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Direct computation of Variable Speed Pumps for water distribution system analysis
Published in Bogumil Ulanicki, Kalanithy Vairavamoorthy, David Butler, Peter L.M. Bounds, Fayyaz Ali Memon, Water Management Challenges in Global Change, 2020
E. Todini, M.E. Tryby, Z.Y. Wu, T.M. Walski
The optimization of operations in consumption or production energy systems has been investigated for some decades, The interest in this area is not only related to the complexity of the problem but also mainly by the economical benefits resulting from the best Solution applied. An optimization problem is a mathematical model in which the main goal is to minimize or maximize a quantity through an objective function constrained by certain restrictions. The optimization models can use several methods, which nowadays are becoming more efficient due to the computer technology evolution. In Firmino el al. (2006) an optimization model using linear programming was developed to improve the pumping stations energy costs in Brazil. The study revealed that the energy costs could be reduced by 15%.
Fractional SIR Epidemic Model of Childhood Disease with Mittag-Leffler Memory
Published in Devendra Kumar, Jagdev Singh, Fractional Calculus in Medical and Health Science, 2020
P. Veeresha, D. G. Prakasha, Devendra Kumar
The kernel of mathematical tools for demonstrating the practical difficulties exist in real life is as old as the conception of the world. The development of science and technology is magnetizing the considerations of the authors with the help of mathematical models to understand, describe, and predict the future behavior of the natural phenomena. A mathematical model is a representation of a system with the aid of mathematical theories, rules, formulas, and methods. Humankind has invented the most influential mathematical concepts known as calculus with the integral and differential operators, which can model and simulate numerous mechanisms that have arisen in environments of past decades. Recently, many researchers pointed out that classical derivatives fail to capture essential physical properties like long-range, anomalous diffusion, random walk, non-Markovian processes, and most importantly heterogeneous behaviours. Hence, many scientists and mathematicians find out that the classical differential operators are not always suitable tools to model the non-linear phenomena.
Governing Equations
Published in Dalia E. E. Khalil, Essam E. Khalil, Sprinklers and Smoke Management in Enclosures, 2020
Dalia E. E. Khalil, Essam E. Khalil
The governing equations of a mathematical model describe how the values of the unknown variables (i.e., the dependent variables) change when one or more of the known (i.e. independent) variables change. A mathematical model describes a system using mathematical concepts and language. The process of developing a mathematical model is termed mathematical modeling. Mathematical models are used in natural sciences (such as physics, biology, earth science, chemistry) and engineering disciplines (such as computer science, electrical engineering), as well as in the social sciences (such as economics, psychology, sociology, political sciences). A model may help to explain a system and study the effects of different components, as well as to make predictions about behavior. A mathematical model usually describes a system by a set of variables and a set of equations that establish relationships between the variables. Variables may be of many types; real or integer numbers, Boolean values or strings. The variables represent some properties of the system, for example, measured system outputs often in the form of signals, timing data, counters, and event occurrence (yes/no). The actual model is the set of functions that describe the relations between the different variables.
An investigative sensitivity study of Ovako working posture analyzing system (OWAS)
Published in Theoretical Issues in Ergonomics Science, 2023
Mangesh Joshi, Vishwas Deshpande
Sensitivity analysis (SA) is a technique that measures how the influence of uncertainties in one or more input variables can lead to uncertainties in the output variables. Sensitivity analysis focuses on determining how the variations in the input variables of a mathematical model affect the response value. The sensitivity analysis is an essential part of any quantitative and qualitative risk assessment (L.G.M. Gorris 2014). In other words, the expected values of various parameters involved can be used to assess the robustness, i.e. the sensitivity of the results from these changes, and to identify the values beyond which the results change significantly (Joshi and Deshpande 2021a, 2021b). It includes a what-if analysis of uncertain model parameters and inputs as well as all essential assumptions. Sensitivity analysis tries to learn things like the sensitivity of the model outputs to changes in the inputs and how that sensitivity might affect decisions (Joshi and Deshpande 2020). A good sensitivity analysis increases the general confidence in a risk assessment. The methodology of the sensitivity analysis essentially consists of three steps. First the inputs/independent variables/parameters were determined. Second, the range of variation was determined. Third, the output/dependent variable is calculated based on the given input variables.
Optimization of the weld characteristics of plasma-arc welded titanium alloy joints: an experimental study
Published in Materials and Manufacturing Processes, 2022
T Pragatheswaran, S. Rajakumar, V. Balasubramanian
Optimization problems generally consist of a well-defined mathematical model to obtain the best possible solutions. The accuracy of the solutions depends on the tool which is employed to solve the optimization problems. response surface methodology employs both statistical and mathematical analysis to narrow down the optimum solutions. In this investigation, the vital variables of the Plasma arc welding process such as current, speed, gas flow rate, and constricted arc length were considered as primary design variables. Each parameter has its effect on the characteristics (weld bead width, penetration and area of fusion zone) of the Plasma arc welded Ti6Al4V joints. The important process parameters which are believed to influence the characteristics of the welding joints are here taken for the analysis. Each process parameter is accounted as the process variable and the desired weld characteristics are regarded as the output response variables. The relation amid the input process variables and the output response variables are expressed in the following Eq. (1).
Marine accident learning with Fuzzy Cognitive Maps: a method to model and weight human-related contributing factors into maritime accidents
Published in Ships and Offshore Structures, 2022
Beatriz Navas de Maya, R. E. Kurt
In addition, to combine the results obtained from both data sources (i.e. historical data and expert judgement), a sensitivity analysis is conducted in the fourth stage of the MALFCMS method. The purpose of a sensitivity analysis is to understand how the uncertainty in the output of a mathematical model or system can be divided and allocated to different sources of uncertainty in its inputs. Hence, as the aim of this stage is to combine the outputs from the historical data and expert opinion analyses, a sensitivity analysis seems adequate to perform this task. Thus, sensitivity analyses have been already applied in the literature to merge the outputs from expert analysis and questionnaires (A. Azadeh et al. 2014). Hence, in order to combine the finding from the historical data analysis stage obtained by de Maya et al. (2019) and the expert opinion stage developed on this study, a sensitivity analysis is performed in this section. Table 13 includes the weights of each HF normalised from both, the historical data analysis stage and the expert opinion stage, and the final weights proposed, in which the same importance has been assigned to both sources of data. In addition, Figure 5 represents the sensitivity analysis to provide a better understanding of the process.