AOHDL: Archimedes Optimization Based Hybrid Deep Learning Model for Soybean Plant Disease Classication

: Bean which is botanically called Phaseolus vulgaris L belongs to the Fabaceae family.During bean disease identification, unnecessary economical losses occur due to the delay of the treatment period, incorrect treatment, and lack of knowledge. The existing deep learning and machine learning techniques met few issues such as high computational complexity, higher cost associated with the training data, more execution time, noise, feature dimensionality, lower accuracy, low speed, etc. To tackle these problems, we have proposed a hybrid deep learning model with an Archimedes optimization algorithm (HDL-AOA) for bean disease classification. In this work, there are five bean classes of which one is a healthy class whereas the remaining four classes indicate different diseases such as Bean halo blight, Pythium diseases, Rhizoctonia root rot, and Anthracnose abnormalities acquired from the Soybean (Large) Data Set.The hybrid deep learning technique is the combination of wavelet packet decomposition (WPD) and long short term memory (LSTM). Initially, the WPD decomposes the input images into four sub-series. For these sub-series, four LSTM networks were developed. During bean disease classification, an Archimedes optimization algorithm (AOA) enhances the classification accuracy for multiple single LSTM networks. MATLAB software implements the HDL-AOA model for bean disease classification. The proposed model accomplishes lower MAPE than other exiting methods. Finally, the proposed HDL-AOA model outperforms excellent classification results using different evaluation measures such as accuracy, specificity, sensitivity, precision, recall, and F-score.


Introduction:
Agriculture is one of the major pillars in the economic sector that contribute toincome, employment generation, and wealth for the country. Plant disease is the major factor to degrade agricultural products all over the world that leads to huge loss each year. The most produced and most important legumein the world is the bean (Phaseolus vulgaris L). On a global scale, the bean is an important legume/grain taken for consumption and was widely dispersed due to its broad adaptation (Argüeso et al. 2020, Mitchell et al. 2009). During the growing season, the plants grow well in about 400 mm of precipitation and moderate growing temperatures (>10 °C and <30 °C). The growing temperatures <30 °C with the tropical highlands and 60-120 days of frost-free growth are permitted by season where the ordinary bean is grown ina moderate growing region . Approximately, 15% soluble fiber, 62% complex carbohydrates, several micronutrients (Ca, Fe, Mg, P, and K), and 22% protein present in the uncooked dry bean. Bean commonly provides trace nutrients, calories, and sources of protein to persons who never give additional expensive sources of nutrition. The dry edible beans are a major kind in contemporary agriculture in which the matured seed is prepared in main dishes and harvested.
Root diseases (such as Fusarium root rot, Pythium diseases, Rhizoctonia root rot, Soybean cyst nematode, and Soybean cyst nematode soil sampling), Stem and wilt diseases (including Bacterial wilt, Fusarium yellows, stem rot, and white mold), and Foliar diseases such as (Anthracnose, Bacterial brown spot, Bean common mosaic, Common bean root dust, common bacterial blight, and halo blight) are the important types of bean diseases , Kabagambe, et al. 2005. Bean disease identification and detection at an early stage is a more important one. Hence, the people quickly take suitable prevention criteria. According to the experience in observing bean disease identification, most forest producers judge a degree and disease species in traditional forestry and agricultural production in which it needs skill and knowledge to detect the symptoms of bean diseases. The unnecessary economical losses are resultant due to delay of the treatment period, incorrect treatment, and lack of knowledge to plant disease identification. It will take little time even if experts are invited to identify a disease  . Hence,the automatic implementation of plant diseases or bean disease identification and classification is essential (Grant et al. 1995, Lindgren et al. 1986).
More computer vision methods were applied to plant disease classification with the development of computational systems in recent years. Nowadays, artificial intelligence and data mining techniques are widely used to solve the prediction and classification issues in agriculture . The execution measurements and 10 fold cross-validation with Decision Tree (DT), k-Nearest Neighbors (kNN), Backing Vector Machine (SVM), and Multilayer perceptron (MLP) models were used . Deep learning techniques play a vital role in plant disease classification. These machine learning and deep learning techniques met few shortcomings in terms of computational complexity, the high cost associated with training data, more execution time, noise, feature dimensionality, lower accuracy, low speed, etc (Uğuz and Uysal 2020, Hernández and Juan 2020. To tackle these issues, we have proposed a hybrid deep learning model with an Archimedes optimization algorithm (HDL-AOA). The major contribution of this paper is summarized as follows:  The combination of wavelet packet decomposition with long short-term memory is proposed as a hybrid deep learning model.  The classification accuracy for multiple single LSTM networks during bean disease classification is boosted up using the Archimedes optimization algorithm (AOA).  The healthy and unhealthy classes such as Bean halo blight, Pythium diseases, Rhizoctonia root rot, and Anthracnose images were collected from Soybean (Large) Data Set.
The rest of the paper is organized as: Various plant disease classifications based on deep learning techniques are delineated in section 2. Section 3 explains the proposed HDL-AOA model for bean disease classification. The experimental investigation based on the proposed model is discussed in section 4. Finally, section 5 concludes the paper.

