend fusion model, and corrects the correlation fitting model between the normalized mass loss rate and corrosion morphology characterization parameters by maintaining the fitting accuracy in the inner region and constraining the trend slope in the extrapolated region. Specifically, it includes the following steps: S1: Data Acquisition and Parameter Processing (1) Obtain corrosion test data from our own sources and corrosion data from several sets of publicly available literature or materials. Referring to Figures 2, 4 and 6, different hollow marks in the figures represent corrosion data from publicly available literature from different sources, while solid dots represent proprietary corrosion test data. Both proprietary corrosion test data and corrosion data from publicly available literature include mass loss rate and corrosion morphology characterization parameters corresponding to the mass loss rate. (2) Calculate the original mass loss rate Specimen quality before corrosion and the quality after removing corrosion products Original mass loss rate Represented as: ; (3) Extracting corrosion morphology characterization parameters The corrosion morphology characterization parameters include uneven corrosion depth, statistical parameters of corrosion pit depth, and statistical parameters of corrosion pit diameter-to-depth ratio. Obtain three-dimensional morphological data of the corrosion specimen surface, and discretize the corrosion test area into... Let the nth measuring point be the th measurement point. The corrosion depth at each measuring point is The corrosion depth corresponding to the location with the lightest corrosion in the test area is Then the first The relative corrosion depth at each measuring point is: ; Uneven corrosion depth Represented as: ; Corrosion pits on the surface of the corrosion test specimen are identified. Let the number of identified corrosion pits be... , No. The depth of the corrosion pits is The pit diameter is The mean of the logarithmic distribution of corrosion pit depth is... Represented as: ; Logarithmic distribution mean of corrosion pit diameter-to-depth ratio Represented as: ; in, Used to characterize the non-uniformity of a corroded surface. The statistical level used to characterize the depth of corrosion pits Used to characterize the relative relationship between the lateral expansion and vertical development of corrosion pits; S2: Normalization processing, correlation fitting model establishment, and construction of empirical trend fusion model (1) Normalization of quality loss rate Since different literature data correspond to different specimen thicknesses, in order to reduce the impact of specimen thickness differences on the mass loss rate, the original mass loss rates obtained from different batches of corrosion tests were normalized according to the specimen size and unified to the same reference thickness scale. The conversion relationship is as follows: ; in, Let be the normalized mass loss rate in the corrosion data of the i-th group of literature. Let be the original mass loss rate in the corrosion data of the i-th group of literature. Let be the specimen thickness corresponding to the corrosion data in the i-th group of literature. For specimen thickness; In this embodiment, the mass loss rates shown in Figures 2, 4, and 6 are all mass loss rates after the above normalization process. For ease of subsequent description, the normalized mass loss rate will be uniformly referred to as... ; (2) Determine the form of the correlation fitting model The correlation fitting model uses a normalized quality loss rate. The parameters are characterized by corrosion morphology as the independent variable. When the corrosion morphology characterization parameter is the statistical parameter of corrosion pit depth, a power function model is used to describe it, with the power function model expressed as: ; When the corrosion morphology characterization parameter is a statistical parameter of uneven corrosion depth or corrosion pit diameter-to-depth ratio, an exponential saturation model is used for description. The exponential saturation model is expressed as follows: ; in, For corrosion morphology characterization parameters, To normalize the quality loss rate, These are the parameters to be fitted; In this embodiment, the uneven corrosion depth shown in Figure 2 is fitted and corrected using an exponential saturation model; the statistical parameters of the corrosion pit depth shown in Figure 4 are fitted and corrected using a power function model; and the statistical parameters of the corrosion pit diameter-to-depth ratio shown in Figure 6 are fitted and corrected using an exponential saturation model. (3) Solving the correlation fitting model for each group of literature data For each set of corrosion data from published literature or materials, the model form of the corresponding corrosion morphology characterization parameters is fitted to obtain the correlation fitting model parameters corresponding to the set of data; referring to Figures 2, 4 and 6, the fitting curves corresponding to the corrosion data from each set of published literature are used to represent the reference trend of corrosion morphology characterization parameters changing with normalized mass loss rate in data from different sources. (4) Parameter fusion of the empirical trend fusion model Since the empirical trend fusion model is used to provide trend slope constraints in the extrapolation region, only the relevant parameters that affect the change of trend slope are fused when the model parameters