Introducing the nth-Order Features Adjoint Sensitivity Analysis Methodology for Nonlinear Systems (nth-FASAM-N): I. Mathematical Framework

This work presents the “nth-Order Feature Adjoint Sensitivity Analysis Methodology for Nonlinear Systems” (abbreviated as “nth-FASAM-N”), which will be shown to be the most efficient methodology for computing exact expressions of sensitivities, of any order, of model responses with respect to features of model parameters and, subsequently, with respect to the model’s uncertain parameters, boundaries, and internal interfaces. The unparalleled efficiency and accuracy of the nth-FASAM-N methodology stems from the maximal reduction of the number of adjoint computations (which are considered to be “large-scale” computations) for computing high-order sensitivities. When applying the nth-FASAM-N methodology to compute the second- and higher-order sensitivities, the number of large-scale computations is proportional to the number of “model features” as opposed to being proportional to the number of model parameters (which are considerably more than the number of features).When a model has no “feature” functions of parameters, but only comprises primary parameters, the nth-FASAM-N methodology becomes identical to the extant nth CASAM-N (“nth-Order Comprehensive Adjoint Sensitivity Analysis Methodology for Nonlinear Systems”) methodology. Both the nth-FASAM-N and the nth-CASAM-N methodologies are formulated in linearly increasing higher-dimensional Hilbert spaces as opposed to exponentially increasing parameter-dimensional spaces thus overcoming the curse of dimensionality in sensitivity analysis of nonlinear systems. Both the nth-FASAM-N and the nth-CASAM-N are incomparably more efficient and more accurate than any other methods (statistical, finite differences, etc.) for computing exact expressions of response sensitivities of any order with respect to the model’s features and/or primary uncertain parameters, boundaries, and internal interfaces.

Experimental study on creep mechanics characteristics of gassy under disturbance conditions

Creep mechanics characteristics of large scale tectonic coal was studied under gas draingae and disturbance conditions by using the new self-developed coal gas cou- pling three axial creep equipment.The results show that when σ_1 is smaller,σ_3 is larger, gas pressure and disturbance load are smaller,gassy coal has no disturbance to creep. When σ_3 is smaller,gas pressure and σ_1 are larger,disturbance load is constant,gassy coal has remarkable effects of disturbance to creep.The concepts of disturbance load sensitive domain and disturbance creep sensitive domain were put forward.Under same amplitude disturbance stress condition,blasting disturbance has a stronger influence on gassy coal deformation is related to frequency of disturbance load;gas drainage,blasting excavation and mining play an important role in coal-gas outbursting.The relationship of gassy coal creep and gas pressure gradient,the creep constitutive equation built with gas pressure gradient and disturbance load as independent variables within the framework of fluid-solid two phases coupling were established.