基于符号语义反向传播的熟料性能显式表征及反向优化OA

Introduction The chemical composition of cement clinker directly affects cement hydration,later-age strength development,and quality stability,and therefore serves as a key basis for clinker quality evaluation and production regulation.Conventional clinker performance analysis mainly relies on chemical composition testing,empirical rules,and mineral-phase estimation methods such as the Bogue calculation.Although these approaches have the physical meanings and practical engineering applicability,their predefined model forms are insufficient to fully capture the complex nonlinear strength relationships arising from the coupled effects of multiple oxide components and the water-to-cement ratio. In recent years,machine learning methods have been widely applied to predict the performance of clinker and cement-based materials,providing some opportunities for modeling complex composition-property relationships.However,the existing black box models usually do not give clear mathematical formulas,which makes it difficult to directly explain how the strength develops.In addition,most studies mainly predict the strength from chemical composition.They are less able to work in the opposite direction,that is,to identify suitable adjustment directions and feasible ranges of clinker chemical components when a strength-improvement target is given,either as a specific value or as an interval.To solve these problems,this study was to develop an explicit modelling and inverse optimization method for clinker performance via combining symbolic regression and semantic backpropagation.This method could provide an interpretable prediction of 28 d compressive strength and target driven inverse regulation of clinker composition. Methods This study proposed an explicit representation and inverse optimization method for clinker performance by combining symbolic regression with semantic backpropagation.This method was designed to address the limited explicit characterization of clinker composition-strength relationships and the difficulty of regulating clinker composition according to the strength requirements.First,clinker samples from different sources were collected,and their chemical compositions and 28 d compressive strengths were used to build a clinker composition performance dataset.Then,a symbolic regression based on genetic programming was used to search for explicit relationships between clinker chemical composition and 28 d compressive strength in an expression space formed by variables,constants,and mathematical operators.Expression trees and their corresponding equations were obtained from the candidate models.To avoid physically unreasonable models or the loss of important variables caused by relying only on prediction error,a model selection strategy was introduced via considering physical prior constraints,model complexity,and variable coverage.This strategy could balance prediction accuracy,physical rationality,structural simplicity,and interpretability.Furthermore,a semantic backpropagation method driven by target strength variation was used to propagate the required strength improvement backward through the explicit expression structure to the input variables.Feasible adjustment intervals for individual chemical components and collaborative optimization schemes for multiple variables were then derived.In this way,the proposed method could transform target strength changes into practical suggestions for inverse regulation of clinker chemical composition. Results and discussion The results show that the symbolic regression model selected by considering physical prior constraints,model complexity,and variable coverage achieves a good balance between prediction accuracy and interpretability.The final model includes all nine key input variables,including CaO,SiO2,Al2O3,Fe2O3,MgO,SO3,K2O,Na2O,and W/C.Its expression is not a simple linear combination,but is composed of product terms,ratio terms,and nonlinear terms.This structure allows the coupled effects of the main clinker oxides and W/C on the 28 d compressive strength to be explicitly described.The sensitivity analysis further shows that K2O,Na2O,W/C,CaO,and Al2O3 have relatively great effects on the model output.Among these variables,W/C shows a mainly negative effect around the most samples,while CaO makes a positive contribution under most local conditions.These results indicate that the obtained explicit model can capture the basic characteristics of strength development controlled by the combined effects of multiple clinker components. The final explicit model demonstrates a satisfactory predictive performance on both the training and test datasets.For the training set,the RMSE,MAE,and R² are 1.303 MPa,0.903 MPa,and 0.811,respectively.For the test set,the corresponding values are 1.409 MPa,1.126 MPa,and 0.817 Compared with multiple linear regression,Ridge regression,random forest,support vector regression,XGBoost,and conventional symbolic regression,the proposed method achieves a better prediction accuracy on the test set.Meanwhile,in contrast to black-box machine learning models,the proposed model retains an explicit expression structure,which can be directly used for variable-relationship analysis and subsequent target-driven input interval back-propagation. The inverse optimization results show that the proposed model can translate requirements for strength improvement into interpretable suggestions for composition adjustment.For a representative sample with a predicted strength of 55.42 MPa,when the target strength increase is set as[1.5,3.0]MPa,single variable backpropagation identifies feasible adjustment intervals for CaO,SiO2,Na2O,W/C,and other variables.Among them,CaO and W/C require smaller minimum adjustment magnitudes,indicating that they may be more suitable for single variable regulation.When CaO,Na2O,and W/C are backpropagated simultaneously,the feasible solutions are not simple combinations of independent adjustment intervals,but appear as several local feasible regions.This result reveals clear synergistic and compensatory effects among clinker components.Sampling validation further confirms that multiple joint adjustment schemes can shift the predicted strength into the target range.These findings indicate that the proposed method can provide practical candidate solutions for clinker strength improvement,quality evaluation,and inverse mix proportion regulation. Conclusions This study demonstrated a potential of symbolic semantic backpropagation in clinker performance prediction,explicit relationship analysis,and strength-target-driven composition regulation.The proposed method established an explicit quantitative relationship between clinker chemical composition and compressive strength at 28 d via combining symbolic regression with semantic backpropagation as well as incorporating physical prior constraints,variable coverage screening and target-interval-based backpropagation.It could also transform strength improvement targets into feasible adjustment intervals for individual variables and collaborative optimization schemes for multiple variables.Compared with conventional black-box models,this method could offer a greater interpretability for the relationship between composition and strength and provides more direct inverse guidance for clinker composition regulation.Overall,it could provide an interpretable and practical approach for clinker strength prediction,quality assessment,and inverse mix proportion regulation.