Weibull Function Research Articles

Equilibrium optimiser for the economic load dispatch problem with multiple fuel option and renewable sources

The integration of thermal units with renewable sources leads to a highly nonlinear and difficult Economic Load Dispatch (ELD) problem. However, dependency of wind speed and solar irradiance, renewable sources like wind-solar plants cannot guarantee their output. It has been possible to anticipate the wind speed and solar irradiation by Weibull and beta probability density functions. Wind and solar energy output powers have been estimated using the 2-m point estimation method. The renewable-based ELD problem has a solution thanks to the equilibrium optimizer (EO) technique. Finding the answer in a relatively short amount of computing time is made possible by the method's exploration and exploitation stages. The suggested technique has been validated in three, five, six, fifteen, and huge 160 thermal units linked to renewable energy sources by meeting restrictions such generator operating restrictions, valve point loading impact, and numerous fuel possibilities.

Compaction-deformation behaviors and breakage characteristics of loose broken coal under various stress–temperature coupling loads

This study probed the compaction-deformation and breakage characteristics of loose broken coal under stress–temperature coupling loads. The constitutive model of loose broken coal under stress–temperature coupling loads was first constructed. Then, we quantificationally investigated the particle size distribution (PSD) evolution for the compacted loose coal using the fractal and Weibull functions. In addition, the relative breakage rate, energy evolution, and particle breakage degree of the loose coal compacted were quantificationally evaluated. Results suggest that stress is the prominent factor leading to the breakage of loose broken coal, while increased temperature exacerbates the particle breakage process in combination with the axial stress. Changes in temperature have a distinctive influence on particle breakage for loose broken coal under low-stress conditions, whereas less conspicuous under high-stress conditions. Finally, the evolution of PSDs and related breakage parameters for the entire loose broken coal compaction process were mathematically predicted utilizing the grey model.

Monitoring and Prediction of Horizontal Displacement of Underground Enclosure Piles in Subway Foundation Pits.

Urban rail transportation and underground space development and utilization are initiatives to solve urban traffic congestion. The monitoring and prediction of the stability of underground enclosure piles in foundation pits is a key index for the dynamic evaluation of the stability of underground space engineering. In this paper, we focused on the problem that the dynamic prediction accuracy and stability of foundation pit retaining piles in the Qingdao area are not high. Based on the analysis of various time function curves and the physical meaning of the parameters, we proposed the Adjusted-Logistic time function model, which introduces three physical parameters to adjust the deformation velocity and deformation acceleration in different stages for better accuracy. It could predict the deformation process of underground enclosure piles under different geological engineering conditions. It was verified in the field that the root-mean-square error (RMSE) of the Adjusted-Logistic function was 0.5316, MAE was 0.3752, and R2 was 0.9937, which were better than those of Gompertz, Weibull, and Knothe time function models. Meanwhile, it showed that with the increase of excavation depth, the maximum horizontal displacement of the underground enclosure piles gradually decreased and finally stabilized at 0.62-0.71 H. We established a catastrophe model of the horizontal displacement cusp at the observation point of the underground enclosure piles by using the time series of the measured data. It could determine the weak location of the underground enclosure pile stability and realize the multipoint warning of the foundation pit stability, which would ensure safe construction.

A Novel Adaptive Manta-Ray Foraging Optimization for Stochastic ORPD Considering Uncertainties of Wind Power and Load Demand