are fused, and the constant term parameters that are unrelated to the slope are not fused. ① When the correlation fitting model is a power function model, its expression is: ; The corresponding slope is: ; Let the parameters of the power function model corresponding to the corrosion data of the j-th group of documents be... If the number of literature corrosion datasets participating in the fusion is M, then only the slope-related parameters are considered. By fusing the data, we obtain the slope-related parameters of the empirical trend fusion model in the form of a power function: ; ; in, Let be the fusion weights of the association fitting model for the j-th group of literature data, and satisfy: ; When using an equal-weight fusion method: ; The trend slope of the empirical trend fusion model in the extrapolation region, in the form of a power function, is expressed as: ; Among them, parameters It does not participate in the fusion of slope-related parameters; In this embodiment, the statistical parameters of the corrosion pit depth shown in Figure 4 are obtained by using the above method to obtain the empirical trend fusion model and the trend slope of its extrapolation area; ② When the correlation fitting model is an exponential saturation model, its expression is: ; The corresponding slope is: ; Let the parameters of the exponential saturation model corresponding to the corrosion data of the j-th group of documents be... If the number of literature corrosion datasets participating in the fusion is M, then only the slope-related parameters are considered. By performing fusion, the slope-related parameters of the empirical trend fusion model in the form of exponential saturation are obtained: ; ; in, Let be the fusion weights of the association fitting model for the j-th group of literature data, and satisfy: ; When using an equal-weight fusion method: ; The reference slope of the exponentially saturated empirical trend fusion model in the extrapolation region is expressed as: ; Among them, parameters It does not participate in the fusion of slope-related parameters; In this embodiment, the statistical parameters of the uneven corrosion depth shown in Figure 2 and the corrosion pit diameter-to-depth ratio shown in Figure 6 are used to obtain the empirical trend fusion model and its extrapolation trend slope in the above manner. S3: Division of Inner Zone and Extrapolation Zone (1) Determine the boundaries of the interval division Let the maximum value of the normalized mass loss rate in the proprietary corrosion test data be... ,Will As the boundary between the inner and outer regions; Referring to Figures 2, 4, and 6, the vertical dashed lines in each figure represent the boundaries between the inner and outer regions; (2) Division of inner and outer regions and setting of outer sampling points The inner region and the extrapolation region are represented as follows: ; ; in, The inner zone is used to maintain the consistency between the corrected fitting model and the proprietary corrosion test data, ensuring that the model has fitting accuracy within the coverage of the proprietary test data. This is the extrapolation region, used to constrain the trend slope of the fitted model, so that the model is constrained by the trend slope of the empirical trend fusion model within the high-quality loss rate range that exceeds the range of its own experimental data. (3) Determine the range of values ​​for the extrapolation region The range of values ​​for the extrapolation region is: ; in, This is the extrapolation range coefficient, used to control the extrapolation range of the trend constraint. In this embodiment... The value is 1.4; (4) Set up sampling points in the extrapolation area Within the extrapolation region, q=50 sampling points are set, and these sampling points are used to calculate the slope error between the fitted model and the empirical trend fusion model. S4: Construction of Joint Objective Function and Screening of Optimal Fitting Model (1) Original fitting model and calculation of original error The original internal zone fitting model was obtained by fitting the corrosion test data with an association fitting model that matches the corresponding corrosion morphology characterization parameters. ; Among them, the power function model was used for the original fitting of the statistical parameters of corrosion pit depth; the exponential saturation model was used for the original fitting of the statistical parameters of uneven corrosion depth and corrosion pit diameter-to-depth ratio. Referring to Figures 2, 4, and 6, the original fitting model is used to represent the fitting results obtained solely based on our own corrosion test data; The original fitting error of the inner region is expressed as: ; The original slope error of the extrapolation region is expressed as: ; in, The original fitting error for the inner region is represented by n, where n is the number of proprietary corrosion test data. Let be the normalized quality loss rate corresponding to the i-th self-owned experimental data. These are the true values ​​of the corresponding corrosion morphology characterization parameters. For the original fitted model in The predicted value at that location; The original slope error of the extrapolation region is given by q, where q is the number of sampling points in the extrapolation region. This represents the normalized quality loss rate corresponding to the k-th sampling point within the extrapolation region. For the original fitted model in The slope at that point For the experience trend fusion