Weibull Distribution Function Research Articles

Optimal reconfiguration, renewable DGs, and energy storage units’ integration in distribution systems considering power generation uncertainty using hybrid GWO-SCA algorithms

ABSTRACT To optimize radial distribution systems, this study suggests the utilization of the Grey Wolf Optimizer (GWO), a hybrid metaheuristic optimization method, combined with the Sine Cosine method (SCA). The primary objective of this work is to enhance the distribution system by determining the most efficient network reconfiguration, sizing, and placement of various distributed energy sources in distribution system. The energy sources considered include capacitors, solar cells, wind turbines, biomass-based distributed generation units, and battery storage units. To achieve this goal, the proposed strategy incorporates the power loss sensitivity technique, which assists in identifying suitable candidate buses and accelerates the resolution process. Moreover, the model considers fluctuations in solar irradiance and wind speed using Weibull and Beta probability distribution functions, compensating for the intermittent nature of renewable energy sources and the variability in demand. To address power fluctuations, voltage surges, significant losses, and inadequate voltage stability challenges, battery energy storage, diesel generators, and dispatchable biomass DGs are employed to mitigate variability and enhance supply continuity. The proposed approach is evaluated and validated by comparing it to existing optimization strategies using IEEE 69-bus and 84-bus RDSs. The results demonstrate that the suggested technique achieves faster convergence to near-optimal solutions. The proposed methodology yields a significant reduction of up to 80% in power losses in the 69-bus system and a 35% reduction in the 84-bus system, signifying higher performance than existing methods.

Fatigue resistance and reliability assessment of hot dip galvanised plates with welded transversal stiffeners

This paper investigates the effect of galvanisation on the fatigue strength of plates with welded transversal stiffeners. A series of 50 fatigue tests were carried out on welded details made of S355 structural steel. For comparison purposes, tests were performed on both hot dip galvanised (HDG) and uncoated joints. In addition, the influence of different cutting methods on the fatigue life was addressed. The experimental fatigue data was analysed, using different statistical methods commonly used in survival analysis. Both the normal distribution function, following the EN1993-1-9 approach, and the two-parameter Weibull distribution function, were considered. For the latter, different methodologies were employed to evaluate its key parameters. Finally, it was concluded that the resulting Wöhler curve for the HDG plates with welded transversal stiffeners matches the fatigue detail category80 of EN1993-1-9. The results of this study were used to propose new revisions of EN 1993-1-9, to extend its scope to galvanised steel details.

Influence of magnetic field on growth kinetics of sodium chlorate crystals from aqueous solution

The results of the study of the influence of a static magnetic field of 55 ± 3 mT on the face growth kinetics of sodium chlorate crystals in the supersaturation range of (0.89–1.78) % are presented. The supersaturation dependence of growth rate was analyzed using different theoretical models and the kinetic parameters of crystal growth in zero and in the applied magnetic field were estimated. It is shown that in both types of experiments the observed crystals grew by a complex dislocation source. Analysis of the growth rate distribution by using the Weibull distribution function was performed to obtain the maximum growth rate Rmax depending on their corresponding initial length lmax. The linear relationship between these quantities is derived from the model of growth by a group of cooperating screw dislocations. It was observed that both the initial size threshold l*max and the slope dRmax/dlmax exhibit higher values in the presence of a magnetic field.

Effects of basalt fibre and rubber particles on the mechanical properties and impact resistance of concrete