The optimal control of reactive powers in electrical systems can improve a system’s performance and security; this can be provided by the optimal reactive power dispatch (ORPD). Under the high penetration of renewable energy resources (RERs) such as wind turbines (WTs), the ORPD problem solution has become a challenging and complex task due to the fluctuations and uncertainties of generated power from WTs. In this regard, this paper solved the conventional ORPD and the stochastic ORPD (SORPD) at uncertainties of the generated power from WTs and the load demand. An Adaptive Manta-Ray Foraging Optimization (AMRFO) was presented based on three modifications, including the fitness distance balance selection (FDB), Quasi Oppositional based learning (QOBL), and an adaptive Levy Flight (ALF). The ORPD and SORPD were solved to reduce the power loss (PLoss) and the total expected PLoss (TEPL), the voltage deviations (VD) and the total expected VD (TEVD). The normal and Weibull probability density functions (PDFs), along with the scenario reduction method and the Monte Carlo simulation (MCS), were utilized for uncertainty representations. The performance and validity of the suggested AMRFO were compared to other optimizers, including SCSO, WOA, DO, AHA, and the conventional MRFO on the IEEE 30-bus system and standard benchmark functions. These simulation results confirm the supremacy of the suggested AMRFO for the ORPD and SORPD solution compared to the other reported techniques.

Investigation and statistical analysis of electrical energy production from the wind farm

Today, the use of wind energy by wind turbines has grown significantly, and this development is due to the production of required energy and tourism attraction of wind turbines. But according to the standard technologies used in this industry, the operating costs are very high. For this reason, before the construction of wind farms, potential measurements should be done along with economic analysis. Therefore, in this research, a statistical analysis of wind farms has been done. In the statistical analysis, Weibull and Rayleigh distribution functions were used to predict the wind speed of the studied area. MATLAB software is used to model prediction functions. Among the important results of wind speed prediction by the Weibull distribution function, it can be mentioned that the wind speed is variable between 0.6 and 7 m/s in the studied area. The total power density and wind energy in the 10 years are equivalent to 28 W/m2 and 810/0534 kWh/m2 at the height of 10 m calculated.

Experimental tests and numerical simulations of ultimate strength on acid etching tempered glass under four-point bending

Acid etching tempered glass (AETG) is a new building material formed by chemical etching of the surface of tempered glass (TG). It is considered that the bending strength of the specimen will show great dispersion due to the comprehensive influence of surface defect distribution. This paper studies the influence of three key factors, including the etching process, age, and loading rate, on bending strength by a four-point bending test. Two-parameter Weibull function is used to analyze the test results so that the characteristic values of the bending strength of specimens in each group can be obtained. The XFEM model of AETG was established based on the experimental results. The results show that the acid etching process changes the surface roughness and surface residual surface stress of TG. The bending strength is improved obviously but can be stabilized gradually after six months. The established XFEM model can better simulate the development of stress corrosion cracking and is close to the characteristics of failure fragments in the experiment.

Asymmetric sex body size and reproductive fitness relation and offspring population parameters of Habrobracon hebetor (Say) (Hymenoptera: Braconidae)

Parasitoids show a strong relationship between body size and fitness, but it is unclear whether the relationship is asymmetric or symmetric in males and females of Habrobracon hebetor (Say) (Hymenoptera: Braconidae). This study investigated the effects of male and female body sizes on the reproductive fitness (e.g., longevity and fecundity) of the F0 generation and the population fitness (e.g., survival rate, body size, longevity, and fecundity) of the F1 generation at 28 ± 1 °C, 75 ± 5% relative humidity and 16:8 h light:dark period based on the age-stage two-sex life table theory. The results showed that the body size of F0 generation males and females significantly affected their reproductive fitness, but not the body size of the F1 generation. Larger females had longer lifetimes and oviposition days, and higher reproductive rates than smaller females. Moreover, only small ♀ × small ♂, but not large ♀ × small ♂, small ♀ × large ♂, and large ♀ × large ♂, had a significant impact on the life history parameters, population parameters, paralysis rate, and parasitism rate of the F1 offspring population. Interestingly, the population size, paralysis rate, and variability of the F1 offspring with different body sizes increased to a stable status after 50 days. The study also found that the Weibull function could not fit the survival rate of the parasitoid wasp well. These findings deepen our understanding of the ecology of H. hebetor population and provide important technical parameters for mass-rearing and application of these parasitoid wasps.

