scholarly journals Reliability Modeling and Estimation of the Gear System

2018 ◽  
Vol 2018 ◽  
pp. 1-9
Author(s):  
Enjun Bai ◽  
Liyang Xie ◽  
Hongyi Ma ◽  
Jungang Ren ◽  
Shijian Zhang
Keyword(s):  
Order Statistics ◽  
Least Square Method ◽  
Small Sample ◽  
Gear System ◽  
Least Square ◽  
Linear Regression Method ◽  
Reliability Model ◽  
Statistical Parameters ◽  
Reliability Modeling ◽  
Reliability Models

Traditional reliability models of the gear system either simplify the gear system unreasonably or are too complicated to be applicable for some gear systems. Therefore, a reliability model of the gear system considering statistically dependent failure based on the theory of the order statistics is developed in this paper. Firstly, the gear bending fatigue test of small sample is implemented to obtain the P-S-N curves that are fitted by using the least square method and the linear regression method of the statistical parameters under the test stress levels. Then, according to stress-strength interference theory and the theory of the order statistics, the reliability models considering the number of load cycles from a gear to gear system are built, which indicates clear modeling process of the gear system. Finally, the proposed reliability model of gear system is validated by using the Monte Carlo Simulation (MCS) and the system reliability under special load history is analyzed qualitatively.

scholarly journals Characteristics and Application of the NHPP Log-Logistic Reliability Model

2018 ◽  
Vol 8 (1) ◽  
pp. 44
Author(s):  
Lutfiah Ismail Al turk
Keyword(s):  
Evaluation Criteria ◽  
Real Data ◽  
Least Square ◽  
Estimation Methods ◽  
Data Sets ◽  
Reliability Model ◽  
Reliability Engineering ◽  
Reliability Models ◽  
Time Domain Data ◽  
Linear Least Square

In this paper, a Nonhomogeneous Poisson Process (NHPP) reliability model based on the two-parameter Log-Logistic (LL) distribution is considered. The essential model’s characteristics are derived and represented graphically. The parameters of the model are estimated by the Maximum Likelihood (ML) and Non-linear Least Square (NLS) estimation methods for the case of time domain data. An application to show the flexibility of the considered model are conducted based on five real data sets and using three evaluation criteria. We hope this model will help as an alternative model to other useful reliability models for describing real data in reliability engineering area.

scholarly journals Developing a Reliability Model of CNC System under Limited Sample Data Based on Multisource Information Fusion

2020 ◽  
Vol 2020 ◽  
pp. 1-10
Author(s):  
Chong Peng ◽  
Yuzhen Cai ◽  
Guangpeng Liu ◽  
T. W. Liao
Keyword(s):  
Information Fusion ◽  
Field Observation ◽  
Prior Information ◽  
Small Sample ◽  
Numerical Control ◽  
Observation Data ◽  
Reliability Model ◽  
Cnc System ◽  
Reliability Models ◽  
Field Observation Data

The reliability of the computer numerical control (CNC) system affects its processing performance and is a major concern in the manufacturing industry today. However, existing reliability models to assess the reliability of the CNC system often exhibit relatively large errors due to inadequate treatment of small samples. In order to get around the constraint of limited lifetime failure data and take full advantage of existing reliability parameters in traditional reliability models, a multisource information fusion-based reliability model grounded on Bayesian inference is proposed to deal with the small sample size. The prior distributions are derived by using the probability encoding method and conjugate distribution based on the idea of multisource information fusion. Then, using the Jensen–Shannon divergence (JSD) to measure the similarity between prior information and field observation data, a constrained optimization problem is established to determine the respective weight of prior information and field observation data. Finally, by conducting the reliability analysis of repairable CNC systems, the validity of the proposed model and its prior distribution derivation method are verified.

scholarly journals Determination of the Sediment Carrying Capacity Based on Perturbed Theory

2014 ◽  
Vol 2014 ◽  
pp. 1-10 ◽  
Author(s):  
Zhi-hui Ni ◽  
Qiang Zeng ◽  
Wu Li-chun
Keyword(s):  
Carrying Capacity ◽  
Influencing Factor ◽  
Least Square Method ◽  
Least Square ◽  
New Method ◽  
Linear Regression Method ◽  
Average Flow Velocity ◽  
New Formula ◽  
Sediment Carrying Capacity

According to the previous studies of sediment carrying capacity, a new method of sediment carrying capacity on perturbed theory was proposed. By taking into account the average water depth, average flow velocity, settling velocity, and other influencing factors and introducing the median grain size as one main influencing factor in deriving the new formula, we established a new sediment carrying capacity formula. The coefficients were determined by the principle of dimensional analysis, multiple linear regression method, and the least square method. After that, the new formula was verified through measuring data of natural rivers and flume tests and comparing the verified results calculated by Cao Formula, Zhang Formula, Li Formula, Engelung-Hansen Formula, Ackers-White Formula, and Yang Formula. According to the compared results, it can be seen that the new method is of high accuracy. It could be a useful reference for the determination of sediment carrying capacity.

