技术领域Technical Field
本发明涉及环氧结构胶技术领域，尤其涉及一种用于环氧结构胶的应力分析及预测系统。The invention relates to the technical field of epoxy structural adhesives, and in particular to a stress analysis and prediction system for epoxy structural adhesives.
背景技术Background Art
环氧结构胶是一种高性能的粘接剂，广泛应用于建筑、汽车、航空航天和电子制造等多个行业，环氧结构胶因其优异的粘接强度、化学稳定性以及耐热性而被广泛采用，胶粘剂能够在广泛的温度和环境条件下维持其机械性能和粘接性能，能有效地将不同或相同材料粘结在一起，此外，环氧结构胶还具有良好的电绝缘性和抗腐蚀性，使其在电子封装和海洋结构等特殊环境中也具有应用价值。Epoxy structural adhesive is a high-performance adhesive widely used in many industries such as construction, automobiles, aerospace and electronic manufacturing. Epoxy structural adhesive is widely used due to its excellent bonding strength, chemical stability and heat resistance. The adhesive can maintain its mechanical properties and bonding properties under a wide range of temperature and environmental conditions, and can effectively bond different or same materials together. In addition, epoxy structural adhesive also has good electrical insulation and corrosion resistance, which makes it also have application value in special environments such as electronic packaging and marine structures.
其中，用于环氧结构胶的应力分析及预测系统的目的是通过计算模型和数据分析技术，分析预测环氧结构胶在不同环境条件和负荷下的行为和性能，从而优化产品设计，提高结构的可靠性和耐久性，同时减少物理测试的需求和成本，可在产品设计阶段即对材料的长期表现进行评估，从而确保结构的安全性和功能性。Among them, the purpose of the stress analysis and prediction system for epoxy structural adhesives is to analyze and predict the behavior and performance of epoxy structural adhesives under different environmental conditions and loads through computational models and data analysis techniques, thereby optimizing product design, improving structural reliability and durability, and reducing the need and cost of physical testing. The long-term performance of materials can be evaluated during the product design stage to ensure the safety and functionality of the structure.
现有技术未能充分整合来自不同环境的数据，限制了其在复杂应用场景下的适应性，现有技术依赖物理测试来评估材料性能，不仅成本高昂，而且效率低下，物理测试的结果难以全面反映材料在实际应用中的表现，尤其是在极端条件下，这导致设计上的缺陷未被及时发现，增加了产品在实际使用中的风险和维护成本。Existing technologies fail to fully integrate data from different environments, limiting their adaptability in complex application scenarios. Existing technologies rely on physical testing to evaluate material properties, which is not only costly but also inefficient. The results of physical tests are difficult to fully reflect the performance of materials in actual applications, especially under extreme conditions. This leads to design defects not being discovered in a timely manner, increasing the risks and maintenance costs of products in actual use.
发明内容Summary of the invention
本发明的目的是解决现有技术中存在的缺点，而提出的一种用于环氧结构胶的应力分析及预测系统。The purpose of the present invention is to solve the shortcomings of the prior art and to propose a stress analysis and prediction system for epoxy structural adhesive.
为了实现上述目的，本发明采用了如下技术方案：一种用于环氧结构胶的应力分析及预测系统，所述系统包括：In order to achieve the above object, the present invention adopts the following technical solution: a stress analysis and prediction system for epoxy structural adhesive, the system comprising:
环境数据整合模块基于环氧结构胶的多源环境数据与历史性能数据，计算环氧结构胶的化学组成与环境稳定性特性，提取时间序列数据的滑动窗口统计量，并筛选与固化条件关联的统计指标，得到环境特性指标集；The environmental data integration module calculates the chemical composition and environmental stability characteristics of epoxy structural adhesives based on multi-source environmental data and historical performance data of epoxy structural adhesives, extracts sliding window statistics of time series data, and screens statistical indicators associated with curing conditions to obtain an environmental characteristic indicator set;
关键特征提取模块基于所述环境特性指标集，利用递归特征消除，筛选影响环氧结构胶粘接性能的关键特征，并进行特征关键性分析，得到关键特征库；The key feature extraction module uses recursive feature elimination based on the environmental characteristic index set to screen key features that affect the bonding performance of the epoxy structural adhesive, and performs feature criticality analysis to obtain a key feature library;
模型训练与验证模块基于所述关键特征库，训练环氧结构胶的预测模型，应用随机森林进行K折交叉验证，验证模型的泛化能力，优化模型预测结果的准确性与稳定性，得到稳健性预测指标；The model training and verification module trains the prediction model of epoxy structural adhesive based on the key feature library, applies random forest to perform K-fold cross validation, verifies the generalization ability of the model, optimizes the accuracy and stability of the model prediction results, and obtains robustness prediction indicators;
不确定性量化模块基于所述稳健性预测指标，采用贝叶斯网络和dropout方法，执行不确定性分析，分析模型输出的概率分布，并计算预测结果的置信区间，得到预测概率置信度。The uncertainty quantification module uses the Bayesian network and dropout method based on the robustness prediction index to perform uncertainty analysis, analyze the probability distribution of the model output, and calculate the confidence interval of the prediction result to obtain the prediction probability confidence.
