امام شعرانیؒ اور شاہ ولی اللہؒ کے فقہی نظریات کا تقابلی مطالعہ

Allah Almighty has created such men in every age for the protection of the religion of Islam whose ijtihād and da'wah deeds have always defeated the false ideologies by proving the legitimacy of Islam on firm grounds. From those blessed ones, Imām Sha'rānī and Shāh Walīullāh are eminent, intellectual, spiritual and rejuvenating personalities of their time. The main purpose of this article is to make a comparative study in the context of the views of each of the above two personalities from different angles regarding the differences in jurisprudence. This paper also aims to highlight the rational and moderate position of these personalities while making their different opinion in comparison to other scholars, so that researchers and scholars of this age may get guidance regarding how to make different opinion. It will help the researchers to take advantage of these blessed attitudes of the ancestors and play an important role in building a peaceful society.

Mode Identification Based Fault Diagnosis of Hybrid Systems

With technological advancements, modern engineering systems are improving in terms of performance, size and cost but at the expense of complexity; making their analysis and control extremely difficult. A fundamental issue regarding these systems is to ensure their safety and reliability due to their vulnerability to faults; owing to their complexity. The situation becomes even worse as the corresponding fault diagnosis algorithms are also becoming more complex and computationally expensive for the online implementation. The problem at hand is to design a simple, reliable and easy to implement fault detection and isolation scheme for these systems. One approach to design such a fault detection scheme for these complex engineering systems is to partition the system into simpler interacting subsystems and designing the desired fault diagnosis scheme for these simpler subsystems. Hybrid modeling provides us a platform to represent these complex engineering systems in simpler subsystems working collectively. Hybrid systems are those having both continuous and discrete dynamics. In these systems, discrete states are known as modes and switching between modes occurs on discrete events. In our proposed scheme, healthy and faulty modes are defined by estimating and analyzing continuous states of the system. This process of state estimation is performed by using Sliding Mode Observers (SMO). The monitoring of system modes is performed by designing a Deterministic Finite Automaton (DFA) that uses modes of the hybrid systems represented as symbols of a language, at its input. The proposed scheme is validated both through simulations and experimental data. Data for the experimental validation of the proposed scheme is acquired from an engine rig of a 1.3L production vehicle compliant with the On-Board Diagnostic II (OBD-II). Proposed scheme is easy to implement on account of being model-based. Instead of Kalman filter, SMO is used for the state estimation that is computationally cheaper. In general, there are two types of faults in hybrid systems; ones related to the current mode behavior and the others affecting the discrete evolution trajectory. In our design, we have detected both these faults using a single scheme by identifying and monitoring system modes. Moreover, detection and isolation of new faults can be easily accommodated by introducing new mode sequences in a fault set.