Three-parameter Weibull Function Research Articles

Constitutive model of viscoelastic dynamic damage for the material of gas obturator in modular-charge howitzer

In order to investigate the mechanical response behavior of the gas obturator of the breech mechanism, made of polychloroprene rubber (PCR), uniaxial compression experiments were carried out by using a universal testing machine and a split Hopkinson pressure bar (SHPB), obtaining stress-strain responses at different temperatures and strain rates. The results revealed that, in comparison to other polymers, the gas obturator material exhibited inconspicuous strain softening and hardening effects; meanwhile, the mechanical response was more affected by the strain rate than by temperature. Subsequently, a succinct viscoelastic damage constitutive model was developed based on the ZWT model, including ten undetermined parameters, formulated with incorporating three parallel components to capture the viscoelastic response at high strain rate and further enhanced by integrating a three-parameter Weibull function to describe the damage. Compared to the ZWT model, the modified model could effectively describe the mechanical response behavior of the gas obturator material at high strain rates. This research laid a theoretical foundation for further investigation into the influence of chamber sealing issues on artillery firing.

A life testing system design and life prediction for plant lighting LED-based luminaires

With the increasing demand for plant lighting LED-based luminaires, the reliability is facing a severe test, and the collection and the research of their life information is imminent. Firstly, the life testing system of plant lighting LED-based luminaires is constructed independently by conducting the preliminary tests of samples. Secondly, the test steps are designed to collect the luminance attenuation data of samples. Finally, the data pretreatment scheme is proposed to optimize the test data under conventional stress, and the life prediction is achieved by three-parameter Weibull right approximation method (TPWRAM). The results indicate that the collected test data well reflect the luminance attenuation characteristics of plant lighting LED-based luminaires, and the developed life test system has higher feasibility. The self-designed data preprocessing scheme is scientific and reasonable, and the processed test data objectively describe the luminance attenuation trend. In addition, the most important thing is that three-parameter Weibull function fits well with test data, which can accurately predict the normal life of plant lighting LED-based luminaires. The above results can provide technical reference for engineers to improve the performance of plant lighting LED-based luminaire.

Обобщенная модель распределения диаметров деревьев в сосновых древостоях

A generalized statistical model for the distribution of tree diameters for pine forest plantations, developed on the basis of a three-parameter Weibull function, is presented. Its parameters were restored using data from 231 distribution series on 24 permanent sample plots in the Forest Experimental Station of the Russian State Agrarian University — Moscow Timiryazev Agricultural Academy from the first and second central moments of the distribution. It is shown that their estimates can be obtained from the equations of connection with the root-mean-square diameter of trunks in a forest stand. It was revealed that the developed model approximates with high accuracy the actual distributions of tree diameters in maturing, middle-aged and mature forest stands, and in young stands there may be deviations between the actual and predicted frequency values. It is shown that the main purpose of the developed model is to predict the distribution of diameters of tree trunks in future ages of forest stands to optimize the management of forest plantations.

Viscosity Approximation of PDMS Using Weibull Function.

The viscosity of a fluid is one of its basic physico-chemical properties. The modelling of this property as a function of temperature has been the subject of intensive studies. The knowledge of how viscosity and temperature variation are related is particularly important for applications that use the intrinsic friction of fluids to dissipate energy, for example viscous torsional vibration dampers using high viscosity poly(dimethylsiloxane) as a damping factor. This article presents a new method for approximating the dynamic viscosity of poly(dimethylsiloxane). It is based on the three-parameter Weibull function that far better reflects the relationship between viscosity and temperature compared with the models used so far. Accurate mapping of dynamic viscosity is vitally important from the point of view of the construction of viscous dampers, as it allows for accurate estimation of their efficiency in the energy dissipation process.

