TY - JOUR AU - Vigneshwari, S AB - Abstract The diseases in plants pose a devastating impact on initiating safety in the production of food and they can lead to a reduction in the quantity and quality of agricultural products. In most cases, plant diseases lead to no grain harvest. Thus, an automatic diagnosis of plant disease is highly recommended for determining agricultural information. Several techniques are devised for plant disease detection wherein deep learning is preferred due to its effective performance. Novel deep learning is presented to spot disease from rice crop images. Here, the rice plant image undergoes pre-processing to remove noise and artifacts contained in the image. Then, the segmentation is performed with Segmentation Network (SegNet) to produce segments. The segments are further adapted for extracting statistical features, convolution neural network (CNN) features and texture features. These features are employed for plant disease detection wherein the deep recurrent neural network (Deep RNN) is utilized. The Deep RNN is trained with the proposed RideSpider Water Wave (RSW) algorithm. The proposed RSW is devised by integrating RWW in Spider monkey optimization. The proposed RWS-based Deep RNN provides superior performance with the highest accuracy of 90.5%, maximal sensitivity of 84.9% and maximal specificity of 95.2%. INTRODUCTION India is rich in agriculture wherein 70% of India’s public relies on agriculture for livelihood. Farmers pose varieties of methods for the selection of apposite crops and for determining the apt pesticide for the growth of plants. Attack of disease on plants causes a substantial decline in the qualitative and quantitative nature of agricultural materials. The scientific study of diseases in plants is known as plant pathology. This study refers to the visually noticeable patterns of the plants. Checking of proper health and illness of plants plays a vital role in effective crop growing. In the olden days, the checking and analyzing of plant diseases are performed manually by a skilled person. Such a process involves more workload and takes extreme time for processing. The methods based on image processing are one of the widely used methods in the detection of disease in plants. Mostly, the symptoms of the disease are spotted on stem, fruit and leave. The plant leaf is known to be one of the important parts for disease detection, which helps to discover the disease symptoms [1]. The accumulation of images seems to be infected in leaves and thus processing images with an automated system result in a promising solution for framers to yield effective crops. For instance, when an automated system is positioned in the farm, in which various camera sensors are placed at an alternate location on the farm, which intermittently captures images, and then the system undergoes processing of captured images to detect any infection. Thus, these systems assist the farmers to be informed about the diseases instantaneously [2]. Rice crop is considered as an imperative food worldwide. Rice acts as the primary food for half of the world’s population. When there is an increase in population and food, the desire for rice maximizes. A critical requirement exists to increase rice yield to manage the world’s rising population. There are several challenges confronted in rice cultivation, which involve a reduction in yield instigated by pests, improper administration of input, irregular usage of nutrients and environment dilapidation [3]. There can be a massive decline in the quantity and quality of agricultural products due to the attack of diseases in plants. There is a certain disease that infects other areas of the tree causing diseases of leaves, branches and twigs. There is a wide range of plant diseases in the whole world. Most of the time, such diseases may lead to contemplative losses in the harvest that may lead to food security [4]. Furthermore, these issues can cause other problems in crop yield. The irregular usage of nutrients, due to poor fertilizer application, may affect the health of the plant. On the other hand, this raises the chance of plants to pests and diseases vulnerability. Such challenges lead to a vital reduction in rice harvest and quality. Attaining the goal of increasing rice yield to cope up with the increasing population is hindered. The symptoms of such diseases can be normally seen in the leaves of rice. The disease attacked rice crop is analyzed by the appearance of rice leaves. The evaluation done manually is based on screening leaf, but this method is burdensome and susceptible to errors [5]. New developments in farming technology have given rise to automated non-destructive techniques for detecting diseases of the plant. It is of great use to farmers when the plant disease detection tool is rapid. An autonomous agricultural vehicle is devised by integrating spectroscopic and imaging techniques, which can be able to offer information on disease detection at prior phases for controlling the spread