The Use of High-Performance Fatigue Mechanics and the Extended Kalman/Particle Filters,for Diagnostics and Prognostics of Aircraft Structures

In this paper,we propose an approach for diagnostics and prognostics of damaged aircraft structures,by combing high-performance fatigue mechanics with filtering theories.Fast&accurate deterministic analyses of fatigue crack propagations are carried out,by using the Finite Element Alternating Method(FEAM)for computing SIFs,and by using the newly developed Moving Least Squares(MLS)law for computing fatigue crack growth rates.Such algorithms for simulating fatigue crack propagations are embedded in the computer program Safe-Flaw,which is called upon as a subroutine within the probabilistic framework of filter theories.Both the extended Kalman as well as particle filters are applied in this study,to obtain the statistically optimal and semi-optimal estimates of crack lengths,from a series of noisy measurements of crack-lengths over time.For the specific problem,a simple modification to the particle filter,which can drastically reduce the computational burden,is also proposed.Based on the results of such diagnostic analyses,the prognostics of aerospace structures are thereafter achieved,to estimate the probabilistic distribution of the remaining useful life.By using a simple example of a single-crack near a fastener hole,we demonstrate the concept and effectiveness of the proposed framework.This paper thus forms the scientific foundation for the recently proposed concepts of VRAMS(Virtual Risk-Informed Agile Maneuver Sustainment)and Digital Twins of aerospace vehicles.

Double Optimal Regularization Algorithms for Solving Ill-Posed Linear Problems under Large Noise

A double optimal solution of an n-dimensional system of linear equations Ax=b has been derived in an affine m-dimensional Krylov subspace with m <<n.We further develop a double optimal iterative algorithm(DOIA),with the descent direction z being solved from the residual equation Az=r0 by using its double optimal solution,to solve ill-posed linear problem under large noise.The DOIA is proven to be absolutely convergent step-by-step with the square residual error ||r||^2=||b-Ax||^2 being reduced by a positive quantity ||Azk||^2 at each iteration step,which is found to be better than those algorithms based on the minimization of the square residual error in an m-dimensional Krylov subspace.In order to tackle the ill-posed linear problem under a large noise,we also propose a novel double optimal regularization algorithm(DORA)to solve it,which is an improvement of the Tikhonov regularization method.Some numerical tests reveal the high performance of DOIA and DORA against large noise.These methods are of use in the ill-posed problems of structural health-monitoring.