A Blind Spot in the Use of the Weibull Function for Modeling Diameter Distributions

Abstract Diameter distribution models based on probability density functions are integral to many forest growth and yield systems, where they are used to estimate product volumes within diameter classes. The three-parameter Weibull function with a constrained nonnegative lower bound is commonly used because of its flexibility and ease of fitting. This study compared Weibull and reverse Weibull functions with and without a lower bound constraint and left-hand truncation, across three large unthinned plantation cohorts in which 81% of plots had negatively skewed diameter distributions. Near-optimal lower bounds for the unconstrained Weibull function were negative for negatively skewed data, and the left-truncated Weibull using these bounds was 14.2% more accurate than the constrained Weibull, based on the Kolmogorov-Smirnov statistic. The truncated reverse Weibull fit dominant tree distributions 23.7% more accurately than the constrained Weibull, based on a mean absolute difference statistic. This work indicates that a blind spot may have developed in plantation growth modeling systems deploying constrained Weibull functions, and that left-truncation of unconstrained functions could substantially improve model accuracy for negatively skewed distributions.

Configuration strategy of shared mitigation equipment for voltage sag considering the demands of users

It is an effective way to mitigate voltage sag by equipping custom power devices in premium power park (PPP), and the key lies in the balance between technology and economy. This study proposes a method to mitigate voltage sags to meet the needs of different sensitive users in PPP to ensure the mitigation effect and reduce mitigation costs. Firstly, a strategy of shared mitigation equipment (ME) and its operation mode is presented, including the multiple stakeholders, the structure of shared ME, and the scheme of the switch on/off to improve the utilisation rate of ME. Secondly, a sensitive equipment (SE) grouping method is proposed, which is suitable for shared ME strategy, considering the minimum compensation voltage magnitude and the economic loss caused by voltage sag. Meanwhile, this study proposes an assessment method of SE failure probability based on the three-parameter Weibull function to design the capacity of ME reasonably. Thirdly, a multi-objective collaborative optimisation model is established based on economic loss assessment to maximise the net income of investors and users. Finally, the effectiveness of the proposed method has been proved through the case study of two sensitive users in PPP.

Modeling the emergence of North African knapweed (Centaurea diluta), an increasingly troublesome weed in Spain

AbstractNorth African knapweed (Centaurea diluta Aiton) is an annual weed that is widespread in southern Spain and is of increasing concern in dryland cropping systems. Despite its expanding range in Spain, there is limited information on the emergence timing and pattern of this species, knowledge of which is critical for developing more timely and effective management strategies. Therefore, there is a need to develop simple and reliable models to predict the timing and emergence of this annual weed under dryland conditions. A multi-location field experiment was established across Spain in 2016 to 2017 to assess the emergence of C. diluta. At each of 11 locations, seeds were sown in the fall, and emergence was recorded. Overall emergence averaged 39% in the first year across all sites and 11% in the second year. In both years, the main emergence flush occurred at the beginning of the growing season. A three-parameter Weibull function best described seedling emergence of C. diluta. Emergence models were developed based on thermal time (TT) and hydrothermal time (HTT) and showed high predictability, as evidenced by root mean-square error prediction values of 10.8 and 10.7, respectively. Three cardinal points were established for TT and HHT at 0.5, 10, and 35 C for base, optimal, and ceiling temperatures, respectively, while base water potential was estimated at −0.5 MPa.

Long-term effects of salvage logging on stand composition in seminatural spruce forests

The tree diameter distribution was used to characterize the impact of forest disturbances and the ecosystem dynamics during the process of regeneration in the absence of any management 44 years after the event. In addition, the impact of salvage logging after windthrow remains unknown, especially on long-term responses. In this study, comparisons were made between the “unsalvaged” and “salvaged” post-storm management scenarios. The study was conducted in Slitere Natural Park in the Northwest part of Latvia, where large-scale windthrow occurred on November 2, 1969. The three-parameter Weibull function was used to describe the diameter distribution of Norway spruce (Picea abies (L.) Karst.) stands formed after large-scale wind storm in two site types (on fertile mineral soils: with normal moisture regime (fresh)—Oxalidosa—and with periodic excess water (wet)—Myrtilloso-sphagnosa) and where salvage logging was or was not carried out (management scenarios). The naturally regenerated stands remained Norway spruce dominated and were independent of the post-storm management scenarios; still, they were significantly affected by a forest type. The three-parameter Weibull distribution function suited well to actual diameter distributions of the sample plots. Diameter distributions significantly differed between the forest types: In Myrtilloso-sphagnosa (wet) forest stands, it was a negative exponential and in Oxalidosa (fresh) stands unimodal and positively skewed. We did not detect distribution differences caused by salvage after a large-scale disturbance, indicating that other factors (like ecological importance of deadwood, a risk of insect outbreaks to neighboring areas, etc.) need to be considered, when deciding on the post-storm management.

