Three-parameter Weibull Distribution Model Research Articles

Prediction of Remaining Fatigue Life of In-Service Bridge Cranes

At present, bridge crane accidents occur frequently, resulting in significant losses and casualties; to ensure the safe use of in-service bridge cranes, it is necessary to predict the residual fatigue life of in-service bridge cranes. Firstly, a static analysis of the most dangerous working conditions of in-service bridge cranes is carried out to find the fatigue failure point. Subsequently, a three-parameter Weibull distribution model is established for the characteristic parameters affecting the acquisition of the stress spectrum. Latin hypercubic sampling is applied to randomly sample the characteristic parameters to produce a random sample set of characteristic parameters for use in obtaining the stress–time history. The amplitude and mean values of the stress spectra are obtained by cycle counting using the rainflow counting method. Finally, Forman’s formula and Miner’s continuous damage accumulation theory were used to derive the remaining life prediction equations for constant and variable amplitude loads. Comparing the remaining life obtained from the simulation and test, the error is about 9.145%, which proves that the remaining life obtained from the simulation is more accurate. The results show that the combined method of simulation and testing is feasible and can predict the remaining life more accurately. In the past, the prediction of residual life was performed with either testing or simulation, which is long and costly. Simulation is low-cost and takes a short time, but the accuracy is not high. In this paper, the combination method of testing and simulation improves the efficiency of production and reduces the cost of use.

Research on parameter estimation methods of fatigue life distribution model of automotive chassis parts

The reliability assessment of fatigue life of automotive chassis parts is an important part of automobile safety. The fatigue endurance tests of automotive half-axles were carried out. The three-parameter Weibull distribution model was established according to the fatigue life distribution of samples. Using the right approximation method and the genetic algorithm to estimate three parameters of the distribution model and a comparative analysis was made. The results show that the initial life unreliability estimated by the median rank in the right approximation method had a large deviation from the true value, which may cause the iterative algorithm fall into the local optimal solution and affect the estimation accuracy. Therefore, a new parameter estimation method based on dual genetic algorithm was proposed. The newly proposed dual genetic algorithm not only improves the iteration speed, but also improves the accuracy of parameter estimation, which provides new ideas and theoretical basis for reliability assessment of mechanical components.

Fatigue properties and S-N curve estimating of 316L stainless steel prepared by SLM

This paper investigates the fatigue properties of 316L stainless steel manufactured by selective laser melting technology (SLM) under hot-isostatic-pressing (HIP) heat-treatment. The fatigue tests of 316L specimens were carried out under pulse tensile cyclic loading to obtain the fatigue performance. To avoid falling into local optima and improve the convergence speed, the dynamic multiswarm particle swarm optimizer (DMS-PSO) algorithm was first introduced for parameter optimization of the three-parameter Weibull distribution model, and then the S-N curves based on the model were obtained. The S-N curves were highly consistent with the metallographic and fractographic phenomena. Besides, both the S-N curves and fractographic analysis show that the resistance of high-stress fatigue fracture is significantly improved by using HIP heat-treatment.

Study on ECC compression fatigue under different constant lateral compression levels

The fatigue performance test was performed on ECC cubic specimens. Three lateral pressure levels and several stress ratios were considered as test variables. S-N curves for all tested specimens were established and a unified S-N equation was proposed for the specimens with biaxial fatigue load. The ECC exhibited a better fatigue performance compared to plain concrete and fiber reinforced concrete. Also, a three-parameter Weibull distribution model was used to calculate the P-S-N curve. Furthermore, the γ-P-S-N curves were obtained for all tested specimens. Finally, the stress–strain, peak deformation development law as well as secondary strain rate were evaluated.

