Estimated Weibull Parameters Research Articles

3-D stochastic modeling approach in thermal inactivation: estimation of thermal survival kinetics of Escherichia coli O157:H7 in a hamburger after exposure to desiccation stress.

Desiccation tolerance of pathogenic bacteria is one strategy for survival in harsh environments, which has been studied extensively. However, the subsequent survival behavior of desiccation-stressed bacterial pathogens has not been clarified in detail. Herein, we demonstrated that the effect of desiccation stress on the thermotolerance of Escherichia coli O157:H7 in ground beef was limited, and its thermotolerance did not increase. E. coli O157:H7 was inoculated into a ground beef hamburger after exposure to desiccation stress. We combined a bacterial inactivation model with a heat transfer model to predict the survival kinetics of desiccation-stressed E. coli O157:H7 in a hamburger. The survival models were developed using the Weibull model for two-dimensional pouched thin beef patties (ca. 1 mm), ignoring the temperature gradient in the sample, and a three-dimensional thick beef patty (ca. 10 mm), considering the temperature gradient in the sample. The two-dimensional (2-D) and three-dimensional (3-D) models were subjected to stochastic variations of the estimated Weibull parameters obtained from 1,000 replicated bootstrapping based on isothermal experimental observations as uncertainties. Furthermore, the 3-D model incorporated temperature gradients in the sample calculated using the finite element method. The accuracies of both models were validated via experimental observations under non-isothermal conditions using 100 predictive simulations. The root mean squared errors in the log survival ratio of the 2-D and 3-D models for 100 simulations were 0.25-0.53 and 0.32-2.08, respectively, regardless of the desiccation stress duration (24 or 72 h). The developed approach will be useful for setting appropriate process control measures and quantitatively assessing food safety levels.IMPORTANCEAcquisition of desiccation stress tolerance in bacterial pathogens might increase thermotolerance as well and increase the risk of foodborne illnesses. If a desiccation-stressed pathogen enters a kneaded food product via cross-contamination from a food-contact surface and/or utensils, proper estimation of the internal temperature changes in the kneaded food during thermal processing is indispensable for predicting the survival kinetics of desiccation-stressed bacterial cells. Various survival kinetics prediction models that consider the uncertainty or variability of pathogenic bacteria during thermal processing have been developed. Furthermore, heat transfer processes in solid food can be estimated using finite element method software. The present study demonstrated that combining a heat transfer model with a bacterial inactivation model can predict the survival kinetics of desiccation-stressed bacteria in a ground meat sample, corresponding to the temperature gradient in a solid sample during thermal processing. Combining both modeling procedures would enable the estimation of appropriate bacterial survival kinetics in solid food.

In-situ synchrotron computed tomography tensile testing of composite specimens to estimate fibre strength Weibull parameters

A methodology is presented for the retrieval of fibre strength Weibull parameters using in-situ synchrotron computed tomography tensile testing of unidirectional composite specimens. Only fibre breaks that did not fail due to stress concentrations caused by other breaks are considered in this methodology. After the selection of the fibre breaks, the Weibull strength parameters were estimated through non-linear regression as well as least-squares fitting of linear regression in logarithmic scale. The two methods yield different estimated parameters, with the non-linear regression showing a better correlation with the observed fibre strength probability. The estimated Weibull parameters differed between specimens of the same fibre and matrix type, indicating that the strength distribution of fibres can vary within a given material batch. The measured Weibull scale parameters of the carbon fibres was estimated to be larger than the parameters measured in the single fibre tensile testing. This strength increase can be evidence of the higher strength of fibres when embedded in resin compared to when tested in air. The effect of fibre pre-selection in single fibre tensile tests was eliminated in the performed impregnated specimen tests, removing one source of uncertainty of the fibre strength Weibull parameters.