本发明改进后，所述化学组成与环境稳定性特性的计算步骤具体为：After the improvement of the present invention, the calculation steps of the chemical composition and environmental stability characteristics are specifically as follows:
基于环氧结构胶的多源环境数据与历史性能数据，计算化学成分的统计描述信息，采用公式：Based on multi-source environmental data and historical performance data of epoxy structural adhesives, the statistical description information of chemical composition is calculated using the formula:
; ;
得到初步的化学成分数据集，其中，是第次观测的第种化学成分值，为观测次数；Get a preliminary chemical composition dataset ,in, It is The first observation Chemical composition values, is the number of observations;
基于所述初步的化学成分数据集，结合温度和湿度环境因素，采用公式：Based on the preliminary chemical composition data set, combined with temperature and humidity environmental factors, the formula is used:
; ;
计算每种化学成分在目标环境下的稳定性指标，其中，是初步的化学成分数据集，和是调节环境因素的敏感度系数；Calculate the stability index of each chemical component in the target environment ,in, is a preliminary chemical composition dataset, and is the sensitivity coefficient of the regulating environmental factor;
基于所述稳定性指标，结合差异化学成分权重，采用公式：Based on the stability index, combined with the weight of the differential chemical composition, the formula is adopted:
; ;
得到化学组成与环境稳定性特性，其中，是稳定性指标，是权重参数，是化学成分的总数。Get chemical composition and environmental stability characteristics ,in, is a stability indicator, is the weight parameter, is the total number of chemical components.
本发明改进后，所述环境特性指标集的获取步骤具体为：After the improvement of the present invention, the steps of obtaining the environmental characteristic index set are specifically as follows:
对收集的所述时间序列数据进行标准化处理，移除异常值，采用公式：The collected time series data are standardized to remove outliers using the formula:
; ;
得到标准化数据集，其中，是原始数据点，是数据的平均值，是标准差；Get a standardized dataset ,in, is the original data point, is the mean value of the data, is the standard deviation;
基于所述标准化数据集，筛选与固化条件关联的统计量，采用公式：Based on the standardized data set, the statistics associated with the curing conditions were screened using the formula:
; ;
得到关联统计量集合，并获得环境特征指标集，其中，和分别代表统计量和固化条件数据，是数据点总数。Get the set of association statistics , and obtain the environmental characteristic index set, among which, and Represent statistics and curing condition data respectively, is the total number of data points.
本发明改进后，所述关键特征库的获取步骤具体为：After the improvement of the present invention, the steps of acquiring the key feature library are specifically as follows:
基于所述环境特性指标集，应用递归特征消除，计算每个特征的贡献度，采用公式：Based on the environmental characteristic index set, recursive feature elimination is applied to calculate the contribution of each feature using the formula:
; ;
得到特征的贡献分数，其中，是第次迭代中第个的特征值，是第次迭代的权重，是迭代次数；Get Features Contribution score ,in, It is In the iteration The characteristic value of It is The weight of the iteration, is the number of iterations;
基于所述贡献分数，计算每个特征与目标变量之间的协方差，结合方差的影响，采用公式：Based on the contribution score, the covariance between each feature and the target variable is calculated, and the influence of the variance is combined, using the formula:
； ;
得到关键性评分，其中，是特征的第个观测值，是目标变量的第个观测值，和分别是和的平均值，是样本数量；Get critical rating ,in, It is a feature No. Observations, is the target variable Observations, and They are and The average value of is the sample size;
基于所述关键性评分，进行关键特征选择，利用判断公式：Based on the criticality score, key feature selection is performed using the judgment formula:
； ;
得到关键特征库，其中，是特征，是关键性评分，是阈值。Get key feature library ,in, It is a feature, is a critical score. is the threshold value.
本发明改进后，所述环氧结构胶预测模型的训练步骤具体为：After the improvement of the present invention, the training steps of the epoxy structural adhesive prediction model are specifically as follows:
使用所述关键特征库中的数据初始化随机森林模型，对模型中的每棵决策树，计算每个特征的信息增益并选择最优分裂点，采用公式：The random forest model is initialized using the data in the key feature library. For each decision tree in the model, the information gain of each feature is calculated and the optimal split point is selected using the formula:
； ;
得到训练后的随机森林模型，其中，表示特征的信息增益，是数据集的熵，是分裂后子集，是子数据集的元素数量，是原始数据集的元素数量；Get the trained random forest model, where Representation characteristics The information gain of It is a dataset The entropy of is the subset after splitting, It is a sub-dataset The number of elements of is the original dataset The number of elements in ;
基于所述训练后的随机森林模型，应用K折交叉验证测试泛化能力，计算每一折的验证准确度，采用公式：Based on the trained random forest model, K-fold cross validation was applied to test the generalization ability, and the validation accuracy of each fold was calculated using the formula:
； ;
得到模型的平均准确度，其中，是第折的准确度，是交叉验证的折数。Get the average accuracy of the model ,in, It is The accuracy of folding, is the number of cross validation folds.