Influence of wind energy utilization potential in urban suburbs: a case study of Hohhot

Given the increasing trend of using wind energy in cities, the utilization of distributed wind energy in cities has been widely concerned by researchers. The related research on the micro-site selection of wind turbines, a sub-project of the Task27 project of the International energy agency, was continued in this paper. The wind speed data of an observation station near Hohhot, Inner Mongolia, with a range of 10–19 m were collected. The evaluation included wind direction, Weibull parameter characteristics, and turbulence intensity. The potential energy output in 10 different heights was estimated using commercial horizontal and vertical axis wind turbines of the same power. Results showed that the following: the three-parameter Weibull distribution model can well describe the statistical properties of the wind speed in this site. The wind speed distribution model constructed from extrapolation parameters reflects the wind speed statistical properties out of detection positions to a certain extent. The wind energy density of the vertical axis wind turbine is slightly lower than that of the horizontal axis wind turbine. Furthermore, more power can be generated from March to May.

Preventive maintenance planning based on Weibull distribution models: The impact of the random scatter behaviour of the threshold parameter

The development of complex technical products also includes the planning of maintenance strategies and maintenance activities regarding the product use phase in field. The planning of maintenance packages within a preventive maintenance strategy is based on prototype testing data, expert knowledge and the statistical analyses of failure data of the previous product generation. The statistical analyses of a failure behaviour contains a statistical distribution model: The use of a three-parameter Weibull distribution model is common in reliability analytics. The Weibull parameters are threshold, scale and shape (hint regarding early failure period, random failure or operation time related failure). The parameter calculation can be done by state-of-the-art estimators (e.g. MLE). The problem is the random scatter range of the estimated parameters, which depends on the underlying data base. Therefore, calculation of parameters confidence interval respectively random dispersion range is obligatory. Especially the threshold parameter gives a hint regarding the upraising risk within a product fleet based on a certain failure behaviour. Consequently, the threshold parameter of a Weibull model, which describes an expected failure behaviour, is essential for the scheduling of maintenance packages regarding the subsequently following product generation to avoid an upcoming risk. This paper shows an empirical study regarding the random scatter behaviour and the characteristics of the threshold parameter and the impact on maintenance package planning within certain maintenance strategies. Furthermore the interdependences to the shape and characteristic life span parameters is worked out. The results of the empirical study are shown within an automotive case study.

Improved environmental contour methods based on an optimization of hybrid models

Estimation of the extreme values of ship and offshore platform responses such as bending moment and mooring tension is important in terms of structural design. Among several such methods, long-term and short-term analyses normally have been used in the industry. In general, long-term relative to short-term analysis is more precise but more time-consuming, because it takes into account all observed sea states. The environmental contour method, which performs a short-term analysis under a few important environmental conditions with an accuracy similar to that of long-term analysis, has been used as an alternative approach. There are several joint distribution models of significant wave height and peak period for environmental contour lines, but it is not known exactly which model most accurately represents actual environmental conditions. A marginal distribution of Hs and a conditional distribution of Tp, which generally are recommended in the rules and standards, have difficulties in drawing contour lines depending on the field. For the three-parameter Weibull distribution of Hs, a proper parameter estimation method should be selected among the several methods according to the observed data, and the distribution parameter of Tp has too little data to fit the given model. Another marginal distribution model is a bivariate lonowe (LOgNOrmal and WEibull) hybrid model of Hs with two distributions that allow for easy and unique estimation of parameters from any data [1]. The process of obtaining the distribution parameters from the existing hybrid model is clarified through the optimization process presented in this paper. And outlier technique is adopted to reduce the influence of some atypical data caused by small samples and, thereby, improve the accuracy of the Tp fitted result. The contour line through this proposed procedure predicts the extreme value similarly to the three-parameter Weibull distribution model, but it can be rather easily drawn. It is shown that the procedure proposed in this paper can be an effective method for drawing of environmental contour lines using any observed sea states.

