Weibull Law Research Articles

Parameters estimation of the Weibull law for reliability modeling of an equipment

Parameters estimation of the Weibull law for reliability modeling of an equipment

Regimes of Precipitation Change Over Europe and the Mediterranean

AbstractThe Mediterranean region is experiencing pronounced aridification and in certain areas higher occurrence of intense precipitation. In this work, we analyze the evolution of the precipitation probability distribution in terms of precipitating days (or “wet‐days”) and all‐days quantile trends, in Europe and the Mediterranean, using the ERA5 reanalysis. Looking at the form of wet‐days quantile trends curves, we identify four regimes. Two are predominant: in most of northern Europe the precipitation quantiles all intensify, while in the Mediterranean the low‐medium quantiles are mostly decreasing as extremes intensify or decrease. The wet‐days distribution is then modeled by a Weibull law with two parameters, whose changes capture the four regimes. Assessing the significance of the parameters' changes over 1950–2020 shows that a signal on wet‐days distribution has already emerged in northern Europe (where the distribution shifts to more intense precipitation), but not yet in the Mediterranean, where the natural variability is stronger. We extend the results by describing the all‐days distribution change as the wet‐days’ change plus a contribution from the dry‐days frequency change, and study their relative contribution. In northern Europe, the wet‐days distribution change is the dominant driver, and the contribution of dry‐days frequency change can be neglected for wet‐days percentiles above about 50%. In the Mediterranean, however, the change of precipitation distribution comes from the significant increase of dry‐days frequency instead of an intensity change during wet‐days. Therefore, in the Mediterranean the increase of dry‐days frequency is crucial for all‐days trends, even for heavy precipitation.

Physical and mechanical properties of two tropical wood (Detarium macrocarpum and Piptadeniastrum africanum) and their potential as substitutes to traditionally used wood in Cameroon

This study aimed to characterise two little-known woods and discuss their potential to replace those heavily exploited in Cameroon's forests. Amouk (Detarium macrocarpum) and Dabema (Piptadeniastrum africanum) were characterised for their physical and mechanical properties. Density, shrinkage, desorption kinetics, shear strength, tensile strength and modulus of elasticity (MOE) in compression and flexion were determined. A Weibull analysis was performed to predict their failure. It was found that Amouk and Dabéma can be classified as medium-heavy wood with low shrinkage and desorption, following Midilli's empirical model. The physical and mechanical characterisations show that the density, strength and MOE parameters of the woods are close to each other and enable them to be classified as medium-strength woods. The probability of failure in compression follows Weibull's law. These woods can, therefore, be used in structural applications such as construction, replacing common woods.

Safety assessment of technical systems based on limit values

Ensuring the safe operation of complex technical systems is an urgent task. Complex technical systems include lifting, mobile, agricultural machinery, etc. Absolutely every complex system fails during operation. At the same time, failures can have different effects not only on reliability indicators, but also on the degree of safety. The degree of safety of operation of complex equipment is directly influenced by the probability and nature of the occurrence of failures. Thus, in order to increase operational safety, it is necessary to reduce the risk of a negative event, which is defined as the possibility of an adverse event occurring, that is, a combination of the degree of negative consequences with the possibility of its occurrence. The article provides an example of calculating the risk of failure; a method for calculating the parameters of the three-parameter Weibull distribution is proposed; an algorithm for determining three parameters of the Weibull law for a sample is given; the results of parameter calculations are presented; Proposals have been put forward for ways to increase the level of reliability and safety, respectively.

From stress concentrations between inclusions to probability of breakage: A two-dimensional peridynamic study of particle-embedded materials.