本发明改进后，所述稳健性预测指标的获取步骤具体为：After the improvement of the present invention, the steps for obtaining the robustness prediction index are specifically as follows:
根据验证的所述模型泛化能力，进行模型参数调整，包括决策树数量和树深度，优化模型泛化能力和性能波动，采用公式：According to the verified generalization ability of the model, the model parameters are adjusted, including the number of decision trees and the tree depth, to optimize the generalization ability and performance fluctuation of the model, using the formula:
； ;
得到优化后的模型参数，其中，表示模型参数，是交叉验证的折数，是在参数下第折的准确度；Get the optimized model parameters ,in, represents the model parameters, is the number of cross validation folds, It is in the parameter Next Folding accuracy;
基于所述优化后的模型参数，重新在数据集上进行训练，并评估模型的稳健性，采用公式：Based on the optimized model parameters, retrain on the data set and evaluate the robustness of the model using the formula:
； ;
得到稳健性预测指标，其中，是优化后模型的平均准确度，是准确度的标准差。Get robust prediction indicators ,in, is the average accuracy of the optimized model, is the standard deviation of accuracy.
本发明改进后，所述概率分布的分析步骤具体为：After the improvement of the present invention, the analysis steps of the probability distribution are specifically as follows:
基于所述稳健性预测指标，使用贝叶斯网络，结合dropout方法模拟输出的概率分布，采用公式：Based on the robustness prediction index, the Bayesian network is used in combination with the dropout method to simulate the probability distribution of the output, using the formula:
； ;
得到模型概率输出结果，表示模型预测的不确定性，其中，是给定输入后，输出的预测概率，是dropout过程中模型参数迭代的次数，是在第次迭代时的模型参数；The model probability output is obtained, which represents the uncertainty of the model prediction, where is a given input After that, output The predicted probability of is the number of model parameter iterations during the dropout process, It is in Model parameters at iteration ;
基于所述模型概率输出结果，计算预测概率的均值，采用公式：Based on the model probability output results, the mean of the predicted probabilities is calculated using the formula:
； ;
得到预测概率的均值，其中，是总样本数，是第个样本的预测概率；Get the mean of the predicted probabilities ,in, is the total number of samples, It is The predicted probability of samples;
基于所述预测概率的均值，建立模型输出概率的密度图，采用公式：Based on the mean of the predicted probabilities, a density map of the model output probability is established using the formula:
； ;
得到概率密度，其中，是预测概率的标准差，是预测概率的均值，是预测概率。Get the probability density ,in, is the standard deviation of the predicted probabilities, is the mean of the predicted probabilities, is the predicted probability.
本发明改进后，所述预测概率置信度的获取步骤具体为：After the improvement of the present invention, the steps for obtaining the prediction probability confidence are specifically as follows:
基于所述模型输出的概率分布，使用分位数方法确定预测结果，使用公式：Based on the probability distribution of the model output, the prediction results are determined using the quantile method, using the formula:
； ;
得到置信区间，其中，表示概率分布中2.5%的分位数，用于确定置信区间的下界，表示概率分布中97.5%的分位数，用于确定置信区间的上界，表示模型预测的概率分布；Get the confidence interval ,in, Represents probability distribution The 2.5% quantile is used to determine the lower bound of the confidence interval. Represents probability distribution The 97.5% quantile is used to determine the upper bound of the confidence interval. represents the probability distribution predicted by the model;
基于所述置信区间，计算当前结果落在预测的置信区间内的比例，并评估置信区间的准确性，采用公式：Based on the confidence interval, calculate the proportion of the current result falling within the predicted confidence interval and evaluate the accuracy of the confidence interval using the formula:
； ;
得到置信区间的覆盖率，其中，是总观测数，是第个观测结果的当前值。Get the coverage of the confidence interval ,in, is the total number of observations, It is The current value of the observation.