The application of waste rubber particles and basalt fibre (BF) in concrete can not only improve the performance of the resulting concrete but also alleviate the environmental pressures related to waste tire disposal. In this study, the impacts of rubber particles and BF on the mechanical and impact performance of concrete are experimentally investigated. Additionally, the macroscopic test phenomenon is explained based on the appearance of the microstructure. The results show that for basalt fibre-reinforced concrete (BFC), when the BF content increases from 0 to 0.4 %, the cube compressive strength and elastic modulus decrease from 71.5 MPa to 62.5 MPa and 44.5 GPa to 41.0 GPa, respectively, while the bending strength increases from 5.9 MPa to 6.6 MPa and then decreases to 6.3 MPa. A BF content of 0.3 % is selected to prepare basalt fibre-reinforced rubber concrete (BFRC). As the rubber particle content of BFRC increases from 0 to 20 %, the cube compressive strength, elastic modulus and bending strength decrease from 64.3 MPa to 51.5 MPa, 41.9 GPa to 33.5 GPa and 6.6 MPa to 5.9 MPa, respectively. However, the reduction rate of the mechanical properties of BFRC is approximately half that of fibre-free rubber concrete at the same rubber content. The shapes of the stressstrain curves of the BFC and normal concrete (NC) are similar, whereas the descending stage of the stressstrain curve of the BFRC is obviously gentler, and the whole BFRC stressstrain curve is much fuller, reflecting typical ductile failure. Both the BF and rubber particles contribute to impact performance improvement, but the effect of the rubber particles is much greater than that of the BF. Compared with that of the NC, the incorporation of 0.3 % BF increases the initial crack impact energy (W1) and final crack impact energy (W2) by 71 % and 79 %, respectively, but when 20 % rubber particles are additionally added, the increase rates of W1 and W2 reach 668 % and 686 %, respectively. The impact life evolutions of BFC and BFRC can be described effectively by a two-parameter Weibull distribution function.

Assessment of wind energy resource in the western region of Somaliland

As the population of Somaliland continues to grow rapidly, the demand for electricity is anticipated to rise exponentially over the next few decades. The provision of reliable and cost-effective electricity service is at the core of the economic and social development of Somaliland. Wind energy might offer a sustainable solution to the exceptionally high electricity prices. In this study, a techno-economic assessment of the wind energy potential in some parts of the western region of Somaliland is performed. Measured data of wind speed and wind direction for three sites around the capital city of Hargeisa are utilized to characterize the resource using Weibull distribution functions. Technical and economic performances of several commercial wind turbines are examined. Out of the three sites, Xumba Weyne stands out as the most favorable site for wind energy harnessing with average annual power and energy densities at 80 m hub height of 317 kW/m2 and 2782 kWh/m2, respectively. Wind turbines installed in Xumba Weyne yielded the lowest levelized cost of electricity (LCOE) of not more than 0.07 $/kWh, shortest payback times (i.e., less than 7.2 years) with minimum return on investment (ROI) of approximately 150%.

A Statistical Evaluation Method Based on Fuzzy Failure Data for Multi-State Equipment Reliability

For complex equipment, it is easy to over-evaluate the impact of failure on production by estimating the reliability level only through failure probability. To remedy this problem, this paper proposes a statistical evaluation method based on fuzzy failure data considering the multi-state characteristics of equipment failures. In this method, the new reliability-evaluation scheme is firstly presented based on the traditional statistical analysis method using the Weibull distribution function. For this scheme, the failure-grade index is defined, and a fuzzy-evaluation method is also proposed by comprehensively considering failure severity, failure maintenance, time, and cost; this is then combined with the time between failures to characterize the failure state. Based on the fuzzy failure data, an improved adaptive-failure small-sample-expansion method is proposed based on the classical bootstrap method and the deviation judgment between distributions of the original and newborn samples. Finally, a novel reliability-evaluation model, related to the failure grade and its membership degree, is established to quantify the reliability level of equipment more realistically. Example cases for three methods of the scheme (the failure-grade fuzzy-evaluation method, the sample-expansion method, and the reliability-evaluation modeling method) are presented, respectively, to validate the effectiveness and significance of the proposed reliability-evaluation technology.