Particle-embedded materials consist of a dispersed phase of particles in a sticking matrix. We used a bond-based peridynamics method to investigate their elastic properties, rupture, and probability of failure. We performed an extensive two-dimensional parametric study where particles are disk-shaped inclusions diluted into a pore-filling matrix. Both particle and matrix are considered to be brittle elastic with a perfectly bonded interface. The inclusion volume fraction φ and the inclusion matrix toughness ratio β (β≥1) were varied from 0.254-0.754 (jamming point) and 1.5-100.0, respectively. A total of 5000 uniaxial tensile tests up to failure were performed. We showed that the Halpin-Tsai model fits well all Young elastic moduli even for nearly in-contact particles. The stress distribution strongly depends on φ and β. As the highest stresses (at the origin of crack nucleation) occur between neighboring particles, we analyzed the average stress in gaps. We found that, regardless of the particle volume fraction, the yield stress is a power law of a grain-scaled stress concentration factor. We also investigated the probability of failure of the samples. We found that whatever φ and β, this probability follows a classical Weibull law. Finally, we showed that Weibull modulus, normalized by its value for infinitely rigid particles, is inversely proportional to a function of the stress concentration factor.

Production Facilities Safety Assessment According to the Maximum Values of Machines Reliability

Introduction. At the stage of designing technical devices and performing appropriate strength calculations of metal structures, sufficiently large reserves of strength are taken, which, theoretically, exclude any failures of parts. In fact, the machines work with frequent failures. Of interest are undiagnosed failures that lead to a critical decrease in safety, especially at hazardous production facilities. It is assumed that the previously applied approaches of selective determination of the maximum (minimum) reliability value, based on point estimates of the distribution parameters of the two-parameter Weibull law, lead to an overestimation of the calculated indicators of the probability of failure-free operation, i.e. underestimation of risk. Therefore, the work objective is to consider an approach to assessing the risk of operating production facilities in a situation of accidental occurrence of dangerous and undiagnosed failures in systems.Materials and Methods. Methods for technical devices safety assessment based on probability theory were used in the work, and the probability of machine failure was determined based on the well-known method of reliability theory. This method consists in calculating and constructing distribution functions of random variables (load-bearing capacity and loading) that influence the occurrence of failure. The level of increase in the reliability index was determined, leading to frequent unpredictable failures of technical devices (machines) and a decrease in the safety of their operation.Results. The signs of inconsistency of strength calculations based on overestimated safety margins, which in theory exclude failures of parts and machines in general, are identified and substantiated. A new approach to risk assessment of operating production facilities in a situation of accidental occurrence of dangerous and undiagnosed failures by safety systems has been developed and implemented. An algorithm for determining the three parameters of Weibull's law for a population based on sample data has been developed. The resource distribution densities of the boom of the single-bucket excavator EK-14 are constructed. The recommendations are given to increase the probability of failure-free operation to 0.9989.Discussion and Conclusion. The results of the conducted research allow us to substantiate a new approach to risk assessment of operating production facilities in the event of dangerous and undiagnosed failures of basic parts by safety systems, leading to negative consequences.

Modelling the Optimal Electricity Mix for Togo by 2050 Using OSeMOSYS

This work uses bottom-up modeling to explore the future evolution trajectories of the electricity mix in Togo by 2050. The objective is to investigate the evolution of the mix and the future investments needed to achieve the sustainable energy and climate change goals. Three scenarios were developed using OSeMOSYS. The reference scenario, named Business As Usual, closely reflects the evolution of the Togolese electricity sector under a business-as-usual assumption and planned capacity increases up to 2030. The second scenario, Net Zero by 2050, is based on the first scenario while ensuring that CO2 emissions cancel out in 2050 by following the Weibull law. The third scenario called Emission Penalty aims not only at the integration of renewable energies like the second one but also at the least cost electricity mix if emission penalties are applied. The results of the cost optimization indicate that photovoltaic and importation are the optimal choices ahead of gas and hydropower. The renewable energy aspect of the electricity mix is more highlighted in the last scenario. At the same time, the model shows that greater energy independence is achievable at the cost of a transitory increase in the cost of the electricity system. A tenfold investment effort is needed in 2030 to ensure either continuity of the status quo or a shift in strategy.

