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1
Tharmabala, T., and Andrzej S. Nowak. "Mathematical models for bridge reliability." Canadian Journal of Civil Engineering 14, no. 2 (April 1, 1987): 155–62. http://dx.doi.org/10.1139/l87-027.
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System reliability of bridge structures is investigated. Three terms are used to describe the standard reliability: structure function, reliability network, and reliability function. A bridge structure is represented by a reliability network which makes it possible to formulate the reliability function of the system. The reliability function is used to evaluate the reliability of the system. Reliability network and the reliability function are formulated for various types of bridges. Effects of component failures on system reliability are illustrated with examples. Key words: bridges, mathematical models, redundancy, system reliability.
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Feinberg, Alec. "Accelerated Reliability Growth Models." Journal of the IEST 37, no. 1 (January 1, 1994): 17–23. http://dx.doi.org/10.17764/jiet.2.37.1.f2u73m8022207868.
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Extending reliability growth so that it can be applied in the area of accelerated testing will enable one to apply all the reliability growth tools and their planning advantages. This paper describes linking these two areas together into what is termed accelerated reliability growth testing (ARGT). Mathematical equations of ARGT for both iso-stress and step-stress accelerated testing are modelled.
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Urbina, Angel, and Thomas Paez. "Statistical Validation of Structural Dynamics Models." Journal of the IEST 46, no. 1 (September 14, 2003): 141–48. http://dx.doi.org/10.17764/jiet.46.1.f430423634885g67.
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There is an increasing reliance in the engineering community on the use of mathematical models to characterize physical system behavior. This is happening even though mathematical models rarely simulate real system behavior perfectly. Due to this reliance, we require objective, well-founded mathematical techniques for model validation. This paper develops a formal approach to the validation of mathematical models of structural dynamics systems. It uses a probabilistic/statistical approach to the characterization of an important measure of behavior of dynamic systems subjected to random excitations, and seeks to validate a mathematical model in a statistical sense. An example is presented.
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Yi, Ping. "Discussion of Mathematical Models of Probabilistic Constraints Calculation in Reliability-Based Design Optimization." Advanced Materials Research 243-249 (May 2011): 5717–26. http://dx.doi.org/10.4028/www.scientific.net/amr.243-249.5717.
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In a reliability-based design optimization (RBDO) problem, most of the computations are used for probabilistic constraints assessment, i.e., reliability analysis. Therefore, the effectiveness, especially the correctness of the reliability analysis is very important. If the probabilistic constraint is misjudged, the optimization iteration would have convergence problems or arrive at erratic solutions. The probabilistic constraint assessment can be carried out using either the conventional reliability index approach (RIA) or the performance measure approach (PMA). In this paper, the mathematical models to calculate the reliability index in RIA and to calculate the probabilistic performance measure (PPM) in PMA are discussed. In RIA, through estimating whether the mean-value point in safe domain or not, we should use a positive or negative reliability index respectively. In PMA, one should always minimize the performance measure to compute PPM whether the performance measure at the mean-value point is positive or negative, which puts right the wrong mathematical model in some literatures and makes it possible to produce effective and efficient approach for RBDO.
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Belov, Alexander, Dmitry Shaforost, and Viktor Chebotarev. "Mathematical Models for Assessing the Thermal Engineering Reliability of Boiler Units of Power Complexes." Известия высших учебных заведений. Электромеханика 64, no. 6 (2021): 88–93. http://dx.doi.org/10.17213/0136-3360-2021-6-88-93.
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The analysis is carried out and the definitions of the concept of thermal engineering reliability, the determining parameter and the determining function of boiler units, are given. A classification has been developed for the determining parameters of steam and hot water boilers by level in the chain of cause-and-effect relationships in the event of a thermal failure. It is proposed to divide the determining parameters and functions of boilers according to their spatial localization into integral and local. A lot of models for defining functions with different mathematical properties (for example, the presence or absence of discontinuities of the second kind) are considered. The defining functions (reliability criteria) currently used in boiler construction have been identified. The analysis of the safety factors for overturning and stagnation in direct-flow and drum boiler units is carried out. The incorrectness of the currently used dependence is shown. A formula has been proposed for these coefficients using internal useful heads, which is especially relevant for boilers with natural circulation at ultrahigh pressure.
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Heydorn, Richard P. "Reliability Engineering: Probabilistic Models and Maintenance Methods." Technometrics 48, no. 3 (August 2006): 446. http://dx.doi.org/10.1198/tech.2006.s412.
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Abdallah, Wafaa, Jacqueline Saliba, Ziubir-Mehdi Sbartaï, Marwan Sadek, Fadi Hage Chehade, and S. Mohammed ElAchachi. "Reliability analysis of non-destructive testing models within a probabilistic approach." MATEC Web of Conferences 281 (2019): 04003. http://dx.doi.org/10.1051/matecconf/201928104003.
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The diagnosis of reinforced concrete is essential to detect the degradation and thus maintain the structural performance of civil engineering structures. This paper aims to establish a mathematical relationship between the ultrasonic pulse velocity UPV (considered as an observable variable) and two concrete properties indicators (compressive strength fc and water content W) within a probabilistic framework. Synthetic simulations are proposed to derive a conversion model between the statistical properties of the output and the input parameters for a reinforced concrete structure by taking into account spatial variability of concrete.
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ROMANCHENKO, Ihor S., Oleh SEMENENKO, Maryna SLIUSARENKO, Mykola VASIANOVYCH, and Ihor LEVCHENKO. "On the development of mathematical models for the reliability evaluation of aircraft operation in combat conditions." INCAS BULLETIN 13, S (August 3, 2021): 169–78. http://dx.doi.org/10.13111/2066-8201.2021.13.s.16.
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The authors of this study propose a methodological approach to modelling the reliability evaluation of aircraft operation in combat conditions. When developing recommendations on operational and strategic requirements for promising aircraft, a very important aspect is the elicitation of the requirements for their reliability, namely no-failure operation. Reliability as a parameter of any equipment should be set in the technical specifications for development together with other operational requirements in the form of reasonable quantitative indicators – reliability standards. The establishment of specific reliability standards stimulates its growth and creates the basis for rational design, taking into account the requirements of reliable operation. The analysis showed that different models can be used to simulate aircraft reliability. In this case, for example, the final values of mean time to failure (MTTF) would be different. The test results show that the methods and mathematical models used to substantiate the values of time and probability of trouble-free operation of aircraft do not fully correspond to the actual processes of changing their state during the use in the military. This is confirmed by a significant discrepancy in the values of reliability indicators implemented in practice. This was due to the fact that the acquainted mathematical models of aircraft reliability do not take into account the combat conditions in which they are supposed to operate. In addition, the reliability indicators used do not take into account possible changes (decrease) in these indicators during the period of aircraft operation. In general, the shortcomings inherent in the methods and mathematical models currently used to describe the aircraft reliability reduce the accuracy of the results obtained, and also do not quite adequately reflect the features of the corresponding process. When using different models, the cost of time to failure differs significantly. The more factors are taken into account, the greater the operating time to failure will be. This means that when designing aircraft, it is necessary to set the value of this indicator greater than indicated in the form. Taking into account additional factors complicates the model, but at the same time makes it more accurate.