Session V:

In this study, work on modelling uncertainty in the tensile properties of two-dimensional plain woven silicon carbide fibre-reinforced silicon carbide matrix (2D SiC/SiC) composite and B-basis values of tensile strength was carried out in the following four aspects. First, the uncertainty law and formation mechanism of the tensile properties of 2D SiC/SiC composites were researched through microstructural analysis. Subsequently, three distribution function models were established for the tensile properties of 2D SiC/SiC composites with Weibull, normal, and log-normal distribution functions. The development of three functional models was based on 30 groups of valid tensile data, linear regression methods, and Kolmogorov hypothesis testing methods. Based on the application of the model validation method, the accuracy of the three functional models was quantitatively evaluated by employing the area index of model validation. B-basis values for the tensile strength of 2D SiC/SiC composites were calculated and finally discussed for three distribution functions. The results indicate that the distribution regularity of tensile properties of 2D SiC/SiC composites could be characterized by using the three function models, and the Weibull distribution function was the most accurate. Therefore, it was preferable to calculate the B-basis values by using the Weibull distribution, with a B-basis value of 266 MPa.

The Analysis of Stress Raisers Affecting the GFRP Strength at Quasi-Static and Cyclic Loads by the Theory of Critical Distances, Digital Image Correlation, and Acoustic Emission.

The purpose of this work is to analyze the stress-raisers that affect the tensile strength and fatigue resistance of GFRP parts using the point and line methods of the theory of critical distances (TCD) to obtain a quantitative measure of the defect size that can be tolerated by the composite before it fails. In the course of the work, a method combining TCD and the Weibull function was developed. In the course of the work, GFRP structural fiberglass for electrical purposes was tested under uniaxial quasi-static and cyclic loading with digital image correlation (DIC) and acoustic emission (AE), as well as a numerical simulation of deformation. The studied specimens were plain (without a stress-raiser) and notched (V-shaped) with different notch root radii and depths. The results were used to determine the material critical distances. In this case, two approaches to TCD were used: line (LM) and point (PM) methods. To analyze the experimental results, finite element modeling was applied using the ANSYS software package. As a result, the linearized maximum principal stresses were obtained on the central line passing through the top of the stress raiser. Thus, the values of the critical distances of the material were determined by PM and LM. Based on the data obtained, the sizes of permissible defects in the studied fiberglass were established that do not affect the tensile and fatigue strength of the material. The paper illustrates the cumulative energy, peak amplitudes, and distributions of the frequency of the spectral maximum of acoustic emission signals obtained after the destruction of specimens by fatigue test. Evolutions of deformation fields on the specimen surface were recorded using a Vic-3D contactless optical video system and the DIC.

Stress-Strain Relationship of Clay in Dongting Lake Area Based on Three Damage Factors

CU test and CD test were performed to capture the stress-strain characteristics of the clay in Dongting Lake area, China. Since the classical constitutive model cannot ideally describe the strain hardening behavior of the clay, an improved constitutive model that involved three damage factors was proposed. The damage first factor D 1 , which represents elemental volume strength F , was fitted by the Weibull function. The second and third damage factors D 2 and D 3 , which represent the porosity ratio e and the drainage rate P ε respectively, were fitted by Harris function. The CD test damage model is constructed by D 1 , D 2 , and D 3 . In the CU test, the porosity ratio e is a constant value, and the drainage volume is 0, so that D 2 is constant value and D 3 is 0. Therefore, the CU test damage model of the clay was constructed using the damage first factor D 1 . In the end, the accuracy of the proposed CU/CD damage constitutive models of the clay was validated with the experimental results. It is found that the results fitted by the proposed methodology are in good agreement with the experimental results.