Direct comparison between monofilament and multifilament tow testing for evaluating the tensile strength distribution of SiC fibers

The tensile strength distributions of five types of silicon carbide (SiC) fiber, namely, Nicalon, Hi-Nicalon, Hi-Nicalon TypeS, Tyranno ZMI and Tyranno SA, were evaluated by monofilament and multifilament tow tensile testing with the estimated Weibull parameters being compared from each method. Whereas values for the Weibull scale parameter were found to be similar for both the monofilament and multifilament test methods, the Weibull shape parameter obtained from multifilament tow testing tended to be greater than that obtained from monofilament testing. The effect of diameter variation within individual fibers on the multifilament tow test results was investigated by Monte-Carlo simulations. In contrast with the experimentally obtained results, the shape parameters calculated by Monte-Carlo simulation exhibited good agreement with the monofilament test results.

Assessing Wind Impact on Noise Level Measurements for Application in Architectural Acoustics: A Preliminary Study

In this study, we have used wind data obtained from an earlier work covering several locations in Nigeria to estimate the possible impact of wind on sound pressure levels. Estimated Weibull parameters were used to compute the most probable wind speed, the average wind speed and the duration for which wind speed exceeds or equal the most probable speed. Adopting the proposed criteria that wind is able to strengthen or weaken sound pressure levels by 3dB depending on wind direction, the effect of wind on sound pressure level was determined. Results showed that wind effect seemed more predominant for the sub-sahelian stations such as Sokoto, Kano, and Maiduguri where the impact was found to be +/- 3dB obviously due to the characteristic high wind speeds recorded at those stations. The situation is almost the same for the midland region except that moderate impacts were found in some of the stations like Yola, Yelwa and Bauchi. However, moderate wind impacts generally characterize the Guinea Savannah and the coastal regions with the exception of Enugu with an impact of +/- 3dB. The result for Warri was found to be insignificant. It was concluded that most locations within the Nigerian environment may attain the wind conditions that would necessitate an adjustment in noise level measurements for application in architectural acoustics. In order to further validate the results of this preliminary study, it was recommended that detailed field survey where all relevant parameters such as wind speeds, wind directions and noise levels are simultaneously measured be conducted.

Long-Term Trends of Planted Loblolly Pine Diameter Distribution Characteristics

Abstract Diameter distributions are fundamental characteristics of stand structure. It is widely assumed that unthinned plantation loblolly pine (Pinus taeda L.) diameter distributions are unimodal and slightly skewed. In this work, the assumption of unimodality is formally tested and confirmed using 413 long-term permanent plots representing three generations of genetics and silviculture across the native range of loblolly pine in the southeastern United States. Approximately 96% of plot measurements had no significant evidence to reject the hypothesis of unimodality. While levels often significantly differed, similar developmental trends of skewness, kurtosis, and estimated Weibull parameters were observed despite the advances of genetics and silviculture. The results of the study indicate the continued need for a flexible distribution for characterizing diameter distributions in plantation loblolly pine.

A techno-economic analysis for power generation through wind energy: A case study of Pakistan

Pakistan needs to overcome the cost of power generation and the ever-increasing demand for energy with environment-friendly renewable energy resources. Several research efforts have been made with the support of Pakistan Meteorological Department in the last two decades for wind resource assessment (WRA) across the country. However, the practical installation of wind farms is quite a fraction of the total forecast wind energy potential. In this feasibility, WRA of Umerkot and Sujawal districts located in Sindh provinces of Pakistan has been analyzed by analyzing mean wind speeds, estimated Weibull parameters, power and energy densities calculation for various heights of selected wind turbines. Further, this paper analyzes the overall energy potential for these locations with implementation cost and pay-back period for investment. These locations are selected by the World Bank initiative of wind profiling campaigns to record wind speed data during 2016 and 2018 with 10 min resolution. It is observed that Umerkot and Sujawal sites are suitable for energy production. The highest values of power and energy densities for Sujawal are 414.18 W/m2 and 3628.22 kWh/m2/Yr and for Umerkot these values are 303.86 W/m2 and 2661.81 kWh/m2/Yr. The results indicate that using Nordex N90/2500 wind turbines are highly beneficial for Umerkot and Sujawal. The associated costs of energy are 0.074 $/kWh and 0.056 $kWh respectively and the payback period is estimated to be around 7 years with 20 years life time of the project. This work suggests the possibility of wind farm installation and commissioning based on power density calculation and cost of land acquisition. This work emphasizes the investment for wind farms at Sujawal and Umerkot for the sustainable growth of the country. This helps out policymakers for long term planning, development of wind energy projects and attracting investment for the country.

