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## Definition

Spiking neural P system (SNPS) is a popular parallel distributed computing model. It is inspired by the structure and functioning of spiking neurons. It belongs to the category of neural-like P systems and is well-known as a branch of the third generation neural networks. SNPS and its variants can perform the task of fault diagnosis in power systems efficiently.

## 1. Introduction

In the 21st century, electrical power systems are associated with the daily necessities of human beings. A network of electrical components is called an electrical power system and such systems help in the supply, transfer, and use of electrical power. However, any accident inside the power systems interrupts the supply of power. In order to perform the task of secure and stable supply of power, it is necessary for the electric devices to have efficient fault diagnosis methods which can identify the faults quickly as well as efficiently. Furthermore, whenever there is a fault in power system, the consoles in the dispatchers receive huge number of messages in a very short span of time from the SCADA (supervisor control and data control) systems. Very often the messages received from SCADA systems are incomplete and uncertain. Power systems are composed of a large number of generators, transmission lines, bus bars, and transformers. These aspects of power systems make very difficult the task of fault diagnosis in power systems. In recent years, the techniques from artificial intelligence have been used to perform the task of fault diagnosis in electric power systems. More specifically, many methods based on Bayesian networks

^{[1]}^{[2]}, artificial neural networks^{[3]}^{[4]}, genetic algorithms^{[5]}, Petri nets^{[6]}^{[7]}^{[8]}^{[9]}, expert systems^{[10]}^{[11]}, fuzzy logic^{[7]}^{[8]}^{[12]}, multi-agent systems^{[13]}^{[14]}, optimization methods^{[5]}^{[15]}^{[16]}, information theory^{[17]}^{[18]}, cause-effect networks^{[19]}^{[20]}have been introduced. P systems or membrane computing models are popular natural computing model. In recent years, many researchers have used different variants of P systems for fault diagnosis in power systems.P system was introduced in 1998 by Gh. Păun

^{[21]}. P system is an abstract mathematical computing model which is inspired by the structure and functioning of the biological cells. The area of study of P systems is well-known as Membrane Computing. In P systems, the objects present inside the cells or membranes are represented by multiset of objects and the evolution processes happening inside these cells are represented by the rules which are applied in maximal parallel manner. P systems models are generally divided into three categories based on their structure, i.e., cell-like, tissue-like and neural-like.Along with finding the analytic solutions for computationally hard problems using the concept of space-time trade-off, in recent years the study of constructing evolutionary algorithms by combining the structure and operations of membrane systems and capabilities of optimization algorithms has gained prominence

^{[22]}. Furthermore, approximate solutions of these problems are obtained by using the algorithms which are popularly known as “membrane algorithms”. In^{[23]}, the solution of an well-known NP -complete problem, i.e., Graph coloring problem (GCP) is obtained by using OLMS (one level membrane structure (OLMS)^{[24]}^{[25]}^{[26]}) membrane algorithm with dynamic operators. Automatic design of P systems is also an attractive work and promising research direction^{[27]}^{[28]}^{[29]}^{[30]}.## 2. Membrane computing models

Membrane computing models have a wide range of real-life applications

^{[22]}^{[31]}^{[32]}^{[33]}^{[34]}^{[35]}and the investigation more problems from different areas of real-life applications which can be solved by these models has drawn huge interest amongst many researchers around the global. One of the most interesting application of membrane computing models has been in the area of “Robotics”. In particular, the use of membrane computing models for designing of membrane controllers for single and multi-robot systems which further helps in navigation of the robot in unknown environments^{[31]}^{[36]}^{[37]}^{[38]}. In recent years, many variants of P systems such as enzymatic numerical P systems, XP-colonies, etc. have been used in single and multiple-robot applications. The membrane controllers based on the membrane computing models are efficient and have comparable performance with respect to traditional robot controllers^{[31]}. Image processing is another area where membrane computing models have been used extensively. Parallel distributed architecture along with the multisets present in the membranes which is useful for encoding of the information, make P systems a suitable model for dealing with digital images. Furthermore, these models can be used in image segmentation, skeletonization, etc.^{[32]}. Moreover, SNPS models can perform binary operations and these models are also suitable to be used in cryptographic applications^{[39]}. Array rewriting P systems can be used as a tool for generation of Peano curve, the Hilbert curve, etc. In^{[40]}, a state-of-the-art based on the P systems with parallel rewriting was introduced for generation of the space-filling curves, and related curves.Membrane computing models also have been used for modelling and simulation of many phenomena existing in Biochemistry, Ecology, Robotics or Engineering

^{[34]}. These models also can model communities of very simple reactive agents living and acting in a joint shared environment. These types of membrane computing models are known as “P colonies”^{[41]}. P colonies can simulate the interactive processes in other mechanisms such as reaction system which is inspired from the different chemical reactions happening in the environment^{[42]}. P systems are also useful in modeling many biological phenomena such as swarming and aggregating behaviour in Myxobacteria bacterial populations^{[43]}^{[44]}.Neural-like P systems/Spiking neural P systems (SNPS)