与现有技术相比，本发明的优点和积极效果在于：Compared with the prior art, the advantages and positive effects of the present invention are:
本发明中，通过整合多源环境数据与历史性能数据并计算环氧结构胶的化学组成与环境稳定性特性，提升了预测准确度，尤其在处理大量数据时的效率和准确性上具有显著优势，利用递归特征消除技术筛选出最关键的特征，显著减少了数据处理过程中的冗余，同时提升了数据分析的焦点和效率，应用随机森林和K折交叉验证不仅优化了模型的泛化能力，也确保了预测结果的稳定性和可靠性，通过贝叶斯网络和dropout技术的应用，系统能够有效地量化预测的不确定性并提供细致的风险评估，减少了对物理测试的依赖，从而在成本和时间上都实现了优化。In the present invention, by integrating multi-source environmental data and historical performance data and calculating the chemical composition and environmental stability characteristics of epoxy structural adhesive, the prediction accuracy is improved, especially in terms of efficiency and accuracy when processing large amounts of data. The most critical features are screened out using recursive feature elimination technology, which significantly reduces redundancy in the data processing process and improves the focus and efficiency of data analysis. The application of random forest and K-fold cross-validation not only optimizes the generalization ability of the model, but also ensures the stability and reliability of the prediction results. Through the application of Bayesian networks and dropout technology, the system can effectively quantify the uncertainty of the prediction and provide a detailed risk assessment, reducing the reliance on physical testing, thereby achieving optimization in both cost and time.
附图说明BRIEF DESCRIPTION OF THE DRAWINGS
图1为本发明的系统流程图；Fig. 1 is a system flow chart of the present invention;
图2为本发明中化学组成与环境稳定性特性的计算流程图；FIG2 is a flow chart showing the calculation of chemical composition and environmental stability characteristics in the present invention;
图3为本发明中环境特性指标集的获取流程图；FIG3 is a flow chart of obtaining an environmental characteristic index set in the present invention;
图4为本发明中关键特征库的获取流程图；FIG4 is a flowchart of obtaining a key feature library in the present invention;
图5为本发明中环氧结构胶预测模型的训练流程图；FIG5 is a training flow chart of the epoxy structural adhesive prediction model in the present invention;
图6为本发明中稳健性预测指标的获取流程图；FIG6 is a flowchart of obtaining robustness prediction indicators in the present invention;
图7为本发明中概率分布的分析流程图；FIG7 is a flow chart of the analysis of probability distribution in the present invention;
图8为本发明中预测概率置信度的获取流程图。FIG8 is a flow chart of obtaining the prediction probability confidence in the present invention.
具体实施方式DETAILED DESCRIPTION
为了使本发明的目的、技术方案及优点更加清楚明白，以下结合附图及实施例，对本发明进行进一步详细说明。应当理解，此处所描述的具体实施例仅仅用以解释本发明，并不用于限定本发明。In order to make the purpose, technical solution and advantages of the present invention more clearly understood, the present invention is further described in detail below in conjunction with the accompanying drawings and embodiments. It should be understood that the specific embodiments described herein are only used to explain the present invention and are not intended to limit the present invention.
在本发明的描述中，需要理解的是，术语“长度”“宽度”“上”“下”“前”“后”“左”“右”“竖直”“水平”“顶”“底”“内”“外”等指示的方位或位置关系为基于附图所示的方位或位置关系，仅是为了便于描述本发明和简化描述，而不是指示或暗示所指的装置或元件必须具有特定的方位、以特定的方位构造和操作，因此不能理解为对本发明的限制。此外，在本发明的描述中，“多个”的含义是两个或两个以上，除非另有明确具体的限定。In the description of the present invention, it should be understood that the terms "length", "width", "up", "down", "front", "back", "left", "right", "vertical", "horizontal", "top", "bottom", "inside", "outside", etc., indicating the orientation or positional relationship, are based on the orientation or positional relationship shown in the drawings, and are only for the convenience of describing the present invention and simplifying the description, rather than indicating or implying that the device or element referred to must have a specific orientation, be constructed and operated in a specific orientation, and therefore cannot be understood as a limitation on the present invention. In addition, in the description of the present invention, the meaning of "multiple" is two or more, unless otherwise clearly and specifically defined.
请参阅图1，本发明提供一种技术方案：一种用于环氧结构胶的应力分析及预测系统包括：Please refer to FIG. 1 . The present invention provides a technical solution: a stress analysis and prediction system for epoxy structural adhesive comprises:
环境数据整合模块基于环氧结构胶的多源环境数据与历史性能数据，计算环氧结构胶的化学组成与环境稳定性特性，提取时间序列数据的滑动窗口统计量，并筛选与固化条件关联的统计指标，得到环境特性指标集；The environmental data integration module calculates the chemical composition and environmental stability characteristics of epoxy structural adhesives based on multi-source environmental data and historical performance data of epoxy structural adhesives, extracts sliding window statistics of time series data, and screens statistical indicators associated with curing conditions to obtain an environmental characteristic indicator set;
关键特征提取模块基于环境特性指标集，利用递归特征消除，筛选影响环氧结构胶粘接性能的关键特征，并进行特征关键性分析，得到关键特征库；The key feature extraction module uses recursive feature elimination based on the environmental characteristic index set to screen the key features that affect the bonding performance of epoxy structural adhesives, and performs feature criticality analysis to obtain a key feature library;
模型训练与验证模块基于关键特征库，训练环氧结构胶的预测模型，应用随机森林进行K折交叉验证，验证模型的泛化能力，优化模型预测结果的准确性与稳定性，得到稳健性预测指标；The model training and verification module trains the prediction model of epoxy structural adhesive based on the key feature library, applies random forest to perform K-fold cross-validation, verifies the generalization ability of the model, optimizes the accuracy and stability of the model prediction results, and obtains robustness prediction indicators;
不确定性量化模块基于稳健性预测指标，采用贝叶斯网络和dropout方法，执行不确定性分析，分析模型输出的概率分布，并计算预测结果的置信区间，得到预测概率置信度。The uncertainty quantification module uses the Bayesian network and dropout method based on the robustness prediction index to perform uncertainty analysis, analyze the probability distribution of the model output, and calculate the confidence interval of the prediction result to obtain the prediction probability confidence.
