Approximate Reasoning Of Modifying Conditional Relation With Distance With Application To Welding Process Decision

Welding is a typical process in shipbuilding.Due to the complexity of its process and mechanism,it is difficult to establish an accurate mathematical model for description.Up to now,the realization of process decision-making,prediction and control still mainly depends on the experience of experts and technicians.Since these empirical knowledge is usually expressed by some fuzzy terms,it is of great significance to apply fuzzy modeling and approximate reasoning technology to the field of welding.For the two widely used methods at present--composition rules of inference（CRI）and similarity-based reasoning,the sole use of the algorithms does not satisfy some important properties,or derives unsatisfactory reasoning results under some conditions because some important information is ignored in the reasoning process.In order to overcome the shortcomings of CRI and similarity-based reasoning,on the basis of considering the relationship between distance function and similarity measure,this paper proposes an approximate reasoning method to modify the conditional relation through the distance between fact and antecedent,which is called reasoning based on distance-modified relation（DMR）.In the proposed method,the distance measure is used as a modification factor to generate a new fuzzy conditional relation,so that any change of fact,antecedent and consequent can be reflected in the reasoning conclusion.We discuss the forms of the modification functions,the selection ways and the fuzzy operators used to construction the conditional relation.Then,we analyze the monotonicity,continuity,approximation and Interchangeability of facts and antecedents of the algorithm,and give the corresponding algorithm of the multiple and multi-dimensional reasoning model.By comparing and analyzing four important properties of three representative methods,the rationality of the proposed algorithm is further proved.In DMR method,a pair of Lukasiewicz operators（T_L,I_L）can be used to construct reduced and expanded modification functions respectively,while left continuous t-norm and continuous implication operators can be regarded as a pair of generalized reduced and extended expanded functions respectively,and left continuous t-norm is also suitable for constructing fuzzy conditional relations.When the above fuzzy logic operators are used and the antecedents are normal sets,the DMR method satisfies monotonicity,reducibility,continuity and approximation property.For mutiple and multi-dimensional reasoning,when expanded modification is adopted,the"union"operation is taken for the complement of the conclusion of each activation rule to obtain the overall conclusion.By comparing and analyzing the four properties of approximate analogical reasoning scheme（AARS）,similarity based reasoning（SAR）and DMR methods,it can be seen that when a pair of（T_L,I_L）operators are taken as the modification function,the accuracy of the conclusion obtained by DMR method is higher than that of the other two methods.AARS and DMR mothods satisfy monotonicity,while SAR method is non-monotonic.If the antecedent is a normal set,the above three methods all satisfy the approximation property;When facts and antecedents are interchanged,unreasonable reasoning conclusions will drawn from AARS and SAR in some cases,while more reasonable results can be derived from DMR method under the same conditions.The DMR algorithm of multiple and multi-dimensional reasoning is applied to CO₂welding specification parameter decision and MAG welding forming prediction of hull plates.Firstly,the modeling data are obtained from KUKA robot welding experimental platform,and the fuzzy process rules of the relationship between welding specification parameters and weld forming geometry are summarized.Secondly,according to the process rule base and DMR algorithm,two reasoning models of process decision and forming prediction are established by using MATLAB.The visual human-computer interaction interface is designed based on GUIDE,and the welding specification parameter decision and weld forming parameter prediction are realized by model calculation.The experimental results show that the average errors between the expected values and the measured values,the predicted values and the measured values of weld forming parameters are within 5%,which can meet the process requirements of hull welding specifications.Finally,the DMR model is compared with the adaptive fuzzy neural network reasoning model,Mamdani reasoning model,the reasoning model based on AARS method and the reasoning model based on SAR method in weld forming prediction.The results show that the calculation accuracy of DMR model is slightly higher than the above four models when using the same rule base.