Partial Differential Equations(PDEs)are model candidates of soft sensing for aero-engine health management units.The existing Physics-Informed Neural Networks(PINNs)have made achievements.However,unmeasurable aero-eng...Partial Differential Equations(PDEs)are model candidates of soft sensing for aero-engine health management units.The existing Physics-Informed Neural Networks(PINNs)have made achievements.However,unmeasurable aero-engine driving sources lead to unknown PDE driving terms,which weaken PINNs feasibility.To this end,Physically Informed Hierarchical Learning followed by Recurrent-Prediction Term(PIHL-RPT)is proposed.First,PIHL is proposed for learning nonhomogeneous PDE solutions,in which two networks NetU and NetG are constructed.NetU is for learning solutions satisfying PDEs;NetG is for learning driving terms to regularize NetU training.Then,we propose a hierarchical learning strategy to optimize and couple NetU and NetG,which are integrated into a data-physics-hybrid loss function.Besides,we prove PIHL-RPT can iteratively generate a series of networks converging to a function,which can approximate a solution to well-posed PDE.Furthermore,RPT is proposed for prediction improvement of PIHL,in which network NetU-RP is constructed to compensate for information loss caused by data sampling and driving sources’immeasurability.Finally,artificial datasets and practical vibration process datasets from our wear experiment platform are used to verify the feasibility and effectiveness of PIHL-RPT based soft sensing.Meanwhile,comparisons with relevant methods,discussions,and PIHL-RPT based health monitoring example are given.展开更多
2-D crustal structure and velocity ratio are obtained by processing S-wave data from two wide-angle reflec-tion/refraction profiles in and around Jiashi in northeastern Pamir, with the result of P-wave data taken into...2-D crustal structure and velocity ratio are obtained by processing S-wave data from two wide-angle reflec-tion/refraction profiles in and around Jiashi in northeastern Pamir, with the result of P-wave data taken into con-sideration. The result shows that: 1) Average crustal velocity ratio is obviously higher in Tarim block than in West Kunlun Mts. and Tianshan fold zone, which reflects its crustal physical property of 'hardness' and stability. The relatively low but normai velocity ratio (Poisson's ratio) of the lower crust indicates that the 'downward thrusting' of Tarim basin is the main feature of crustal movement in this area. 2) The rock layer in the upper crust of Tianshan fold zone is relatively 'soft', which makes it prone to rupture and stress energy release. This is the primary tectonic factor for the concentration of small earthquakes in this area. 3) Jiashi is located right over the apex or the inflection point of the updoming lower crustal interface C and the crust-mantle boundary, which is the deep struc-tural background for the occurrence of strong earthquakes. The alternate variation of vp/vs near the block bounda-ries and the complicated configuration of the interfaces in the upper and middie part of the upper crust form a par-ticular structural environment for the Jiashi strong earthquake swarm. vp/vs is comparatively high and shear modulus is low at the focal region, which may be the main reason for the low stress drop of the Jiashi strong earthquake swarm.展开更多
基金supported in part by the National Science and Technology Major Project of China(No.2019-I-0019-0018)the National Natural Science Foundation of China(Nos.61890920,61890921,12302065 and 12172073).
文摘Partial Differential Equations(PDEs)are model candidates of soft sensing for aero-engine health management units.The existing Physics-Informed Neural Networks(PINNs)have made achievements.However,unmeasurable aero-engine driving sources lead to unknown PDE driving terms,which weaken PINNs feasibility.To this end,Physically Informed Hierarchical Learning followed by Recurrent-Prediction Term(PIHL-RPT)is proposed.First,PIHL is proposed for learning nonhomogeneous PDE solutions,in which two networks NetU and NetG are constructed.NetU is for learning solutions satisfying PDEs;NetG is for learning driving terms to regularize NetU training.Then,we propose a hierarchical learning strategy to optimize and couple NetU and NetG,which are integrated into a data-physics-hybrid loss function.Besides,we prove PIHL-RPT can iteratively generate a series of networks converging to a function,which can approximate a solution to well-posed PDE.Furthermore,RPT is proposed for prediction improvement of PIHL,in which network NetU-RP is constructed to compensate for information loss caused by data sampling and driving sources’immeasurability.Finally,artificial datasets and practical vibration process datasets from our wear experiment platform are used to verify the feasibility and effectiveness of PIHL-RPT based soft sensing.Meanwhile,comparisons with relevant methods,discussions,and PIHL-RPT based health monitoring example are given.
基金State Key Basic Development and Programming Project (G1998040702)the Project (9691307) from Ministry of Science and Technology and China Seismological Bureau.
文摘2-D crustal structure and velocity ratio are obtained by processing S-wave data from two wide-angle reflec-tion/refraction profiles in and around Jiashi in northeastern Pamir, with the result of P-wave data taken into con-sideration. The result shows that: 1) Average crustal velocity ratio is obviously higher in Tarim block than in West Kunlun Mts. and Tianshan fold zone, which reflects its crustal physical property of 'hardness' and stability. The relatively low but normai velocity ratio (Poisson's ratio) of the lower crust indicates that the 'downward thrusting' of Tarim basin is the main feature of crustal movement in this area. 2) The rock layer in the upper crust of Tianshan fold zone is relatively 'soft', which makes it prone to rupture and stress energy release. This is the primary tectonic factor for the concentration of small earthquakes in this area. 3) Jiashi is located right over the apex or the inflection point of the updoming lower crustal interface C and the crust-mantle boundary, which is the deep struc-tural background for the occurrence of strong earthquakes. The alternate variation of vp/vs near the block bounda-ries and the complicated configuration of the interfaces in the upper and middie part of the upper crust form a par-ticular structural environment for the Jiashi strong earthquake swarm. vp/vs is comparatively high and shear modulus is low at the focal region, which may be the main reason for the low stress drop of the Jiashi strong earthquake swarm.