Reliability analysis of respirators based on the analytic hierarchy process and multicriteria decision-making

This study examined the reliability of respirators using hierarchical analysis and multicriteria decision-making. The hierarchical structure, which consists of three assessment criteria and six product assemblies as decision possibilities, reveals that the priority of evaluation criteria follows the trend of cost, complexity and technology. Face-piece, triple-piece and visor assemblies have the highest failure rate, according to an analysis of product reliability at the assembly level. However, according to the analysis at the parts level, the most likely failures are found in the face-piece, upper and lower visor frames, visor, head-harness, exhalation valve disc and exhalation valve seat. In addition, the Weibull distribution function (with a shape parameter >1) can be utilized to predict product reliability. Among the six defined product assemblies, according to the sensitivity analysis, the overall weight of the triple-piece assembly and the visor assembly has the most sensitivity to changes in the priority of evaluation criteria.

Evaluation and Improvement of the Accuracy of Reanalysis and Analysis Datasets for Wind Resource Assessment in Sudan

Wind speed datasets are used to evaluate wind resources and energy production of wind farms. In locations where measured data are not available, reanalysis and analysis datasets can be used as an alternative to assess wind resources. This study evaluated the accuracy of wind speed data collected from reanalysis and analysis datasets against mast-measured data between 1975 and 1985 in Sudan, using monthly statistical analyses. Three bias correction methods, based on Measure-Correlate-Predict (MCP) and Linear Adaptation (LA1 and LA2), were applied to determine the original wind speed. The results indicate that LA1 outperformed MCP and LA2. Furthermore, the Weibull distribution function was employed to analyze the wind speed characteristics. In addition, wind power density was calculated using data from different sources. The findings show that although the wind power potential of the chosen locations is not suitable for large wind turbines, wind power can still be exploited with small wind turbines. Consequently, this study introduces a wind energy roadmap to attract investors in clean energy for sustainable development in Sudan, address energy problems, and meet domestic demands. The study also identifies the most important grid datasets for assessing the country's wind potential, enhancing the accuracy of assessments for investors and policymakers.

About the Necessity to Consider Membrane Electrolyte Degradation Statistically

Polymer Electrolyte Membrane Fuel Cells (PEMFCs) are subjected to aging under pure mechanical, pure chemical and the combination of both stressors. Progression of degradation leads to membrane failures. In this study, seven different accelerated stress test (AST) protocols are applied to degrade two types of commercially available membrane electrode assemblies (MEAs) to demonstrate the necessity to evaluate lifetime of this system with statistical methods. In total, data from 56 samples is reported. Membrane lifetime is derived from hydrogen crossover and open circuit voltage (OCV) which is tracked over the course of degradation. The characteristic membrane lifetime distribution of each AST protocol is described via a cumulative Weibull distribution function (CDF). As a result, the scatter of lifetime distribution correlates with the lifetime itself and thus conclude that less repeats are required for ASTs creating short lifetimes compared to those causing long lifetimes. As the latter is required especially for membrane lifetime prediction, these conclusions are relevant for anybody designing the lifetime of PEMFC stacks.

Analysis of the Interference Effects in CMOS Image Sensors Caused by Strong Electromagnetic Pulses

With the electromagnetic environment becoming increasingly complex, it is crucial to address the risk posed by electromagnetic pulse, which critically impairs the performance and reliability of electronic systems based on complementary metal oxide semiconductor (CMOS) image sensors. In this context, research on the failure types of CMOS image sensors in a high-power electromagnetic environment, caused by strong electromagnetic pulses and the rapid evaluation method of interference immunity, has garnered significant interest. This paper conducts electromagnetic pulse simulation experiments on CMOS image sensors to first study their failure types, such as image abnormalities and functional interruption, and then identify the corresponding failure criteria. Furthermore, this study builds on the small sample test evaluation method to investigate the interference threshold of functional interruptions in CMOS image sensors by calculating the failure probability at different field strengths. The obtained data were combined with the Weibull distribution function for fitting, the results of which found the interference threshold to be at 40.4 kV/m. The findings of this study provide a basis for evaluating the survivability of CMOS image sensors and their associated reinforcement technology in high-power electromagnetic environments.