Estimation of Weibull parameters for wind energy analysis across the UK

Harvesting wind energy resources is a major part of the UK strategy to diversify the power supply portfolio and mitigate environmental degradation. Based on wind speed data for the period 1981–2018, collected at 38 surface observation stations, this study presents a comprehensive assessment of wind speed characteristics by means of statistical analysis using the Weibull distribution function. The estimated Weibull parameters are used to evaluate wind power density at both station and regional levels and important, turbine-specific wind energy assessment parameters. It is shown that the Weibull distribution function provides satisfactory modeling of the probability distribution of daily mean wind speeds, with the correlation coefficient generally exceeding 0.9. Site-to-site variability in wind power density and other essential parameters is apparent. The Weibull scale parameter lies in the range between 4.96 m/s and 12.06 m/s, and the shape parameter ranges from 1.63 to 2.97. The estimated wind power density ranges from 125 W/m2 to 1407 W/m2. Statistically significant long-term trends in annual mean wind speed are identified for only 15 of the 38 stations and three of the 11 geographical regions. The seasonal variability of Weibull parameters and wind power density is confirmed and discussed.

Artificial Intelligence Techniques for Estimation of Optimum Weibull Parameters for Wind Speed Distribution

The main objective of this study is to estimate the optimum Weibull scale and shape parameters for wind speed distribution at three stations of the state of Tamil Nadu, India using Nelder-Mead, Broyden–Fletcher–Goldfarb–Shanno, and Simulated annealing optimization algorithms. An attempt has been made for the first time to apply these optimization algorithms to determine the optimum parameters. The study was conducted for long term wind speed data (38 years), short term wind speed data (5 years) and also with single year’s wind speed data to assess the performance of the algorithm for different quantum of data. The efficiency of these algorithms are analyzed using various statistical indicators like Root mean square error (RMSE), Correlation coefficient (R), Mean absolute error (MAE) and coefficient of determination (R2). The results suggest that the performance of three algorithms is similar irrespective of the quantum of the dataset. The estimated Weibull parameters are almost similar for short term and long term dataset. There is a marginal variation in the obtained parameters when only single year’s wind data is considered for the analysis. The Weibull probability distribution curve fits very well on the wind speed histogram when only single year’s wind speed data is considered and fits marginally well when short term and long term wind speed data is considered

Influence of linearity in Weibull plot on accuracy of parameter estimation

Abstract This paper deals with influence of linearity in Weibull plot on accuracy of parameter estimation. Random numbers were generated as fracture probability, and transformed into virtual strength data at given Weibull parameters (m = 20, β= 100 MPa). The data was analyzed by Weibull plot method to estimate its Weibull parameters (m*, β*). This type of numerical simulation was repeated 1000 times at the number of specimens between 5 and 100. Comparison between the estimated Weibull parameters (m*, β*) and the given Weibull parameters (m = 20, β= 100 MPa) shows us that parameter estimation by Weibull plot method has sufficient accuracy when the square of correlation factor R2 ≥ 0.90 in Weibull plot.

A stand table projection system for interior Douglas-fir in British Columbia, Canada

Abstract This study developed a stand table projection system for interior Douglas-fir (Pseudotsuga menziesii (Mirb.) Franco var. glauca (Beissn.) Franco) in British Columbia, Canada. Simulation data, obtained by running PrognosisBC (with 150 year projections) using input derived from 140 permanent sample plots, were utilized for model construction. First, a whole-stand attributes (number of trees per ha, quadratic mean diameter, and arithmetic mean diameter) prediction model was constructed. Weibull parameters for the diameter distribution of the future stand were estimated from the predicted stand attributes using two parameter prediction methods (via seemingly unrelated regression and the cumulative distribution function) and one parameter recovery method. The future stand table was projected with the estimated Weibull parameters and compared with two stand diameter distribution adjustment algorithms, yielding a total of nine parameter estimation-diameter adjustment combinations. The outputs from the stand table projection model were evaluated with repeated measures data covering 20 years from 18 independent plots, as well as compared with the outcomes predicted by PrognosisBC for those plots. The diameter class adjustment procedure applying tree mortality prior to growth, combined with the cumulative distribution parameter prediction method, performed best among the nine combinations we compared. The stand table projection system yielded similar results to PrognosisBC on the evaluation data and is expected to be a useful tool for managing forests sustainably and effectively.

