scholarly journals A time-dependent probabilistic fatigue analysis method considering stochastic loadings and strength degradation

2018 ◽  
Vol 10 (7) ◽  
pp. 168781401878556 ◽  
Author(s):  
Chunbo Su ◽  
Shui Yu ◽  
Zhonglai Wang ◽  
Zafar Tayyab
Keyword(s):  
Density Estimation ◽  
Failure Probability ◽  
Safety Margin ◽  
Estimation Method ◽  
Kernel Density ◽  
Strength Degradation ◽  
Probability Density Functions ◽  
Time Dependent ◽  
Density Functions ◽  
Dependent Failure

This article proposes two strategies for time-dependent probabilistic fatigue analysis considering stochastic loadings and strength degradation based on the failure transformation and multi-dimensional kernel density estimation method. The time-dependent safety margin function is first established to describe the limit state of the time-dependent failure probability for mechatronics equipment with stochastic loadings and strength degradation. Considering the effective safety margin points and the corresponding number of the load cycles, two strategies for transforming the time-dependent failure probability calculation to the static reliability calculation are then proposed. Multi-dimensional kernel density estimation method is finally employed to build the probability density functions and the reliability is estimated based on the probability density functions. An engineering case of a filtering gear reducer is presented to validate the effectiveness of the proposed methods both in computational efficiency and accuracy.

scholarly journals Log-Transform Kernel Density Estimation of Income Distribution

2016 ◽  
Vol 91 (1-2) ◽  
pp. 141-159 ◽  
Author(s):  
Arthur Charpentier ◽  
Emmanuel Flachaire
Keyword(s):  
Income Distribution ◽  
Density Estimation ◽  
Kernel Density Estimation ◽  
Kernel Density ◽  
Estimation Methods ◽  
Density Functions ◽  
Income Distributions ◽  
Heavy Tailed Distributions ◽  
Heavy Tailed ◽  
Positive Support

Standard kernel density estimation methods are very often used in practice to estimate density functions. It works well in numerous cases. However, it is known not to work so well with skewed, multimodal and heavy-tailed distributions. Such features are usual with income distributions, defined over the positive support. In this paper, we show that a preliminary logarithmic transformation of the data, combined with standard kernel density estimation methods, can provide a much better fit of the density estimation.

Nonholonomic Motion Planning Using Diffusion of Workspace Density Functions

2003 ◽  
Author(s):  
Yu Zhou ◽  
Gregory S. Chirikjian
Keyword(s):  
Planck Equation ◽  
Probability Density Functions ◽  
Time Dependent ◽  
Density Functions ◽  
Value Of Time ◽  
Nonholonomic Mobile Robots ◽  
Planning Algorithm ◽  
The Fourier Transform ◽  
Nonholonomic Motion Planning ◽  
Closed Form Approximation

This paper introduces a trajectory planning algorithm for nonholonomic mobile robots which operate in an environment with obstacles. An important feature of our approach is that the planning domain is the workspace of the mobile robot rather than its configuration space. The basic idea is to imagine the robot being subjected to Brownian motion forcing, and to generate evolving probability density functions (PDF) that describe all attainable positions and orientations of the robot at a given value of time. By planning a path that optimizes the value of this PDF at each instant in time, we generate a feasible trajectory. The PDF of robot pose can be constructed by solving the corresponding Fokker-Planck equation using the Fourier transform for SE(N). A closed-form approximation of the resulting time-dependent PDF is then used to plan a trajectory based on the observation that the evolution of this “workspace density” is a diffusion process. Examples are provided to illustrate the algorithm.

Effect of the geometrical size on time dependent failure probability of the solid oxide fuel cell

2019 ◽  
Vol 44 (21) ◽  
pp. 11033-11046 ◽  
Author(s):  
Yu-Cai Zhang ◽  
Min-Jie Lu ◽  
Wenchun Jiang ◽  
Shan-Tung Tu ◽  
Xian-Cheng Zhang
Keyword(s):  
Fuel Cell ◽  
Solid Oxide Fuel Cell ◽  
Failure Probability ◽  
Solid Oxide ◽  
Time Dependent ◽  
Oxide Fuel ◽  
Geometrical Size ◽  
Dependent Failure

scholarly journals A Multivariate Statistics-Based Approach for Detecting Diesel Engine Faults with Weak Signatures

Energies ◽  
2020 ◽  
Vol 13 (4) ◽  
pp. 873
Author(s):  
Jinxin Wang ◽  
Chi Zhang ◽  
Xiuzhen Ma ◽  
Zhongwei Wang ◽  
Yuandong Xu ◽  
...  
Keyword(s):  
Diesel Engine ◽  
Multivariate Statistics ◽  
Kernel Density ◽  
Principal Component ◽  
Probability Density Functions ◽  
Density Functions ◽  
Detection Approach ◽  
Marine Diesel ◽  
Adaptive Kernel ◽  
Control Limits

The problem of timely detecting the engine faults that make engine operating parameters exceed their control limits has been well-solved. However, in practice, a fault of a diesel engine can be present with weak signatures, with the parameters fluctuating within their control limits when the fault occurs. The weak signatures of engine faults bring considerable difficulties to the effective condition monitoring of diesel engines. In this paper, a multivariate statistics-based fault detection approach is proposed to monitor engine faults with weak signatures by taking the correlation of various parameters into consideration. This approach firstly uses principal component analysis (PCA) to project the engine observations into a principal component subspace (PCS) and a residual subspace (RS). Two statistics, i.e., Hotelling’s T 2 and Q statistics, are then introduced to detect deviations in the PCS and the RS, respectively. The Hotelling’s T 2 and Q statistics are constructed by taking the correlation of various parameters into consideration, so that faults with weak signatures can be effectively detected via these two statistics. In order to reasonably determine the control limits of the statistics, adaptive kernel density estimation (KDE) is utilized to estimate the probability density functions (PDFs) of Hotelling’s T 2 and Q statistics. The control limits are accordingly derived from the PDFs by giving a desired confidence level. The proposed approach is demonstrated by using a marine diesel engine. Experimental results show that the proposed approach can effectively detect engine faults with weak signatures.

Sign in / Sign up

Export Citation Format

Share Document