J. Nig. Soc. Phys. Sci. 4 (2022) 945 Journal of the Nigerian Society of Physical Sciences Efficient and Intelligent Decision Support System for Smart Irrigation Monika Sainia, Ashish Kumara,∗, Vijay Singh Maana, Deepak Sinwarb aDepartment of Mathematics & Statistics, Manipal University Jaipur, Jaipur-303007, India bDepartment of computer and Communication, Manipal University Jaipur, Jaipur-303007, India Abstract The main aim of present analysis is to develop a novel efficient and intelligent irrigation system (EIIS). The proposed irrigation system configured using five components arranged in a series configuration along with the internal cold standby redundancy on sensor unit. The failure and repair rates are exponentially distributed. By using the Markovian birth-death process differential difference equations of the model are developed to derive the availability expressions and estimation of parameters. The availability of the system is optimized by employing Grey-Wolf optimization (GWO) and Dragon Fly algorithm (DA) for efficiency and performance evaluation. The derived results are helpful for the system designers. DOI:10.46481/jnsps.2022.945 Keywords: Markov model, Availability, Cold standby redundancy, Intelligent irrigation system Article History : Received: 20 July 2022 Received in revised form: 28 September 2022 Accepted for publication: 14 October 2022 Published: 11 November 2022 c© 2022 The Author(s). Published by the Nigerian Society of Physical Sciences under the terms of the Creative Commons Attribution 4.0 International license (https://creativecommons.org/licenses/by/4.0). Further distribution of this work must maintain attribution to the author(s) and the published article’s title, journal citation, and DOI. Communicated by: T. Latunde 1. Introduction Agriculture is one of the oldest occupations done by human being. It is one of the strong pillars that contribute to the de- velopment of the economic development of any country. A big portion of the population of any country depends on the agricul- ture for survival. In most of the countries traditional methods of irrigation are adopted for farming but these methods suffer due to several drawbacks. The wasteful use of water and inap- propriate irrigation are the major drawbacks while smart irriga- tion technology ensures the efficient use of water in irrigation. The traditional method of irrigation is very challenging due to several factors like soil nature, crop requirement, etc. while in ∗Corresponding author tel. no: +917725922864 Email address: ashish.kumar@jaipur.manipal.edu (Ashish Kumar) smart irrigation system based on soli and environmental mea- surements irrigation decision can be made. Several researchers like Morais et al. [1], Vellidis et al. [2], Kehui et al. [3], Giusti and Marsili-Libelli [4], Navarro-hellı́n et al. [5], and Sinwar et al. [6] proposed model for smart irrigation systems in var- ious aspects. Nasikou et al. [7] proposed a model for smart energy utilization in smart irrigation systems. Gu et al. [8] de- veloped a software for irrigation scheduling that work on the crop water stress. Shekhar et al. [9] developed an automated irrigation system using intelligent IoT. Goap et al. [10] used machine learning and open source technologies in development of a internet based irrigation management systems. Nawandar and Satpute [11] devloped a smart irrigation system based on IoT . A lost cost intelligent module has beem utilized in the de- velopment of the system. Wang et al. [12] proposed a decision support system to manage the canal irrigation. It is observed 1 Saini et al. / J. Nig. Soc. Phys. Sci. 4 (2022) 945 2 that the performance aspects of these smart system has not been