Abstract 5786: Spatial relationships in the tumor microenvironment predict response to immune checkpoint inhibitors in urothelial and head and neck cancer

Abstract Background: Immune checkpoint inhibitors (ICI) can achieve remarkable clinical responses in urothelial cancer (UC). However, it remains unclear which aspects of the tumor microenvironment (TME) determine a patient’s response. The TME is usually characterized by immune cell density, which ignores cells’ spatial relationships relative to each other. Methods: Using multiplex immunofluorescence data (PanCK, CD20, CD68, CD3, CD8, and FoxP3 antibody panel) of 24 pre-ICI UC transurethral resections retrieved from the NABUCCO trial (NCT03387761), we spatially profiled cancer cells, macrophages, B-cells, and distinct T-cell populations. We first quantified the TME immune cell densities at the tumor and stroma tissue compartments. We then quantified the TME spatial relationships with a novel approach based on fitting a Weibull function to the first nearest neighbor (1-NN) distance distribution, allowing us to uniquely summarize spatial relationships with two parameters (Weibull approach). We compared this approach to conventional techniques (G-functions) that rely upon a predefined distance threshold. We performed a simulation study to identify sources of variation in the spatial relationship parameters. Lastly, we associated the TME parameters with ICI (ipilimumab + nivolumab) response. Results: Unlike the Weibull approach, the G-function quantifications manifested a variable effect size and statistical power in association studies because of its distance threshold dependence. We found that variation in density affected the spatial relationship metrics of rare cell types (i.e., B-cells) but not of abundant cell types (i.e., cancer cells). The spatial relationship metrics from the Weibull approach outperformed immune cell density in ICI response prediction. Specifically, immune cell density did not discriminate between ICI response groups (FDR>10%). In contrast, the spatial relationship between either CD8+ T-cells or macrophages to their closest cancer cell did associate with response to ICI (FDR=1%). Furthermore, non-responding tumors were characterized by CD8+ T-cells close to B-cells (FDR=9%). Importantly, we validated the association between proximity and response from CD8+ T-cells to cancer cells (FDR=1%) and from macrophages to cancer cells (FDR=1%) using data from 25 pre-ICI head and neck squamous cell carcinoma tumors from the IMCISION trial (NCT03003637, arm B, ipilimumab + nivolumab). Conclusion: We created a framework to quantify, study, interpret and analyze spatial relationships in the TME and illustrated its superior clinical relevance compared to density metrics for predicting ICI treatment response. Our findings emphasize the importance of spatial relationships in the TME for response and suggest that proximity between either macrophages or CD8+ T-cells to cancer cells are candidate biomarkers for ICI response. Citation Format: Alberto Gil-Jimenez, Nick van Dijk, Yoni Lubeck, Maurits L. van Montfoort, Dennis Peters, Erik Hooijberg, Annegien Broeks, Joris L. Vos, Charlotte L. Zuur, Bas van Rhijn, Daniel J. Vis, Michiel S. van der Heijden, Lodewyk F. Wessels. Spatial relationships in the tumor microenvironment predict response to immune checkpoint inhibitors in urothelial and head and neck cancer. [abstract]. In: Proceedings of the American Association for Cancer Research Annual Meeting 2023; Part 1 (Regular and Invited Abstracts); 2023 Apr 14-19; Orlando, FL. Philadelphia (PA): AACR; Cancer Res 2023;83(7_Suppl):Abstract nr 5786.

Weibull distribution-based prediction model for compression after impact (CAI) strength of CFRP laminates

The aim of this research was to assess the appropriateness of the two-parameter Weibull distribution-based model to predict the compression after impact (CAI) strength and to develop both efficient and secure prediction scheme for laminated composite. Four levels of impact energy were considered (10 J, 25 J, 40 J and 55 J) and CAI tests were conducted. The scanning electron microscope were used to evaluate the representative damage pattern. Two-parameter Weibull function was utilized for statistically evaluating the CAI strength results. Experiment results showed that the wildest variance was observed at the impact energy range of 25–40 J for both layups. It was found fiber damage accompanied with high variance while the matrix and delamination damage corresponded to lower variance. To predict the CAI strength more efficiently, the time to first failure (TTFF) concept was used to draw CAI strength versus impact energy graphics under different reliabilities for reference. It was verified that the safe design strength curve under 0.99 reliability level was capable and secure enough to predict the residual strength in actual application considering the variance of composite.