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Ya-jun, Wang, and Wang Jun. "Generalised Reliability On Hydro-Geo Objects." Open Civil Engineering Journal 9, no. 1 (July 31, 2015): 498–503. http://dx.doi.org/10.2174/1874149501509010498.
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This study established the fuzzy logic modeling of the stochastic finite element method based on the first-order approximation theorem. Fuzzy mathematical models of safety repertories were incorporated into the stochastic finite element method to analyze the stability of embankments and foundations in order to describe the fuzzy failure procedure for the random safety performance function. The fuzzy models were developed with membership functions with half depressed gamma distribution, half depressed normal distribution, and half depressed echelon distribution. The result shows that the middle region of the dike is the principal zone of concentrated failure due to local fractures. There is also some local shear failure on the dike crust. This study provides a referential method for solving complex multi-uncertainty problems in engineering safety analysis.
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Guo, R., and E. Love. "Reliability Modelling with Fuzzy Covariates." International Journal of Reliability, Quality and Safety Engineering 10, no. 02 (June 2003): 131–57. http://dx.doi.org/10.1142/s0218539303001056.
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In this research, we focus on covariate modelling to explore the interactions between industrial system and its enviroment in terms of the modelling fundamental characteristic — random and fuzzy uncertaity with an intention to decrease the fatal weakness of the modern dissection methodology. We extend the additive and multiplicative covariate models from these considering randomness alone into these considering both randomness and fuzziness in the sense as a mathematical extension to the existing covariate modelling. In terms of the form of logical function an engineering oriented fuzzy reliability model which could potentially count all the aspects associated with an operating system and its environment is proposed. Statistical estimation on the parameters of system fuzzy reliability is considered based on the general theory of the point processes. The impacts on the optimal plant maintenance from the engineering oriented fuzzy reliability modelling is also discussed. Finally we use an industrial example to illustrate the main theoretical developments.
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Liu, Ying, Yao Ma, Zhigang Qu, and Xiaozhong Li. "Reliability Mathematical Models of Repairable Systems With Uncertain Lifetimes and Repair Times." IEEE Access 6 (2018): 71285–95. http://dx.doi.org/10.1109/access.2018.2881210.
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Obzherin, Yuriy E. "Semi-Markov and hidden semi-Markov models of energy systems." E3S Web of Conferences 58 (2018): 02023. http://dx.doi.org/10.1051/e3sconf/20185802023.
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The problem of information control systems creation for energy systems and transition to intelligent control and engineering is one of the important problems of reliability and efficiency theory for energy systems. The solution of this problem is possible based on construction of mathematical models concerning different aspects of these systems structure and operation. The possibilities of application of semi-Markov processes with common phase space of states, hidden Markov and semi-Markov models for energy system modeling are considered in the paper.
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Wang, Wanting, Zubair Ahmad, Omid Kharazmi, Clement Boateng Ampadu, E. H. Hafez, and Marwa M. Mohie El-Din. "New generalized-X family: Modeling the reliability engineering applications." PLOS ONE 16, no. 3 (March 31, 2021): e0248312. http://dx.doi.org/10.1371/journal.pone.0248312.
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As is already known, statistical models are very important for modeling data in applied fields, particularly in engineering, medicine, and many other disciplines. In this paper, we propose a new family to introduce new distributions suitable for modeling reliability engineering data. We called our proposed family a new generalized-X family of distributions. For the practical illustration, we introduced a new special sub-model, called the new generalized-Weibull distribution, to describe the new family’s significance. For the proposed family, we introduced some mathematical reliability properties. The maximum likelihood estimators for the parameters of the new generalized-X distributions are derived. For assessing the performance of these estimators, a comprehensive Monte Carlo simulation study is carried out. To assess the efficiency of the proposed model, the new generalized-Weibull model is applied to the coating machine failure time data. Finally, Bayesian analysis and performance of Gibbs sampling for the coating machine failure time data are also carried out. Furthermore, the measures such as Gelman-Rubin, Geweke and Raftery-Lewis are used to track algorithm convergence.
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Mazūra, Mindaugas, and Olga Fadina. "THE RELIABILITY OF FORECASTS IN TRANSPORTATION." TRANSPORT 17, no. 6 (December 31, 2002): 219–22. http://dx.doi.org/10.3846/16483840.2002.10414046.
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Major problems of forecasting the economic characteristics of transportation (i.e. the amount of freight and passengers carried, the turnover rate of freight and passengers, etc. in transportation as a whole and in particular areas using various transport facilities) are demonstrated. Methods for predicting the development of transportation based on multidimensional regression and correlation analysis and realizing mathematical models for choosing linear and nonlinear regression equations, more accurately approximating the empirical data, are presented. The research conducted has demonstrated that the most reliable forecasts may be made when the methods of choosing the proper non-linear regression equation described in Section 2 of the present paper are used.
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Li, Xiao Quan, Run Ling Li, and Yi Jing Xie. "Reliability Analysis Based on Markov Process for Repairable Systems." Applied Mechanics and Materials 571-572 (June 2014): 241–44. http://dx.doi.org/10.4028/www.scientific.net/amm.571-572.241.
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The problems of reliability and maintainability for repairable systems are investigated in this paper, and Markov process is employed to build the mathematical models of availability and reliability for the repairable systems. Firstly, the formulas of availability and reliability for single repairable systems are deduced. Then, the repairable system with two parallel components and one standby are investigated, which is common in engineering application. Finally, simple approaches are summarized for availability of complicated repairable systems. Since the two approaches has the same result, which provides theoretical proof for the study of repairable systems’reliability and availability.
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Pugacheva, Natalya, Tatyana Kirillova, Olga Kirillova, Aleksandr Lunev, and Oksana Pavlova. "Forming the Basic Mathematical Knowledge among Technical Students." International Journal of Emerging Technologies in Learning (iJET) 15, no. 03 (February 18, 2020): 34. http://dx.doi.org/10.3991/ijet.v15i03.11686.
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Mathematical knowledge plays a system-forming role in education. The aim of this paper is to find out the didactic features of mathematical knowledge formation. The study involved 50 professors, 300 students. The criteria of mathematical knowledge acquisition include reliability, autonomy, and stability. The main study objectives are as follows. First, to clarify and scientifically substantiate special functions of mathematical knowledge in the process of engineering activity (bijection, formalization, relativity, and robustness). Second, to determine the formation of academic and applied mathematical knowledge. Technical knowledge can be applied using the special functions of mathematical knowledge. For example, in the form of mathematical models, or in a stable mathematical component in the professional outlook. The academic mathematical knowledge is focused on the systematic integrity of purpose, content, forms, methods and means of education. Along with transdisciplinary holistic worldview formation. Applied mathematical knowledge is focused on integration of teaching, educating, developing functions of education to acquire common cultural and professional competences. In modern conditions of rapid computerization, the opportunities to use mathematical analysis and modeling are increasing. However, basic mathematical knowledge is needed to assess the reliability of computer solutions.