Modal characterization of crack network development in an MgO containing refractory castable

Damage due to MgO hydration in castables has been studied by bar resonance and recently by Digital Image Correlation (DIC). The hydration reaction kinetics was studied via principal component analyses (PCA) applied to DIC results of images acquired during 60 h of curing and drying of an MgO containing refractory castable. The experiment was carried out in a in-house climatic chamber at 50°C and 50% of relative air humidity. The displacement and maximum eigen strain fields were obtained via DIC. Their PCA revealed the crack network as the most relevant component, with a temporal development of a sigmoidal curve where a two-parameter Weibull law was satisfactorily fitted. The reaction duration was virtually identical for both fields, and only a time shift in reaction initiation and saturation was attributed to the choice of field. The approach allows the need for user-defined thresholds to be avoided for crack quantification.

OPTIMIZATION OF CUTTING MODES ON HEAVY MACHINES

The optimization of the cutting process is of great importance for metalworking in ensuring the high quality of products and increasing its competitiveness. Increasing the efficiency of metalworking is based on the designation of optimal cutting parameters. It is determined that the economic criterion is the criterion of optimality: discounted costs, prime cost and productivity. The objective functional of the discounted costs and productivity which considers feature of cutting on heavy machines is generated. The limitations of the design of the machine and tool, work material and tool material, tool life, as well as the limitations caused by the quality of the tool operation is taken into account. Optimization of cutting modes is carried out simultaneously by two variables - feed S and cutting speed V. Optimal cutting modes should provide the maximum average productivity and minimum average cost. If several optimality criteria are used, optimization is performed for each of them. The final decision is made by comparing the obtained values. The average actual tool life is a random value. It was accepted that the durability period of carbide tools on heavy machine tools was distributed according to the Weibull law. It is established that the cutting process is characterized by a large number of interrelated factors influencing both the course and the result of the process. With increased requirements to the stability of the technological process of machining of parts, in determining the rational cutting parameters, the tool reliability is also taken into account

On the Control of Metal Strength of Structural Elements of Floating Cranes

Introduction. The article is devoted to the issues of non-destructive testing of mechanical characteristics of metal structural elements of cranes. The reliability of cranes largely determines their safety. The main manifestations of operational failures of floating cranes are analyzed on the example of the UMK-2 crane. It is noted that 27% of failures occur due to the loss of metal strength of their structural elements. Determination of the causes of such failures is possible by conducting non-destructive testing of the mechanical characteristics of the failing structural elements metal. The paper provides the principle of one of the methods of non-destructive strength control based on the impact insertion of a conical indenter into the metal under study with the subsequent analysis of the intermediate parameters of this insertion. The results of measurements of the mechanical characteristics of the metal deformed during the operation of the boom strut of a floating crane are given. The current measured values of the mechanical characteristics of the metal obtained at various points of the strut are processed for compliance with the three-parameter Weibull law to obtain the minimum values of these characteristics. As a result of such processing, it is stated that the minimum values of yield strength, strength and elongation are lower than those claimed by the design documentation for the crane. This may be one of the reasons for the deformation of the structural element during operation.Problem Statement. The application of the method of non-destructive testing of the metal of the boom strut is considered in order to assess the mechanical characteristics and establish possible causes of its deformation when analyzing the operational reliability of the crane.Theoretical Part. When identifying possible causes of deformation or destruction of steel elements of crane structures, it is proposed to apply a method of non-destructive testing of mechanical characteristics based on the impact insertion of a conical indenter into the test surface. Further, it is proposed to process the obtained sample of values of the measured characteristic for compliance with the three-parameter Weibull law to estimate the shift parameter or the minimum value of this characteristic.Conclusions. The minimum values of the tensile strength, yield strength and relative elongation of the metal of the deformed boom strut of the UMK-2 crane were obtained on the basis of the application of the method of non-destructive testing with subsequent approximation of statistical information by the Weibull distribution law. A conclusion was made about the reduced strength characteristics of the metal relative to those stated in the technical documentation, which could cause deformation of the crane boom element.

Proposal of an analytical method based on linear regression for modeling reliability by Weibull law

The paper aims to identify a sufficiently precise and easy method that will ultimately lead to a working tool easily accessible and used for modeling reliability through the most widely used mathematical law in the field of reliability - the Weibull law. An analytical method for linearizing the Weibull function is proposed in order to allow, by using the linear regression function of the Microsoft Office software, to obtain the parameters of the reliability model. The calculation program created in Microsoft Excel allows the identification of the 3 parameters of the Weibull model and based on the Weibull model thus determined, the validation or invalidation of the reliability objectives. The application presented reveals that the proposed working tool is easy to use and the Weibull model obtained has a very good probability.