of diseases, and such technology can be adapted for identifying stress levels and deficiencies of nutrient in plants [6]. Exceptional usage of computer vision and image processing are analyzed, but there is no noteworthy solicitation of methods detected in agriculture. Moreover, the International Rice Research Institute successfully devised software namely Rice Doctor [7] that mentioned disease name by employing pragmatic information noted from an infected plant. Moreover, prototype system using intelligent decision with machine vision is devised for automatic recognition of cotton insect pest [8], while remote sensing method is employed for managing farm pest [9]. Other methods help to detect the deficiency of mineral using analysis of colour texture [10]. In conventional method, disease is discovered visually by a knowledgeable skilled person who poses capability to determine minor variations in plant colour. Scout and plant canopy are measured to access infection percentage [11]. Moreover, the method is labour oriented and consumes more time, and it is impracticable to precisely evaluate stained areas and harshness in huge-scale farming [12]. Thus, it is essential to devise novel cost effectual and productive methods that could increase the efficiency of conventional method for detecting plant disease. The goal is to present a plant disease detection strategy using rice plants for which the proposed RideSpider Water Wave (RSW)-based Deep RNN is employed. The major contribution of the research is the detection of plant disease. Here, the segmentation is performed which is carried out using SegNet, and features from each segment are extracted. The extracted features involves convolution neural network (CNN) features, statistical features which involves mean, variance, standard deviation, entropy, skewness, kurtosis and texture features involves Local Optimal Oriented Pattern (LOOP). In addition, Deep RNN is employed for detecting the plant disease using the features. Finally, the Deep RNN is trained by proposed RSW in such a way that the model parameters are learned optimally. RSW is the proposed algorithm, which is developed through the inheritance of the high global convergence property of RSW in the Spider monkey optimization (SMO) algorithm. Hence, the proposed RSW-based Deep RNN renders effective accuracy while facilitating plant disease detection. The training of Deep RNN is done using proposed RSW. The major contribution of the paper has follows: Proposed RSW-based Deep RNN for disease detection in rice plant: The major contribution of this work is the development of the classifier, named RSW-based Deep RNN by modifying the training algorithm of Deep RNN with RSW algorithm. Proposed RSW algorithm: The RSW algorithm is developed by combining RWW and SMO algorithm, for the optimal tuning of weights and biases of the Deep RNN. Other sections of the paper are arranged as: Section 2 elaborates the description of the conventional plant disease detection strategies utilized in literature and Section 3 provides the motivation of the proposed technique. The proposed method for plant disease detection using modified Deep RNN is portrayed in Section 4. The outcomes of proposed strategy with other methods are illustrated in Section 5 and Section 6 present conclusion. RELATED WORK Agriculture is essential for growing population and is imperative energy source. However, the plant diseases impact the quantity and quality of crops for agricultural growth. Thus, the diagnosis of plant disease is important in prior stages for preventing and controlling them. The observation done manually by experts is the strategy adapted for plant disease detection, but it is time-consuming and requires many efforts. To remove these issues, an automatic plant disease detection model is devised. In a current image processing technology, deep learning (DL) has been effectively applied in several tasks, such as object detection, disease detection and scene analysis. DL is kind of machine learning, depends on representation learning of data, which recognizes artificial intelligence in the form of artificial neural networks (ANNs) with several hidden layers and very big training data. ANNs have an increasing popularity for estimating and forecasting water resources. The benefit of ANNs over conventional techniques is the lesser needs of information about the complex nature of the underlying process [13,14]. DL utilizes the multi-level abstraction to discover complex feature representations from raw data and generates components automatically. Also, the strong learning ability of DL methods enables them to implement various kinds of problems especially well and flexibly adapt to numerous highly complex problems [15]. Here, the eight machine learning methods employed for the plant disease diagnosis is illustrated along with its limitations. Chen et al. [16] devised a method using transfer learning with deep convolutional neural networks (DCNNs) for identifying the plant leaf disease. The