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Isametova, Madina E., Rollan Nussipali, Nikita V. Martyushev, Boris V. Malozyomov, Egor A. Efremenkov, and Aysen Isametov. "Mathematical Modeling of the Reliability of Polymer Composite Materials." Mathematics 10, no. 21 (October 26, 2022): 3978. http://dx.doi.org/10.3390/math10213978.
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An urgent task in creating and using composite materials is the assessment and prediction of their performance properties and reliability. Currently, when studying the reliability of the materials, there is little experimental data, mathematical descriptions, and models for both probabilistic and deterministic methods to assess reliability. Based on the obtained experimental data, this article discusses the development of a methodology for predicting reliability. The article also proposes a statistical model for assessing reliability by the criterion of the structural strength of products made of polymer composite materials. The characteristics of the reliability changes in the materials when in operation are presented. The calculation allowed obtaining graphs showing the dispersion and statistical variability of the characteristics of polypropylene-based polymeric materials at the design, production, and operation stages of the product life cycle. The computational experimental results for determining the influence of the shape of inclusions and mass on the mechanical properties of a polymer composite material aimed at improving the strength characteristics of the products are presented. Based on a computational experiment in the MSC Digimat MF nonlinear solver, equations are provided to demonstrate the regression dependence of the strength of a part made of a polymer composite material on technological factors.
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Al-Mutairi, Norah N., Lutfiah I. Al-Turk, and Sharifah A. Al-Rajhi. "A New Reliability Model Based on Lindley Distribution with Application to Failure Data." Mathematical Problems in Engineering 2020 (November 6, 2020): 1–11. http://dx.doi.org/10.1155/2020/4915812.
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Software reliability is an important feature that influences systems’ reliability. Software reliability models are a common tool to evaluate software reliability quantitatively. Various reliability models have been suggested based on the NHPP (nonhomogeneous Poisson process). In this article, a new NHPP model based on the Lindley distribution is proposed. The mathematical formulas for its measures of reliability are obtained and graphically illustrated. The proposed model’s parameters are estimated using both the NLSE (nonlinear least squares estimation) and the WNLSE (weighted nonlinear least squares estimation) methods. The model is then validated based on several different reliability datasets. The methods of estimation are evaluated and compared using three different criteria. The performance of the new model is also evaluated and compared, both objectively and subjectively, with three previously suggested models. The application results show that our new model demonstrates good performance in our selected failure data.
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Semenenko, Oleg, Maryna Sliusarenko, Tatyana Akinina, Roman Legkohod, and Oleksandr Paiuk. "ASSESSMENT OF COMPLIANCE OF MATHEMATICAL MODEL OF RELIABILITY OF COMBAT MEANS OF ANTI-AIRCRAFT MISSILE FORCES WITH REQUIREMENTS TO MATHEMATICAL MODELS." Collection of scientific works of Odesa Military Academy, no. 15 (September 30, 2021): 144–51. http://dx.doi.org/10.37129/2313-7509.2021.15.144-151.
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The article presents a variant of the procedure for assessing the compliance of the mathematical model of the reliability of anti-aircraft missile warfare equipment with the requirements for mathematical models using the example of the Buk self-propelled fire launcher. Parameters affecting change of serviceability of self-propelled fire plant operation in conditions of combat situation are determined. The use of the Weibull distribution allows, by varying the parameter values, to increase the guarantee of the implemented self-propelled fire plant reliability indicators, stated in technical conditions, during its operation in the troops. If necessary, this model can also take into account factors that arise suddenly, for example, taking into account the staffing of the self-propelled fire plant of the anti-aircraft missile regiment to assess the possible (predicted) value of average daily losses, taking into account various measures to reduce the values of the predicted average daily losses. Values calculated using this model react markedly to changes in model parameters, are set within the specified restrictions. In addition, it is possible to determine the time between failures. The accuracy of the results of calculating certain quantities using the mathematical model was estimated by absolute and relative errors. The calculations indicate the relative simplicity of the mathematical model, because it uses simple mathematical methods. The ability to vary the parameters of scale and shape parameters (taking into account aging), the mathematical model of IED failure makes it possible to obtain individual (partial) results obtained using previously used similar models, which emphasizes the evolution of this model. The improved method of mathematical modeling quite adequately reflects the trouble-free operation of the anti-aircraft missile system "Buk" taking into account the conditions of hostilities and meets the requirements for mathematical models. Keywords: probability of failure-free operation, parameters of mathematical model, combat situation, absolute error, time between failures, average daily combat losses.
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Tsitsiashvili, Gurami. "Construction and Analysis of Queuing and Reliability Models Using Random Graphs." Mathematics 9, no. 19 (October 7, 2021): 2511. http://dx.doi.org/10.3390/math9192511.
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In this paper, the use of the construction of random processes on graphs allows us to expand the models of the theory of queuing and reliability by constructing. These problems are important because the emphasis on the legal component largely determines functioning of these models. The considered models are reliability and queuing. Reliability models arranged according to the modular principle and reliability networks in the form of planar graphs. The queuing models considered here are queuing networks with multi server nodes and failures, changing the parameters of the queuing system in a random environment with absorbing states, and the process of growth of a random network. This is determined by the possibility of using, as traditional probability methods, mathematical logic theorems, geometric images of a queuing network, dual graphs to planar graphs, and a solution to the Dirichlet problem.
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Puzanov, A. V. "Transdisciplinary models of hydraulic drives of mobile machinery." «System analysis and applied information science», no. 4 (February 6, 2019): 51–55. http://dx.doi.org/10.21122/2309-4923-2018-4-51-55.
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Modern drive engineering requires a comprehensive analysis of all work processes in hydraulic drives, solving the problems of modeling the technological processes of their production using mathematical and software tools of various physicality.The article proposes an approach to the development of hydrodrives of mobile equipment based on transdisciplinary models of instruments and control systems. These models are designed to unite in a single information space a methodical and mathematical apparatus of various physicality: mechanics, kinematic, hydromechanics, heat engineering, and methods for their solution. These measures will increase their adequacy, reduce assumptions and reduce the safety factor as a measure of imperfection of the scientific and technical understanding of the facility.The article gives an example of the use of this approach in the development of volumetric hydraulic drives of mobile equipment a technique for calculating the indicator diagram of an axial-plunger hydraulic machine at a micro level using the Matlab / Simulink, Autodesk Simulation CFD and Autodesk Simulation Mechanical software complexes. The indicator diagram of the hydraulic machine is a clear characteristic of the dynamic qualities of the product. From the correctness of the calculation of this characteristic, the dynamic properties, reliability and resource of the drive as a whole depend.
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Belostotsky, Mikhail A., and Anatoly M. Korolenok. "Совершенствование методов планирования ремонтных работ на основе анализа надежности нефтепроводной системы." SCIENCE & TECHNOLOGIES OIL AND OIL PRODUCTS PIPELINE TRANSPORTATION, no. 5 (December 9, 2021): 562–68. http://dx.doi.org/10.28999/2541-9595-2021-11-5-562-568.