环境特性指标集包括化学性质指标、环境适应性指标、固化过程指标，关键特征库包括粘接力度因子、时间敏感性特征、环境响应特征，稳健性预测指标包括预测准确率指标、稳定性评分、模型效能指标，预测概率置信度包括置信区间范围、不确定性等级、预测准确性评估结果。The environmental characteristic indicator set includes chemical property indicators, environmental adaptability indicators, and curing process indicators. The key feature library includes bonding strength factors, time sensitivity characteristics, and environmental response characteristics. The robustness prediction indicators include prediction accuracy indicators, stability scores, and model effectiveness indicators. The prediction probability confidence includes confidence interval range, uncertainty level, and prediction accuracy evaluation results.
请参阅图2，化学组成与环境稳定性特性的计算步骤具体为：Please refer to Figure 2. The calculation steps of chemical composition and environmental stability characteristics are as follows:
基于环氧结构胶的多源环境数据与历史性能数据，计算化学成分的统计描述信息，采用公式：Based on multi-source environmental data and historical performance data of epoxy structural adhesives, the statistical description information of chemical composition is calculated using the formula:
； ;
得到初步的化学成分数据集，其中，是第次观测的第种化学成分值，为观测次数；Get a preliminary chemical composition dataset ,in, It is The first observation Chemical composition values, is the number of observations;
基于初步的化学成分数据集，结合温度和湿度环境因素，采用公式：Based on the preliminary chemical composition data set, combined with temperature and humidity environmental factors, the formula is used:
； ;
计算每种化学成分在目标环境下的稳定性指标，其中，是初步的化学成分数据集，和是调节环境因素的敏感度系数；Calculate the stability index of each chemical component in the target environment ,in, is a preliminary chemical composition dataset, and is the sensitivity coefficient of the regulating environmental factor;
基于稳定性指标，结合差异化学成分权重，采用公式：Based on the stability index, combined with the weight of the different chemical components, the formula is adopted:
； ;
得到化学组成与环境稳定性特性，其中，是稳定性指标，是权重参数，是化学成分的总数。Get chemical composition and environmental stability characteristics ,in, is a stability indicator, is the weight parameter, is the total number of chemical components.
假设对于某种化学成分，有5次观测值：Suppose for a certain chemical composition, there are 5 observations:
100，120，110，130，90；100, 120, 110, 130, 90;
； ;
。 .
计算过程：Calculation process:
； ;
表示这种化学成分的平均观测值为110，这是一个统计描述，用来反映该化学成分在观测期间的一般水平。 It means that the average observed value of this chemical component is 110, which is a statistical description used to reflect the general level of this chemical component during the observation period.
设；set up ;
； ;
。 .
计算过程：Calculation process:
； ;
表示该化学成分在当前环境条件下具有较高的稳定性，值越接近1，表示稳定性越高。 It indicates that the chemical composition has a higher stability under the current environmental conditions. The closer the value is to 1, the higher the stability.
假设有三种化学成分：Assume there are three chemical components:
； ;
权重分别为：The weights are:
； ;
计算过程：Calculation process:
； ;
； ;
表示综合了不同化学成分的环境稳定性得分和权重后，整体的化学组成与环境稳定性特性的评分。 It represents the score of the overall chemical composition and environmental stability characteristics after combining the environmental stability scores and weights of different chemical components.
请参阅图3，环境特性指标集的获取步骤具体为：Please refer to FIG3 , the steps for obtaining the environmental characteristic index set are as follows:
对收集的时间序列数据进行标准化处理，移除异常值，采用公式：The collected time series data are standardized and outliers are removed using the formula:
； ;
得到标准化数据集，其中，是原始数据点，是数据的平均值，是标准差；Get a standardized dataset ,in, is the original data point, is the mean value of the data, is the standard deviation;
基于标准化数据集，筛选与固化条件关联的统计量，采用公式：Based on the standardized data set, the statistics associated with the curing conditions were screened using the formula:
； ;
得到关联统计量集合，并获得环境特征指标集，其中，和分别代表统计量和固化条件数据，是数据点总数。Get the set of association statistics , and obtain the environmental characteristic index set, among which, and Represent statistics and curing condition data respectively, is the total number of data points.
