scholarly journals A Well-Designed Parameter Estimation Method for Lifetime Prediction of Deteriorating Systems with Both Smooth Degradation and Abrupt Damage

2015 ◽  
Vol 2015 ◽  
pp. 1-9
Author(s):  
Chuanqiang Yu ◽  
Cheng Jiang
Keyword(s):  
Parameter Estimation ◽  
Estimation Method ◽  
Prediction Method ◽  
Estimation Procedure ◽  
Cumulative Distribution ◽  
Lifetime Prediction ◽  
Unknown Parameters ◽  
Lifetime Distributions ◽  
Random Coefficient Regression ◽  
Deteriorating Systems

Deteriorating systems, which are subject to both continuous smooth degradation and additional abrupt damages due to a shock process, can be often encountered in engineering. Modeling the degradation evolution and predicting the lifetime of this kind of systems are both interesting and challenging in practice. In this paper, we model the degradation trajectory of the deteriorating system by a random coefficient regression (RCR) model with positive jumps, where the RCR part is used to model the continuous smooth degradation of the system and the jump part is used to characterize the abrupt damages due to random shocks. Based on a specified threshold level, the probability density function (PDF) and cumulative distribution function (CDF) of the lifetime can be derived analytically. The unknown parameters associated with the derived lifetime distributions can be estimated via a well-designed parameter estimation procedure on the basis of the available degradation recordings of the deteriorating systems. An illustrative example is finally provided to demonstrate the implementation and superiority of the newly proposed lifetime prediction method. The experimental results reveal that our proposed lifetime prediction method with the dedicated parameter estimation strategy can get more accurate lifetime predictions than the rival model in literature.

scholarly journals Parameter estimation in a Black Scholes

2018 ◽  
Vol 22 (Suppl. 1) ◽  
pp. 117-122
Author(s):  
Mustafa Bayram ◽  
Buyukoz Orucova ◽  
Tugcem Partal
Keyword(s):  
Parameter Estimation ◽  
Maximum Likelihood ◽  
Parametric Method ◽  
Estimation Method ◽  
Parametric Estimation ◽  
Likelihood Method ◽  
Observation Data ◽  
Unknown Parameters ◽  
Black Scholes ◽  
Non Parametric

In this paper we discuss parameter estimation in black scholes model. A non-parametric estimation method and well known maximum likelihood estimator are considered. Our aim is to estimate the unknown parameters for stochastic differential equation with discrete time observation data. In simulation study we compare the non-parametric method with maximum likelihood method using stochastic numerical scheme named with Euler Maruyama.

A Dynamic Material Parameter Estimation Procedure for Soft Tissue Using a Poroelastic Finite Element Model

1994 ◽  
Vol 116 (1) ◽  
pp. 19-29 ◽  
Author(s):  
J. P. Laible ◽  
D. Pflaster ◽  
B. R. Simon ◽  
M. H. Krag ◽  
M. Pope ◽  
...  
Keyword(s):  
Finite Element ◽  
Parameter Estimation ◽  
Finite Element Model ◽  
Three Dimensional ◽  
Estimation Method ◽  
Estimation Procedure ◽  
Element Model ◽  
Sequential Optimization ◽  
Displacement Control ◽  
Starting Values

A three-dimensional finite element model for a poroelastic medium has been coupled with a least squares parameter estimation method for the purpose of assessing material properties based on intradiscal displacement and reactive forces. Parameter optimization may be based on either load or displacement control experiments. In this paper we present the basis of the finite element model and the parameter estimation process. The method is then applied to a test problem and the computational behavior is discussed. Sequential optimization on different parameter groups was found to have superior convergence properties. Some guidelines for choosing the starting parameter values for optimization were deduced by considering the form of the objective function. For load control experiments, in which displacement data is used for the optimization, the starting values for the elastic modulus should be lower in magnitude than an “anticipated” modulus. The permeability starting values should be higher than an anticipated permeability. For displacement control experiments, the reverse is true. The optimization scheme was also tested on data with random variations.

scholarly journals The complementary Poisson-Lindley class of distributions

2015 ◽  
Vol 3 (2) ◽  
pp. 146 ◽  
Author(s):  
Amal Hassan ◽  
Salwa Assar ◽  
Kareem Ali
Keyword(s):  
Information Matrix ◽  
Real Data ◽  
Formal Proof ◽  
Cumulative Distribution ◽  
Likelihood Method ◽  
Unknown Parameters ◽  
Data Set ◽  
Lifetime Distributions ◽  
New Class ◽  
Rate Functions