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The author presents the methodology for identifying risks in operation of main oil pipelines, which can be based upon in improvement of methods for planning overhauls of the main pipelines. A method for calculating reliability indicators of the system is reviewed, including analysis of the type distributions of the system elements failures pattern. The reliability of the system is determined by purely mathematical operations on the obtained distributions. Such an approach is typical for the system (structural, mathematical) theory of reliability, the key task thereof being the transition from the elements reliability indicators to the system reliability indicators. It is advisable to resolve the problems of calculating the actual reliability of a complex technical system taking for consideration the dependencies of its elements, based on the approach assuming that reliability of the elements and the system shall be calculated in the general multi-level simulation process wherein both physical and structural models are used. Physical models of elements reliability are used at lower levels, while structural models are used at higher ones. Установлена своевременность и актуальность идентификации и формализации структурно-логических связей показателей эксплуатации линейной части магистральных нефтепроводов. Представлена методология идентификации рисков при эксплуатации магистральных нефтепроводов, которая может быть положена в основу совершенствования методов планирования их капитальных ремонтов. Рассмотрен метод для расчета показателей надежности технической системы, предусматривающий анализ типовых распределений отказов ее элементов. Надежность системы находится чисто математическими операциями над полученными распределениями. Подобный подход характерен для системной (структурной, математической) теории надежности, основной задачей которой является переход от показателей надежности элементов к показателям надежности системы. Задачи расчета реальной надежности сложной технической системы с учетом зависимостей ее элементов целесообразно решать на основе подхода, который состоит в том, что расчет надежности элементов и системы проводится в общем многоуровневом имитационном моделирующем процессе с применением физических и структурных моделей. Физические модели надежности элементов используются на низших уровнях, а структурные модели – на высших.
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Kumar, Rajiv, A. K. Gupta, and M. Naveen. "Compartment Fires: BFD Curve and Mathematical Models." Journal of Applied Fire Science 17, no. 1 (January 1, 2007): 73–95. http://dx.doi.org/10.2190/af.17.1.e.
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Melcher, Thomas, and Ulrich Krause. "A Mathematical Approach to Estimate the Error During Calculating the Smoke Layer Height in Industrial Facilities." TRANSACTIONS of the VŠB – Technical University of Ostrava, Safety Engineering Series 11, no. 1 (March 1, 2016): 1–7. http://dx.doi.org/10.1515/tvsbses-2016-0001.
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Abstract Engineering based calculation procedures in fire safety science often consist of unknown or uncertain input data which are to be estimated by the engineer using appropriate and plausible assumptions. Thereby, errors in this data are induced in the calculation and thus, impact the number as well as the reliability of the results. In this paper a procedure is presented to directly quantify and consider unknown input properties in the process of calculation using distribution functions and Monte-Carlo Simulations. A sensitivity analysis reveals the properties which have a major impact on the calculation reliability. Furthermore, the results are compared to the numerical models of CFAST and FDS.
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Nikulina, E., V. Severin, and D. Lukinova. "Mathematical Models for Investigation of WWER-1000/320 Transients." Nuclear and Radiation Safety, no. 1(77) (February 19, 2018): 18–23. http://dx.doi.org/10.32918/nrs.2018.1(77).03.
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The paper presents mathematical models of the reactor WWER-1000/320, which are designed to investigate non-stationary operating modes of the reactor. The models in relative state variables include a point model of neutron kinetics with six groups of delayed neutrons and models of thermal processes, gradual heat generation, change in xenon concentration. The effects of reactivity on the movement of control rods and changes in reactor power, the effects of reactivity on changes in fuel and coolant temperatures, effect of change in the concentration of xenon are taken into account. The values of the constant parameters of the models are given for the start of stationary fuel loading.
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INOUE, SHINJI, SHIHO HAYASHIDA, and SHIGERU YAMADA. "EXTENDED HAZARD RATE MODELS FOR SOFTWARE RELIABILITY ASSESSMENT WITH EFFECT AT CHANGE-POINT." International Journal of Reliability, Quality and Safety Engineering 20, no. 02 (April 2013): 1350009. http://dx.doi.org/10.1142/s0218539313500095.
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A software hazard rate model is known as one of the important and useful mathematical models for describing the software failure occurrence phenomenon observed in a testing phase. It is difficult to say that the testing environment always constant during a testing phase due to changing the specification and fault target and so forth. Therefore, taking into consideration of the effect of the change in software reliability growth modeling is expected to conduct more accurate software reliability assessment. In this paper, we develop extended software hazard rate models based on well-known Jelinski–Moranda and Moranda models, by considering with a change of testing environment. Especially in this paper, we incorporate the uncertainty of the effect of the change on the software reliability growth process into the software hazard rate modeling. Finally, we show numerical examples for our models and results of model comparisons by using actual data.
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Lukianchuk, Vadim, Boris Lanetskii, Hennadii Khudov, Ivan Terebuha, Oleksii Zvieriev, Oleh Shknai, Denys Zapara, Serhii Petruk, Valentyn Dyptan, and Oleksandr Piavchuk. "Development of an experimental-estimation method for estimating indices of residual life of a radio technical complex." Eastern-European Journal of Enterprise Technologies 3, no. 9(111) (June 30, 2021): 27–39. http://dx.doi.org/10.15587/1729-4061.2021.233538.
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To implement the operation of a radio technical complex according to its technical condition, it is necessary to jointly evaluate its reliability and residual life indices with required accuracy and reliability and minimization of the scope of special tests. The known methods are focused on separate solutions to the problems of estimating these indices as applied to the regulated strategy. To solve this problem, general provisions have been developed for estimating the indices of residual life of the radio technical complex including the accepted assumptions and limitations for developing the method, the estimated indices, and criteria of limiting state. The developed experiment-calculated method is a set of mathematical models of change of the reliability indices of a radio technical complex depending on calendar duration of operation or total operating time and analytical models of estimating the indices of its residual life. The mathematical models of change of mean time between failures, the probability of failure-free switching, and the parameter of the flow of failures of the radio technical complex depending on calendar duration of operation or the total operating time were presented in a form of regressive dependences. Analytical models of estimating the residual life indices are ratios for calculating the "average residual service life (resource)" according to the technical and economic criterion using regression-time dependences of the reliability indices. The developed experiment-calculated method can be used to estimate the indices of residual life of the radio technical complex with acceptable accuracy (no more than 2 quarters) and reliability (no worse than 0.8). In this case, the duration of the intervals of predicting the reliability indices should be 0.5 to 1 year and the corresponding observation intervals should be more than 1 year
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PADBERG, FRANK. "MAXIMUM LIKELIHOOD ESTIMATES FOR THE HYPERGEOMETRIC SOFTWARE RELIABILITY MODEL." International Journal of Reliability, Quality and Safety Engineering 10, no. 01 (March 2003): 41–53. http://dx.doi.org/10.1142/s0218539303000981.
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We present a fast and exact novel algorithm to compute maximum likelihood estimates for the number of defects initially contained in a software, using the hypergeometric software reliability model. The algorithm is based on a rigorous and comprehensive mathematical analysis of the growth behavior of the likelihood function for the hypergeometric model. We also study a numerical example taken from the literature and compare the estimate obtained in the hypergeometric model with the estimates obtained in other reliability models. The hypergeometric estimate is highly accurate.