extensively explored so far. Reliability and availability are the major concern with the perofrmance of these systems. Many researchers worked in the direction of reliability evaluation and optimization of performance of systems. Maihulla and Yusuf [13] examined the reliability, availability, maintainability and dependability to check the sensitivity effect in a grid-connected photovoltaic systems. This sensitivity analysis shows that close attention and close monitoring are needed to ensure the dis- tribution board’s reliability of the system. Venkatakrishnan et al. [14] compare the effect of modified differential evolution algorithm (MDE) on wind turbine system along with GA and PSO techniques. It concludes that in addition to meet energy demand, the modified DE algorithm assists in finding the sys- tem’s most cost-effective solution. Kumar et al. [15] proposed an efficient model for availability optimization of cooling tower using metaheuristic algorithms. Saini et al. [16] optimized the performance of a biological and chemical processing unit us- ing genetic algorithm and particle swarm optimization. Saini et al. [17] proposed a stochastic model for availability optimiza- tion of condenser used in steam turbine power plants using GA and PSO. Though area of reliability optimization of smart irri- gation systems is still untouched. But efficient and intelligent irrigation-based systems are necessary nowadays for optimum utilization of fresh water. So, the work is proposed develop such an efficient and intelligent irrigation system which ensures the availability of the system as and when required for irrigation. The rest of the work is arranged in six sections: Section 2 devoted to the novelty claims by the investigators, section 3 explained the notations and section 4 briefed the system de- scription. Mathematical model proposed in section 5 and in section 6 numerical discussion and graphical representation is made followed by concluding section 7. A very less efforts have been made so far for development of efficient and intelligent irrigation systems. So, here an effort is made to develop and efficient and intelligent irrigation sys- tem. The efficiency of the system is evaluated in terms of avail- ability of the system for use. By probabilistic arguments and Markov methodology, a mathematical model is developed and optimized using Grey-Wolf optimization (GWO) and Dragon Fly algorithm (DA). The state transition diagram of proposed system is shown in Figure 2. The blow mentions points are claimed as the novelty by the inventors. 1. Design: A novel design of the proposed system is de- veloped for efficiency improvement. The cold standby redundancy is used at sensor level, and it is verified that it performed better. 2. Efficient: The availability of the proposed irrigation sys- tem is optimized using various algorithms like Grey-Wolf optimization (GWO) and Dragon Fly algorithm (DA). In literature so far these algorithms are not employed on availability optimization of irrigation systems. The sys- tem is proved efficient when it is operated with the pa- rameters estimated by GWO parameters. 3. Intelligent: The proposed system is capable of taking intelligent decisions for irrigation based on the data cap- tured by sensors in real time. 2. Notations The nomenclatures used in the development of the model are as follows: S i: ithstate of smart irrigation system Pi(t): Probability that smart irrigation system is in state i at time t P ′ i (t): Derivative of first order of Pi(t) A, B1, B2, C, D, E: Description of the operative states of smart irrigation system a, b1, b2, c, d, e: Description of the failed states of smart irriga- tion system αi/βii = 1, 2, 3, 4, 5: Failure/repair rates of A, B1, B2, C, D, E respectively. 