Cold Atmospheric plasma treatments trigger changes in sun-dried tomatoes mycobiota by modifying the spore surface structure and hydrophobicity

The contamination of sun-dried tomatoes during processing can have a decisive impact on the quality of the finished product. In this study we investigated how Cold Atmospheric Plasma (CAP) under high surface power density (SPD) values can reduce fungal contamination in sun-dried tomatoes. In the application of this innovative processing method, the established “regime” for air plasma chemistry was the transition regime or NOx regime. First, we isolated and identified the mycobiota present on the tomatoes surfaces by mean of the analysis of the ITS region. The analysis revealed 32 different species, with A. niger , A. tubingensis, A. chevalieri , A. flavus, and A. alternata being the most abundant. Then, to reduce the fungal population, CAP-NOx was applied for 5, 10, 20 and 30 min on the surface of dried tomatoes. After incubation for 10 days, we observed that the antifungal effect was species and dose-dependent. In vitro investigation on the most abundant species revealed that A. chevalieri PSJ144 was the most sensitive species (almost 90%) immediately after 5 min of CAP treatment. With the increase of the exposure time up to 30 min, a strong reduction (p ≤ 0.05) of spore germination of A. alternata PSJ77 and A. tubingensis PSJ100 was observed (98 and 92%, respectively). However, spores of A. niger PSJ38 and A. flavus PSJ30 showed the highest resistance to the treatment. Moreover, the reparameterized Weibull function allowed to obtain useful information about germination kinetics as a function of time of CAP-NOx treatment, revealing that the resistance of the spores was: A. chevalieri < A. alternata < A. tubingensis < A . flavus < A. niger . In situ analyses confirmed a significant effect on natural fungal contamination by CAP-NOx treatment (76.5% of reduction), likely due to cell membrane rupture and cell death caused by plasma radicals. In addition, Pearson correlation analysis showed that spore resistance was highly correlated (p = 0.98) with their hydrophobicity. In a nutshell, our results clearly indicate that CAP-NOx treatment is an effective technique to reduce fungal contamination in sun-dried tomatoes. Among non-thermal processing methods, CAP shows promising perspectives of application in the tomato industry, to mitigate the effects of energy price rises. • A. niger , A. tubingensis, were most abundant species in dried tomatoes. • CAP reduced the fungal contamination on the dried tomatoes by 76.5%. • A. niger and A. flavus spores were more resistant ones to CAP. • A. chevalieri spores were inactivated after 0.1 min of CAP-NOx. • Spore hydrophobicity was correlated with the spore resistant to CAP.

Machine Learning Classification and Prediction of Wind Estimation Using Artificial Intelligence Techniques and Normal PDF

Estimating wind energy at a specific wind site depends on how well the real wind data in that area can be represented using an appropriate distribution function. In fact, wind sites differ in the extent to which their wind data can be represented from one region to another, despite the widespread use of the Weibull function in representing the wind speed in various wind locations in the world. In this study, a new probability distribution model (normal PDF) was tested to implement wind speed at several wind locations in Jordan. The results show high compatibility between this model and the wind resources in Jordan. Therefore, this model was used to estimate the values of the wind energy and the extracted energy of wind turbines compared to those obtained by the Weibull PDF. Several artificial intelligence techniques were used (GA, BFOA, SA, and a neuro-fuzzy method) to estimate and predict the parameters of both the normal and Weibull PDFs that were reflected in conjunction with the actual observed data of wind probabilities. Afterward, the goodness of fit was decided with the aid of two performance indicators (RMSE and MAE). Surprisingly, in this study, the normal probability distribution function (PDF) outstripped the Weibull PDF, and interestingly, BFOA and SA were the most accurate methods. In the last stage, machine learning was used to classify and predict the error level between the actual probability and the estimated probability based on the trained and tested data of the PDF parameters. The proposed novel methodology aims to predict the most accurate parameters, as the subsequent energy calculation phases of wind depend on the proper selection of these parameters. Hence, 24 classifier algorithms were used in this study. The medium tree classifier shows the best performance from the accuracy and training time points of view, while the ensemble-boosted trees classifier shows poor performance regarding providing correct predictions.