model in The slope of the trend at that point; (2) Calculate the basic weights The basic weights of the inner region are determined based on the original fitting error of the inner region, and are expressed as follows: ; The basic weights of the extrapolation region are determined based on the original slope error of the extrapolation region, and are expressed as follows: ; in, As the basic weight of the inner area, As the basic weight for the extrapolation region, To prevent positive numbers with a denominator of zero, the range of values ​​is [value missing]. ; (3) Introduce extrapolation weight amplification factor The extrapolation weight amplification factor λ is used to adjust the basic weights of the extrapolation region. The adjusted extrapolation region weights are expressed as follows: ; in, The adjusted extrapolation weights are λ, where λ is the extrapolation weight amplification factor. (4) Construct the joint objective function Based on the aforementioned inner region base weights and adjusted extrapolation region weights, a joint objective function is constructed that includes the inner region fitting error and the extrapolation region slope error: ; in, For the joint objective function, The corrected fitting model parameters are to be solved. To correct the in-zone fitting error of the model, To correct the slope error in the extrapolation region of the model; The fitting error of the inner region and the slope error of the extrapolation region are expressed as follows: ; ; Given the extrapolation weight amplification factor λ, the corresponding corrected fitting model parameters are expressed as follows: ; in, The corrected fitting model parameters are those corresponding to the extrapolation weight amplification factor of λ. (5) Traversal extrapolation weight amplification factor Multiple candidate values ​​for extrapolation weight amplification coefficients are set, and the extrapolation weight amplification coefficients are iterated. For each candidate value, the corresponding corrected fitting model parameters are re-solved, and the in-zone fitting error and extrapolation zone slope error of the corresponding model are calculated. Referring to Figures 3, 5, and 7, the three types of corrosion morphology characterization parameters correspond to a set of extrapolation weight amplification coefficients for evaluation results. Figure 3 corresponds to the uneven corrosion depth, Figure 5 to the statistical parameters of corrosion pit depth, and Figure 7 to the statistical parameters of corrosion pit diameter-to-depth ratio. The horizontal axis in each figure represents the extrapolation weight amplification coefficient λ, and the subfigures show the fitting error of the inner region under different λ values. extrapolation zone slope error The changes in the comprehensive evaluation index IC and the screening results; The vertical dashed lines in Figures 3, 5 and 7 represent the final selected extrapolation weight amplification coefficients, and the errors and indicators at the positions corresponding to the dashed lines are the evaluation results corresponding to the final optimal corrected fitting model. (6) Screening for internal error limits Candidate modified fitting models are screened based on the inner region error constraint, which is expressed as follows: ; in, To correct the in-zone fitting error of the candidate fitted model. This represents the inner region fitting error of the original unconstrained fitting model. This is the allowable coefficient for amplification of errors in the inner region; when a candidate corrected fitting model does not meet this constraint, it is removed from the candidate set. In this embodiment, Referring to Figures 3, 5, and 7, as the extrapolation weight amplification factor λ increases, the inner region fitting error of the candidate model gradually increases; when the inner region fitting error exceeds the limit, the model no longer participates in the optimal model selection. (7) Determination of comprehensive evaluation indicators and optimal model A comprehensive evaluation index is calculated for the candidate corrected fitting model that meets the inner region error constraint condition. The comprehensive evaluation index is expressed as follows: ; Where IC is the comprehensive evaluation index, n is the number of proprietary corrosion test data, and p is the number of parameters in the corrected fitting model. This represents the inner region fitting error of the candidate model. The slope error of the extrapolation region of the candidate model; In the set C of candidate corrected fitting models that meet the inner region error constraint, the candidate corrected fitting model with the smallest comprehensive evaluation index is determined as the optimal corrected fitting model; the parameters of the optimal corrected fitting model are expressed as: ; in, To determine the optimal fitted model parameters, C represents the set of candidate models that satisfy the inner region error constraint. Referring to Figures 2, 4, and 6, the final corrected fitting curves correspond to the optimal corrected fitting models for the three types of corrosion morphology characterization parameters, respectively. The area to the left of the vertical dashed line in the figures is the inner region, where the corrected fitting curve maintains consistency with the original corrosion test data. The area to the right of the vertical dashed line is the extrapolation region, where the corrected fitting curve is constrained by the trend slope of the empirical trend fusion model.

