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.

scholarly journals Adaptive Kernel Density Estimation

2003 ◽  
Vol 3 (2) ◽  
pp. 148-156 ◽  
Author(s):  
Philippe Van Kerm
Keyword(s):  
Density Estimation ◽  
Kernel Density Estimation ◽  
Kernel Method ◽  
Kernel Density ◽  
Density Functions ◽  
Adaptive Kernel ◽  
Kernel Approach

This insert describes the module akdensity. akdensity extends the official kdensity that estimates density functions by the kernel method. The extensions are of two types: akdensity allows the use of an “adaptive kernel” approach with varying, rather than fixed, bandwidths; and akdensity estimates pointwise variability bands around the estimated density functions.

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 Modeling Diameter Distributions with Six Probability Density Functions in Pinus halepensis Mill. Plantations Using Low-Density Airborne Laser Scanning Data in Aragón (Northeast Spain)

2021 ◽  
Vol 13 (12) ◽  
pp. 2307
Author(s):  
J. Javier Gorgoso-Varela ◽  
Rafael Alonso Ponce ◽  
Francisco Rodríguez-Puerta
Keyword(s):  
Probability Density ◽  
Linear Models ◽  
Pinus Halepensis ◽  
Beta Function ◽  
Probability Density Functions ◽  
Lidar Data ◽  
Density Functions ◽  
Minimum Diameter ◽  
Location Parameters ◽  
Diameter Distributions

The diameter distributions of trees in 50 temporary sample plots (TSPs) established in Pinus halepensis Mill. stands were recovered from LiDAR metrics by using six probability density functions (PDFs): the Weibull (2P and 3P), Johnson’s SB, beta, generalized beta and gamma-2P functions. The parameters were recovered from the first and the second moments of the distributions (mean and variance, respectively) by using parameter recovery models (PRM). Linear models were used to predict both moments from LiDAR data. In recovering the functions, the location parameters of the distributions were predetermined as the minimum diameter inventoried, and scale parameters were established as the maximum diameters predicted from LiDAR metrics. The Kolmogorov–Smirnov (KS) statistic (Dn), number of acceptances by the KS test, the Cramér von Misses (W2) statistic, bias and mean square error (MSE) were used to evaluate the goodness of fits. The fits for the six recovered functions were compared with the fits to all measured data from 58 TSPs (LiDAR metrics could only be extracted from 50 of the plots). In the fitting phase, the location parameters were fixed at a suitable value determined according to the forestry literature (0.75·dmin). The linear models used to recover the two moments of the distributions and the maximum diameters determined from LiDAR data were accurate, with R2 values of 0.750, 0.724 and 0.873 for dg, dmed and dmax. Reasonable results were obtained with all six recovered functions. The goodness-of-fit statistics indicated that the beta function was the most accurate, followed by the generalized beta function. The Weibull-3P function provided the poorest fits and the Weibull-2P and Johnson’s SB also yielded poor fits to the data.

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