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BROGGI, MATTEO, ADRIANO CALVI, and GERHART I. SCHUËLLER. "RELIABILITY ASSESSMENT OF AXIALLY COMPRESSED COMPOSITE CYLINDRICAL SHELLS WITH RANDOM IMPERFECTIONS." International Journal of Structural Stability and Dynamics 11, no. 02 (April 2011): 215–36. http://dx.doi.org/10.1142/s0219455411004063.
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Cylindrical shells under axial compression are susceptible to buckling and hence require the development of enhanced underlying mathematical models in order to accurately predict the buckling load. Imperfections of the geometry of the cylinders may cause a drastic decrease of the buckling load and give rise to the need of advanced techniques in order to consider these imperfections in a buckling analysis. A deterministic buckling analysis is based on the use of the so-called knockdown factors, which specifies the reduction of the buckling load of the perfect shell in order to account for the inherent uncertainties in the geometry. In this paper, it is shown that these knockdown factors are overly conservative and that the fields of probability and statistics provide a mathematical vehicle for realistically modeling the imperfections. Furthermore, the influence of different types of imperfection on the buckling load are examined and validated with experimental results.
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Poliakov, Andriy, Volodymyr Kryvtsun, Maksym Kalenyk, and Viacheslav Nagachevskyi. "A formalized representation of exponential models of the main indicators of reliability, the limitations of their use for the characteristics of engineering weapons." Journal of Mechanical Engineering and Transport 12, no. 2 (February 2021): 100–105. http://dx.doi.org/10.31649/2413-4503-2020-12-2-100-105.
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The article deals with the solution of a scientific and applied problem to study the possibility of using existing exponential models to determine the reliability indicators of engineering weapons. Exponential models are widely used to assess the reliability of objects, mainly consisting of radio electronic elements, which led to their mass distribution in the aviation industry, air defense facilities, etc. Experimental operation of typical samples of military road-building equipment and experimental studies of the operating time of the main blocks and assemblies of engineering weapons show that the rate of failure and restoration of these products are functions of time. This state of affairs is associated with the design features of engineering weapons, which are characterized by the complex use of electrical, mechanical, hydraulic and other systems, while during use these systems can often experience significant overloads. At the same time, it should be borne in mind that today the engineering weapons that are in the units generally have a service life longer than that guaranteed by the manufacturer, which significantly affects the parameters of failure rates and recovery. The article shows the procedure for obtaining expressions for calculating the main indicators of the reliability of complex technical systems with an exponential distribution of operating time to failure and their recovery time and it is allowed to use them only for minimal periods of time (from several hours to several days, depending on the intensity of the use of machines) due to for the non-ergodic nature of the process of failures and restorations. In addition, the use of these models should be accompanied by an assessment of the adequacy of the results obtained to the real process with the adjustment of the duration of the corresponding time intervals. Thus, the construction of mathematical models of the technical state of engineering equipment will be accompanied by a search for other conceptual approaches to determining the reliability indicators of engineering equipment and methods for calculating these indicators.
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Kulyk, Mykola, Olexiy Kucher, and Vladimir Miltsov. "MATHEMATICAL MODELS OF THE CALCULATION OF AIRCRAFT STRUCTURAL RELIABILITY / ORLAIVIŲ KONSTRUKCINIŲ ELEMENTŲ STIPRUMO PATIKIMUMO SAVYBIŲ SKAIČIAVIMO MATEMATINIAI MODELIAI." Aviation 15, no. 1 (April 14, 2011): 11–20. http://dx.doi.org/10.3846/16487788.2011.566315.
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The mathematical models of damageability under static and cyclic loadings are investigated. The parameters of damageability and endurance are considered necessary for the calculation of long-term durability wear and low-cycle and high-cycle fatigue, thermo-cyclic endurance and deformation as well as general models, taking into account multi-axis and multicomponent loads. The models of damageability at loading range, the probabilistic models of endurance and accumulation of damage at random influence are given. Probabilistic criteria for service life estimation and their connection with accumulated damageability are researched. Santrauka Darbe išanalizuoti pažeidimų matematiniai modeliai, kai veikia statinės ir ciklinės apkrovos. Išnagrinėti pažeidimų modelių parametrai bei ilgaamžiškumo savybės, reikalingos ilgalaikio stiprumo išnaudojimui, mažacikliam ir daugiacikliam nuovargiui, termocikliniam ilgaamžiškumui ir takumui įvertinti. Apibendrinti modeliai, įvertinantys daugiaašių ir daugiakomponenčių apkrovų ypatybes. Pateikti pažeidimų modeliai, esant apkrovų spektrui, tikimybiniai stiprumo ir pažeidimų kaupimo modeliai, esant atsitiktiniams poveikiams. Išanalizuoti resurso išnaudojimo kriterijai, parodytas jų ryšys su sukauptais pažeidimais.
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Milani, Abbas S., and James A. Nemes. "On Identification of Material Models When Nonrepeatability of Test Data is Present: Application to Textile Composites." Journal of Engineering Materials and Technology 126, no. 4 (October 1, 2004): 443–49. http://dx.doi.org/10.1115/1.1789963.
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Engineering test data occasionally violate assumptions underlying standard material model identification. Consequently, one has to apply appropriate remedies with respect to each violation to enhance the reliability of identified material parameters. This paper generalizes the use of the signal-to-noise weighting scheme when heteroscedasticity of test data are suspected. Different mathematical and practical aspects of the approach are discussed. Additionally, the ensuing weighted identification process is simplified to an equivalent standard form by means of a space transformation. Finally, the approach is applied to the identification of a nonlinear material model for textile composites, on both qualitative and quantitative levels.
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Catelani, Marcantonio, Lorenzo Ciani, Giulia Guidi, Gabriele Patrizi, and Diego Galar. "Estimate the useful life for a heating, ventilation, and air conditioning system on a high-speed train using failure models." ACTA IMEKO 10, no. 3 (September 30, 2021): 100. http://dx.doi.org/10.21014/acta_imeko.v10i3.1058.
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<p class="Abstract">Heating, ventilation, and air conditioning (HVAC) is a widely used system used to guarantee an acceptable level of occupancy comfort, to maintain good indoor air quality, and to minimize system costs and energy requirements. If failure data coming from company database are not available, then a reliability prediction based on failure rate model and handbook data must be carried out. Performing a reliability prediction provides an awareness of potential equipment degradation during the equipment life cycle. Otherwise, if field data regarding the component failures are available, then classical reliability assessment techniques such as Fault Tree Analysis and Reliability Block Diagram should be carried out. Reliability prediction of mechanical components is a challenging task that must be carefully assessed during the design of a system. For these reasons, this paper deals with the reliability assessment of an HVAC using both failure rate model for mechanical components and field data. The reliability obtained using the field data is compared to the one achieved using the failure rate models in order to assess a model which includes all the mechanical parts. The study highlights how it is fundamental to analyze the reliability of complex system integrating both field data and mathematical model.</p>
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Kong, Gangqiang, Hanlong Liu, Qing Yang, Robert Y. Liang, and Hang Zhou. "Mathematical Model and Analysis of Negative Skin Friction of Pile Group in Consolidating Soil." Mathematical Problems in Engineering 2013 (2013): 1–11. http://dx.doi.org/10.1155/2013/956076.