method utilized pre-trained model with massive datasets and then relocate the prescribed task for own data. The VGGNet was trained with Inception module and ImageNet were chosen for initializing the weights in random manner. The method showed better performance with improved validation accuracy. However, the method was inapplicable on mobile devices and unable to recognize the plant disease automatically. Ahmed et al. [17] devised CNN-based dual phase method for spotting the rice grain disease from the rice grain disease dataset. Here, the Faster RCNN technique is adapted to crop out desired portion from images. The first phase result to secondary dataset of rice grain. Moreover, the classification of disease was carried out on derived samples with CNN model. The method showed better performance but failed to increase the accuracy of prediction. Rahman et al. [18] devised deep learning-based method for determining the diseases from the images of rice plants. The goal of the method tends to be 2-fold. One was the usage of conventional huge-scale architectures such as InceptionV3 and VGG16 for determining and spotting the rice diseases. The method showed that it provided improved performance with two-stage small CNN architecture. However, the method failed to incorporate weather, location and soil data for diseased plant detection. Chen et al. [19] devised a deep learning model, namely DENS-INCEP for detecting rice disease. The ImageNet and DenseNet were integrated with Inception model using transfer learning, and top layers were removed by describing fully connected Softmax layer for number of classifications. In addition, Focal Loss function was adapted in network for improving the ability of learning. The method improved the ability of extracting features and reduced the complexity of computation without losing dormant information. However, the method was inapplicable to real-world applications. Li et al. [20] designed deep learning-enabled video detection architecture for plant disease detection with custom backbone. Initially, the video was transformed into the still frame and then forwarded still frame for image detector for the detection purposes. At last, frames were synthesized to video. However, the faster RCNN was introduced for the detection of still image. Then, the image-training models were employed for detecting blurred videos. In addition, the machine learning classifier was established to detect the video effectively. The method was failed to apply other crop diseases and pests. Bakar et al. [21] devised a method to detect RLB disease using multi-level colour image thresholding. This framework includes image pre-processing, segmentation and the image analysis in which the Hue saturation value colour space was employed. Then, the Region of Interest extraction was done, and finally, the pattern recognition was performed using the developed model. The method was unable to measure the incidence of RLB disease in the field. Atole and Park [22] employed the DCNN to classify the rice plants to unhealthy, normal and the golden apple by applying pre-trained biases and weights. Here, the image dataset consists of images captured from various rice fields around district and public images from the Internet. The method failed to use the multispectral high-altitude images. Ramesh and Vydeki [23] presented an approach based on K-Nearest Neighbour or the ANNs to detect the early stage disease of crop. This approach is utilized to identify blast disease and mitigate loss of crop and thus improves the production of rice agriculture effectively. The paddy field images were captured and the eight features were extracted for differentiating healthy and disease affected leaves. Here, the accuracy was found better but failed to apply other affecting rice plants diseases. Ramesh and Vydeki [24] have developed an optimized Deep Neural Network with Jaya Algorithm for the recognition and classification of paddy leaf diseases. The proposed method provides the high performance than the other classifiers, such as ANN, DAE and DNN. However, the false classification rate needs to be reduced. Goluguri et al. [25] have utilized a DCNN with support vector machine (SVM), DCNN with ANN and DCNN with long short-term memory (LSTM) for detecting the rice diseases. Here, artificial fish swarm optimization (AFSO), particle swarm optimization and efficient AFSO were used to identify optimal weights of LSTM. This method offered the high accuracy. Anyhow, the performance of this method need to enhanced further. Zema et al. [13] developed an ANN model to predict the hydrological response of a forest after wildfire and soil treatments. This model provides accurate runoff and erosion predictions in burned and non-burned soils as well as for all soil treatments. However, the performance of this model was reduced in the condition with the combination of treatments, which provide the worst performance, mulching, burning and logging. MOTIVATION Rice is a vital crop used as a staple food in