[0019] As shown in Figures 2 to 7, through the above steps, this embodiment obtains the optimal corrected fitting models corresponding to the statistical parameters of uneven corrosion depth, corrosion pit depth, and corrosion pit diameter-to-depth ratio, which can be used to predict corrosion morphology characterization parameters under different normalized mass loss rates.

Claims

1. A method for fitting and correcting corrosion morphology parameters in small samples based on empirical trend fusion constraints, characterized in that: Includes the following steps: S1: Obtain proprietary corrosion test data and corrosion data from several sets of publicly available literature or materials. Both proprietary corrosion test data and publicly available literature corrosion data include mass loss rate and corrosion morphology characterization parameters corresponding to the mass loss rate. S2: Normalize the mass loss rate obtained from different batches of corrosion tests according to the sample size; establish a correlation fitting model between various corrosion morphology characterization parameters and normalized mass loss rate; fuse the model parameters of the correlation fitting model of corrosion morphology characterization parameters in multiple sets of literature data to obtain an empirical trend fusion model. S3: Using the maximum normalized mass loss rate in the proprietary corrosion test data as the boundary, the fitting interval is divided into an inner region and an extrapolation region. Within the inner region, the optimal fit is performed using an association fitting model that is compatible with the proprietary corrosion test data. In the extrapolation region, the slope of the empirical trend fusion model is used as the trend constraint. S4: Based on the fitting error of the inner zone fitting model using proprietary corrosion test data, construct the basic weights of the inner zone. Based on the difference between the slope of the inner zone fitting model and the slope of the empirical trend fusion model, construct the basic weights of the extrapolation zone. Introduce an extrapolation weight amplification coefficient to adjust the basic weights of the extrapolation zone, construct a joint objective function that includes the fitting error of the inner zone and the slope error of the extrapolation zone, and obtain a corrected fitting model of the relationship between corrosion morphology parameters and normalized mass loss rate by traversing the extrapolation weight amplification coefficient, limiting the inner zone error, and screening the comprehensive evaluation index.

2. The method for fitting and correcting small-sample corrosion morphology parameters based on empirical trend fusion constraints according to claim 1, characterized in that, In step S1, the corrosion morphology characterization parameters include uneven corrosion depth, corrosion pit depth statistical parameters, and corrosion pit diameter-to-depth ratio statistical parameters. The corrosion pit depth statistical parameters and corrosion pit diameter-to-depth ratio statistical parameters are represented by logarithmic distribution mean or logarithmic distribution characteristic values. The specific definitions and calculation methods of each parameter are as follows: Obtain three-dimensional morphological data of the corrosion specimen surface, and discretize the corrosion test area into... Let the nth measuring point be the th measurement point. The corrosion depth at each measuring point is The corrosion depth corresponding to the location with the lightest corrosion in the test area is Then the first The relative corrosion depth at each measuring point is: ； Uneven corrosion depth Represented as: ； Corrosion pits on the surface of the corrosion test specimen are identified. Let the number of identified corrosion pits be... , No. The depth of the corrosion pits is The pit diameter is The mean of the logarithmic distribution of corrosion pit depth is... Represented as: ； Logarithmic distribution mean of corrosion pit diameter-to-depth ratio Represented as: ； in, Used to characterize the non-uniformity of a corroded surface. The statistical level used to characterize the depth of corrosion pits It is used to characterize the relative relationship between the lateral expansion and vertical development of corrosion pits.

