Line-of-sight tunable-diode-laser absorption spectroscopy（LOS-TDLAS） with multiple absorption lines is introduced for non-uniform temperature measurement. Temperature binning method combined with Gauss–Seidel itera...Line-of-sight tunable-diode-laser absorption spectroscopy（LOS-TDLAS） with multiple absorption lines is introduced for non-uniform temperature measurement. Temperature binning method combined with Gauss–Seidel iteration method is used to measure temperature probability distribution function（PDF） along the line-of-sight（LOS）. Through 100 simulated measurements, the variation of measurement accuracy is investigated with the number of absorption lines, the number of temperature bins and the magnitude of temperature non-uniformity. A field model with 2-T temperature distribution and15 well-selected absorption lines are used for the simulation study. The Gauss–Seidel iteration method is discussed for its reliability. The investigation result about the variation of measurement accuracy with the number of temperature bins is different from the previous research results.展开更多
Firstly,this paper proposes a generalized log-determinant optimization model with the purpose of estimating the high-dimensional sparse inverse covariance matrices.Under the normality assumption,the zero components in...Firstly,this paper proposes a generalized log-determinant optimization model with the purpose of estimating the high-dimensional sparse inverse covariance matrices.Under the normality assumption,the zero components in the inverse covariance matrices represent the conditional independence between pairs of variables given all the other variables.The generalized model considered in this study,because of the setting of the eigenvalue bounded constraints,covers a large number of existing estimators as special cases.Secondly,rather than directly tracking the challenging optimization problem,this paper uses a couple of alternating direction methods of multipliers(ADMM)to solve its dual model where 5 separable structures are contained.The first implemented algorithm is based on a single Gauss–Seidel iteration,but it does not necessarily converge theoretically.In contrast,the second algorithm employs the symmetric Gauss–Seidel(sGS)based ADMM which is equivalent to the 2-block iterative scheme from the latest sGS decomposition theorem.Finally,we do numerical simulations using the synthetic data and the real data set which show that both algorithms are very effective in estimating high-dimensional sparse inverse covariance matrix.展开更多
基金Project supported by the National Natural Science Foundation of China(Grant No.61108034)the Young Scientists Fund of the National Natural Science Foundation of China(Grant No.61205151)
文摘Line-of-sight tunable-diode-laser absorption spectroscopy（LOS-TDLAS） with multiple absorption lines is introduced for non-uniform temperature measurement. Temperature binning method combined with Gauss–Seidel iteration method is used to measure temperature probability distribution function（PDF） along the line-of-sight（LOS）. Through 100 simulated measurements, the variation of measurement accuracy is investigated with the number of absorption lines, the number of temperature bins and the magnitude of temperature non-uniformity. A field model with 2-T temperature distribution and15 well-selected absorption lines are used for the simulation study. The Gauss–Seidel iteration method is discussed for its reliability. The investigation result about the variation of measurement accuracy with the number of temperature bins is different from the previous research results.
基金the National Natural Science Foundation of China(No.11971149).
文摘Firstly,this paper proposes a generalized log-determinant optimization model with the purpose of estimating the high-dimensional sparse inverse covariance matrices.Under the normality assumption,the zero components in the inverse covariance matrices represent the conditional independence between pairs of variables given all the other variables.The generalized model considered in this study,because of the setting of the eigenvalue bounded constraints,covers a large number of existing estimators as special cases.Secondly,rather than directly tracking the challenging optimization problem,this paper uses a couple of alternating direction methods of multipliers(ADMM)to solve its dual model where 5 separable structures are contained.The first implemented algorithm is based on a single Gauss–Seidel iteration,but it does not necessarily converge theoretically.In contrast,the second algorithm employs the symmetric Gauss–Seidel(sGS)based ADMM which is equivalent to the 2-block iterative scheme from the latest sGS decomposition theorem.Finally,we do numerical simulations using the synthetic data and the real data set which show that both algorithms are very effective in estimating high-dimensional sparse inverse covariance matrix.