<p>This paper proposed a new general class of continuous lifetime distributions, which is a complementary to the Poisson-Lindley family proposed by Asgharzadeh et al. [3]. The new class is derived by compounding the maximum of a random number of independent and identically continuous distributed random variables, and Poisson-Lindley distribution. Several properties of the proposed class are discussed, including a formal proof of probability density, cumulative distribution, and reliability and hazard rate functions. The unknown parameters are estimated by the maximum likelihood method and the Fisher’s information matrix elements are determined. Some sub-models of this class are investigated and studied in some details. Finally, a real data set is analyzed to illustrate the performance of new distributions.</p>

scholarly journals Multi-Parameter Estimation of Uncertain Systems Based on the Extended PID Control Method

2021 ◽  
Author(s):  
Jinping Feng ◽  
Wei Wang
Keyword(s):  
Complex System ◽  
Parameter Estimation ◽  
Convergence Analysis ◽  
Control Method ◽  
Estimation Method ◽  
Pid Controllers ◽  
Unknown Parameters ◽  
State Observation ◽  
New States ◽  
Nonlinear Pid Controller

Parameter estimation is an important step in the identification of systems. With the extension of systems, there needs the multi-parameter estimation of systems. The estimation of multi parameters of complex systems based on the extended PID controllers is considered in this chapter. As the related references proved that the integral item of the nonlinear PID controller could deal with the uncertain part of the complex system (which can also be called new stripping principle, simple notes as NSP). Based on this theory, new multi-parameter estimation method is given. Firstly, the unknown parameters are expanded to new states of the system. Two cases, parameters are constant or changing with time, are separately analyzed. In the time-variant case, the unknown parameters are extended to functions which actual forms are uncertain. Secondly the method NSP could be applied to cope with the uncertain part, and then reconstruction state observation to estimate the states. If the states are observed, the unknown parameters are obtained at the same time. Finally the convergence analysis of the error systems and some simulations will be given in this chapter to indicate the effectiveness of the proposed method.

An Inverse Problem for Parameter Estimation in a Bend Stiffener System

2018 ◽  
Author(s):  
Yangye He ◽  
Murilo Augusto Vaz ◽  
Marcelo Caire
Keyword(s):  
Inverse Problem ◽  
Parameter Estimation ◽  
Measurement Errors ◽  
Production Systems ◽  
Mathematical Formulation ◽  
Estimation Procedure ◽  
Flexible Pipe ◽  
Unknown Parameters ◽  
Maximum Curvature ◽  
Angle Measurements

The top connection of the flexible pipe attached to the platform supporting structure is considered to be a critical area as it sustains the highest forces and often the maximum curvature in the riser system. Bend stiffener, a polymeric structure with conical shape, is employed to limit the maximum curvature of the riser at the uppermost connection, and protect it against excessive bending and accumulative fatigue damage. In this work, an inverse problem methodology is proposed for estimating unknown parameters in the bend stiffener system, based on a large displacement beam theoretical model combined with the Levenberg-Marquardt Method. The global mathematical formulation is used for nonlinear analysis of the riser/bend stiffener system considering linear elastic symmetric material. A case study is given considering simulated angle measurements in five monitoring positions to estimate two unknown parameters in the system, top tension and polyurethane Young’s modulus. Monte Carlo method is employed to analyze the statistic properties of the estimated parameters with measurement errors. The effects of sensor locations and measurement error ranges on the accuracy of parameter estimation are investigated. It is shown that the proposed procedure can estimate efficiently and accurately unknown parameters in a bend stiffener system. The parameter estimation procedure can also be used to assess other mechanical parameters of the bend stiffener system by angle measurements in certain monitoring positions in realistic production systems.

A Study of Gearbox Residual Life Prediction Method Based on Stochastic Filtering and Recursive Expectation Maximization Model

2014 ◽  
Vol 1030-1032 ◽  
pp. 1133-1137
Author(s):  
Xin Liu ◽  
Yun Xian Jia ◽  
Jie Zhou
Keyword(s):  
Expectation Maximization ◽  
Life Prediction ◽  
Residual Life ◽  
Estimation Method ◽  
Prediction Method ◽  
Likelihood Estimation ◽  
Difficult Problem ◽  
Unknown Parameters ◽  
Stochastic Filtering ◽  
Residual Life Prediction

Residual life prediction is a critical and difficult problem in condition-based maintenance decision-making. Aiming to deal with the problems that practical data is limited and the estimation of initial parameters is not accurate in maintenance practice, a residual life prediction method for gearbox based on stochastic filtering (SF) is proposed. In this method, recursive expectation maximization (REM) algorithm is introduced to update the parameters, and a maximum likelihood estimation method is designed to update the unknown parameters. Finally, the validity and practicability of the model are validated by an example.

scholarly journals A modified truncated distribution for modeling the heavy tail, engineering and environmental sciences data

PLoS ONE ◽  
2021 ◽  
Vol 16 (4) ◽  
pp. e0249001
Author(s):  
Ahtasham Gul ◽  
Muhammad Mohsin ◽  
Muhammad Adil ◽  
Mansoor Ali
Keyword(s):  
Hazard Function ◽  
Real Life ◽  
Estimation Method ◽  
Likelihood Estimation ◽  
Cumulative Distribution ◽  
Statistical Characteristics ◽  
Model Parameters ◽  
Truncated Distribution ◽  
Unknown Parameters ◽  
Proposed Model