3. The method for fitting and correcting small-sample corrosion morphology parameters based on empirical trend fusion constraints according to claim 1, characterized in that, In step S1, the mass loss rate is calculated as follows: Obtain the quality of the specimen before corrosion and the quality after removing corrosion products Original mass loss rate Represented as: 。 4. The method for fitting and correcting small-sample corrosion morphology parameters based on empirical trend fusion constraints according to claim 1, characterized in that, In step S2, the original mass loss rates obtained from different batches of corrosion tests are normalized, that is, the original mass loss rates are converted according to the thickness ratio of the specimens in each batch. The conversion relationship is as follows: ； in, Let be the normalized mass loss rate in the corrosion data of the i-th group of literature. Let be the original mass loss rate in the corrosion data of the i-th group of literature. Let be the specimen thickness corresponding to the corrosion data in the i-th group of literature. The thickness is the specimen thickness.

5. The method for fitting and correcting small-sample corrosion morphology parameters based on empirical trend fusion constraints according to claim 1, characterized in that, In step S2, the literature reference model uses a normalized quality loss rate. The parameters are characterized by corrosion morphology as the independent variable. The dependent variable is determined according to the type of corrosion morphology characterization parameter. Among them, the statistical parameter of corrosion pit depth is described by a power function model, and the statistical parameters of uneven corrosion depth and corrosion pit diameter-to-depth ratio are described by an exponential saturation model. Power function model: ; Exponential saturation model: ; in, For corrosion morphology characterization parameters, To normalize the quality loss rate, These are the parameters to be fitted.

6. The method for fitting and correcting small-sample corrosion morphology parameters based on empirical trend fusion constraints according to claim 1, characterized in that, In step S2, when fusing the model parameters of the correlation fitting models of corrosion morphology characterization parameters in each group of literature data, the fusion object is the relevant parameters affecting the change of trend slope in the multiple correlation fitting models obtained. The purpose of fusion is to provide the empirical trend slope of the extrapolation region. (1) When the correlation fitting model of the corrosion morphology characterization parameters in the literature is a power function model, its expression is: ； The corresponding slope is: ； Let the parameters of the power function model corresponding to the corrosion data of the j-th group of documents be... If the number of literature corrosion datasets participating in the fusion is M, then only the slope-related parameters are considered. By fusing the data, we obtain the slope-related parameters of the empirical trend fusion model in the form of a power function: ； ； in, Let be the fusion weights of the association fitting model for the j-th group of literature data, and satisfy: ； When using an equal-weight fusion method: ； The trend slope of the empirical trend fusion model in the extrapolation region, in the form of a power function, is expressed as: ； Among them, parameters It does not participate in the fusion of slope-related parameters; (2) When the correlation fitting model of the corrosion morphology characterization parameters in the literature is an exponential saturation model, its expression is: ； The corresponding slope is: ； Let the parameters of the exponential saturation model corresponding to the corrosion data of the j-th group of documents be... If the number of literature corrosion datasets participating in the fusion is M, then only the slope-related parameters are considered. By performing fusion, the slope-related parameters of the empirical trend fusion model in the form of exponential saturation are obtained: ； ； in, Let be the fusion weights of the association fitting model for the j-th group of literature data, and satisfy: ； When using an equal-weight fusion method: ； The reference slope of the exponentially saturated empirical trend fusion model in the extrapolation region is expressed as: ； Among them, parameters It does not participate in the fusion of slope-related parameters.

7. The method for fitting and correcting small-sample corrosion morphology parameters based on empirical trend fusion constraints according to claim 1, characterized in that, In step S3, the maximum normalized mass loss rate in the proprietary corrosion test data is used as the boundary. The maximum value of the normalized mass loss rate in the proprietary corrosion test data is set as follows: Then the inner region and the extrapolated region are represented as follows: ； ； in, For the inner area, The extrapolation region is defined as follows: the inner region is used to maintain consistency between the correlation fitting model and the proprietary corrosion test data; the extrapolation region is used to constrain and correct the trend slope of the fitting model; and the value range of the extrapolation region is as follows: ； in, This is the extrapolation range coefficient, used to control the extrapolation range of the modified fitted model for trend constraints.