Reliability of Life Calculation Laws for Materials under Variable Amplitude Loading

For many years, researchers have been looking for a reliable law that will take into account the type of loading, the mechanical characteristics of the material, the geometric configuration in the determination of the service life of mechanical parts. The service life of structures at risk (automotive, aeronautics, among others.) in service, subjected to variable solicitations in time, are random for a same type of loading. This article proposes to highlight the influence of this variation in service life on the reliability of structures by a probabilistic approach. The characteristics of the proposed law are satisfactory compared to the classical laws because it takes into account the parameters of the classical laws (Weibull law) and the dispersions of the lifetimes of a same material.

Improvement of trawler hull structure under condition of ensuring fatigue strength

The structure of the hull of the project 1288 trawler in a region of fore hold was improved to ensure fatigue strength of assemblies of the intersection of main frames with the second bottom. To this end, a study of the fatigue strength of these assemblies was carried out for the original side structure and two versions of its modernization. Values of internal forces at the points of appearance of fatigue cracks in the compartment have been determined for three design versions of the side. It was found that the greatest forces act in the middle of the fore half of the compartment. Calculations of parameters of the long-term distribution of magnitudes of ranges of total equivalent operating stresses according to the Weibull law in the points of occurrence of fatigue cracks for different design versions of the side grillage have been performed. These parameters were determined for the middle of the fore hold of the vessel and for the areas in which maximum values of bending moment ranges are in effect with and without corrosive wear. Values of total fatigue damage and durability of the studied assemblies were determined. Calculations were carried out by nominal stress method, hot spot stress method, and experimental and theoretical method. It was shown that in order to ensure fatigue strength of the assembly under consideration, it is necessary to extend the intermediate frames of the original version of the side structure to the level of the second bottom fixing them to the deck. It is also necessary to attach a cargo platform to the side thus reducing the frame span. As a result, the level of fatigue damage over 25 years of operation will decrease by about 3.5 times. As it was found, approximate consideration of the slamming effect does not significantly increase the amount of fatigue damage to the assembly. The results of the development of recommendations for modernization of the side structure can be implemented both on ships of the 1288 project and on other ships with a transverse side framing system.

ОЦЕНКА УРОВНЯ НАДЕЖНОСТИ ВАРИАНТОВ УСИЛЕНИЯ СТРОИТЕЛЬНЫХ МЕТАЛЛОКОНСТРУКЦИЙ С ИСПОЛЬЗОВАНИЕМ МАТЕМАТИЧЕСКОЙ МОДЕЛИ ВЕРОЯТНОСТИ ИХ БЕЗОТКАЗНОЙ РАБОТЫ

The article is devoted to the issues of assessing the level of reliability of options for strengthening building metal structures using mathematical models of the probability of their uninterrupted operation. The increasing requirements for the structural safety of building metal structures, the need to use justified mathematical calculations confirming their performance and safety, taking into account various reinforcement options determine the relevance of this study. The content of the article is based on the platform of the theoretical basis for the design of reinforcement of metal structures. It is predetermined by the subsequent synthesis of innovative solutions in assessing the level of reliability building structures taking into account the use of mathematical modeling of the probability of uninterrupted operation. The article presents an analysis of the problem points of using the probabilistic method for calculating the level of reliability of building metal structures. This allows to assess the compliance of the existing loads with standard values and guarantee the reliable operation of building metal structures. The characteristics that influence the assessment of the level of reliability of options for strengthening building metal structures using mathematical modeling are highlighted. A critical review of the amplification options from the point of view of the use of mathematical models of the probability of the operation of a metal structure is presented. Attention is focused on the construction of an optimization mathematical model of the bearing capacity of a metal structure using probability theory, Gram-Charlier series, Gumbel's law, Weibull's law. An example of strengthening of a load-bearing truss using a mathematical model for assessing the level of reliability of a metal structure is described. The proposed option will improve the safety, bearing capacity of the structure while ensuring the perception of the maximum possible load and at the same time will reduce the cost of this type of structure in construction.