Estimating the asymptotic characteristic time scales for diffusion-controlled drug release systems using partially sampled data

Drug release experiments and numerical simulations only give access to partial release data (i.e., within a finite time range t∈[0,tf]). In this article, we propose fitting-based procedures to estimate the asymptotic time scales of the release process, namely the global relaxation time τ∗ and the longest (or terminal) relaxation time τ0, from partially sampled data of diffusion-controlled drug release systems. We test these procedures on both synthetic and experimental data using, as an example, the well-known Weibull function. Our results show that the Weibull function must be used with great care because the values of the fitting parameters can vary significantly depending on the ratio tf/τ0. Beyond their practical simplicity, the usefulness of our procedures is evidenced by the fact that: (1) the initial loading profile does not need to be known and (2) the chosen fitting function does not require any physical basis. These two advantages allow us to determine the diffusion coefficient of the molecules directly from the characteristic time τ0.

Magnetic force prediction of hybrid magnet with Halbach array using generalized regression neural network optimized by a modified aquila optimizer

This paper addresses the balancing of global and local searches in the recently proposed AO (Aquila Optimizer) algorithm. The original random algorithm is modified using normal-distribution parameters, and an adaptive function represented by a Weibull function is added to the motion law of the predator. Sixteen benchmark functions are used to test the improved algorithm against several recently developed algorithms. The results show that the accuracy and convergence speed of the modified algorithm are improved while the advantages of the original algorithm are retained. In solving the problems of a complex calculation and limited solution in the design of a hybrid electromagnetic structure based on a Halbach array, a prediction model based on the improved algorithm and generalized regression neural network (GRNN) is designed for improved prediction accuracy of the GRNN. Thirty groups of data are obtained using Ansoft, and the prediction accuracy of the improved GRNN is verified using the data. The mean squared error (MSE) of normalized prediction results reaches 0.1404. The improved prediction model has the prediction error less than 10% and its performance is better than the RBF and the KCV-GRNN.

ALGORITHM FOR THE PROJECTION OF FOREST GROWTH AND PRODUCTION

The modeling of forest growth and production is an essential tool for forestry management because it allows us to perform simulations and project forest biometric variables in the future, thus assisting in stock planning and economic analyses. In this work, a growth and production model by diameter distribution was proposed with the application of the Weibull function based on the recovery of parameters through simplified functions between the forest attributes and the parameters of the Weibull function. The algorithm was developed in Excel’s VBA language. Validation was performed with data from the Continuous Forest Inventory (CFI) in a stand of Khaya grandifoliola and in rows of Eucalyptus spp. in the ILPF system, which were ordinarily organized into seven date combinations, from the most distant from to the closest to the projection date. The results were evaluated by the percentage standard error (SE%) applied to the projected and observed volumes and by the Kolmogorov‒Smirnov test applied to the diameter distributions to verify adherence. It was possible to identify an exact relationship for parameter c of the Weibull function as a function of the percentiles and for parameter b, improving the parameter recovery method. Another methodological improvement was the use of maximum diameter and maximum height for age to adjust the hypsometric function. The algorithm presented results for total volume with errors up to 20% in 85% of the tests.