Dynamics of the diameter distribution after selection cutting in uneven- and even-aged northern hardwood stands: a long-term evaluation

Selection cutting is defined as a tool for uneven-aged silviculture. Dependence on diameter distribution by forestry practitioners for identifying stand conditions has led to misuse of selection-like cuttings in even-aged northern hardwood stands. Our study used several long-term data sets to investigate the temporal stability in numbers of trees per diameter class in uneven-aged northern hardwood stands treated with single-tree selection and in 45-year-old second-growth stands treated with selection-like cuttings. We analyzed data from New York, Michigan, and Wisconsin to determine changes through time in number of trees across 2.5 cm diameter classes, shifts in the shape and scale of the three-parameter Weibull function used to describe the diameter distributions, and dynamics of associated stand attributes. Findings showed that single-tree selection cutting created and sustained stable diameter distributions and uniformity of conditions through consecutive entries in uneven-aged stands. By contrast, these characteristics varied through time in the second-growth stands that had been treated with selection-like cuttings. Analysis also showed that the Weibull shape and scale parameters for stands under selection system migrated towards those of the recommended target diameter distribution in the uneven-aged stands. These parameters diverged from the target with repeated use of selection-like cuttings in the second-growth even-aged stands.

Dynamics of Eucalyptus Diameter Distribution in the State of Minas Gerais

ABSTRACT The aim of this study was to evaluate the effects of age, site, and density factors on the dynamics of eucalyptus diameter distribution. Data were obtained from a continuous forest inventory measured at different occasions, stratified according to the factors evaluated and adjusted by the three-parameter Weibull function using nonthinned clonal plots of eucalyptus stands located in the Central region of the state of Minas Gerais. In order to evaluate the diameter distribution behavior, asymmetry and kurtosis measures and graphical analysis for fitted curves were used. In general, an increase was observed in diameter amplitudes with aging, as well as with improvement of site productivity and higher densities. The number of trees decreased in the lower classes and increased in the upper classes, resulting in diameter distribution curves, being displaced to the right and flattened with aging.

Fatigue Deformation Model of Plain and Fiber-Reinforced Concrete Based on Weibull Function

AbstractA novel model based on the three-parameter Weibull function is proposed to describe the three-stage fatigue deformation behavior of plain and fiber-reinforced concrete. The fatigue strain a...

Біометричні ознаки таксаційної будови за діаметром ялицевих деревостанів Закарпаття

Проаналізовано літературні джерела з проблематики дослідження таксаційної будови насаджень в Україні та за її межами. Розглянуто питання, пов'язані з дослідженням біометричних ознак будови ялицевих деревостанів Закарпаття за діаметром у різних вікових групах. На підставі аналізу матеріалів 119 кругових пробних площ на території Закарпатського обласного управління лісового та мисливського господарства наведено аналіз біометричних ознак (середнього значення, основного відхилення, коефіцієнтів варіації, точності досліду, асиметрії та ексцесу) рядів розподілу дерев ялиці білої за діаметром та розподілу дерев за природними ступенями товщини у зв'язку з віковою зміною середніх діаметрів. З'ясовано, що серед усіх функцій, які використано у цих дослідженнях, найточніше будову ялицевих деревостанів за діаметром моделює функція Вейбулла. Здійснено перевірку узгодженості фактичних і теоретичних чисельностей за критерієм згоди Пірсона. За допомогою функції Вейбулла визначено теоретичні чисельності за ступенями товщини. На основі трипараметричної функції Вейбулла опрацьовано математичну модель рядів розподілу дерев за діаметром та віковими групами. Встановлено, що для будови ялицевих деревостанів Закарпаття за ступенями товщини характерне значне варіювання їхніх біометричних показників. Внаслідок виконаних досліджень побудовано узагальнені ряди розподілу дерев за діаметром, що є основою для подальшого розроблення нормативів товарної структури деревостанів.

Is a three-parameter Weibull function really necessary for the characterization of the statistical variation of the strength of brittle ceramics?