8. The method for fitting and correcting small-sample corrosion morphology parameters based on empirical trend fusion constraints according to claim 1, characterized in that, In step S4, the basic weight of the inner zone is determined based on the error of the inner zone fitting model of the proprietary corrosion test data; firstly, an adapted correlation fitting model is used to fit the proprietary corrosion test data to obtain the inner zone fitting model. And calculate the fitting error of the inner region fitting model: ； in, The fitting error of the inner zone fitting model is represented by , and n is the number of self-owned corrosion test data. Let i be the normalized mass loss rate corresponding to the i-th self-owned corrosion test data. These are the true values ​​of the corresponding corrosion morphology characterization parameters. For the inner region fitting model in The predicted value at that location; The basic weights of the extrapolation region are determined based on the slope difference between the inner region fitting model and the empirical trend fusion model within the extrapolation region; q sampling points are set within the extrapolation region, and the slope error of the extrapolation region is calculated. ； in, The slope error of the extrapolation region is given by q, where q is the number of sampling points in the extrapolation region. This represents the normalized quality loss rate corresponding to the k-th sampling point within the extrapolation region. For the inner region fitting model in The slope at that point For the experience trend fusion model in The trend slope at that point.

9. The method for fitting and correcting small-sample corrosion morphology parameters based on empirical trend fusion constraints according to claim 1, characterized in that, In step S4, the basic weight of the inner region is expressed as: ； The basic weights of the extrapolation region are represented as follows: ； in, As the basic weight of the inner area, As the basic weight for the extrapolation region, To prevent positive numbers with a denominator of zero, the value is taken as... ; Introducing an extrapolation weight amplification factor λ, the basic weights of the extrapolation region are adjusted. The adjusted extrapolation region weights are expressed as follows: ； in, The adjusted extrapolation weights are denoted by λ, where λ is the extrapolation weight amplification factor. A joint objective function is constructed based on the inner region basic weights and the adjusted extrapolation region weights. The corrected model parameters are then solved under a given extrapolation weight amplification coefficient λ. The joint objective function is expressed as: ； in, For the joint objective function, The corrected model parameters are to be solved. As the basic weight of the inner area, The adjusted extrapolation region weights, This represents the fitting error in the inner region. This refers to the slope error in the extrapolation region; The corresponding corrected model parameters are expressed as follows: ； in, The extrapolation weight amplification factor is λ, which corresponds to the corrected fitting model parameters.

10. The method for fitting and correcting small-sample corrosion morphology parameters based on empirical trend fusion constraints according to claim 1, characterized in that, In step S4, multiple candidate values ​​for the extrapolation weight amplification coefficient are set, and the extrapolation weight amplification coefficients are iterated. For each candidate value, the corresponding modified fitting model parameters are re-solved, and the in-zone fitting error and extrapolation slope error of the corresponding modified fitting model are calculated. Simultaneously, the candidate modified fitting models are screened according to the in-zone error constraint condition, which is expressed as follows: ； in, To correct the fitting error in the inner region of the fitted model, β represents the inner-zone fitting error of the original unconstrained fitting model, and β is the allowable coefficient for amplification of the inner-zone error. When the modified fitting model does not meet the inner-zone error constraint, it is removed from the candidate modified fitting models. A comprehensive evaluation index is calculated for the candidate modified fitting models that meet the inner-zone error constraint, and the candidate modified fitting model with the smallest comprehensive evaluation index is determined as the optimal modified fitting model. The comprehensive evaluation index is expressed as: ； Where IC is the comprehensive evaluation index, n is the number of proprietary corrosion test data, and p is the number of parameters in the corrected fitting model. To correct the in-region fitting error of the candidate fitted model, To correct the slope error of the extrapolation region corresponding to the candidate fitted model; The optimal corrected fitting model parameters are expressed as follows: ； in, Let C be the parameters of the optimal corrected fitting model, and let C be the set of candidate corrected fitting models that satisfy the inner region error constraint.

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