Research on freeze-thaw damage and life prediction model of polyethylene fiber-reinforced cementitious composites based on reliability analysis

Engineered Cementitious Composite (ECC), is a fiber-reinforced cementitious composite with excellent ductility, toughness, impact resistance and multi-crack development characteristics. In addition to the excellent mechanical properties, the durability of ECC has also received equal attention. In order to investigate the frost resistance of polyethylene fiber-reinforced cementitious composites (PE-ECC), PE-ECC and normal concrete (NC) specimens were subjected to different numbers of freeze-thaw cycles, and the changes in compressive strength, mass loss rate and relative dynamic modulus of elasticity of the specimens before and after freezing and thawing were tested, so as to compare the freeze-resistant properties of PE-ECC and NC. A freeze-thaw damage model was established using the two-parameter Weibull distribution function, and the freeze-thaw reliability of NC and PE-ECC was analyzed based on the Wiener process analysis, based on which a life prediction model was established to predict the life of NC and PE-ECC under freeze-thaw environment. The results show that after 200 freeze-thaw cycles, the compressive strength loss rate, mass loss rate and the relative dynamic elastic modulus loss rate of NC and PE-ECC are 32.97%, 2.35%, 50.28% and 17.28%, 0.71%, 6.57%, respectively, and the damage indexes of PE-ECC are lower than that of NC, and the NC after 200 freeze-thaw cycles has reached the standard of freeze-thaw damage, while PE-ECC is still at a lower level of freeze-thaw damage; it shows that the frost resistance of PE-ECC is better than that of NC, and the addition of PE fibers can effectively improve the frost resistance of concrete; the results of the damage model and the reliability analysis coincide well with the experimental results, and the results of life prediction are given in some cold regions, which can provide a basis for the application of PE-ECC in practice.

Calculating Weibull Coefficients Using the Maximum Likelihood Method and Comparing Performance Across Sites

In this study, the compliance of the Weibull Distribution Function (WDF) and actual wind data (WD) from three different locations were investigated. The coefficients of the WDF were calculated using the Maximum Likelihood Method (MLM) in the Adana, Osmaniye, and Hatay regions. The main purpose of this study is to observe the performances of the MLM in determining the coefficients of the WDF in different regions in different years and to examine the success of this method in estimating the mean wind power and speed of the determined regions. The performance of the indicated approach in all three selected locations was evaluated using the Root Mean Square Error (RMSE), Coefficient of Determination (R2), and Mean Percentage Error (MPE). Also wind power densities were estimated for all three regions, which are one of the most essential metrics for estimating a region's wind energy (WE) potential. WDF power densities were estimated and compared to real wind power densities generated from measured WD for three different places. The performance of the method described in this paper was investigated in depth in various places with varying geographic characteristics. In addition, in the same years, the performance of the chosen method was evaluated in detail in three distinct places, and it was seen how geographical factors affected the method's performance.

Using of the Weibull distribution in developing global solar radiation forecasting models

AbstractIn this study, a solar radiation prediction model was developed using the Weibull distribution function (WDF). The main purpose of this study is to develop a new model for solar radiation (SR) estimation using the WDF and to bring this model to the literature. Although the WDF is widely used in wind energy forecasting due to its compatibility with wind speed data, it has not been used before in solar radiation forecasting model development. In this study, it is aimed to make SR estimation with the WDF for the first time. SR data for all regions where this new model was developed and its performance was examined were obtained from the General Directorate of Meteorology. In order to decide the success of these developed models, five different statistical metrics (RPE, MPE, MAPE, SSRE, and t‐stat) were discussed in the study. When the results are evaluated in general, it is seen that the new developed model has an acceptable performance. According to all test results in the region where the model was developed, it is seen that the new developed model showed the best performance with 0.0353, 0.4068, 7.1851, 0.1144, and 0.0162 values, respectively. The performance of this new developed model was observed in three different regions. When the statistical test results in these regions were examined, it was seen that the new model developed had a similar performance to the popular solar forecasting models widely used in the literature.