3. System Description In this section, the configuration of the efficient and intelli- gent irrigation system is presented. A smart irrigation system is presented in Figure 1 that depicts five main components viz. power unit, active and cold standby sensor unit, Raspberry pi, water pump, and irrigation unit. As the name suggest, power unit is needed to provide the power supply to the smart irriga- tion systems. The power may come directly or through solar power supply. On the other hand, sensor unit indicates a col- lection of sensors (i.e., moisture, temperature, water, humidity, etc.) needed for decision making by the control unit. The heart of this smart irrigation system is Raspberry pi that is responsible for taking efficient irrigation decisions based on data captured by sensor unit. In addition, Raspberry pi is utilized to trigger the water pump whenever required. Once the water pump is turned on, the irrigation unit (i.e., sprinklers) start working to- wards irrigation of the field. Upon reaching the threshold values by sensor units, Raspberry pi initiates actions to turn off the wa- ter pump. It is evident that sensor unit is more prone to failures, that’s why the redundancy has been utilized in sensor unit of the system. If primary sensor failed in fetching information any one or more of these than standby sensor starts immediately and failed sensor undergoes for repair. The concept of cold standby redundancy and exponential distributed random variable have been utilized in development of the stochastic model. The re- pair and switch devices are perfect and sufficient repair facility is available with system. The architecture and state transition diagram of smart irrigation system is depicted in Figure 1 and Figure 2 respectively. 4. Mathematical Modelling and Analysis Here, mathematical model for the smart irrigation system is developed using Markov birth-death process. The Chapman- Kolmogorov differential difference equations derived based on Figure 2. P0 (t+∆t) = (1−α1∆t−α2∆t−α3∆t−α4∆t−α5∆t) P0 (t) 2 Saini et al. / J. Nig. Soc. Phys. Sci. 4 (2022) 945 3 Figure 1. Framework of intelligent decision support system for smart irrigation Figure 2. State Transition Diagram +β1P1 (t) ∆t+β2P2 (t) ∆t+β3P3 (t) ∆t+β4P4 (t) ∆t+β5P5(t)∆t lim ∆t→0 P0 (t+∆t)−P0 (t) ∆t = − (α1+α2+α3+α4+α5) P0+β1P1 (t) +β2P2 (t) +β3P3 (t) +β4P4 (t) +β5P5(t) P ′ 0 (t) = − (α1+α2+α3+α4+α5) P0+β1P1 (t) +β2P2 (t) +β3P3 (t) +β4P4 (t) +β5P5(t) 3 Saini et al. / J. Nig. Soc. Phys. Sci. 4 (2022) 945 4 lim t→∞ P ′ 0 (t) = − (α1+α2+α3+α4+α5) P0+β1P1+β2P2 +β3P3+β4P4+β5P5 − (α1+α2+α3+α4+α5) P0+β1P1+β2P2 +β3P3+β4P4+β5P5 = 0 (1) P1 = α1P0 β1 (2) P2 = β1P6+β2P7+β3P8+β4P9+β5P10 + α2P0( α1+α2+α3+α4+α5 + β2 ) (3) P3 = α3P0 β3 (4) P4 = α4P0 β4 (5) P5 = α5P0 β5 (6) P6 = α1P2 β1 (7) P7 = α2P2 β2 (8) P8 = α3P2 β3 (9) P9 = α4P2 β4 (10) P10 = α5P2 β5 (11) The initial conditions are as follows: P0 (0) = 1 Pi (0) = 0 where i = 1 to 10 (12) The set of linear equations [1]-[11] along with initial con- ditions [12] constitute the mathematical model for smart irriga- tion system. After simplification the probabilities at respective states are derived as follows: P0 = P0, P1 = α1 β1 P0, P2 = α2 β2 P0, P3 = α3 β3 P0, P4 = α4 β4 P0, P5 = α5 β5 P0, P6 = α1 β1 α2 β2 P0, P7 = α2 β2 α2 β2 P0, P8 = α3 β3 α2 β2 P0, P9 = α4 β4 α2 β2 P0, P10 = α5 β5 α2 β2 P0 (13) By normalizing criteria that sum of all are transition proba- bilities is equal to 1 10∑ i=0 Pi = 1 (14) we get P0 = [ 1 + ( 1 + α2 β2 ) ( α1 β1 + α2 β2 + α3 β3 + α4 β4 + α5 β5 )]−1 (15) The system availability function is defined as: A0 = P0 + P2 = ( 1 + α2 β2 ) [ 1 + ( 1 + α2 β2 ) ( α1 β1 + α2 β2 + α3 β3 + α4 β4 + α5 β5 )]−1 (16) 5. Numerical Results and Discussion In this section, parameter estimation of the failure and re- pair rates of the smart irrigation system is done using swarm- intelligence based algorithms namely Gray Wolf Optimization (GWO) and Dragon Fly algorithm (DA). The possible search space of the decision variables is appended in Table 1. The estimated values of the parameters with respect to 30 iteration levels at several population sizes is derived and appended in Table 2. The availability of smart irrigation system derived at various population sizes are appended in Figure 3-6. The exe- cution time of the program taken by algorithms are appended in Table 6. The simulation study is performed using R software on Windows 10 64-bit operating system having 8 GB of RAM and Intel Core i5 8th generation CPU. The range of these decision variables is provided in Table 1 as follows: Here parameters of failure and repair rates for GWO are constant for different population sizes and system attains its maximum availability in early stage of simulation process. Pa- rameters values change rapidly when using DA algorithm. It is seen that failure rate of Controller Arduino uno increase rapidly for population size 600 and water pump failure increase with population size 400 and 1000. Table 3 appended the various parameters values after 50 iterations corresponding to various population sizes. It also shows that by using GWO, parameters for failure rates and re- pair rates have its minimum and maximum value simultane- ously and system attains its maximum availability. for DA, range of parameters of failure rates increase for sub-system sensor/standby sensor unit, Controller Arduino uno and water pump for population size 800 and 1000. Table 4 highlights the estimated values after 70 iterations on different population sizes. For GWO, system attains its maxi- mum availability. While using DA, range of parameters of fail- ure rates increase rapidly for sub-system sensor/standby sensor unit for population size 800. Table 5 reported the estimated parametric values of failure and repair rates after 90 iterations at various population sizes. For GWO, system attains its maximum availability. While us- ing DA, range of parameters of failure rates increase rapidly for sub-system Controller Arduino uno for population size 600 and 1000. The best parameter values of failure and repair rates, derived by simulation process done in R studio for GWO and DA optimizations. Parameters obtained for different popula- tion sizes and various iterations. These are the best parameters 4 Saini et al. / J. Nig. Soc. Phys. Sci. 4 (2022) 945 5 Table 1. Range of the decision variables Sub-system Range of failure-rate (α) Range of repair-rate (β) Power unit α1 = [0.000003, 1.99] β1 = [0.000009, 2.11] Sensor unit &Stand by Sensor unit α2= [0.000005, 1.89] β2 = [0.000006, 2.30] Controller Arduino uno α3 = [0.000001, 1.53] β3 = [0.000008, 2.57] Water pump α4 = [0.000004, 1.24] β4 = [0.000007, 2.08] Smart valve α5 = [0.000002, 1.32] β5 = [0.000019, 2.34] Table 2. Parameter estimation of various failure and repair rates after 30 iterations and different population sizes by using GWO and DA Iter\NP 400 600 800 1000 GWO α1 0.0000030 0.0000030 0.0000030 0.0000030 α2 0.0000050 0.0000050 0.0000050 0.0000050 α3 0.0000010 0.0000010 0.0000010 0.0000010 α4 0.0000040 0.0000040 0.0000040 0.0000040 α5 0.0000020 0.0000020 0.0000020 0.0000020 β1 1.86464 2.11 2.11 2.11 β2 2.3 2.3 2.3 2.3 β3 2.57 2.57 2.57 2.57 β4 2.08 2.08 2.08 2.08 β5 2.34 2.34 2.34 2.34 DA α1 0.0000030 0.0000030 0.0000030 0.0000030 α2 0.0000050 0.0000050 0.243093 0.0000050 α3 0.0000010 1.53 0.0000010 0.0000010 α4 1.24 0.0000040 0.0000040 1.24 α5 0.0000020 