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In order to calculate negative skin friction (NSF) of pile group embedded in a consolidating soil, the dragload calculating formulas of single pile were established by considering Davis one-dimensional nonlinear consolidation soils settlement and hyperbolic load-transfer of pile-soil interface. Based on effective influence area theory, a simple semiempirical mathematical model of analysis for predicting the group effect of pile group under dragload was described. The accuracy and reliability of mathematical models built in this paper were verified by practical engineering comparative analysis. Case studies were studied, and the prediction values were found to be in good agreement with those of measured values. Then, the influences factors, such as, soil consolidation degree, the initial volume compressibility coefficient, and the stiffness of bearing soil, were analyzed and discussed. The results show that the mathematical models considering nonlinear soil consolidation and group effect can reflect the practical NSF of pile group effectively and accurately. The results of this paper can provide reference for practical pile group embedded in consolidating soil under NSF design and calculation.
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Lyapichev, Yury P., Guido Mazza, Enrique Mateu, Gerald Zenz, and Alain J. Carrère. "Reliability and applicability of modern numerical analyses of dams." Structural Mechanics of Engineering Constructions and Buildings 15, no. 6 (December 15, 2019): 458–69. http://dx.doi.org/10.22363/1815-5235-2019-15-6-458-469.
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Relevance. At present the application of numerical analyses to real problems of dam engineering has suffered at times from the gaps between the specialists of mathematical modeling and dam engineers and managers. The first group usually includes information system specialists because they are able to develop the computer models to their full potential. The professionals belonging to the second group often prefer to revert to traditional methods of calculation and empirical methods based on their proven experience. The aim of the work - based on recommendations of International workshops seminars, organized by the ICOLD Committee on Computational Aspects of Dam Analysis and Design, help dam engineers to interact with mathematical modeling specialists and to work with them without language barriers or gaps in knowledge. In this relation the assessment of reliability and applicability of numerical analyses of dams allows engineers to develop the optimal dam design. Methods. Assessment of the reliability of numerical methods of analyses of dam behavior was based on data of 10 International benchmark-workshop seminars, organized by the Committee in Italy (1991 and 1992), France (1994 and 2009), Spain (1996), USA (1999), Austria (2001), Romania (2003), China (2005), Russia (2007), in which specialists of these countries also took part.
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Мaidaniuk, V. "Analysis of problems of small-angle approximation in mathematical models of projectile flight." Military Technical Collection, no. 27 (November 30, 2022): 19–26. http://dx.doi.org/10.33577/2312-4458.27.2022.19-26.
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The article deals with the topical issue of developing mathematical models of projectile flight, which accurately describe the projectile motion in the air. It is shown that the nature of the mathematical models presentation varies depending on the required reliability degree of the real physical projectile flight process representation by the mathematical model, the adequate consideration of certain forces (moments) acting on the projectile, as well as the level of information about the external flight conditions which include the parameters of the air in which the projectile moves.At the same time, the use of the shape coefficient - the agreement coefficient in the differential equation system leads to "rough" mathematical models, which does not allow to adequately describe the projectile flight trajectory and its individual elements. The solution to this problem is especially relevant during developing and implementing procedures, technical solutions in the interest of achieving the necessary level of interoperability with NATO forces, the gradual abandonment of the standard functions of air resistance, the transition to individual functions and mathematical models of projectile motion, which are currently accepted in the member states of the Alliance. The conducted analysis of modern mathematical models showed that their construction is based on an approximate approach, which was called the small-angle approximation, in which, for an axisymmetric rotating projectile, it is considered that the nutation angles are sufficiently small, the aerodynamic forces (moments) depend only on the speed of its flight and the nutation angle, and only the linear terms of their Taylor series expansion are used in the calculations. The nutation-precessional behavior of the projectile was considered and the nonlinear dependencies of the coefficients of the aerodynamic forces (moments) of the projectile on the angles of nutation were revealed.
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Zambon, Ivan, Anja Vidović, and Alfred Strauss. "Reliability of Existing Concrete Structures Determined with Physical Models - Carbonation Induced Corrosion." Solid State Phenomena 259 (May 2017): 255–60. http://dx.doi.org/10.4028/www.scientific.net/ssp.259.255.
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The main goal of transportation infrastructure management is to optimize the use of infrastructure in the most beneficiary way while respecting the predefined requirements. One of the crucial parts in management strategy is the prediction of behaviour of vital transportation elements. Used prediction models should accurately describe the process of degradation and allow forecasting of structural condition by considering environment, usage and maintenance actions. Deterioration models can be divided into mathematical (statistical), physical and empirical models. Statistical models are based on data that describe condition of structure, such as for example condition rating. Physical models describe damage-causing processes and empirical models are experience based. The focus of this paper is to present the physical model of carbonation in assessment of performance of existing reinforced concrete structures in transportation networks. Assessment is done through determining the probability of limit state of depassivation. In order to determine the carbonation without testing, a special attention has to be given to environmental and material parameter identification. Herein, the identification takes into account weather specifics and construction practice in Austria. Finally, the reliability of existing reinforced concrete structures for combination of different exposure classes and material characteristics is analysed. Based on the analysis of reliability, the carbonation nomogram for engineering use is presented, showing the reliability indices β for the service life of 50 years.
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Lyashenko, B. A., Z. A. Stotsko, O. A. Kuzin, M. O. Kuzin, and V. A. Mechnik. "Analysis of friction interaction and optimisation of detail surface hardening technologies using non-local mathematical models." Journal of Achievements in Materials and Manufacturing Engineering 1, no. 100 (May 1, 2020): 20–25. http://dx.doi.org/10.5604/01.3001.0014.1960.
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Purpose: The aim of the work is to build physically sound engineering and design schemes that take into account the behaviour of polycrystalline metal systems under intense loads and allow optimization of surface treatment technologies to increase the operational reliability parameters of products. Design/methodology/approach: Using the approaches of thermodynamics, a methodological scheme is proposed, on the basis of which it is possible to optimize surface engineering technologies to increase the contact durability of details. Findings: It was found that the maximum increase in the durability of steel 40X13 (AISI 420) is achieved with thermocyclic ion nitriding in a cycle of ± 50°C, and the minimum with isothermal nitriding. Research limitations/implications: In this paper, the optimization of technological solutions to increase the contact durability of structural elements operating under prevailing power loads is given. Practical implications: Using the proposed mathematical relationships, optimal technological regimes of ion-plasma nitriding were established for various operating conditions, under which the maximum durability and wear resistance of 40X13 (AISI 420) steel are ensured. Originality/value: The paper proposes an approach to the formation of functionally gradient surface layers of steel with specified operational parameters when choosing optimal nitriding technology modes based on nonlocal mathematical models.
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Igi, Tomislav S., and Natasa Ž. Veljkovi. "Design of a System for Monitoring Reliability of Structures and Constructions in Civil Engineering." International Journal of Engineering Pedagogy (iJEP) 1, no. 2 (June 30, 2011): 19. http://dx.doi.org/10.3991/ijep.v1i2.1634.