Systematic Monte Carlo simulations were performed in the present study to examine the effectiveness of two-parameter Weibull function in the characterization of the strength variation and fracture reliability of a material whose strength follows a three-parameter Weibull distribution. It was shown that two-parameter Weibull function is sufficiently suitable for the description of the statistical variation of the conventionally adopted small strength sample, regardless of whether the strength follows a two-parameter or a three-parameter Weibull distribution. Furthermore, for a material whose strength follows a three-parameter Weibull distribution, accurate determinations of the fracture stress corresponding to a given fracture probability may be obtained based on two-parameter Weibull analysis. Therefore, it is concluded that three-parameter Weibull function is not necessary for the analysis of the statistical variation of the fracture strength of brittle ceramics.

Effect of temperature on longevity and fecundity of Phyllonorycter ringoniella (Lepidoptera: Gracillariidae) and its oviposition model

Asiatic apple leafminer, Phyllonorycter ringoniella, is an important insect pest in apple orchards. However, information on its temperature-dependent reproductive behavior and oviposition model is lacking. The longevity and fecundity of P. ringoniella were investigated at seven constant temperatures (13.7, 15.6, 20.5, 23.7, 26.1, 30.2, and 32.3°C), 60–80% RH, and a photoperiod of 14:10 (L:D) h. The longevity and fecundity of P. ringoniella were significantly influenced by temperature. Female adult longevity ranged from 6.3days at 32.3°C to 18.3days at 15.6°C. The fecundity ranged from 9.9 eggs at 32.3°C to 65.2 eggs at 15.6°C. The preoviposition (1.5–4.1days) and oviposition (1.8–12.6days) periods were significantly affected by temperature, while the postoviposition (1.2–2.2days) period was not. Female adult aging rates (1/mean longevity) were well described by an inverse second-order polynomial function (r2=0.98), which was used to calculate the physiological ages of female adults. The oviposition model of P. ringoniella comprised four components: adult aging rate model, total fecundity model, age-specific oviposition rate model, and age-specific survival rate model. The relationship between mean total fecundity and temperature was well described by an extreme value function (r2=0.95). Age-specific cumulative oviposition rate was well fitted to a three-parameter Weibull function (r2=0.98) and age-specific survival rate to a sigmoid function (r2=0.99), respectively. The model would be useful in predicting egg occurrence of P. ringoniella and establishing a management strategy against P. ringoniella in apple orchards.

Bursa-Kestel Ormanlarında Çap Dağılımlarının Weibull Fonksiyonu ile Modellenmesi

Detailed data about forest stands are needed for economic and silvicultural interpretation of forest enterprises for a long time. Diameter distribution models (DDMs) allow to predict number of trees, basal area and stand volume at level of diameter classes. So, both effects of silvicultural treatments on forest stands and economic analysis of forest enterprise can be made with more details. In this study, diameter distributions were predicted by three-parameter Weibull function. The parameters of the Weibull function were predicted by maximum likelihood and percentile-based methods. According to the comparison based on Reynold’s error index, the method based on 31 th and 63 rd percentiles with an average success order of 2.61 was assessed as the most successful in prediction of parameters of the Weibull function. The eligible of the predicted distribution by the most successful method for the observed distribution was tested by Kolmogorov-Simirnov analyze, and the results showed that the Weibull function was suitable for 305 of total 312 sample plots.

A Model to Explain Temperature Dependent Systemic Infection of Potato Plants by Potato virus Y

The effect of temperature on the rate of systemic infection of potatoes (Solanum tuberosum L. cv. Chu-Baek) by Potato virus Y (PVY) was studied in growth chambers. Systemic infection of PVY was observed only within the temperature range of 16°C to 32°C. Within this temperature range, the time required for a plant to become infected systemically decreased from 14 days at 20°C to 5.7 days at 28°C. The estimated lower thermal threshold was 15.6°C and the thermal constant was 65.6 degree days. A systemic infection model was constructed based on experimental data, using the infection rate (Lactin-2 model) and the infection distribution (three-parameter Weibull function) models, which accurately described the completion rate curves to systemic infection and the cumulative distributions obtained in the PVY-potato system, respectively. Therefore, this model was useful to predict the progress of systemic infections by PVY in potato plants, and to construct the epidemic models.

Re-evaluation of individual diameter : height allometric models to improve biomass estimation of tropical trees.