0.0000020 0.0000020 0.0000020 β1 2.11 2.11 2.11 2.11 β2 0.6341965 2.118504 2.3 2.3 β3 2.57 2.57 1.130091 2.57 β4 2.08 2.08 2.08 2.08 β5 2.34 2.34 1.496042 2.34 Table 3. Parameter estimation of various failure and repair rates after 50 iterations and different population sizes by using GWO and DA Iter\NP 400 600 800 1000 GWO α1 0.0000030 0.0000030 0.0000030 0.0000030 α2 0.0000050 0.0000050 0.0000050 0.0000050 α3 0.0000010 0.0000010 0.0000010 0.0000010 α4 0.0000040 0.0000040 0.0000040 0.0000040 α5 0.0000020 0.0000020 0.0000020 0.0000020 β1 2.11 2.11 2.11 2.11 β2 2.3 2.3 2.3 2.3 β3 2.57 2.57 2.57 2.57 β4 2.08 2.08 2.08 2.08 β5 2.34 2.34 2.34 2.34 DA α1 0.0000030 0.0000030 0.0000030 0.0000030 α2 0.0000050 0.0000050 1.047884 1.414718 α3 0.0000010 0.8860956 1.190195 0.02381295 α4 0.0000040 0.0000040 0.0000040 1.24 α5 0.0000020 0.0000020 0.2853557 0.0355639 β1 0.239885 2.11 0.7081718 2.11 β2 2.3 2.3 2.3 2.3 β3 0.6369218 1.704359 2.57 2.57 β4 2.08 0.1690187 2.08 2.08 β5 2.34 1.701183 2.34 2.34 5 Saini et al. / J. Nig. Soc. Phys. Sci. 4 (2022) 945 6 Table 4. Parameter estimation of various failure and repair rates after 70 iterations and different population by using GWO, DA Iter\NP 400 600 800 1000 GWO α1 0.0000030 0.0000030 0.0000030 0.0000030 α2 0.0000050 0.0000050 0.0000050 0.0000050 α3 0.0000010 0.0000010 0.0000010 0.0000010 α4 0.0000040 0.0000040 0.0000040 0.0000040 α5 0.0000020 0.0000020 0.0000020 0.0000020 β1 2.11 2.11 2.11 2.11 β2 2.3 2.3 2.3 2.3 β3 2.57 2.57 2.57 2.57 β4 2.08 2.08 2.08 2.08 β5 2.34 2.34 2.34 2.34 DA α1 0.0000030 0.0000030 0.0000030 0.0000030 α2 0.0000050 0.05620236 1.89 0.0000050 α3 0.0000010 0.0000010 0.0000010 0.0000010 α4 0.4775554 0.1183404 0.0000040 0.1965477 α5 0.0000020 0.8200995 0.0000020 0.0000020 β1 2.11 0.00640018 2.11 2.11 β2 0.1106202 2.3 2.3 2.3 β3 2.57 0.7383446 1.424582 2.267976 β4 1.718693 1.26267 2.08 0.8067474 β5 1.063321 2.34 2.34 2.34 Table 5. Parameter estimation of various failure and repair rates after 90 iterations and different population sizes by using GWO and DA Iter\NP 400 600 800 1000 GWO α1 0.0000030 0.0000030 0.0000030 0.0000030 α2 0.0000050 0.0000050 0.0000050 0.0000050 α3 0.0000010 0.0000010 0.0000010 0.0000010 α4 0.0000040 0.0000040 0.0000040 0.0000040 α5 0.0000020 0.0000020 0.0000020 0.0000020 β1 2.11 2.11 2.11 2.11 β2 2.3 2.3 2.3 2.3 β3 2.57 2.57 2.57 2.57 β4 2.08 2.08 2.08 2.08 β5 2.34 2.34 2.34 2.34 DA α1 1.059087 0.0000030 0.5533655 0.0000030 α2 0.0000050 0.4501209 0.0000050 0.0000050 α3 0.6671488 1.53 0.0000010 1.53 α4 0.0000040 0.4808177 0.0000040 0.1965477 α5 0.0000020 0.1602266 0.0000020 0.0000020 β1 2.11 1.725929 2.11 2.11 β2 0.5978837 1.181086 2.3 2.3 β3 1.702016 2.57 2.57 2.57 β4 1.457232 1.438981 0.2638387 2.08 β5 2.34 2.34 2.34 2.34 Table 6. Elapsed time (in seconds) of the GWO and DA algorithms used in finding the optimum availability with respect to iterations at various population size Iteration Population size 400 600 800 1000 GWO DA GWO DA GWO DA GWO DA 30 3.96 9.37 3.72 7.01 4.5 8.52 4.32 7.89 50 4.18 7.75 4.61 7.82 7.98 7.69 4.2 12.61 70 3.81 9.8 3.55 7.1 3.79 7.05 3.58 7.39 90 3.37 7.17 3.92 7.75 3.63 7.2 4.35 7.84 6 Saini et al. / J. Nig. Soc. Phys. Sci. 4 (2022) 945 7 Figure 3. Availability of Smart Irrigation System at various iterations at Pop. Size =400 Figure 4. Availability of Smart Irrigation System at various iterations at Pop. Size =600 Figure 5. Availability of Smart Irrigation System at various iterations at Pop. Size =800 for which system attains its maximum availability. For GWO, parameters for failure rates and repair rates have its minimum and maximum value simultaneously and system attains its max- imum availability at early stage of simulation. For DA the val- ues of parameters