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<span style="font-family: "Times New Roman"; font-size: 10pt; mso-fareast-font-family: 'Times New Roman'; mso-ansi-language: EN-US; mso-fareast-language: EN-US; mso-bidi-language: AR-SA;" lang="EN-US">Monitoring of civil engineering structures and constructions requires techniques which can produce high precision and accuracy, reliable measurements and fast processing speed. The development of information and communication systems as well as of microprocessor controllers has enabled a creation of monitoring systems that can be used for tracking reliability of structures and constructions in civil engineering, with described key features. This paper describes in detail the architecture of the Civil Engineering Structures Reliability Monitoring (CERM) system. The system has been designed for the purposes of the Technical Mechanics and Theory of Constructions Department at the Faculty of Civil Engineering and Architecture, University of Nis. Unlike general commercial monitoring systems, the CERM system has been specially designed for the purpose of reliability monitoring, and its potential will be further exploited in this paper. It is based on usage of universal microprocessor controllers Integraf of series 10X, along with specially designed software package. This system provides real time acquisition of measurements for observed civil engineering structures and analysis of received values based on developed mathematical models.</span>
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Pollard, P. C., E. v. Münch, P. A. Lant, and P. F. Greenfield. "The impact of microbiological tools on mathematical modelling of biological wastewater treatment." Water Science and Technology 36, no. 10 (November 1, 1997): 97–108. http://dx.doi.org/10.2166/wst.1997.0368.
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Biological systems are being used to treat an increasing range of complex wastes; domestic and industrial wastewaters containing nutrients and refractory organic compounds, soil sites and groundwater contaminated by organics, and organic solid residues. These treatment processes rely on micro-organisms and, more than ever before, must deliver higher quality outcomes at higher levels of reliability to protect the environment. At the same time, pressures to deliver cost-effective treatment have increased. The challenge for these biological treatment technologies and the associated engineering is to achieve the environmental and economic goals simultaneously. Mathematical modelling is an essential component in developing a detailed understanding of such processes, as well as design guidelines and suitable operating and control strategies. This paper provides a brief summary of the development of mathematical models for biological waste treatment systems, why they have become increasingly complex and how certain microbiological tools can provide the experimental means to validate more complex segregated and structured models of biological behaviour. With a number of specific modelling examples in the field of wastewater treatment, we illustrate the potential of these modern microbiological tools and their implications for gaining an improved understanding of biological waste treatment.
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Rapatskiy, Yurii, and Victoria Lipka. "APPLICATION OF THE SEMI-MARKOV MODEL FOR INVESTIGATION THE PARAMETERS OF MECHANICAL ASSEMBLY PRODUCTION TAKING INTO ACCOUNT DIFFERENT TYPES OF FAILURES." Voronezh Scientific-Technical Bulletin 3, no. 3 (February 2, 2022): 52–64. http://dx.doi.org/10.34220/2311-8873-2022-52-64.
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A technique is proposed for studying the productivity and reliability of technological processes of mechanical assembly production at the stages of the life cycle of mechanical engineering products. A semi-Markov mathematical model is proposed that makes it possible to analyze, for example, the technological processes of manufacturing threaded connections. In the proposed model, the distribution functions (DF) of the service time of a unit of production are determined, taking into account failures. FDs make it possible to ensure informational consistency of models of various hierarchical levels and to study the relationship between the stages of the life cycle of mechanical engineering products.
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Iqbal, Muhammad Zafar, Muhammad Zeshan Arshad, Gamze Özel, and Oluwafemi Samson Balogun. "A better approach to discuss medical science and engineering data with a modified Lehmann Type – II model." F1000Research 10 (August 17, 2021): 823. http://dx.doi.org/10.12688/f1000research.54305.1.
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Background: Modeling with the complex random phenomena that are frequently observed in reliability engineering, hydrology, ecology, medical science, and agricultural sciences was once thought to be an enigma. Scientists and practitioners agree that an appropriate but simple model is the best choice for this investigation. To address these issues, scientists have previously discussed a variety of bounded and unbounded, simple to complex lifetime models. Methods: We discussed a modified Lehmann type II (ML-II) model as a better approach to modeling bathtub-shaped and asymmetric random phenomena. A number of complementary mathematical and reliability measures were developed and discussed. Furthermore, explicit expressions for the moments, quantile function, and order statistics were developed. Then, we discussed the various shapes of the density and reliability functions over various model parameter choices. The maximum likelihood estimation (MLE) method was used to estimate the unknown model parameters, and a simulation study was carried out to evaluate the MLEs' asymptotic behavior. Results: We demonstrated ML- II's dominance over well-known competitors by modeling anxiety in women and electronic data.
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Popovych, P. V., Volodymyr Dzyura, and O. S. Shevchuk. "Reliability Estimation of Transport Means Elements Under the Action of Cyclic Loads and Corrosive Environment." International Journal of Automotive and Mechanical Engineering 15, no. 4 (December 24, 2018): 5793–802. http://dx.doi.org/10.15282/ijame.15.4.2018.6.0443.
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The approach for determining the residual life of the vehicles’ thin-walled metal elements with cracks under the action of cyclic loads and corrosive environment is developed based on the first law of thermodynamics and the fracture mechanics principles. Based on the results of the mathematical description of electrochemical reactions and separate data of fracture mechanics, the equation describing the kinetics of the corrosion-fatigue cracks propagation is deduced. This equation and the initial and final conditions are a mathematical model for determining the residual life of structural elements. The correctness of the developed analytical models is confirmed by the experimental data known in the literature. The performance of this model is demonstrated on the example of determining the residual life of a plate made of 17G1S steel. The plate was diluted by a crack in a 3% NaCl solution and subjected to cyclic loading. An increase in the initial size of corrosion-fatigue cracks is significant to reduce the period of their subcritical growth.
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Zhdanov, Alexey A., Oleg A. Kursin, and Pham Xuan Bach. "The mathematical models for cutting force calculation during structural and corrosion-resistant steels` parts processing." MATEC Web of Conferences 298 (2019): 00099. http://dx.doi.org/10.1051/matecconf/201929800099.
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The paper shows that conventional mathematical models for calculating the cutting force components during the turning process, represented in reference guides on engineering, give drastic errors reaching 100 percent or more for various tool-workpiece couples. These errors interfere with applying reference values of the cutting force for any further calculations, equipment selection, workpiece positioning scheme, workpiece deformation value due to the elastic of the technological system elements during processing and etc., because of the insufficient reliability of the results of such calculations. The paper proposes mathematical models obtained as a result of experimental studies, which allow for increasing the accuracy of the calculation of the components of the cutting force by introducing an additional parameter – i.e., the value of thermo EMF of the test running into the calculation formulas. This approach enables to reduce the error in the calculation of the components of the cutting force up to ± 15%. In addition, the need for the development of specific mathematical models for various groups of materials machined is shown, which is due to the peculiarities of contact processes in the machining of various groups of steels, as well as to qualitative and quantitative indicators of the thermo-physical properties of the materials of tool-workpiece contact couples.