假设有以下五个数据点：Suppose there are the following five data points:
10，20，30，40，50；10, 20, 30, 40, 50;
计算平均值：Calculate the average :
； ;
计算标准差：Calculate standard deviation :
； ;
为20： For 20:
； ;
标准化值-0.63表示原始数据点20在平均值以下0.63个标准差的位置。The normalized value of -0.63 means that the original data point 20 is 0.63 standard deviations below the mean.
假设：Assumptions:
为[1.0，0.0，-1.0]； is [1.0, 0.0, -1.0];
为[2，1，0]； is [2, 1, 0];
。 .
计算各部分：Calculate the parts:
； ;
； ;
； ;
； ;
； ;
； ;
该相关系数1表示和之间有完美的正相关关系。The correlation coefficient of 1 indicates and There is a perfect positive correlation between them.
请参阅图4，关键特征库的获取步骤具体为：Please refer to Figure 4, the steps for obtaining the key feature library are as follows:
基于环境特性指标集，应用递归特征消除，计算每个特征的贡献度，采用公式：Based on the environmental characteristic index set, recursive feature elimination is applied to calculate the contribution of each feature using the formula:
； ;
得到特征的贡献分数，其中，是第次迭代中第个的特征值，是第次迭代的权重，是迭代次数；Get Features Contribution score ,in, It is In the iteration The characteristic value of It is The weight of the iteration, is the number of iterations;
基于贡献分数，计算每个特征与目标变量之间的协方差，结合方差的影响，采用公式：Based on the contribution score, the covariance between each feature and the target variable is calculated, and the influence of the variance is combined, using the formula:
； ;
得到关键性评分，其中，是特征的第个观测值，是目标变量的第个观测值，和分别是和的平均值，是样本数量；Get critical rating ,in, It is a feature No. Observations, is the target variable Observations, and They are and The average value of is the sample size;
基于关键性评分，进行关键特征选择，利用判断公式：Based on the criticality score, key feature selection is performed using the judgment formula:
； ;
得到关键特征库，其中，是特征，是关键性评分，是阈值。Get key feature library ,in, It is a feature. is a critical score. is the threshold value.
假设有一个特征在三次迭代中的值分别为0.5，0.8，0.3；Suppose there is a feature whose values in three iterations are 0.5, 0.8, and 0.3 respectively;
权重分别为0.2，0.5，0.3；Weight They are 0.2, 0.5, and 0.3 respectively;
计算公式如下：The calculation formula is as follows:
； ;
； ;
； ;
得分0.59表示该特征在递归特征消除过程中的综合重要性，表明该特征对模型的影响较大。The score of 0.59 indicates the comprehensive importance of this feature in the recursive feature elimination process, indicating that this feature has a greater impact on the model.
假设：Assumptions:
为[1，2，3]； is [1, 2, 3];
为[3，2，1]； is [3, 2, 1];
计算和：calculate and :
计算：calculate :
； ;
； ;
关键性指数-1.414表示特征与目标变量的关联性，这里的负值表示反向关系，大小表明较强的关联性。The criticality index of -1.414 indicates the correlation between the feature and the target variable. The negative value here indicates an inverse relationship, and the size indicates a stronger correlation.
假设：Assumptions:
； ;
； ;
计算是否包含：Calculate whether it contains :
； ;
； ;
因，特征被包含在关键特征库中，表示特征对目标变量有显著影响。because ,feature Being included in the key feature library indicates that the feature has a significant impact on the target variable.
请参阅图5，环氧结构胶预测模型的训练步骤具体为：Please refer to Figure 5, the training steps of the epoxy structural adhesive prediction model are as follows:
使用关键特征库中的数据初始化随机森林模型，对模型中的每棵决策树，计算每个特征的信息增益并选择最优分裂点，采用公式：Use the data in the key feature library to initialize the random forest model. For each decision tree in the model, calculate the information gain of each feature and select the optimal split point using the formula:
； ;
得到训练后的随机森林模型，其中，表示特征的信息增益，是数据集的熵，是分裂后子集（左或右），并且表示子集的大小，是子数据集的元素数量，是原始数据集的元素数量；Get the trained random forest model, where Representation characteristics The information gain of It is a dataset The entropy of is the subset after splitting (left or right ),and represents the size of the subset, It is a sub-dataset The number of elements of is the original dataset The number of elements in ;
基于训练后的随机森林模型，应用K折交叉验证测试泛化能力，计算每一折的验证准确度，采用公式：Based on the trained random forest model, K-fold cross validation is applied to test the generalization ability and calculate the validation accuracy of each fold using the formula:
； ;
得到模型的平均准确度，其中，是第折的准确度，是交叉验证的折数。Get the average accuracy of the model ,in, It is The accuracy of folding, is the number of cross validation folds.