most parts of the world and mainly in Asia. Rice plants are affected by several diseases, which destroy 10–15% of production in Asia. Every disease has diverse stages of growth. In the manual disease detection techniques, farmers use the guide books or their experiences to discover the diseases. Every time the disease occurs on a plant, farmers have to keep eyes on the infection. This technique is time-consuming and needs some safety measure during the selection of pesticides. Hence, an automated system can be used which can inform the farmers about diseases instantly. FIGURE 1. Open in new tabDownload slide Schematic view of plant disease detection with proposed RSW-based Deep RNN. The existing automated systems for diseases have some issues. The artificially devised features need costly works and skilled knowledge that poses certain subjectivity. Moreover, it is complex to detect the features that are optimal for reliable disease detection. Due to complicated background, much method failed to efficiently segment the leaf and its corresponding lesion image from the background [16]. The collection of field data based on agriculture is a major issue in contrast to the poor and developing countries. These issues involve lack of tools and experts as the farmers of these areas are unaware of technology usage which makes it more complex to accumulate crop disease data with smart devices. Thus, the plant disease scarcity is major issue in discovering the disease [17]. The detection of rice plant diseases in a timely manner is the major issue in agriculture. Thus, a requirement exists for automatic rice disease detection with voluntarily accessible mobile devices with rural areas [18]. Transfer learning is a type of deep learning technique wherein a CNN is trained for a specific task and is used as preliminary model. However, the method utilized deep learning model that required long time and computing resources for training huge attributes. Moreover, the training of massive dataset is a complex process [19]. Numerous plant disease techniques are devised for spotting the disease of plant using the set of plant images and classifier. The classifier classifies the image into diseased or healthy images. However, the method is costly and requires extensive knowledge. Hence, this paper develops an automated system for rice plant disease detection with the aim of addressing the drawbacks in the conventional methods. PROPOSED RSW-BASED DEEP RNN FOR PLANT DISEASE DETECTION Figure 1 portrays the plant disease detection framework using proposed RSW-based Deep RNN. Initially, input plant images are pre-processed for making image apposite for consequent processing. The pre-processed images are subjected to segmentation module wherein the pre-processed image undergoes segmentation using SegNet. Once the segments are obtained, then the feature extraction is performed considering each segment. From each segment, the CNN features, statistical features which involve mean, variance, kurtosis, standard deviation, entropy and the texture features, such as LOOP are extracted. The extracted features obtained from each segment are formulated in a feature vector. Finally, plant disease detection is performed with Deep RNN using the feature vector, wherein the Deep RNN is trained using the proposed RSW. The proposed RSW is the integration of the standard ROA, WWO and SMO in order to inherit the merits of both the optimizations, towards the effective training of the classifier. Assume a plant disease dataset |$A$| with |$a$| number of images and is formulated as $$\begin{equation} A=\left\{{I}_1,{I}_2,...,{I}_c,...,{I}_a\right\}, \end{equation}$$1 where |${I}_c$|represents the cth input image and |$a$| represents total images. Pre-processing using input plant images The significance of pre-processing is to enable smoother processing with input image. Pre-processing is considered as an essential step for processing the images to make it suitable for detection process. Additionally, the pre-processing is performed for eliminating noise and artifacts contained in image. Moreover, pre-processing can be aided as image enhancement module, which poses the capability to enhance the contrast of the image for plant disease detection. Segmentation of pre-processed image for relevant feature extraction The pre-processed rice image is fed to the segmentation module considering SegNet [26] to provide high-dimensional data segmentation. The pre-processed image contains a different segment each indicating individual regions. In the plant disease detection strategy, the SegNet is applied for determining the disease regions considering each segment. In segmentation, the decision is taken for each pixel contained in the image. Semantic segmentation is defined as a method, which can understand the image at its pixel level. Moreover, the model classifies each pixel according to the pre-determined class. SegNet consists of decoder, and encoder and a pixel-wise layer. Thus, the SegNet provides segments of the input