Durability of air-entrained shotcrete exposed to cyclic freezing and thawing effect

In this study, the long-term performance of air-entrained shotcrete under cyclic freezing and thawing (F-T) is investigated and predicted. The dynamic modulus of elasticity and cohesive fracture energy of shotcrete at different F-T cycles are determined following ASTM C215 and RILEM TC 50-FMC, respectively. Both the test methods are found to be capable of examining material deterioration as a result of accumulative F-T damage; however, the fracture energy property tends to be more sensitive and degrades faster than the dynamic modulus of elasticity under the same number of F-T cycles. Probabilistic damage analysis is conducted to establish the relationship between the life (i.e., the number of F-T cycles in this study) and the damage parameter using the three-parameter Weibull distribution model. An exponential trend between the degradation of dynamic modulus of elasticity and the number of F-T cycles is observed at any given damage level. The failure rate of shotcrete increases as the number of F-T cycles increases, indicating that shotcrete exhibits more potential risk of failure and becomes less reliable when undergoing more F-T actions. The predicted results based on the polynomial probability model at 50% reliability level are consistent with the experimental results. Overall, the proposed probabilistic damage model is competent in evaluating freeze-thaw durability and predicting life of shotcrete.

Fatigue Failure Analysis on Precracked 304 Stainless Steel Components Repaired by Laser with Addition of Nanocomposites

Abstract The service life of components can be extended by repairing fatigue crack with laser so as to improve resource utilization rate. However, the effect of laser repair may be influenced by the instability of laser treatment. To investigate the addition of nanocomposites on the laser repairing effect, fatigue test under uniaxial tension was carried out to evaluate the fatigue life of precracked 304 stainless steel components repaired by laser. According to the results obtained from fatigue tests, a probabilistic fatigue life distribution model considered the sampling size and discreteness of data was established based on the three-parameter Weibull distribution model and three-parameter stress-life equation. The results of probabilistic fatigue life distribution model show that the fatigue life of components repaired by laser with addition of WC nanocomposites can be enhanced significantly, especially the high cycle fatigue life. Moreover, the microstructure of repaired region show that the WC nanoparticles could refine the recrystallized grains and lead to the improvement of strength and toughness of material around crack tip, which are the main reason of improved fatigue life. Meanwhile, smooth surface of repaired region caused by WC nanoparticles can also prevent the initiation of microcracks.

Rotating Bending Fatigue Microscopic Fracture Characteristics and Life Prediction of 7075-T7351 Al Alloy

Rotating bending fatigue tests were carried out by using the 7075-T7351 Al alloy with a microarc oxidation (MAO) coating (h = 10 μm) and with no coating. Tests were conducted in air and 5.0% NaCl aqueous solution conditions. The fatigue microscopic fracture behavior of the metals was investigated by using scanning electron microscope and three-dimensional digital microscope technologies. The empirical formulas between the stress intensity factor ΔK and the fatigue life Nf in the different conditions were obtained. In addition, the reason for data scattering in the fatigue lives of uncoated 7075-T7351 samples under the same stress amplitude in air was analyzed. Furthermore, the fatigue characteristic life of 7075-T7351 alloy was predicted by the three-parameter Weibull distribution model.

Probability Analysis of Wave Run-Ups and Air Gap Response of a Deepwater Semisubmersible Platform Using LH-Moments Estimation Method

The air gap response in harsh environments, a critical design issue for offshore platforms, is related to the wave run-ups attributable to wave-platform interactions and has the potential to result in serious wave impacts. Therefore, the reliable prediction of wave run-ups and air gap response in harsh environments is a challenging task and needs further study. In this study, probability analysis of the wave run-up data from an experimental study of a deepwater semisubmersible platform was conducted based on the three-parameter Weibull distribution model using the LH-moments method for parameter estimation. One of the highlights in the present study is that the explicit relationships between the first three LH-moments at arbitrary levels and the parameters of the Weibull distribution were established analytically. The accuracy of LH-kurtosis estimation was proposed to determine the appropriate level for probability analysis. The air gap response was found to be more serious in quartering and beam seas than in head seas. In front of the columns along the incoming-wave direction, especially the aft one, the wave run-ups showed higher probability distributions than did the other platform areas, leading to higher likeliness of suffering from negative air gap and wave impact accidents. At the platform center, the wave run-up was found to be significantly lower than the incident wave. This research shows that the probability distributions based on LH-moments at the appropriate level can well represent large wave run-ups, except for that beyond the still-water air gap, where both measurement methods and probability analyses warrant further research.

