Variance of a Nonstationary Random Process

2006 ◽  
Author(s):  
Lorenzo Galleani ◽  
Leon Cohen
Keyword(s):  
Random Process ◽  
Nonstationary Random Process

Information Theoretic Equivalent Bandwidths of Random Processes and Their Applications

2007 ◽  
Vol 46 (02) ◽  
pp. 110-116 ◽  
Author(s):  
S. Kikkawa ◽  
H. Yoshida
Keyword(s):  
Random Process ◽  
Random Processes ◽  
Systolic Murmur ◽  
Nonstationary Random Process ◽  
Frequency Distributions ◽  
Copula Theory ◽  
Information Theoretic ◽  
Time Frequency ◽  
New Class ◽  
Stationary Random Processes

Summary Objectives : Since most of the biomedical signals, such as electroencephalogram (EEG), electromyogram (EMG) and phonocardiogram (PCG), are nonstationary random processes, the time-frequency analysis has recently been extensively applied to those signals in order to achieve precise characterization and classification. In this paper, we have first defined a new class of information theoretic equivalent bandwidths (EBWs) of stationary random processes, then instantaneous EBWs (IEBWs) using nonnegative time-frequenc distributions have been defined in order to track the change of the EBW of a nonstationary random process. Methods : The new class of EBWs which includes spectral flatness measure (SFM) for stationary random processes is defined by using generalized Burg entropy. Generalized Burg entropy is derived from the relation between Rényi entropy and Rényi information divergence of order α. In order to track the change of EBWs of a nonstationary random process, the IEBWs are defined on the nonnegative time-frequency distributions, which are constructed by the Copula theory. Results : We evaluate the IEBWs for a first order stationary auto-regressive (AR) process and three types of time-varying AR processes. The results show that the IEBWs proposed here properly represent a signal bandwidth. In practical application to PCGs, the proposed method was successful in extracting the information that the bandwidth of the innocent systolic murmur was much smaller than that of the abnormal systolic murmur. Conclusions : We have defined new information theoretic EBWs and have proposed a novel method to track the change of the IEBWs. Some computer simulation showed effectiveness of the methods. Applying the IEBWs to PCGs, we could extract some features of a systolic murmur.

scholarly journals Wear reliability of spur gear based on the cross-analysis method of a nonstationary random process

2018 ◽  
Vol 10 (12) ◽  
pp. 168781401881929 ◽  
Author(s):  
Zhe Yuan ◽  
Yuhou Wu ◽  
Ke Zhang ◽  
Mircea-Viorel Dragoi ◽  
Minghe Liu
Keyword(s):  
Random Process ◽  
Estimation Method ◽  
Tooth Wear ◽  
Spur Gear ◽  
Reliability Estimation ◽  
Tooth Surface ◽  
Time Varying ◽  
Reliability Model ◽  
Analysis Method ◽  
Nonstationary Random Process

Tooth wear is one of the main reasons that lead to gear failure. The amount of wear is nonlinearly related to temperature, lubrication, load, and various random factors of materials, with obvious randomness and slow time-varying characteristics. Wear is a nonstationary random process, which has no accurate mathematical model or accurate reliability estimation method. This article proposes a reliability model of spur gears which works under a nonstationary random process that exceeds the limit, and the time-varying wear reliability is studied based on the level crossing analysis method. The wear at tooth root is revised in the calculation under the nonstationary random process, and the reliability curves are obtained afterwards. An experiment is carried out on the spur gear meshing test rig, and the reliability model and wear performance are verified and analyzed. Results obtained with the proposed tooth surface wear reliability model match well with the experimental results. Therefore, this model is applicable for situations under a nonstationary random process. The new method makes contribution to the assessment of gear running status and is of great significance in the prediction of wear life under a nonstationary random process.

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