Truncated models are imperative to efficiently analyze the finite data that we observe in almost all the real life situations. In this paper, a new truncated distribution having four parameters named Weibull-Truncated Exponential Distribution (W-TEXPD) is developed. The proposed model can be used as an alternative to the Exponential, standard Weibull and shifted Gamma-Weibull and three parameter Weibull distributions. The statistical characteristics including cumulative distribution function, hazard function, cumulative hazard function, central moments, skewness, kurtosis, percentile and entropy of the proposed model are derived. The maximum likelihood estimation method is employed to evaluate the unknown parameters of the W-TEXPD. A simulation study is also carried out to assess the performance of the model parameters. The proposed probability distribution is fitted on five data sets from different fields to demonstrate its vast application. A comparison of the proposed model with some extant models is given to justify the performance of the W-TEXPD.

Dynamically Adjusting Diversity in Ensembles for the Classification of Data Streams with Concept Drift

2021 ◽  
Vol 16 (2) ◽  
pp. 1-30
Author(s):  
Juan I. G. Hidalgo ◽  
Silas G. T. C. Santos ◽  
Roberto S. M. Barros
Keyword(s):  
Parameter Estimation ◽  
Real World ◽  
Data Streams ◽  
Data Stream ◽  
Concept Drift ◽  
Estimation Method ◽  
Estimation Procedure ◽  
Dynamic Parameter ◽  
Real World Datasets ◽  
Concept Drifts

A data stream can be defined as a system that continually generates a lot of data over time. Today, processing data streams requires new demands and challenging tasks in the data mining and machine learning areas. Concept Drift is a problem commonly characterized as changes in the distribution of the data within a data stream. The implementation of new methods for dealing with data streams where concept drifts occur requires algorithms that can adapt to several scenarios to improve its performance in the different experimental situations where they are tested. This research proposes a strategy for dynamic parameter adjustment in the presence of concept drifts. Parameter Estimation Procedure (PEP) is a general method proposed for dynamically adjusting parameters which is applied to the diversity parameter (λ) of several classification ensembles commonly used in the area. To this end, the proposed estimation method (PEP) was used to create Boosting-like Online Learning Ensemble with Parameter Estimation (BOLE-PE), Online AdaBoost-based M1 with Parameter Estimation (OABM1-PE), and Oza and Russell’s Online Bagging with Parameter Estimation (OzaBag-PE), based on the existing ensembles BOLE, OABM1, and OzaBag, respectively. To validate them, experiments were performed with artificial and real-world datasets using Hoeffding Tree (HT) as base classifier. The accuracy results were statistically evaluated using a variation of the Friedman test and the Nemenyi post-hoc test. The experimental results showed that the application of the dynamic estimation in the diversity parameter (λ) produced good results in most scenarios, i.e., the modified methods have improved accuracy in the experiments with both artificial and real-world datasets.

THE REALIZATION OF THE ITERATIVE METHOD OF THE LEAST SQUARES FOR THE ESTIMATION OF STATIC OBJECT PARAMETERS IN MATLAB ENVIRONMENT

2017 ◽  
pp. 28-36
Author(s):  
Galina Vasil’evna Troshina ◽  
Alexander Aleksandrovich Voevoda
Keyword(s):  
Parameter Estimation ◽  
Iterative Method ◽  
Least Squares ◽  
Input Signal ◽  
Layer Structure ◽  
Estimation Procedure ◽  
Parameter Estimation Procedure ◽  
Noise Simulation ◽  
Static Object ◽  
Object Parameters

It was suggested to use the system model working in real time for an iterative method of the parameter estimation. It gives the chance to select a suitable input signal, and also to carry out the setup of the object parameters. The object modeling for a case when the system isn't affected by the measurement noises, and also for a case when an object is under the gaussian noise was executed in the MatLab environment. The superposition of two meanders with different periods and single amplitude is used as an input signal. The model represents the three-layer structure in the MatLab environment. On the most upper layer there are units corresponding to the simulation of an input signal, directly the object, the unit of the noise simulation and the unit for the parameter estimation. The second and the third layers correspond to the simulation of the iterative method of the least squares. The diagrams of the input and the output signals in the absence of noise and in the presence of noise are shown. The results of parameter estimation of a static object are given. According to the results of modeling, the algorithm works well even in the presence of significant measurement noise. To verify the correctness of the work of an algorithm the auxiliary computations have been performed and the diagrams of the gain behavior amount which is used in the parameter estimation procedure have been constructed. The entry conditions which are necessary for the work of an iterative method of the least squares are specified. The understanding of this algorithm functioning principles is a basis for its subsequent use for the parameter estimation of the multi-channel dynamic objects.

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