Weibull model for wind speed data analysis of different locations in India

Wind speed data should be fitted by a suitable statistical model like Weibull to determine expected number of hours per year in the critical wind speed range for a slender structure, which is required to determine the expected number of stress cycles in the projected working life of the structure. Apart from this, for the assessment of wind energy potential wind speed data should be fitted by an appropriate probability distribution. In the present scope of study, wind data of various locations of India have been fitted by Weibull model. Wind speed data are initially sampled in knot by Indian Meteorological Department and later converted into integer km/h before supplying them to the end user. Due to this conversion, wind speed data cannot be properly fitted by Weibull distribution and in this regard, the choice of appropriate class width becomes very much important. Without the choice of appropriate class width, estimated Weibull parameters become biased which would yield incorrect estimation of expected number of hours in critical wind speed ranges as well as wind energy potential. After taking appropriate class width of 4 km/h, it has been found that Weibull model is an adequate model to describe wind speed distributions of India. Weibull model has also been compared with other models such as Gamma and inverse Weibull distributions to establish its suitability than the others. In this study, the values of Weibull shape parameters vary from 1.3 to 2.3, whereas the values of scale parameters vary from 1.4 m/s to 6.5 m/s. The validity of Weibull model is also verified with a target confidence interval of 90%. The uncertainties involved in the estimation of available wind energy potential as well as the expected number of hours per year in critical wind speed ranges have also been considered due to random variation of wind climate in each year.

Conditional Weibull Control Charts Using Multiple Linear Regression

Because in Weibull analysis, the key variable to be monitored is the lower reliability index (R(t)), and because the R(t) index is completely determined by both the lower scale parameter (η) and the lower shape parameter (β), then based on the direct relationships between η and β with the log‐mean (μx) and the log‐standard deviation (σx) of the analyzed lifetime data, a pair of control charts to monitor a Weibull process is proposed. Moreover, because the fact that in Weibull analysis, right censored data is common, and because it gives uncertainty to the estimated Weibull parameters, then in the proposed charts, μx and σx are estimated of the conditional expected times of the related Weibull family. After that both, μx and σx are used to monitor the Weibull process. In particular, μx was set as the lower control limit to monitor η, and σx was set as the upper control limit to monitor β. Numerical applications are used to show how the charts work. Copyright © 2016 John Wiley & Sons, Ltd.

Tree height distribution dynamics in young naturally regenerated study plots

Abstract Growth assessment of young stands gives the possibility of assessing forest site potential, tree species-dependent competition and developing realistic predictions for the following periods. The study is conducted in naturally regenerated broadleaves dominated stands in 2005 at Järvselja Training and Experimental Forest Center. The current study material is collected from 9 study plots established in three forest stands (regeneration felling years respectively 1996, 2000 and 2002). The study plots were re-measured 4–6 times respectively between the years of 2006 and 2012. The Weibull distribution function fit for empirical height distributions in consecutive years was tested and the estimated Weibull parameters were analysed. Results indicate that empirical height distributions of young regenerated forests do not fit well to theoretical distributions, but in many cases, empirical and theoretical distribution are similar. The Weibull distribution shape parameter was related to the maximum height and range of the height, and the scale parameter was related to the mean, quadratic mean and median height.

Weibull statistical analysis of splitting tensile strength of concretes containing class F fly ash, micro/nano-SiO2

Despite the importance of the Weibull modulus in reliability analysis of brittle materials, the majority of the studies are focused on plain concrete; the data being especially scarce for nano-SiO2-concrete. Therefore, this paper investigates the concrete tensile strength up to quaternary designs containing fly ash, micro- and/or nano-SiO2. Splitting failures were carried out at 3, 7, 28, 56 and 90-days. Quadratic class goodness-of-fit tests of composite hypothesis were applied to investigate the accuracy of the two- (We2) and three-parameter (We3) Weibull models. The estimated Weibull parameters were obtained using maximum likelihood (MLE) and other nonlinear methodologies. This practice enables to overcome divergences in some datasets associated with the solely use of MLE-We3. Results showed that the We3 represented the model with the best fit (71%) in comparison to the We2 (25%). However, differences through time in the mean Weibull moduli were not significant based on ANOVA analyses.