Accurate estimation of tree biomass is necessary to provide realistic values of the carbon stored in the terrestrial biosphere. A recognized source of errors in tree aboveground biomass (AGB) estimation is introduced when individual tree height values (H) are not directly measured but estimated from diameter at breast height (DBH) using allometric equations. In this paper, we evaluate the performance of 12 alternative DBH : H equations and compare their effects on AGB estimation for three tropical forests that occur in contrasting climatic and altitudinal zones. We found that fitting a three-parameter Weibull function using data collected locally generated the lowest errors and bias in H estimation, and that equations fitted to these data were more accurate than equations with parameters derived from the literature. For computing AGB, the introduced error values differed notably among DBH : H allometric equations, and in most cases showed a clear bias that resulted in either over- or under-estimation of AGB. Fitting the three-parameter Weibull function minimized errors in AGB estimates in our study and we recommend its widespread adoption for carbon stock estimation. We conclude that many previous studies are likely to present biased estimates of AGB due to the method of H estimation.

Discussion of “Compressibility Behavior of Soils: A Statistical Approach” by Syed Iftekhar Ahmed and Sumi Siddiqua [Geotechnical and Geological Engineering, doi: 10.1007/s10706-016-9996-7

Ahmed and Siddiqua (2016) introduced a new regression-based relationship in the form of a three-parameter Weibull function, herein referred to as the 3P-W model, for modeling the compressibility behavior (i.e. the void ratio-effective stress relationship) of soils. In this discussion, important drawbacks associated with the newly proposed 3P-W model were outlined. In addition, an attempt was made to extend the practicality of the proposed model by introducing a simple analytical solution to derive regression-based equations for determining the compressibility curve variables (i.e. the recompression index, pre-consolidation pressure and compression index). The proposed analytical concept is primarily intended to replace the current conventional graphical method by providing consistent-error free results. The proposed equations in this discussion accompanied by the original 3P-W model construct a unique regression aided-analytical framework which can be employed for advance numerical simulations.

Effect of Temperature on the Fecundity and Longevity of Ascotis selenaria (Lepidoptera: Geometridae): Developing an Oviposition Model.

The fecundity and longevity of Ascotis selenaria (Denis & Schiffermüller 1775) female adults were examined at constant temperatures ranging from 13-35°C. Adult longevity decreased as the temperature increased and ranged from 26.2 d at 13.1°C to 5.2 d at 34.3°C. The maximum observed fecundity of A. selenaria was 2,420 eggs per female at 19.4°C, which decreased to ca 100 eggs per female at 34.3°C. Female adult aging rates (one per median longevity) were well described by a sigmoid equation in the range of 13-35°C used to calculate the physiological age of adults. The relationship between total fecundity and temperature was well described by an extreme value function. Age-specific cumulative oviposition rate and age-specific survival rate curve were fitted to a three-parameter Weibull function. An oviposition model for A. selenaria was developed using the estimated three temperature-dependent submodels: total fecundity, age-specific cumulative oviposition, and age-specific survival rate models. The oviposition model was simulated using pheromone catches of A. selenaria females as input value. Simulated egg populations were subjected to egg stage emergence model to project first-instar populations. Overall, the output of our simulation described the field occurrence pattern of A. selenaria first-instar populations in 2009 and 2010.

An improved modeling for life prediction of high-power white LED based on Weibull right approximation method

Aiming at precisely predicting the life of the high-power white light LED (HPWLED), a three-parameter Weibull function and the right approximation method were employed to establish the luminance degradation model. The lumen maintenance data collected according to the IES LM-80-08 lumen maintenance test standard were fitted with and without error corrections, and the pseudo failure time of each HPWLED sample was extrapolated. The statistical analysis on the failure time was achieved by using Weibull distribution, normal distribution, lognormal distribution and Akaike Information Criterion (AIC). Then the life information was acquired. The results indicate that Weibull right approximation luminance degradation model (WRALDM) accurately reflects the variation of the lumen law with time. The failure time is accurately obtained. The best life distributions before and after the error correction to the lumen maintenance data are identified, based on AIC, as Weibull distribution and lognormal distribution, respectively. It is further confirmed by comparing the widths of life confidence interval and the life provided by the IES TM-21-11 method that the HPWLED life using WRALDM has a better accuracy. The optimized model provides researchers and manufacturers with significant guidelines for the further development of life prediction methodology.