On the use of a new probabilistic model and machine learning methods with applications to reliability and music engineering

In this paper, we considered a new probability distribution with new applications in the field of engineering, in particular, in music engineering. The new probability distribution is mainly based on the Weibull distribution and cosine function. We call this the weighted cosine flexible Weibull distribution. The point estimators for the new distribution are obtained. We evaluate these point estimators for three sets of parameter values. The illustration of the weighted cosine flexible Weibull distribution is provided for two practical data set which are drawn from the reliability and music engineering. In addition, to dual robust machine learning approaches, we implement the Lasso (Least Absolute Shrinkage and Selection Operator) and Elastic Net (ENet) to improve the predictive performance of the data. This was done in response to the existence of outliers in the same datasets. We provide comparative analysis to see how well these approaches performed in comparison to the Step Indicator Saturation (SIS) method.

Meso-damage behaviour of cement-stabilised macadam after long-time immersion based on particle flow theory

Water can cause a certain degree of damage to cement-stabilised macadam (CSM), and the degree of damage is greater if CSM is immersed in water for a long time. In order to study CSM damage after lengthy water immersion, a discrete-element model of CSM was established. The Weibull distribution function was used to simulate the heterogeneous contacts between particles. The parallel bond model was used to simulate the material constitutive relationship. The microscopic parameters of CSM were obtained by trial-and-error method. The stress–strain curve was obtained from immersion tests. The micromechanical behaviour of the CSM after immersion was analysed. The results showed that the contact area and strength of the CSM immersed for 30 days were, respectively, 31.4% and 46% less than those of the non-immersed macadam. The force chains between particles were evenly distributed. At peak loading, the normal contact force between particles was much larger than the tangential contact force, and the vertical force chain was much larger than the transverse force chain. The distributions of cementation energy, friction energy and impact energy were not uniform in the middle/peak loading stage.

A Comparative Study on the Estimation of Wind Speed and Wind Power Density Using Statistical Distribution Approaches and Artificial Neural Network-Based Hybrid Techniques in Çanakkale, Türkiye

In recent years, wind energy has become remarkably popular among renewable energy sources due to its low installation costs and easy maintenance. Having high energy potential is of great importance in the selection of regions where wind energy investments will be made. In this study, the wind power potential in Çanakkale Province, located in the northwest of Türkiye, is examined, and the wind speed is estimated using hourly and daily data over a one-year period. The data, including 12 different meteorological parameters, were taken from the Turkish State Meteorological Service. The two-parameter Weibull and Rayleigh distributions, which are the most widely preferred models in wind energy studies, are employed to estimate the wind power potential using hourly wind speed data. The graphical method is implemented to calculate the shape (k) and scale (c) parameters of the Weibull distribution function. Daily average wind speed estimation is performed with artificial neural network–genetic algorithm (ANN-GA) and ANN–particle swarm optimization (ANN-PSO) hybrid approaches. The proposed hybrid ANN-GA and ANN-PSO algorithms provide correlation coefficient values of 0.94839 and 0.94042, respectively, indicating that the predicted and measured wind speed values are notably close. Statistical error indices reveal that the ANN-GA model outperforms the ANN-PSO model.

Damage constitutive model of rock and application based on strength theory

Abstract Extending the one-dimensional damage constitutive model of rock materials to 3 dimensions using classical methods fails to capture the significant differences in tensile, compressive, and shear strengths exhibited by the rock materials. Consequently, it is necessary to revise the existing damage constitutive model to describe the damage evolution law and constitutive relationship of rock materials more accurately and provide a theoretical basis for the safety and stability analysis of underground engineering more scientifically, thus ensuring the sustainable development of underground engineering. By introducing the Weibull distribution function and building upon strength theory, a correction function was established. This correction function adjusted the equivalent strain, enabling the development of a 3-dimensional damage constitutive model that accounted for the varying tensile, compressive, and shear strengths of rock materials. The impact of various parameters on the model's fitting effectiveness was evaluated, and a comparative analysis was conducted against pertinent experimental results. Using the theory of neutral axis deviation, the relationship between bending moment and damage variables in a purely bending rock beam was derived. The study revealed that all parameters of the damage constitutive model could be derived from the uniaxial stress-strain curve, and its theoretical findings exhibited strong agreement with experimental results obtained from rock and rock-like materials under uniaxial tension, compression and triaxial compression. Based on the examined cases, it was concluded that, when considering both tensile and compressive damage, the ultimate bending moment of a rock beam was approximately one-third of its elastic limit bending moment in an undamaged state. The results have verified the feasibility of the damage constitutive model.