Method for Determining the Reliable Life Parameter of Turbine Wheel of Turbocharger with Over-Speed Failure Mode

2012 ◽  
Vol 544 ◽  
pp. 251-255
Author(s):  
Zheng Wang ◽  
A Na Wang ◽  
Kai Guo ◽  
Li Zhuang ◽  
Lin Hua
Keyword(s):  
Failure Mode ◽  
Design Parameters ◽  
Series System ◽  
Reliability Model ◽  
Turbine Wheel ◽  
Reliability Modeling ◽  
Reliability Models ◽  
Modeling Process ◽  
Life Parameter ◽  
The Relationship

For the over-speed failure mode, the method for determining the reliable life parameter of turbine wheel of turbocharger is proposed in this paper. The shortage of design criteria based on conventional safety factor for turbine wheel with over-speed failure mode is analyzed. In order to embody the characteristics of structure and over-speed failure mode, the turbine wheel is taken as a series system consisting of several blade symmetrical components in the reliability modeling process. The time-reliability models of turbine wheel are derived and the relationship between the reliability and failure rate of turbine wheel and life parameter is studied. Then, the method for determining the reliable life parameter of turbine wheel of turbocharger with over-speed failure mode is proposed based on the reliability model and reliability curve. As long as the design parameters including the number of blades, speed, stress, and strength are given, the reliable life of turbine wheel of turbocharger with over-speed failure mode can be determined with the method proposed.

Researches on Lifetime Modeling of LED Luminaires

2014 ◽  
Vol 1061-1062 ◽  
pp. 662-665
Author(s):  
Hua Jing Li ◽  
Lei Nie ◽  
Fei Huang ◽  
Wen Jing Xiang
Keyword(s):  
Mathematical Reasoning ◽  
Great Influence ◽  
Least Square Method ◽  
Exponential Model ◽  
Least Square ◽  
Linear Regression Method ◽  
Testing Method ◽  
Accelerate Life Testing ◽  
Vibration Stress ◽  
Arrhenius Function

The temperature and vibration have great influence on the properties and materials of LED luminaires. Therefore, the bi-stress accelerate life testing method under temperature and vibration stress was designed and demonstrated. Based on the large amounts of experimentally obtained data and Arrhenius function, life models of LED luminaires were built rapidly by using mathematical reasoning (least square method and unary linear regression method). The results showed that the method we mentioned can sharply reduce the test life test and the life curve of LED luminaires obey to exponential model.

Functional Availability Modelling of CNC Machine Tools

2014 ◽  
Vol 915-916 ◽  
pp. 395-399 ◽  
Author(s):  
Xiao Bing Li ◽  
Jun Gao ◽  
Zheng Zhang ◽  
Xiao Cui Zhu
Keyword(s):  
Least Square Method ◽  
Smoothing Method ◽  
Least Square ◽  
Cnc Machine Tools ◽  
Linear Regression Method ◽  
Cnc Machine ◽  
Basis System ◽  
Functional Linear Regression ◽  
Availability Model ◽  
Fitting Parameters

A new method for calculating the instantaneous availability was proposed based on Functional Data Analysis method. It introduced the Quadratic Bernstein Polynomial into the smoothing method firstly for the reliability which estimated by median rank method and estimated the fitting parameters by least square method. Then, under the assumption that the maintenance difficult of the CNCs was decreasing over the work time, chosen the appropriate smoothing basis function based on the trend after the time section adjustment for the estimated maintainability value. The Fourier basis system and the non-linear least squares were selected for the maintainability function smoothing method and the fitting parameters. Finally, the instantaneous availability model of CNCs was built based on the functional linear regression method, and a case example of 15 CNCs was given.

scholarly journals Least Squares Consensus for Matching Local Features

Information ◽  
2019 ◽  
Vol 10 (9) ◽  
pp. 275
Author(s):  
Qingming Zhang ◽  
Buhai Shi ◽  
Haibo Xu
Keyword(s):  
Least Squares ◽  
Order Statistics ◽  
Random Sampling ◽  
Sampling Methods ◽  
Least Square Method ◽  
Least Square ◽  
Nearest Neighbour ◽  
Data Set ◽  
Alternative Scheme ◽  
New Approach