pre-processed image. Assume the segments obtained from the image be represented as $$\begin{eqnarray} S=\left\{{s}_1,{s}_2,...,{s}_d,...,{s}_n\right\}, \end{eqnarray}$$2 where |$n$| indicate the total segments present in the image and |${s}_d$| is the dth segment of input image. Feature extraction using statistical features and texture features The extraction of features guarantees effective plant disease detection for which the CNN features, statistical features and texture features are adapted. For the features extraction, each segment is adapted in such a way that the features assure improved accuracy in plant disease detection. The features extracted from the segments include CNN features, statistical features, which involve mean, variance, standard deviation, kurtosis, entropy and texture features, such as LOOP, which are explained below. (a) Mean: The mean is calculated by computing the average of pixels contained in the image that are formulated as $$\begin{eqnarray} \mu =\frac{1}{\mid d\left({S}_n\right)\mid}\times \sum \limits_{n=1}^{\mid d\left({S}_n\right)\mid }d\left({S}_n\right), \end{eqnarray}$$3 where |$n$| is the total segments, |$d({S}_n)$| indicates the values of pixel of each segment and |$\mid d({S}_n)\mid$| indicates the total pixels contained in the segment. (b) Variance: The variance feature |$\sigma$| is calculated based on the mean value that is expressed as $$\begin{eqnarray} \sigma =\frac{\sum \limits_{n=1}^{\mid d\left({S}_n\right)\mid}\mid{S}_n-\mu \mid }{d\left({S}_n\right)}. \end{eqnarray}$$4 (c) Standard deviation: It is square root of variance and is expressed as |$\rho$|⁠. (d) Kurtosis: Kurtosis |$\kappa$| represents the evenness that defines the sharpness of the peak. The connotation of kurtosis is that it describes object shape based on the arithmetical value. The kurtosis represents the relative peakedness of the probability distribution. (e) Entropy: The entropy [27] is a standard measure used for determining the uncertainty in any data and is utilized for maximizing mutual information in different operations. The entropy is expressed as $$\begin{eqnarray} \varepsilon =-Q\log (Q), \end{eqnarray}$$5 where |$Q$| denotes the probability distribution of pixels in an image. (f) LOOP: The LOOP [27,28] provides a non-linear combination of LDP and LBP, which overwhelms the issues while protecting the strengths of each. Consider |${k}_l$| represents image intensity |$I$| at pixel location |$({u}_o,{v}_o)$| and |${k}_j(j=0,1,\dots, 7)$| be the intensity of pixel in |$(3\times 3)$| neighbourhood of |$({u}_o,{v}_o)$| excluding center pixel |${k}_o$|⁠, and thus the LOOP feature is expressed as $$\begin{eqnarray} L=\mathrm{LOOP}\left({u}_o,{v}_o\right)=\sum \limits_{j=0}^7z\left({k}_j-{k}_o\right){2}^{\omega_j} \end{eqnarray}$$6 $$\begin{eqnarray} z(s)=\{{\displaystyle \begin{array}{l}1\kern0.48em \mathrm{If}\kern0.24em s\ge 0\\{}0\kern0.36em \mathrm{Otherwise}\end{array}}. \end{eqnarray}$$7 (g) CNN features: CNN is the multilayered network with the special architecture used to detecting the complex features from the result of the segmented image. The architecture of CNN consists of three different layers, namely convolution layer, pooling layer and fully connected layer. Convolution is the first layer, which helps to mine essential features from segmented image. It preserves relations between the image features and the pixel values. It takes the segmented result |$S$| as input and extracts the CNN features through the convolution layer. The features that are extracted at the first convolution layer are termed as CNN features and are represented as |${f}_{\omega }$| with the dimension of |$[1\times 256]$|⁠, respectively. Thus the CNN feature is represented as |$C.$| Formation of feature vector Equation (8) demonstrates the set of CNN, statistical and texture feature. Thus, the features extracted from each segment are given as $$\begin{eqnarray} J=\left\{\mu, \sigma, \rho, \kappa, \varepsilon, L,C\right\}, \end{eqnarray}$$8 where |$J$| indicates the feature vector that is extracted using each segment, |$\mu$|⁠, |$\sigma$|⁠, |$\rho$|⁠, |$\kappa$| and |$\varepsilon$|⁠, which indicates mean, variance, standard deviation, kurtosis and entropy which are statistical features, whereas texture features include the LOOP, which is denoted as |$L$| and the CNN feature is indicated by |$C.