Study Of Model Factors Grouping Based On Second-order Indices Of Sensitivity Analysis

Sensitivity Analysis methods are invaluable tools for model validation,model optimization and model diagnosis,so that to study model complexity described by mathematical models,such as how a model response is sensitive to a parameter or parameter interaction.However,for decades after Sobol's method was proposed,the SA work of using Sobol's indices mostly focuses on the aim of factor priorization using first-order Sobol's index and factor fixing using total-order Sobol's index.Only the first-order and total-order indices are quantitatively used for modelling processing,while the use of second-order index is so rare.The advantage of using second-order Sobol's index to quantitatively describe the interaction has been largely underestimated.The use is only qualitatively limited to check which pair of factors' interaction is 'larger' or 'smaller'.What's more,the performance after these interaction mapping has been ignored.In such case,the potential usefulness of identifying the interaction quantitatively for second-order Sobol's index is not fully investigated.Network clustering is widely applied in system network models,used for detecting commu-nity structure,and make us understanding the structure of the system model more deeply.The second-order Sobol's index evaluates the interaction between parameters.Such interaction re-flects the effect strength between factors.It is the intrinsic property of the system that the model describes.Such interaction can be seen as a similarity measure,thus we can build the network be-tween the model factors through the second-order indices,then we can detect the clustering groups by network clustering methods.In this case,the second-order Sobol's index can be used for fac-tor clustering that can reveal the interaction network within the model.As such,we proposed a new method of model factor clustering based on second-order sensitivity index in this paper.The method is a combination of second-order Sobol's index matrix and network clustering.Our method can make factor clustering 'blindly' to expert knowledge of modelling while revealing the model mechanisms.The significance of such method is that it can provide a configuration of putting factors into naturally clustering according to the intrinsic interaction property of the model itself,instead of the subjective knowledge of the modellers.The uncertainty of expert knowledge could be avoided in this way,because if the clustering work by expert knowledge is not validated,the modules analysis result could be misleading.