Three-parameter Weibull distribution model for tensile strength of GFRP bars based on experimental tests

Concrete structures with fibre-reinforced plastic bars can solve steel corrosion problems very effectively. At present, glass fibre-reinforced plastic bars are more widely used among fibre-reinforced plastic bars. Different from steel bars, glass fibre-reinforced plastic bars have no yield stage before fracture, which means concrete structures with glass fibre-reinforced plastic bars will not suffer ductile failure but only brittle failure without warning. Therefore, it is of particular importance to accurately obtain a standard value of the tensile strength of glass fibre-reinforced plastic bars. This paper carried out tensile tests of glass fibre-reinforced plastic bars with different diameters, measured the ultimate tensile strength and elasticity modulus of glass fibre-reinforced plastic bars, and conducted regression analyses. Based on the test results, a three-parameter Weibull probability distribution model was proposed, model parameters were fitted, and the results of the experimental tests were compared to that of the Weibull distribution model and the normal distribution model. At last, the relationship between the tensile strength and effective volume of glass fibre-reinforced plastic bars was discussed and a formula which can calculate the standard values of tensile strength of glass fibre-reinforced plastic bars with different diameters was obtained.

Probabilistic damage modeling and service-life prediction of concrete under freeze–thaw action

The long-term performance of concrete subjected to freezing and thawing damage is experimentally studied. The ASTM procedures for rapid freezing and thawing are followed to condition all the test samples. Dynamic modulus of elasticity and fracture energy for different numbers of freeze/thaw (F/T) cycles are measured through nondestructive modal and cohesive fracture tests, respectively. Nonlinear regression analysis is adopted to analyze the test data, and the relationship between the relative dynamic modulus and the number of F/T cycles is established. Based on the three-parameter Weibull distribution model, the probabilistic damage analysis is performed, from which the relationships between the number of F/T cycles and damage parameter for different probabilities of reliability are established. Based on the correlations between the available field environment and the indoor laboratory experiment, the field service-life of the considered structural concrete is predicted and validated with the fracture energy test data.

Statistical distribution of crankshaft fatigue: Experiment and modeling

Crankshaft fatigue problem has long been a headache and frequent phenomenon in combustion engine which attracts various efforts especially including fundamental fatigue experimental data. In this paper, the rational experimental method is employed to study the crankshaft fatigue phenomenon based on a customized experiment platform, mimicking the real-world crankshaft working condition physically. Then, based on the experiment data, the statistical regression analysis of eight commonly used hypothesis distributions is conducted. The degrees of fitting effects of the chosen statistical model are evaluated individually. Results show that the three-parameter Weibull distribution model fits the data best which may be used as the fundamental model in future analysis. This study provides a solid foundation for better understanding the mechanism of crankshaft fatigue phenomenon.

Cohesive fracture and probabilistic damage analysis of freezing–thawing degradation of concrete

The durability of concrete with low-degradation aggregates due to cyclic freezing and thawing effect is experimentally studied by characterizing the variance of fracture energy with respect to the number of freeze/thaw (F/T) cycles. Cohesive fracture test is conducted for notched concrete beams subjected to different F/T cycles, and the fictitious crack model-based approach is employed to calculate the fracture energy from the testing data. The relationship between the relative fracture energy and the number of F/T cycles is established using the nonlinear regression analyses. Based on the three-parameter Weibull distribution model, the probabilistic damage analysis is conducted, and the life distribution diagrams are produced according to the probability of reliability/survival concept. The relationships between the life (i.e., the number of F/T cycles) and damage parameter for different probabilities of reliability are obtained, from which the service life of concrete due to cyclic freezing and thawing actions can be determined at any given reliability index. The validation and accuracy of the present models are demonstrated through comparisons between the predicted data by the present models and the test data. The present probabilistic damage model can serve as a reference for maintenance, design and life prediction of concrete structures with low-degradation aggregates in cold regions subjected to cyclic freezing and thawing actions.

