Construction of a probability function for a given random data is the main theme of several branches of human knowledge, where it is an active area of study. In spite of great developments, the solution needs extensive effort and the results contain epistemic uncertainty. In this study, making use of the logical reasoning and concise mathematical logics, a method called the change of state philosophy, which is digested in the Persian curves, is derived. The Persian curves that have the necessary and sufficient condition for a probability function, are explicitly derived, via the ordinates of four specific points on the random data. The proposed Persian curves are free of epistemic uncertainty and their flexibility provide the possibility for the insertion of the expert's will. The work is validated via concise logical formulation and comparison of the results with those of the others.
Glass is being increasingly used as a structural material. Its favorable aesthetic qualities have made it popular with modern designers. Recently glass is used for major structural elements such as beams and columns in modern and innovative architectural applications. High slenderness ratios and brittle behavior in tension contribute to the complexity of stability and ultimate strength analysis of glass structures. Moreover the available design curves and methods of ultimate strength analysis of glass structure contain epistemic uncertainty, therefore are not reliable. In this study, based on logical reasoning, concise mathematics and reliable data, a reliable method called the change of state philosophy is developed and expressed in the Persian curve. The Persian curve is used for reliable analysis of glass structures. The validity of the work is verified via its sound basic formulation and comparison of the results with those of the others in the literature.
The Monte Carlo Simulation method is a powerful tool for solving problems including random variables. The basic idea to implement a Monte Carlo simulation is to first generate samples of random inputs from their assumed distribution functions and then perform a deterministic calculation on the generated random inputs, based on mathematical modeling of the system, to obtain output results. An early version of Monte Carlo simulation is the famous needle experiment. The idea of random experiment, have been used for solving many complex problems. Simulation based approaches have some disadvantages. Its implementation needs a massive use of computational resource and long calculation times. Moreover, providing linkage between input to the system and its output is difficult. Toward remedy, the phenomenon is considered as the change in the state of the system. Via logical reasoning, concise mathematics and using real world data, the output is related to the input via the Persian Curve. The Persian Curve provided a simple, cheap and exact solution to the problem. Consequently the Persian Curve is proposed as a replacement for the Monte Carlo Simulation. The validity of the work is verified via concise mathematics and comparison of the results with those of the others.
Geotechnical engineering is the art of making decisions in the presence of uncertainty, where real world problems are treated and this is associated with uncertainties arising from various sources. The sources of uncertainty may be divided into uncertainties of nature and uncertainties of mind. The uncertainties of nature are due to variation of encountered phenomena, e.g., the shear strength in a soil. This is reduced by obtaining more reliable data via the results of tests. The uncertainties of mind are related to the modelling, which may be reduced by change of philosophy.Here, the data is considered as variable instead of random so is reliable. Based on logical reasoning and concise mathematics a reliable formulation, i.e., the change of state philosophy which is digested in the Persian curve is proposed. The Persian curve method is free of uncertainties of mind. In the presented paper the Persian curve method is used to manage the variable geotechnical data in a form that can easily be used in practical geotechnical work for decision making and design.
A conventional tool for assessing the integrity of structures containing flaws is, the Failure Assessment Diagram (FAD). The (FAD) is a combination of the limiting conditions for load, the flaw size and fracture toughness or yielding stress. The abscissa is the load ratio and the ordinate is the toughness ratio. The toughness ratio is defined as a function of the load ratio. Three options are available for this function. The (FAD) drive is based on parameters of fracture mechanics. Classical fracture mechanics contains epistemic uncertainty and is unreliable. As a result, the state of the art for the (FAD) is also unreliable. The present authors' team, conducted an extensive investigation in the past two decades, which led to the birth of the change of state philosophy that is digested in the Persian Curve. In the present paper the Persian Curve is used for development of a reliable (FAD). The validity of the work is verified via concise mathematical logics and comparison of the results with those of the others.
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