Study of the influence of dust deposits on photovoltaic solar panels: Case of Nouakchott

Degradation performance of photovoltaic (PV) modules by real weather conditions has become increasingly problematic. In the desert climate, dust accumulation is one of the main concerns that may cause a significant deterioration of PV efficiency. In the present work, experimental investigations were carried out to understand the effect of dust on the electrical performance of PV modules under Toujounine, Nouakchott, Mauritania weather conditions. The measurements were performed with an I-V tracer ftv200. The measured parameters were I-V and P-V curves, open-circuit voltage (Voc), short-circuit current (Isc), current and voltage at maximum power (Imp and Vmp) and maximum power (Pmax); as well as the measurement of temperature of panels and Irradiation. The study was carried out according to the following cleaning scenarios: panels cleaned before each measurement (Clean panels 01), panels undergoing systematic cleaning with the central unit (Clean panels 02) and chains undergoing no cleaning (Dusty panels 03). Then, the modeling of reliability as a function of maximum power by Weibull's law, for clean and dusty panels is evaluated. According to the experimental results, disturbances in I-V and P-V curves for dusty panels were noticed. Also, a decrease in the Isc and the Imp for dusty panels compared to clean panels was found. These results are explained by the effect of dust accumulation on the module's surface, which blocks the solar radiation and thus reduces the conversion efficiency of PV modules. Again, dust reduces the output power of photovoltaic modules by 21.57% for dusty panels per clean panels. Finally, a low reliability for dusty panels compared to clean panels was found, due to the loss in the output power under the dust effect. These results clearly show the importance of properly maintaining and servicing the photovoltaic modules to avoid their degradation by dust deposits.

Breakage of flawed particles by peridynamic simulations

In this paper, we use a 2D bond-based peridynamic model to investigate the strength of disk-shaped particles including pre-cracks. We use a diametral (or Brazilian) test to break the particles. For the flawless particles, we find that the stress distribution compares well with an analytical model accounting for the size of the contact zone, and the particle stiffness tends linearly to a well-defined value for increasingly resolved meshing. We then introduce cracks, which are numerically defined by reducing the Young modulus of the bonds crossing linear segments. We consider in detail the effect of a single vertical crack on the yield stress as a function of its position. We also consider a randomly distributed population of cracks with sizes generated from a Gaussian size distribution. For a parametric study with a hundred particles, we found a probability of failure that is well fit by a Weibull law. Finally, using an image analysis algorithm, we investigate the statistics of cracks and the resulting fragments.

Modeling the Propagation of Flood Waves at the Mouth of the Comoé River in Grand-Bassam (South East of Côte d’Ivoire)

This study was carried out in order to determine the areas at risk of flooding during high water periods at the mouth of the Comoé River in Grand-Bassam. The database is essentially made up of hydro-climatic data, satellite images and topographic data. According to the various criteria, the Weibull law was selected to estimate the maximum frequency flows. According to this law, the flows at the return periods of 2, 10, 50 and 100 years are respectively 634, 733, 781 and 797 m3 / s. The modeling results showed that the areas exposed to the risk of flooding are located near the Ouladine lagoon and the Ebrié lagoon at the mouth of the Comoé river. The extent of the floodplains varies with flooded areas of the order of 85.63 km²; 89.42 km²; 101.67 km²; 107.10 km² for the return periods of 2; 10; 50 and 100 years old.

