Building Probability Functions by Persian Curve

Abstract

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.

Building Design Rule for Glass Structures by Persian Curve

“…This is the main shortcoming of all conventional methods of analysis in different branches of human knowledge. This shortcoming is removed, in the change of state philosophy (Ranjbaran et al, 2020a), as follows. The first step was deletion of (F) and (), from the conventional equations, as in Eq.…”

“…Therefore Equation ( 14) is rewritten in a unified form as in Eq. (15), in terms of the positive control parameters (aM) and (b) (Ranjbaran et al, 2020a). The control parameters are to be determined from calibration of reliable data:…”

“…Finally, via logical reasoning, a unified equation for capacity (design) and fragility (assessment) curve is proposed as follows. Extensive research of the author's team (Ranjbaran et al, 2020a) concluded into the fact that the Persian curve for complete failure is defined in Eq. (21) (We looked for reliable capacity data in different codes, theses, dissertations, papers and reports (Ranjbaran et al, 2020a).…”

“…The current authors research team detected the need for remedy and after extensive research (Ranjbaran et al, 2008;Ranjbaran, 2010;Ranjbaran et al, 2011;Ranjbaran, 2012a-b;2013;Ranjbaran and Rousta, 2013a-b;Ranjbaran et al, 2013a-b;Ranjbaran and Ranjbaran, 2014;Ranjbaran, 2014;2016;Ranjbaran and Ranjbaran, 2016;2017a-c;Hosseini et al, 2018;Amirian and Ranjbaran, 2020;Baharvand and Ranjbaran, 2020a-b;Ranjbaran et al, 2020a-d), in the last two decades, proposed the Change of State Philosophy (CSP) which expressed in the Persian Curves (PC) (Ranjbaran et al, 2020a). The aim of the presented paper is to derive and validate the (PC) and then apply it for analysis of structural glass members as follows.…”

Development of a Reliable Failure Assessment Diagram by Persian Curve

“…The state of the art of the (FAD) contains epistemic uncertainty, that should be modified. The current authors research team detected the need for remedy and after extensive research (Ranjbaran, 2010;Ranjbaran et al, 2013;Ranjbaran and Ranjbaran, 2014;Ranjbaran et al, 2020a;2020b;2020c;2020d;2021;Amirian and Ranjbaran, 2019;Baharvand and Ranjbaran, 2020), in the last two decades, proposed the Change of State Philosophy (CSP) which digested in the Persian Curves (PC) (Ranjbaran et al, 2020a), that is used for the 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 as follows.…”