Army-Materiel-System-Analysis-Activity Maturity Projection Model Based on a Subsystem Stein Estimator

A reliability-growth test is often used to assess complex systems under development.Reliability-growth models are usually used to quantify the achievable reliability indices and predict the expected reliability values.The Crow army-materiel-system-analysis-activity(Crow-AMSAA)projection model and the AMSAA maturity projection(AMPM)-Stein model are suitable for modelling delayed corrective strategies.The AMPM-Stein model,which involves more failure data and requires limited assumptions,is more robust than the Crow-AMSAA projection model.However,the rationality of the Stein factor introduced in the AMPM-Stein model has always been controversial.An AMPM-Stein extended projection model,derived from data regrouping based on similar failure mechanisms,is presented to alleviate the problem.The study demonstrated that the proposed model performed well,the prediction results were credible,and the robustness of the proposed model was examined.Furthermore,the Stein-shrinkage factors,which are derived from components with similar inherent failure mechanisms,are easier to understand and accept in the field of engineering.An example shows that the proposed model is more suitable and accurate than the Crow-AMSAA model and the AMPM-Stein model,by comparing the projection values based on the failure data of the previous phases with the actual values of the current phases.This study provides a technical basis for extensive applications of the proposed model.

Degrees of freedom in low rank matrix estimation

The objective of this paper is to quantify the complexity of rank and nuclear norm constrained methods for low rank matrix estimation problems. Specifically, we derive analytic forms of the degrees of freedom for these types of estimators in several common settings. These results provide efficient ways of comparing different estimators and eliciting tuning parameters. Moreover, our analyses reveal new insights on the behavior of these low rank matrix estimators. These observations are of great theoretical and practical importance. In particular, they suggest that, contrary to conventional wisdom, for rank constrained estimators the total number of free parameters underestimates the degrees of freedom, whereas for nuclear norm penalization, it overestimates the degrees of freedom. In addition, when using most model selection criteria to choose the tuning parameter for nuclear norm penalization, it oftentimes suffices to entertain a finite number of candidates as opposed to a continuum of choices. Numerical examples are also presented to illustrate the practical implications of our results.

De-Noising Stochastic Noise in FOG Based on Second-Generation DB4 Wavelet and SURE-Threshold

An effective de-noising method for fiber optic gyroscopes （FOGs） is proposed. This method is based on second-generation Daubechies D4 （DB4） wavelet transform （WT） and level-dependent threshold estimator called Stein＇s unbiased risk estimator （SURE）. The whole approach consists of three critical parts： wavelet decomposition module, parameters estimation module and SURE de-noising module. First, DB4 wavelet is selected as lifting base of the second-generation wavelet in the decomposition module. Second, in the parameters estimation module, maximum likelihood estimation （MLE） is used for stochastic noise parameters estimation. Third, combined with soft threshold de-noising technique, the SURE de-noising module is designed. For comparison, both the traditional universal threshold wavelet and the second-generation Harr wavelet method are also investigated. The experiment results show that the computation cost is 40% less than that of the traditional wavelet method. The standard deviation of de-noised FOG signal is 0.012 and the three noise terms such as angle random walk, bias instability and quantization noise are reduced to 0.007 2°/√h, 0.004 1° / h, and 0.008 1°, respectively.