MODELAGEM DA DISTRIBUIÇÃO DIAMÉTRICA DE ESPÉCIES ARBÓREAS EM FRAGMENTO DE FLORESTAS ESTACIONAL SEMIDECIDUAL

ABSTRACT Modeling diameter distribution in natural forests is an important tool for understanding the native woody species dynamics, supporting decision-making for degraded lands management and restoration. Therefore, this work aimed to fit probabilistic density functions to evaluate the diameter structure of three tree species with economic interest, such as Campomansesia xanthocarpa Marl. Ex. O. Berg, Piptadenia gonoacantha (Mart.) J.F. Macbr. and Zeyheria tuberculosa (Vell.) Bureau ex Verl., in a Semideciduous Seasonal Forest fragment at São Paulo State, Brazil. The data came from 83 temporary plots of 10 m x 20 m systematically distributed along 164 ha. Log-normal, Gamma, and Weibull functions were fitted to the three species using the fitdistrplus-package in the R program. Kolmogorov-Smirnov's adherence test was used to evaluate the fits at a 5% probability level. The functions were selected employing Akaike's Information Criterion (AIC) and Schwarz's Bayesian Information Criterion (BIC), in addition to a graphical analysis of the fitted functions. The results indicated that the three species diameter structure is positively asymmetric, representing the exponential pattern, representing continuous natural regeneration. AIC and BIC statistics indicated the Log-normal function to describe the diameter distribution of C. xanthocarpa and Z. tuberculosa, while the Gamma function was the most appropriate for P. gonoacantha. For the three species, the graphical analysis showed the Gamma function results in the best fit without tendency for estimating frequency density per diameter class.

A lunar surface scenario simulation applying adaptive operating systems (revised version)

There is much discussion about the further exploration of the moon and its implementation by autonomous robots and rovers. Prognostics and health management approaches are considered for autonomous systems to assure reliable operation. In this context, the reliability-adaptive systems approach deals with the prediction of the remaining useful life (RUL) to avoid maintenance conflicts. The proposed paper introduces a multi-system scenario on the lunar surface consisting of six rovers maintained by a single base. The rovers drill into the lunar surface and bring soil samples back to the base. To estimate the RUL as precisely as possible, the wear of the drill is monitored. Soil density, radiation, and soil versus rover temperature are just a few random aspects which are considered in the calculation of the drill failure rate. The simulation applies different values to the Weibull function shape parameter b > 1. This modeling represents the pessimistic assumption of an increasing soil density per drilling depth on the Moon. The base can maintain only one rover at a time. To avoid maintenance conflicts and to maximize the total scenario soil output, some rovers are derating their performances in order to extend their RUL so that all rovers reach the base preferably one after the other. When predicting the RUL, all previous failures, the current performances, and RUL prognoses of all rovers are considered. The paper discusses the operation algorithm including the rover procedures. The proposed contribution compares the efficiency of systems operated either conventionally in a non-derating mode or in a reliability-adaptive mode. The scenario-wide workload performed by all rovers is the evaluation measure in this approach. The following results have been obtained: Reliability-adaptive systems are operating more efficiently in the given lunar context than the conventional systems operate as the adaptive rovers continuously achieve higher up times in total. The longer the simulation time, the higher is the efficiency of reliability-adaptive operation. It has also been shown that reliability-adaptive systems have a significant influence on reducing delay times when returning to the drilling sites.

Using Weibull distribution function to determine the design bounds for carburized 4320 steel shafts subjected to bending dominated fatigue loading

The differential pinion shaft in an axle is often heat-treated to high surface hardness to withstand the extreme bending fatigue loading conditions. The carburized pinion shaft made of 4320 steel material was identified as the primary fracture mode when subjected to various fatigue loading conditions. However, minimal data is available to understand the fatigue behavior of carburized 4320 steel shafts. This research proposes a prediction approach to determine the fatigue life of carburized 4320 steel shafts. Since hardness varies rapidly through the carburized specimen's depth, subsurface crack initiations are likely. The fatigue prediction at the shaft subsurface was made possible by creating a set of hardness-based strain-life curves through the depth of the shaft specimen. Since all the carburized shafts in the experiment had electroless nickel plating, this research could capture the unique fatigue behavior by introducing a surface correction factor. Mean stress correction to the strain-life curves was investigated to account for the shaft failure in the case of tensile-dominated loading conditions. The performance of prominent mean stress correction models was compared by correlating with the experimental data. An analytical model was proposed since the standard models were unable to capture the physics completely. This proposed model showed excellent correlation with test data. Finally, this research implemented a Weibull-statistics-based reliability estimation approach to determine the design bounds for the carburized pinion shaft.