Analytical and numerical assessments of probabilities of fatigue fracture of pipeline components under internal pressure

The paper presents analytical and numerical approaches to assessing the probability of failure of structural components of technical systems subjected to cyclic loading. The kinetics of the crack is described by the modified Paris equation. The analytical solution is based on the inverse extrapolation of the critical crack depth. In this case, the only probabilistic parameter is considered to be the initial crack depth, which is assumed to be distributed according to an exponential law. The numerical solution uses the Monte-Carlo method. The initial crack depth, fracture toughness of the structural material, and parameters C and m of the Paris equation are taken as probabilistic parameters. For the statistical description of the process of fatigue crack growth in structural components, a computer code was developed in the Matlab environment, which allows using appropriate random number generators to simulate various laws of distribution of random parameters, including the laws of uniform density, exponential law, normal law, Weibull's law, etc. An example of analytical and numerical calculation of the probability of fatigue failure of a pipeline component containing an axial crack on the inner surface and loaded with internal pressure is given. Comparison of the obtained results of analytical and numerical solutions allows us to conclude that an approximate analytical estimate of the fracture probability can be used for preliminary calculations at the design stage of structural components, as well as for obtaining a prior estimates of the fracture probability when implementing Bayesian updating procedures for specifying the fracture probability and determining the frequency of technical inspections of the condition of the components under consideration as part of the implementation of risk-oriented approaches to ensuring their strength and safety.

Theoretical principles of redundancy and patterns of transport and technological complexes’ adaptation to the operating conditions

The paper addresses the issues of improving the performance of the handling and transport complex at a mining enterprise. It presents statistical estimates for the general standard reliability of the transport system, which should correspond to similar indicators of subsystems of equipment, machinery, etc. We studied the operation of a rock mass transportation system used in open-pit mines. The handling and transport complex includes dump trucks of various capacities and a single-bucket elevator. The process of rock mass excavation and transportation depends on weather and climatic conditions. Among the factors that affect the transport system performance, the following can be distinguished: air temperature, snowdrifts, gas accumulation in the pits, and, as a result, reduction of the visibility range, leading to a decrease in the average speed of vehicles. The mathematical models of transportation are based on the well-known methods of forming excavator and truck fleets. To calculate the reliability of the transport system in the pit, it is necessary to have data on the probability of no-failure operation and the mean time between failures for each vehicle. Information about the state of the vehicles was obtained based on the results of statistical analysis. During optimization calculations, the following restrictions and assumptions were accepted: the limit state of a vehicle was determined by the mileage of 250,000 km; the distribution of the fleet vehicles’ mileage was subject to the Weibull law with the variation factor approximately equal to 1. In this case, the distribution of the mean time between failures can be considered exponential. Analysis of statistical data on the operational reliability of vehicles showed that random failures prevail. When simulating the operation of handling and transport complexes, it is necessary to take into account the parametric and technological connection between individual machines operating within these systems. The developed methodology for justification of the level of equipment adaptation to the operating conditions is aimed at improving the reliability of handling and transport complexes involved in mining production.

Reliability assessment of power supply systems with powerful nonlinear loads

Purpose. To substantiate the expediency of applying distribution laws to model the reliability of power supply systems with powerful nonlinear loads. Methodology. Application of exponential and normal distribution laws, and Weibull's law. Findings. In a comprehensive assessment of the problem of electromagnetic compatibility and the development of multicriteria parameters of energy efficiency of power supply systems of industrial enterprises, it is most appropriate to use the reliability of the elements that are mathematically described by the Weibull distribution. At the same time, the results of modeling of typical electrical modes and variations of substitution schemes of enterprises showed the sensitivity of reliability indicators to changes in power system capacity. Originality. New theoretical foundations for research in modern power supply systems with increasing nonlinear load capacity have developed the scientific basis for analysis and synthesis of energy processes in multiphase electrical systems and propose methods of correction taking into account the complex action of sources of electromagnetic interference. And also to offer methods of estimation of their influence on reliability and efficiency of work of the basic electrotechnological equipment. Practical value. The possibility of applying the obtained results to assess the reliability of power supply systems with powerful nonlinear loads is substantiated. The necessary accuracy and reliability of the decision at the levels of random events, quantities and processes is provided. The mathematical apparatus for the analysis of the main indicators of reliability in the presence of non-sinusoidal voltage is given. Conclusions are made on the adequacy of the calculation results at different stages of electricity distribution. It is shown that the simultaneous optimization of reliability and voltage quality are components of a complex scientific problem of ensuring energy efficiency of electrical networks in the implementation of decentralized models of the energy system.