假设有一个数据集，包含10个元素，5个元素的类标为1，5个为0，使得：Suppose there is a data set containing 10 elements, 5 of which are labeled 1 and 5 are labeled 0, such that:
； ;
现在基于特征分裂数据集，左子集包含3个类标为1的元素和2个类标为0的元素，右子集包含2个类标为1的元素和3个类标为0的元素。Now based on the feature Split the dataset, left subset Contains 3 elements with class label 1 and 2 elements with class label 0, the right subset Contains 2 elements with class label 1 and 3 elements with class label 0.
计算如下：The calculation is as follows:
； ;
； ;
； ;
信息增益为0.03，表示选择该特征进行数据集分裂带来的不确定性减少非常小，表明该特征不是非常有用的分裂特征。Information Gain It is 0.03, which means that the uncertainty reduction brought by selecting this feature for data set splitting is very small, indicating that this feature is not a very useful splitting feature.
假设进行了3折交叉验证，每折的精确度分别为0.95，0.92，0.93；Assume that a 3-fold cross validation is performed, and the accuracy of each fold is 0.95, 0.92, and 0.93 respectively;
； ;
平均精确度为0.93，表示模型在未见数据上有很好的表现，具有较高的稳定性和泛化能力。Average accuracy It is 0.93, indicating that the model performs well on unseen data and has high stability and generalization ability.
请参阅图6，稳健性预测指标的获取步骤具体为：Please refer to Figure 6. The specific steps for obtaining the robustness prediction index are as follows:
根据验证的模型泛化能力，进行模型参数调整，包括决策树数量和树深度，优化模型泛化能力和性能波动，采用公式：According to the verified model generalization ability, the model parameters are adjusted, including the number of decision trees and the tree depth, to optimize the model generalization ability and performance fluctuation, using the formula:
； ;
得到优化后的模型参数，其中，表示模型参数，是交叉验证的折数，是在参数下第折的准确度；Get the optimized model parameters ,in, represents the model parameters, is the number of cross validation folds, It is in the parameter Next Folding accuracy;
基于优化后的模型参数，重新在数据集上进行训练，并评估模型的稳健性，采用公式：Based on the optimized model parameters, retrain on the data set and evaluate the robustness of the model using the formula:
； ;
得到稳健性预测指标，其中，是优化后模型的平均准确度，是准确度的标准差。Get robust prediction indicators ,in, is the average accuracy of the optimized model, is the standard deviation of accuracy.
假设进行了3折交叉验证，模型参数调整后在三个不同的折上的精确度分别为0.90，0.92，0.91。Assuming a 3-fold cross validation, the model parameters After adjustment, the accuracies on three different folds are 0.90, 0.92, and 0.91 respectively.
计算过程：Calculation process:
； ;
得到为0.91，表明模型在各个子集上表现出相对稳定且高效的预测性能。get It is 0.91, indicating that the model exhibits relatively stable and efficient prediction performance on each subset.
基于上述假设值，的计算如下：Based on the above assumptions, The calculation of is as follows:
； ;
计算稳健性预测指标：Calculate the robustness forecast indicator:
； ;
得到为110.98，该高值表明模型在不同的测试条件下具有非常高的性能一致性和可信度，说明预测模型非常稳健。get The high value is 110.98, which indicates that the model has very high performance consistency and credibility under different test conditions, indicating that the prediction model is very robust.
请参阅图7，概率分布的分析步骤具体为：Please refer to Figure 7, the analysis steps of probability distribution are as follows:
基于稳健性预测指标，使用贝叶斯网络，结合dropout方法模拟输出的概率分布，采用公式：Based on the robustness prediction index, the Bayesian network is used, combined with the dropout method to simulate the probability distribution of the output, using the formula:
； ;
得到模型概率输出结果，表示模型预测的不确定性，其中，是给定输入后，输出的预测概率，是dropout过程中模型参数迭代的次数，是在第次迭代时的模型参数；The model probability output is obtained, which represents the uncertainty of the model prediction, where is a given input After that, output The predicted probability of is the number of model parameter iterations during the dropout process, It is in Model parameters at iteration ;
基于模型概率输出结果，计算预测概率的均值，采用公式：Based on the model probability output results, calculate the mean of the predicted probabilities using the formula:
； ;
得到预测概率的均值，其中，是总样本数，是第个样本的预测概率；Get the mean of the predicted probabilities ,in, is the total number of samples, It is The predicted probability of samples;
基于预测概率的均值，建立模型输出概率的密度图，采用公式：Based on the mean of the predicted probabilities, a density map of the model output probability is constructed using the formula:
； ;
得到概率密度，其中，是预测概率的标准差，是预测概率的均值，是预测概率。Get the probability density ,in, is the standard deviation of the predicted probabilities, is the mean of the predicted probabilities, is the predicted probability.
假设进行3次迭代，每次的预测概率分别为0.6，0.65，0.7。Assume that three iterations are performed, and the predicted probabilities of each are 0.6, 0.65, and 0.7 respectively.