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Sharma, Shivom, Iftekhar A. Karimi, Shamsuzzaman Farooq, Lakshminarayanan Samavedham, and Rajagopalan Srinivasan. "Health Monitoring of Pressure Regulating Stations in Gas Distribution Networks Using Mathematical Models." Energies 15, no. 17 (August 28, 2022): 6264. http://dx.doi.org/10.3390/en15176264.
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Many cities have extensive distribution networks that supply natural or town gas to domestic, industrial, and power plant consumers. A typical network may have hundreds of pressure regulating stations that are of different types and capacities, but most legacy networks are sparsely instrumented. The reliability of these stations is the first priority for ensuring uninterrupted gas supplies; hence, condition monitoring and prescriptive maintenance are critical. In this study, mathematical models were developed for two types of commonly used regulators: spring-loaded and lever-type regulators. We also considered three faults that are typically of interest: filter choking, valve seat damage, and diaphragm deterioration. The proposed methodologies used the available measured data and mathematical models to diagnose faults, track prognoses, and estimate the remaining useful life of the regulators. The applicability of our proposed methodologies was demonstrated using real data from an existing distribution network. To facilitate industrial use, the methodologies were packaged into a user-friendly dashboard that could act as an interface with the operational database and display the health status of the regulators.
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Wang, Zi Bo. "Optimization Design of PV/ Wind Hybrid System Considering Power Supply Reliability." Advanced Materials Research 805-806 (September 2013): 293–98. http://dx.doi.org/10.4028/www.scientific.net/amr.805-806.293.
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In order to give full play to PV/Wind hybrid system, a mathematic model of optimization design considering power supply reliability is proposed in this paper. Firstly, the structure of PV/Wind hybrid system is given, so are the mathematical models of wind generators, PV modulesand batteries are. Then,the mathematic model of optimization design is determined: in the case of meeting the power supply reliability, an objective function is constructed to minimize the total costs of system investment costs, operation and maintenance costs and system power loss cost, which are limited by realistic constraints. Finally, an PV/Wind hybrid system is employed to validate the model, results show that the mathematic model proposed in this paper is suitable to design a PV/Wind hybrid system.
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Wang, Song, Chuan Gui Yang, Fei Chen, Zhao Jun Yang, Zhuang Tan, and Guang Zhu. "Research on Modeling and Parameter Identification of Electro-Hydraulic Servo Loading System." Advanced Materials Research 889-890 (February 2014): 970–77. http://dx.doi.org/10.4028/www.scientific.net/amr.889-890.970.
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In order to improve the mathematical models accuracy of the electro-hydraulic servo loading system from the high-speed motorized spindle reliability test bench. This paper establishes the mathematical model based on the dynamic characteristics of the test bench, then establishes discrete mathematical model of the system based on the Z-transform, and finally uses particle swarm optimization (PSO) algorithm to identify the parameters of the discrete model. Additionally, the least square method is applied to identify the parameters of the model for measuring the PSO algorithm parameter identification capability in our paper. The experimental results show that the mathematical model, identified by the PSO algorithm, can simulate the loading process very well under the strong interference signals, and the result is better than that gotten by the least square method, which proves that the PSO algorithm has high identification accuracy and better capability in parameters identification .
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Kalanta, Stanislovas. "DUAL MATHEMATICAL MODELS OF LIMIT LOAD ANALYSIS PROBLEMS OF STRUCTURES BY MIXED FINITE ELEMENTS." JOURNAL OF CIVIL ENGINEERING AND MANAGEMENT 3, no. 10 (June 30, 1997): 43–51. http://dx.doi.org/10.3846/13921525.1997.10531683.
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The general and discrete dual mathematical models of the limit load analysis and optimization problems of rigid-plastic body are created in the article. The discrete models are formulated by mixed finite elements and presented in terms of kinematic and static formulation. In these models the velocity of the energy dissipation is estimated not only within the volume of finite elements, but also at the plastic surfaces between elements, where the discontinuities of displacement velocities functions appear. The theory of plastic flow, the theory of duality and mathematical programming are applied. The mixed energy functional (1) and (3) of both problems are formulated using the general static formulations of these problems, presented in the article [10], and Lagrangian multipliers method. The mixed finite elements are used for their discretization. The discrete expressions (8), (9) and (13) of mixed functionals are given choosing the interpolation functions (7) for the stress, displacement velocities, plastic multipliers and external load. Stationary conditions are created by static variables (stress and load vectors) of theses functionals. The discrete expressions of the geometric compatibility equations and constraint of load power are received from them. Using them as preliminary conditions for the functionals (8) and (9), the mathematical models (14), (15) and (17) of kinematic formulation of limit load analysis and optimization problems are formulated. The model (20) with a smaller number of unknowns is formed by elimination the displacement velocities. Using Lagrangian multipliers method, the mathematical models (21)-(23) of static formulation for the limit load parameter analysis problem and the models (24)-(26) for the load optimization problem are derived. All of them are the problems of mathematical programming. The mathematical models of static formulation for engineering purposes are more important and fit better. They are easier solved (a smaller quantity of unknowns), besides, they allow to determine the optimum distribution of the load. The formulated mathematical models allow to determine upper values of limit load, stresses, displacement and plastic multipliers velocities. Together with equilibrium models of these problems, presented in the article [10], they allow to determine the lower and upper values of aforementioned parameters. So, a good possibility is created to check reliability and exactness of numerical calculation results and to establish, if the computing net density of finite elements is sufficient.
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Biegańska, Jolanta, and Krzysztof Barański. "Experiments with Pyrotechnic Compositions Based on a Mathematical Model—Part I Evaluation of the Applicability of Mathematical Models in Developing Pyrotechnic Compositions Producing an Acoustic Effect." Energies 14, no. 24 (December 18, 2021): 8548. http://dx.doi.org/10.3390/en14248548.
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This paper presents research on the development of pyrotechnic compositions producing an acoustic effect. These types of compositions are used in firecrackers to imitate a cannon shot—they are most frequently used during military exercises. The research was based on a mathematical model of an experiment. For environmental reasons, the replacement of the harmful oxidant Ba(NO3)2 by KClO4 and NH4ClO4 was modelled. The compositions were tested for reliability and evaluated in terms of friction sensitivity and burning rate. This allowed for the verification of the effectiveness of the modelling carried out. Optimum compositions were selected for further research.
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Hu, Jiqiang, Chunming Ji, Shuai Chen, Shuai Li, Bing Wang, and Zhengong Zhou. "Novel Mathematical-Statistical Models for the Distribution of Fatigue Life and Residual Strength for Fiber Reinforced Polymer Composites." International Journal of Applied Mechanics 12, no. 09 (November 2020): 2050104. http://dx.doi.org/10.1142/s1758825120501045.
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For the distribution prediction of fatigue life and residual strength of fiber reinforced polymer composites, the existing models have the disadvantages of imprecision, instability and single applicability. A novel S–N curve model and a residual strength degradation model were first developed, which are independent and uncorrelated. After verifying their reliability, the statistical distribution models of fatigue life and residual strength were further derived and verified by using experimental data from literature. Compared with the other models, the proposed models can perfectly predict the probability distribution of fatigue life and residual strength under different materials, stacking sequences and stress levels, showing excellent prediction accuracy, stability and applicability.