are fluctuating rapidly, and sub-systems need adequate maintenance at time. In Figure 3, graphical representation of the optimum avail- ability of system using GWO and DA with respect to various iterations with population size 400 is shown. It is seen that at iteration 30 and 50 both techniques attain the same and max- imum availability after that availability for DA is decreasing with increasing the iteration size and for GWO it remains same at 0.9999954. In Figure 4, graphical representation of the optimum avail- ability of system using GWO and DA with respect to various it- erations with population size 600 is shown. Here availability for GWO remains constant at 0.9999954 for each iteration. Avail- ability for DA slightly increase from 0.6268276 to 0.6919241 for iteration 30 and 70 respectively but iteration 90 availability decreases rapidly to 0.4754869. Figure 5 shows the graphical representation of the optimum availability of system using GWO and DA with respect to var- ious iterations with population size 800 is shown. Availabil- ity for GWO remains constant at 0.9999954 for each iteration. Figure 6. Availability of Smart Irrigation System at various iterations at Pop. Size =1000 Availability for DA decreases rapidly from 0.9899925 to 0.5788153 in-between iteration 30 to 50. Then after it increases to 0.7922205 for iteration 90. Figure 6 is the representation of the optimum availability of system using GWO and DA with respect to various itera- tions with population size 1000. System attains its maximum availability 0.9999954 in early stage of population size and it- eration by using GWO and then remain constant for higher pop- ulation size and iterations. For DA availability varies between 0.804096 at iteration 70 to 0.5391205 at iteration 50. Table 6 show elapsed time taken by optimization techniques which includes time taken by system and optimization tech- nique and provide the total execution time. The variation in time taken to complete the task by using GWO and DA can be easily seen. Time taken by GWO is almost half of the time taken by DA. It is also seen that GWO attains the maximum availability at early stage with respect to DA. 6. Conclusion In present work, a novel efficient and intelligent irrigation system is developed using the concept of cold standby redun- dancy. The availability expression for the model is derived and optimized using the Grey-Wolf optimization (GWO) and Dragon Fly (DA) algorithms. The parameters of all failure and repair rates are estimated by both algorithms. The maxi- mum availability derived is 0.9999954 in the search space by both the algorithms. It is observed that Dragon fly algorithm is not given sustain results with the increase of number of itera- tions. Though the elapse time taken by Grey-Wolf optimization (GWO) is sufficiently less in comparison to Dragon Fly (DA) algorithm. So, it is recommended that the system when oper- ated according to the parameters estimated by grey wolf opti- mization perform more efficiently. The present work may be further extended to the component level investigation by using some other nature inspired algorithms. The concept of simulta- neous failure and redundancy can be involved in further study. The proposed methodology may be opted in other process in- dustries. Acknowledgement The authors are extremely grateful to the insightful com- ments provided by the reviewers and section editor to improve the quality of this study. 7 Saini et al. / J. Nig. Soc. Phys. Sci. 4 (2022) 945 8 References [1] R. Morais, A. Valente & C. Serôdio, A wireless sensor network for smart irrigation and environmental monitoring: A position article. 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