Adaptive salp swarm algorithm for sustainable economic and environmental dispatch under renewable energy sources

Many developing nations face energy crises, in addition to the global warming issue, owing to the recent increase in oil prices, accordingly, identifying the alternate energy sources. As a result, scientists around the globe are investigating new computational techniques for the energy dispatch under hybrid power systems. The aim of this research is to explore the integration of green energy sources (GESs) such as wind and solar in the conventional hydro–thermal coordination problem (CHTCP) to reduce the energy production cost along with the environmental benefits. The proposed hybrid energy coordination problem considers a probabilistic model for incorporating GESs uncertainties by using the point-estimation technique. Weibull and Beta distribution functions are utilized for the treatment of uncertain input variables of wind and solar sources, and the overall energy production cost is optimized via an improved heuristic swarm-based paradigm, namely, adaptive salp swam algorithm (ASSA). Three complex test systems are chosen (with and without GESs) to demonstrate the effectiveness of ASSA on hybrid power systems. The control parameters of ASSA are modified to maintain a balance between the exploration and exploitation phases to improve the convergence and to achieve better solution. The simulation results indicate that the integration of GESs into CHTCP has lowered the operational expenses by 10 percent and emissions by 64 percent. The findings have been compared with the existing techniques to show the effectiveness of the proposed approach.

Impact resistance of macro and micro steel fibre reinforced self-compacted concrete (SFRSCC) with modelling and reliability analysis

Adding steel fibres can transform the brittle characteristic of concrete into a ductile state. The objective of the current study is to test the impact resistance of macro and micro steel fibre-reinforced self-compacting concrete (SFRSCC) experimentally by applying a simulated drop-weight impact, as well as statistically and through reliability studies. Cube specimens were used for the experiment. The inclusion of macro and micro steel fibre greatly increased the concrete mixture’s impact resistance. It is observed that the volume fraction of 0.75 and 0.50% of macro and micro steel fibre has improved impact resistance with an increase in the percentage of energy absorption of 216.21 and 240.53%, respectively. All the concrete samples exhibited the same failure pattern. Using Response Surface Methodology, the impact resistance of SFRSCC mixtures can be accurately predicted. The first and failure cracks (N1 and N2) follow a two-parameter Weibull distribution function of drop-weight impact test.

Study of convective air turbulence based on the probability distribution function of angle of arrival fluctuations

This study investigates the probability density function (PDF) of angle of arrival (AoA) fluctuations of a laser beam propagating through convective air turbulence in two settings: indoor turbulence and atmospheric surface layer. The indoor turbulence is generated by an electric heater with a 50 cm × 100 cm surface area placed horizontally on the bottom. The atmospheric turbulence experiments are conducted over a level at 60 cm height from an asphalted area using a slightly divergent laser beam that propagates along 350 m. Image motion monitoring of four sub-apertures installed in front of the receiving telescope aperture is used to record the AoA fluctuations and their PDFs over the entrance pupil at the sub-aperture locations for both types of turbulence. The observations are made in two perpendicular directions to the propagation of the laser beam. The experimental PDFs of the AoA fluctuations are fitted with Gaussian, Lognormal, Weibull, and Gamma distribution functions. The results show that the Weibull and Gamma models are more consistent with the experimental data for the indoor convective air and atmospheric turbulence respectively. For the indoor convective turbulence, the full width at half maximum and the peak location of the measured PDFs increase with the heater temperature, as well as the goodness of fit, which saturates at high temperatures.