A Finite Mixture Three-Parameter Weibull Model for the Analysis of Wind Speed Data

This article presents a mixture three-parameter Weibull distribution to model wind speed data. The parameters are estimated by using maximum likelihood (ML) method in which the maximization problem is regarded as a nonlinear programming with only inequality constraints and is solved numerically by the interior-point method. By applying this model to four lattice-point wind speed sequences extracted from National Centers for Environmental Prediction (NCEP) reanalysis data, it is observed that the mixture three-parameter Weibull distribution model proposed in this paper provides a better fit than the existing Weibull models for the analysis of wind speed data under study.

Reliability Evaluation on Machining Center Based on Three-Parameter Weibull Distribution

In order to improve the model accuracy of reliability evaluation, the Three-Parameter Weibull Distribution model of time between fault was established by introducing location parameters. The correlation coefficient optimization method based on the adaptive genetic algorithm was firstly applied to estimate the location parameter of the Three-Parameter Weibull Distribution. Shape parameter and scale parameter were obtained by the least square method. The time between failures of these series machining center submitting to three-parameter weibull Distribution was checked by the test hypothesis of goodness-of-fit distribution. Finally, the machining center was carried out reliability evaluation based on the Three-Parameter Weibull Distribution model.

Development of TRIPLEX-Management model for simulating the response of forest growth to pre-commercial thinning

In order to simulate forest growth response to pre-commercial thinning (PCT), TRIPLEX1.0 – a process-based model designed to predict forest growth as well as carbon (C) and nitrogen (N) dynamics – was modified and improved to also simulate managed forest ecosystem thinning practices. A three-parameter Weibull distribution model was integrated to simulate thinning treatments within the newly developed TRIPLEX-Management model. The thinning intensity component within the model allows users to simulate thinning treatments by applying basal area, stand density and volume to quantify thinning intensity. Natural mortality decreased following thinning due to an increase in growing space for residual stems. Predicted litterfall pools also increased after thinning events took place. The TRIPLEX-Management model was tested against published observational data for Jack Pine ( Pinus banksiana Lamb.) stands subjected to PCT in Northwestern Ontario, Canada. The coefficients of determination ( R 2) between the predicted and observed variables including stand density, mean DBH (diameter at breast height), the quadratic mean DBH, total volume and merchantable volume as well as belowground, aboveground, and total biomass ranged from 0.50 to 0.88 ( n = 20, P < 0.001) with the exception of mean tree height ( R 2 = 0.25, n = 20, P < 0.05). Overall, the Willmott index of agreement between predicted and observed variables ranged from 0.97 to 1.00. Results show that the TRIPLEX-Management model is generally capable of simulating growth response to PCT for Jack Pine stands.

Temperature‐dependent developmental model of Neoseiulus californicus (McGregor) (Acari, Phytoseiidae)

AbstractThe developmental time and survival of immature stages of Neoseiulus californicus were studied at nine constant temperatures (12, 16, 24, 24, 28 32, 36, 38 and 40°C), 60–70% RH, and a photoperiod of 16 : 8 (L : D) h. The total mortality of immature N. californicus was lowest at 24°C (4.5%) and highest at 38°C (15.2%). The total developmental time decreased with increasing temperature between 12°C (18.38 days) and 32°C (2.98 days), and increased beyond 32°C. The relationship between the developmental rate and temperature was fitted by five nonlinear developmental rate models (Logan 6, Lactin 1, 2 and Briere 1, 2). The nonlinear shape of temperature development was best described by the Lactin 1 model (r2 = 0.98). The developmental variation of each stage was well described by the three‐parameter Weibull distribution model (r2 = 0.91–0.93). The temperature‐dependent developmental models of N. californicus developed in this study could be used to determine optimal temperature conditions for its mass rearing, to predict its seasonal population dynamics in fruit tree orchards or greenhouse crops, or to develop a population dynamics model of N. californicus.