^{[45]}have gained popularity amongst the researchers because of its similarities with third-generation neural networks, i.e., spiking neural networks (SNNs)^{[46]}. In recent years, the research in SNPS also has gained huge momentum and many variants of SNPS have been introduced inspired by the properties present in the biological neurons. Many variants of it already have been introduced along with investigations regarding their computational power^{[47]}^{[48]}, efficiency in solving computationally hard problems^{[49]}and real-life applications^{[50]}^{[51]}^{[52]}. A new variant of SNPS is introduced in^{[53]}where the firing and forgetting rules are applied in generalized manner. In these models, if a rule is applied at any step of the computation, then it will be applicable any number of times. These models are also computational complete. Matrix representation and simulation algorithm of different variants of SNPS are investigated in^{[54]}. Another novel variant of SNPS is recently introduced in^{[55]}and it is called as dynamic threshold neural P systems. These models are inspired from the spiking and dynamic threshold mechanisms of neurons. Moreover, it has been proved that the sequential variant of this model is capable of generating/accepting Turing universal numbers. Some of the well-known variants of SNPS are SNPS with asynchronous systems^{[56]}, astrocytes^{[57]}, rule on synapses^{[58]}, communication on request^{[59]}, synapses with schedules^{[60]}, structural plasticity^{[61]}^{[62]}, weighted synapses^{[63]}, inhibitory synapses^{[64]}, anti-spikes^{[65]}, etc. Furthermore, SNPS have been used extensively in solving many real-world problems in many areas such as fault diagnosis of power systems^{[66]}^{[67]}^{[68]}^{[69]}^{[70]}^{[71]}^{[72]}^{[73]}^{[74]}^{[75]}, pattern recognition^{[76]}^{[77]}^{[78]}, computational biology^{[79]}, performing arithmetic and logical operations and hardware implementation^{[80]}^{[81]}^{[82]}^{[83]}^{[84]}^{[85]}^{[86]}^{[87]}, biochip design^{[88]}, programming for logic controllers^{[89]}^{[90]}, etc. In^{[91]}, SNPS models have been used for computing finite-state functions.In the last few decades, although significant progress has been made in obtaining many theoretical results as well as real-life applications of membrane computing models, very little progress has been made towards in vivo implementation of these models. In

^{[33]}, a mechanism was introduced where multivesicular liposomes can be experimentally produced through electroformation of dipalmitoylphosphatidylcholine films. It can be further used in ‘real’ P-systems.Over the years one of the most interesting direction of research in membrane computing has been constructing simulation tools for different variants of P systems and their applications

^{[92]}. Many researchers have focused on developing softwares^{[93]}based on P-Lingua which can simulate different variants of membrane systems efficiently such as (1) Cell-like P systems^{[94]}; (2) P-Systems with String Replication^{[95]}; (3) Tissue P systems^{[96]}(4) Cell-like SNPS^{[97]}; (5) Spiking Neural P Systems^{[98]}; (6) Asynchronous Spiking Neural P Systems^{[99]}. P-Lingua is an efficient tool. Recently, there has been significant progress towards constructing P-Lingua language, pLinguaCore library and MeCoSim environment. These tools also have been used for experimentally validate solutions of computationally hard problems^{[100]}. Furthermore, many simulators have been proposed which are based on different programming languages other than P-Lingua and following is the list of some simulators: (1) CuSNP^{[101]}; (2) UPSimulator^{[102]}; (3) Psim^{[103]}; (4) SNUPS^{[104]}; (5) GPUPeP^{[105]}. The P systems simulators work as an important tool for formally creating a framework for real-life applications. The simulators based on the requirements of the users and specific application abstract the concepts of different variants of P systems. The researchers in membrane computing community have constructed many types of simulators^{[106]}and used it for simulation of the simple kernel P systems solution to the graph 3-colouring problem^{[107]}. Moreover, testing methods for membrane computing models such as kernel P systems have been introduced^{[108]}.The process of fault diagnosis in power systems is based on processing of uncertain and incomplete information. General SNPS models are not capable of handling these type of information. So a new variant of SNPS was introduced in order to serve this purpose. In

^{[68]}, a new variant of SNPS, i.e., FRSNPS (fuzzy reasoning spiking neural P systems) was introduced, aiming to handle fuzzy diagnosis knowledge and reasoning. Furthermore, a methodology for fault diagnosis in transformers was presented. There has been only a few investigations regarding incorporating the idea of machine learning in SNPS. It is also difficult to introduce machine learning mechanisms in SNPS because of its formal language theory framework. Recently, a new method based on learning Spiking Neural P System with Belief AdaBoost^{[75]}is introduced for fault diagnosis in transformers. Moreover, SNPS models and their variants have been introduced for identification of faults in power transmission networks^{[109]}, traction power supply systems of high-speed railways^{[72]}, metro traction power systems^{[66]}, electric locomotive systems^{[71]}. Moreover, these models have been used for fault location estimation of power systems^{[110]}and fault line detection^{[69]}.The entry is from 10.3390/app11104376

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