$| The feature vector is fed to Deep RNN, which classifies the input images on the basis of provided features and derives label of class. The classifier derives label of class and classifies disease or healthy plant corresponding to the input image. Proposed RSW-based Deep RNN for plant disease detection The features extracted are given to classification with Deep RNN [29] and training of classifier is done with proposed RSW, which is a combination of ROA [30], SMO [27] and WWO [31]. The goal of the proposed RSW-based Deep RNN is to detect the disease from input image based on features extracted. The proposed RSW is the incorporation of SMO in RWW, which is the combination of WWO and ROA. The SMO [27] is motivated from the foraging behaviour of spider monkeys and is said to be flexible with other swarm intelligence algorithm. This method helps to make a tradeoff between the exploration and exploitation by handling the speed of convergence. In addition, the SMO helps to balance the population diversity and thus considered as a candidate for population-based techniques. On the other hand, the RWW is the integration of the ROA in the WWO and poses the benefits of both algorithms. Moreover, this method speeded the process of convergence and increased the diversity of solution and attained improved balance between exploitation and exploration. Thus, the RWW is done to improve the overall system performance. Thus, the integration of RWW and SMO is done to enhance overall algorithmic performance. The architecture of Deep RNN and steps of proposed RSW are portrayed below. Architecture of Deep RNN The features |$F$| that are mined from input plant data are given as the input to the Deep RNN classifier. Deep RNN [29] is the network architecture that contains multiple recurrent hidden layers in the layer of network hierarchy. The structure of Deep RNN is made by considering the input vector of bth layer at rth time as |${F}^{(b,r)}=\{{F}_1^{(b,r)},{F}_2^{(b,r)},...{F}_i^{(b,r)},...{F}_y^{(b,r)}\}$| and the output vector of bth layer at rth time as |${J}^{(b,r)}=\{{J}_1^{(b,r)},{J}_2^{(b,r)},...{J}_i^{(b,r)},...{J}_y^{(b,r)}\}$|⁠, respectively. The pair of each element of input and the output vectors is termed as the unit. Here, |$i$| denotes the arbitrary unit number of bth layer, and |$y$| represents the total number of units of bth layer. In addition to this, the arbitrary unit number and the total number of units of (b−1)th layer are denoted as |$j$| and |$E$|⁠, respectively. At this time, the input propagation weight from (b−1)th layer to bth layer is indicated as |${W}^{(b)}\in{H}^{y\times E}$|⁠, and the recurrent weight of bth layer is represented as |${w}^{(b)}\in{H}^{y\times y}$|⁠. Here, |$H$| signifies set of weights. However, the components of the input vector are expressed as $$\begin{eqnarray} {F}_i^{\left(b,r\right)}=\sum \limits_{z=1}^E{p}_{iz}^{(b)}\;{J}_z^{\left(b-1,r\right)}+\sum \limits_{i^{\prime}}^y{x}_{i{i}^{\prime}}^{(b)}\;{J}_{i^{\prime}}^{\left(b,r-1\right)}, \end{eqnarray}$$9 where |${p}_{iz}^{(b)}$| and |${x}_{i{i}^{\prime}}^{(b)}$| are the elements of |${W}^{(b)}$| and |${w}^{(b)}$|⁠. |${i}^{\prime }$| denotes the arbitrary unit number of bth layer. The elements of the output vector of bth layer are represented as $$\begin{eqnarray} {J}_i^{\left(b,r\right)}={\beta}^{(b)}\;\left({F}_i^{\left(b,r\right)}\right), \end{eqnarray}$$10 where |${\beta}^{(b)}$| denotes the activation function. However, the activation functions, such as sigmoid function as |$\beta (F)=\tanh (F)$|⁠, rectified linear unit function as |$\beta (F)=\max (F,0)$| and the logistic sigmoid function as |$\beta (F)=\frac{1}{(1+{e}^{-F})}$|⁠, are the frequently used activation function. To simplify the process, 0th weight as |${p}_{i0}^{(b)}$|and 0th unit as |${J}_0^{(b-1,r)}$| are introduced and hence the bias is represented as $$\begin{eqnarray} {J}^{\left(b,r\right)}={\beta}^{(b)}.\left({W}^{(b)}{J}^{\left(b-1,r\right)}+{w}^{(b)}.{J}^{\left(b,r-1\right)}\right). \end{eqnarray}$$11 Here, |${J}^{(b,r)}$|denotes the output of classifier. Training of Deep RNN with proposed RSW The training procedure of Deep RNN classifier is done using the proposed optimization algorithm named RSW algorithm. However, the weight of the classifier is trained using the proposed RSW for obtaining optimal solution. RSW modifies the Deep RNN by integrating the RWW with the SMO to select optimal weights to achieve update process. For detecting disease in plant, the optimization, namely RSW, is proposed in this research. The proposed RSW optimization is used to train the weight of Deep RNN classifier in order to generate the optimal solution. By integrating the RWW with SMO, the parametric features from both the optimization are inherited, which boost the performance of classification accuracy. The algorithmic procedure for plant disease detection is given as Step 1) Initialization: The foremost step is the initiation of solution, which is given as $$\begin{eqnarray} G=\left\{{G}_1,{G}_2,\cdots, {G}_e,\cdots{G}_f\right\};1\le e\le f, \end{eqnarray}$$12 where |$f$| denotes the total number of solutions and |${G}_e$| indicate the eth solution. Step2) Evaluation of the error: The optimal solution is detected using error, which is modelled as the minimization problem, and thus, the solution with least Mean Square Error (MSE) is chosen as an optimal solution. Here, MSE is computed as follows: $$\begin{eqnarray} {\mathrm{MS}}_{\mathrm{err}}=\frac{1}{a}\sum \limits_{c=1}^{at}{\left[{N}_c-{N}_c^{\ast}\right]}^2, \end{eqnarray}$$13 where |${N}_c$|denotes expected output and |${N}_c^{\ast }$| signifies predicted output, |$c$| denotes the count of data samples, where |$1