计算过程：Calculation process:
； ;
在Dropout方法引入随机性后，预测概率的平均值为0.65，表明模型在给定输入下，预测的平均概率。After the Dropout method introduces randomness, the average value of the predicted probability is 0.65, indicating that the model is Next, prediction The average probability of .
假设有5个样本，其预测概率为0.5，0.6，0.55，0.65，0.7。Suppose there are 5 samples, and their predicted probabilities are 0.5, 0.6, 0.55, 0.65, and 0.7.
计算过程：Calculation process:
； ;
均值0.6表示模型在所有样本上的平均预测概率。The mean value of 0.6 represents the average predicted probability of the model over all samples.
假设和，计算的概率密度。Assumptions and ,calculate The probability density of .
计算过程：Calculation process:
； ;
结果解释：Result interpretation:
概率密度为，显示是最可能的预测结果，因为位于概率分布的中心。Probability density for ,show is the most likely prediction because it is in the center of the probability distribution.
请参阅图8，预测概率置信度的获取步骤具体为：Please refer to FIG8 , the specific steps for obtaining the prediction probability confidence are as follows:
基于模型输出的概率分布，使用分位数方法确定预测结果，使用公式：Based on the probability distribution of the model output, the prediction results are determined using the quantile method, using the formula:
； ;
得到置信区间，其中，表示概率分布中2.5%的分位数，用于确定置信区间的下界，表示概率分布中97.5%的分位数，用于确定置信区间的上界，表示模型预测的概率分布；Get the confidence interval ,in, Represents probability distribution The 2.5% quantile is used to determine the lower bound of the confidence interval. Represents probability distribution The 97.5% quantile is used to determine the upper bound of the confidence interval. represents the probability distribution predicted by the model;
基于置信区间，计算当前结果落在预测的置信区间内的比例，并评估置信区间的准确性，采用公式：Based on the confidence interval, calculate the proportion of the current result falling within the predicted confidence interval and evaluate the accuracy of the confidence interval using the formula:
； ;
得到置信区间的覆盖率，其中，是总观测数，是第个观测结果的当前值，是用于检测某一条件是否为真，若为真（即观测值落在置信区间内）则返回1，否则为0。Get the coverage of the confidence interval ,in, is the total number of observations, It is The current value of observations, It is used to test whether a condition is true. If it is true (i.e. the observed value Falls within the confidence interval 1 if the value is within the range specified in the query, otherwise 0.
假设概率分布如下，以10个数据点表示：Assume the following probability distribution, represented by 10 data points:
； ;
计算：calculate :
在10个数据点中，2.5%分位数是第个数据点，取最接近的较大值，即0.2。Of the 10 data points, the 2.5% quantile is the data points, take the closest larger value, which is 0.2.
计算：calculate :
在10个数据点中，97.5%分位数是第个数据点，取最接近的较小值，即1.0。Of the 10 data points, the 97.5% quantile is data points, take the closest smaller value, which is 1.0.
置信区间CI为[0.2，1.0]，此置信区间表示在给定模型的预测概率分布情况下，可以95%的置信度预计实际结果将落在0.2到1.0的范围内。The confidence interval CI is [0.2, 1.0], which means that given the predicted probability distribution of the given model, it can be expected with 95% confidence that the actual result will fall within the range of 0.2 to 1.0.
假设有5个观测结果：Assume there are 5 observations:
； ;
置信区间CI=[0.2，1.0]。Confidence interval CI=[0.2, 1.0].
对每个观测结果，检查是否在置信区间内：For each observation , check whether it is within the confidence interval:
； ;
； ;
； ;
； ;
； ;
； ;
此覆盖率表示，在5次观测中，有80%的观测结果落在预测的置信区间内，说明置信区间的设置是相对准确的。This coverage rate means that among the 5 observations, 80% of the observations fall within the predicted confidence interval, indicating that the setting of the confidence interval is relatively accurate.
以上，仅是本发明的较佳实施例而已，并非对本发明作其他形式的限制，任何熟悉本专业的技术人员可能利用上述揭示的技术内容加以变更或改型为等同变化的等效实施例应用于其他领域，但是凡是未脱离本发明技术方案内容，依据本发明的技术实质对以上实施例所做的任何简单修改、等同变化与改型，仍属于本发明技术方案的保护范围。The above are only preferred embodiments of the present invention and are not intended to limit the present invention in other forms. Any technician familiar with the profession may use the technical contents disclosed above to change or modify them into equivalent embodiments with equivalent changes and apply them to other fields. However, any simple modification, equivalent change and modification made to the above embodiments based on the technical essence of the present invention without departing from the technical solution of the present invention still falls within the protection scope of the technical solution of the present invention.
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| CN202411109840.1ACN118629546A (en) | 2024-08-14 | 2024-08-14 | A stress analysis and prediction system for epoxy structural adhesive |
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| CN202411109840.1ACN118629546A (en) | 2024-08-14 | 2024-08-14 | A stress analysis and prediction system for epoxy structural adhesive |
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