Criteria of optimality for sensors' location based on adjoint transformation of observation data interpolation error

Abstract

SUMMARYCriteria of optimality for sensors' location are addressed using an interpolation error transformed by especial adjoint problems. The considered criteria correspond to the analysis error in certain Hessian-based metrics and to the error of some forecast aspect. Both criteria are obtained using adjoint problems that provide computation without the direct use of the Hessian. For a linear inverse heat conduction problem, these criteria are compared and demonstrated promising results when compared with a criterion based on the norm of the interpolation error of observation data. Approaches to sensor set modification using either redistribution of sensors' or refinement of the sensors grid (insertion of additional sensors) are also compared.

Real‐time updating of structural mechanics models using Kalman filtering, modified constitutive relation error, and proper generalized decomposition

“…According to sensor placement, identification results can be partially exact as for example with the configuration 2 where only the κ 1 value is correctly identified whereas there is no sensor in the corresponding area. In order to ensure an optimal sensor placement, different approaches can be used, for example, the approach based on observability Grammian , the method using the information entropy , or adjoint‐based approaches . Another way, that we will certainly explore in future works, is to use the spatial PGD modes to localize sensors which probably hold most of the information.…”

Efficient computation of operator‐type response sensitivities for uncertainty quantification and predictive modeling: illustrative application to a spent nuclear fuel dissolver model

“…As the expressions in Eqs. (15) through (27) indicate, the aforementioned predictive modeling methodology calibrates simultaneously all model parameters and responses, over all spatial locations and over the entire time interval from the start to the end of the transient physical phenomenon under consideration. Notably, these expressions generalize and significantly extend the "data adjustment" methods customarily used in nuclear engineering, as well as those underlying the 4D-VAR data assimilation procedures in the geophysical sciences (e.g., Lahoz et al [29], and Cacuci, Navon and Ionescu-Bujor [1]).…”

“…The sensitivities computed as discussed in the previous Section were used in Eqs. (15,(17)(18)(19)(20)(21)(22)(23)(24)(25)(26) to compute the optimally predicted nominal parameter values ("model calibration" along with the corresponding (reduced) predicted covariance matrices, as well as the optimally predicted nominal response values and the reduced predicted uncertainties in the responses. Thus, the optimally predicted "best-estimate" nominal values for the model parameters result from applying Eq.…”

“…and ocean sciences, particularly regarding data assimilation, a-posteriori pointwise error estimation for adaptive mesh modeling, proper orthogonal decomposition, and reduced order modeling. He has co-authored two books [1,2] and numerous peer-reviewed journal articles, a sample of which [2][3][4][5][6][7][8][9][10][11][12][13][14][15][16][17][18][19] is referenced herein. The common theme in his work has been the use of adjoint models, which have enabled the practical solution of large-scale problems by substantially reducing the amount of computational effort.…”

An ensemble method for sensor optimisation applied to falling liquid films

“…The deterministic methods , such as direct method, FSAP (Forward Sensitivity Analysis Procedure) and ASAP (Adjoint Sensitivity Analysis Procedure), involve differentiation of the system under investigation 65 and exactly computing the sensitivities; while the statistical methods, such as sampling based methods, variance based methods, and FAST (Fourier Amplitude Sensitivity Test), rely on multiple simulations to obtain statistically reliable results . By operating backward in time to describe the propagation of information, adjoint models can be used for sensitivity 70 analysis and adaptive observations (Errico, 1997;Palmer et al, 1998;Baker and Daley, 2000;Daescu and Navon, 2004;Alekseev and Navon, 2010;Godinez and Daescu, 2011). In our previous study, we presented an ensemble method to study the sensitivity (Che et al, 2013), which is simple to implement, and can be used for different target functions for various purposes.…”