This paper presents a new approach to estimate the consensus in a data set. Under the framework of RANSAC, the perturbation on data has not been considered sufficiently. We analysis the computation of homography in RANSAC and find that the variance of its estimation monotonically decreases when the size of sample increases. From this result, we carry out an approach which can suppress the perturbation and estimate the consensus set simultaneously. Different from other consensus estimators based on random sampling methods, our approach builds on the least square method and the order statistics and therefore is an alternative scheme for consensus estimation. Combined with the nearest neighbour-based method, our approach reaches higher matching precision than the plain RANSAC and MSAC, which is shown in our simulations.

scholarly journals The Reliability Evaluation of Electromagnetic Valve of EMUs Based on Two-Parameter Exponential Distribution

2015 ◽  
Vol 9 (1) ◽  
pp. 630-636 ◽  
Author(s):  
Jianwei Yang ◽  
Chunqing Zhao ◽  
Xi Li ◽  
Fumin Wang
Keyword(s):  
Exponential Distribution ◽  
Small Sample Size ◽  
Least Square Method ◽  
Reliability Evaluation ◽  
Small Sample ◽  
Bayes Estimation ◽  
Least Square ◽  
Electromagnetic Valve ◽  
Reliability Parameters ◽  
Two Parameter

In order to solve reliability evaluation of life of electromagnetic valve of EMUs, this paper evaluated the life of electromagnetic valve under small sample size based on zero-failure data. Firstly, prior distribution of the failure probability was taken into consideration and then the posteriori distribution was obtained by using the Bayes method so that the Bayes estimation could be received under the square loss. Finally, according to the pi received, the reliability parameters of two-parameter exponential distribution were estimated based on weighted least square method. In addition, this paper applied the reliability theory to the reliability life evaluation of electromagnetic valve of EMUs which shows that this method can solve the reliability assessment problem providing certain theoretical basis for the reliability of electromagnetic valve.

scholarly journals Nonlinear regression analysis of length growth in cultured rainbow trout

2020 ◽  
Vol 72 (5) ◽  
pp. 1778-1788
Author(s):  
P.C. Janampa-Sarmiento ◽  
R. Takata ◽  
T.M. Freitas ◽  
M.M.B. Pereira ◽  
L. Sá-Freire ◽  
...  
Keyword(s):  
Rainbow Trout ◽  
Logistic Model ◽  
Performance Metrics ◽  
Model Performance ◽  
Least Square Method ◽  
Absolute Error ◽  
Small Sample ◽  
Least Square ◽  
Von Bertalanffy ◽  
Length Growth

ABSTRACT Length growth as a function of time has a non-linear relationship, so nonlinear equations are recommended to represent this kind of curve. We used six nonlinear models to calculate the length gain of rainbow trout (Oncorhynchus mykiss) during the final grow-out phase of 98 days under three different feed types in triplicate groups. We fitted the von Bertalanffy, Gompertz, Logistic, Brody, Power Function, and Exponential equations to individual length-at-age data of 900 fish. Equations were fitted to the data based on the least square method using the Marquardt iterative algorithm. Accuracy of the fitted models was evaluated using a model performance metrics combining mean squared residuals (MSR), mean absolute error (MAE) and Akaike's Information Criterion corrected for small sample sizes (AICc). All models converged in all cases tested. Evaluation criteria for the Logistic model indicated the best overall fit (0.67 of combined metric MSR, MAE and AICc) under all different feeding types, followed by the Exponential model (0.185), and the von Bertalanffy and Brody model (0.074, respectively). Additionally, ∆AICc results identify the Logistic and Gompertz models as being substantially supported by the data in 100% of cases. The logistic model can be suggested for length growth prediction in aquaculture of rainbow trout.

scholarly journals Reliability Analysis on Domestic Special CNC Machine Tools Based on Weibull Distribution

2021 ◽  
Vol 2101 (1) ◽  
pp. 012024
Author(s):  
Zhanghu Shi ◽  
Xi Zhao ◽  
Huang Zhang ◽  
Hailong Sun ◽  
Chao Zeng ◽  
...  
Keyword(s):  
Machine Tool ◽  
Model Building ◽  
Hypothesis Test ◽  
Least Square Method ◽  
Least Square ◽  
Test Method ◽  
Cnc Machine Tools ◽  
Model Parameters ◽  
Reliability Model ◽  
Cnc Machine

Abstract Mean time between failures (MTBF), regarded as an important target to evaluate the performance of machine tool, is widely applied in analysis of reliability, especially in reliability model building. Taking Huazhong CNC HNC-848C Complex Machine Tool as research object, this paper conducted censored test to collect MTBF data during a period of 226 days. Based on the data and presupposed Weibull reliability model. Parameters of the model were estimated by least square method. Graph test Method and Kolmogorov-Smirnov Method are implemented to perform the hypothesis test on obtained parameters, which provides evaluation on MTBF of complex machine tool with theoretical basis and data reference.

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