Maximum likelihood estimation for the three-parameter Weibull cdf of strength in presence of concurrent flaw populations

Abstract For a correct strength characterization of brittle materials, not only the maximum stress at fracture, but also the geometry of the specimens has to be considered thus taking into account the variable stress state and the size effect. Additionally, fracture may occur due to different fracture modes, as for example surface or edge defects. The authors propose a maximum likelihood estimator to obtain the cumulative distribution functions of strength for surface and edge flaw populations separately, both being three-parameter Weibull cdfs referred to an elemental surface area or elemental edge length, respectively. The method has been applied to simulated 3-point bending test data. The estimated Weibull parameters have been used to compute the cdfs of strength for specimens with different size, providing also the confidence bounds calculated by means of the bootstrap method. Finally, fracture data of 4-point bending tests on silicon carbide have been evaluated with the proposed method.

Unbiased estimation of Weibull parameters with the linear regression method

Monte Carlo simulations were used to search for the probability estimator for the unbiased estimate of the Weibull parameters in the linear regression method. Compared with commonly-used probability estimators, the estimator proposed gives a more accurate estimation of the Weibull modulus and the same estimation precision of the scale parameter. It is found that the estimator proposed is more conservative than the estimator P i = ( i − 0.5)/ n recommended by previous authors, and hence results in a higher safety in reliability predictions. The unbiased properties of the estimated Weibull parameters were validated with actual experimental data. It is also concluded that the estimated Weibull modulus from actual experimental data is more dispersive than that from Monte Carlo simulation, which arises from the fact that the strength data from actual experiments does not perfectly follow the Weibull statistics.

In search of convenient techniques for reducing bias in the estimation of Weibull parameters for uncensored tests

Techniques for estimating the parameters of the 2-parameter Weibull distribution from data obtained from uncensored tests are compared. This will allow the most convenient method to be chosen by considering the data's characteristics and the level of algorithm complexity. It is shown that common techniques, such as least squares regression and maximum likelihood, may give rise to very significant errors in terms of the bias of the estimated Weibull parameters. The estimator suggested by Jacquelin (1993) for /spl alpha/ and the correction factor suggested by Ross (1994) for /spl beta/ usually give errors of <5 and <1%, respectively and are to be recommended, because they are straightforward to implement. Techniques are available which will eliminate virtually all bias in the estimation of the parameters, but these may be at the expense of considerable complexity in implementation.

Relationship of stand attributes of some plantation mahoganies with estimated Weibull parameters

The Weibull parameters of location, scale and shape were obtained for diameter data collected from plantations of Lovoa trichilioides, Khaya ivorensis and Entandrophragma cylindricum in Nigeria. The coefficients obtained were then expressed as linear functions of stand attributes, viz. age, number of trees in stand, basal area and diameter. The individual models obtained were then pooled together by replacing their estimated coefficients with the established linear relationships to obtain a composite diameter model for each species. Cumulative frequencies generated from the composite model compared favourably with those obtained from other sets of data not used in the original formulation.

Within-stand seedling dispersal for isolated pinnsstrobus within hardwood stands

White pine (Pinusstrobus L.) seedling distributions were sampled around isolated seed trees located on 12 study areas within hardwood stands. Seedling densities were found to differ significantly in different directions from the apparent seed source. Pooled densities from all study areas were lowest and highest in the southwest and northeast quadrants, respectively. With some exceptions, the Weibull probability density function was helpful in describing the general shape of the seedling distributions. Correlations between estimated Weibull parameters and stand characteristics surrounding each seed source suggest that the shape of seedling density distributions is not strongly related to stand characteristics. Implications for modeling seed dispersal are also discussed.