Related work:
This section reviews a few of the existing works based on plant disease classification using deep learning techniques.A deep convolutional neural network (DCNN) was proposed by Uğuz et al. (Uğuz et al. 2020) for olive peacock spot and aculeus olearius diseases classification. There are 3400 olive leaves sampleschosen in which three classes namely healthy, olive peacock spot and aculeus olearius disease were present. The VGG16 and VGG19 architectures based on the DCNN model are used. The network's performance was improved with the help of the RMS Prop optimization algorithm and Stochastic gradient descent. The multi-task system based on Convolutional Neural Networks (CNN) was suggested by  to detect the stress severity caused by biotic agents on coffee leaves. A more accurate and robust detection system was performed using computational experiments. As a result of 86.51% severity estimation and 95.24% of biotic stress classification accuracy were obtained using multi-task system-based CNN with ResNet50 architecture. Hence, this method is appropriate for biotic stresses in coffee plantation identification and quantification.
A pre-trained Convolutional Neural Network (CNN) was proposed by  for crop disease identification. This pre-trained CNN includes models such as DenseNet201, ResNet101, GoogLeNet, VGG19, Visual Geometry Group 16 (VGG16), and AlexNet. The author chose four kinds of crops with ten diseases such as leafhopper, yellow vein mosaic virus, citrus canker, citrus Hindu mite, brown spot, Cercospora leaf spot, two-spotted spider mite, Epilachna beetle, little leaf disease, and Tobacco Mosaic Virus TMV. For each disease class, they evaluated the prediction scores and classified images in realtime. Hernández et al. (2020) proposed a Bayesian Deep Learning technique for the detection of plant diseases. When compared to the state of art methods, higher classification performance is achieved using Bayesian inference. The uncertainty of the predictions is quantified and posterior density for the plant disease detection problem was approximated.
The transfer learning of the deep convolutional neural networks (DCNN) was introduced by Chen et al. (2020) for plant leaf disease identification. They selected the Inception module and VGGNet pre-trained on ImageNet for experimental investigation. According to the experimental investigation, 92.00% classification accuracy is obtained for rice plant images. For classification, the high-dimensional features are extracted and the experimental results provided better results in terms of both own dataset and public dataset. Finally, 91.83% validation accuracy is achieved during disease classification. Li et al. (2020) proposed Convolutional Neural Network (CNN) for Ginkgo leaf disease detection. They combined and used Inception V3 and VGGNet-16 models. Based on laboratory conditions, 98.44% accuracy was accomplished and the VGG model provided 92.19% accuracy. Nevertheless, data overfitting with more processing time takes place. The existing work based on the plant disease classification using deep learning techniques is delineated in Table 1.

Hybrid deep learning with AOA model for bean disease classification:
In this section, we have proposed hybrid deep learning with AOA (HDL-AOA) model forthe bean disease classification. For this work, the normal healthybean with four unhealthy classes such as Bean halo blight, Pythium diseases, Rhizoctonia root rot, Anthracnose were chosen. The steps involved in the proposed HDL-AOA model for bean disease classification are briefly explained in the following section.

Wavelet Packet Decomposition:
The time-frequency localization function with orthogonal wavelet packet bases and image properties are analyzed using an efficient tool called Wavelet Packet Decomposition (WPD). The original images are decomposed into sub-layers in which WPD is a kind of wavelet decomposition (WD). The low pass components of frequencies are segregated (Coifman et al. 1994). The timefrequency planes more than wavelet decompositionare divided and WPD accomplished a more precise analysis of images. When compared to WD, the WPD is more efficient for singular components, instantaneous, unbalanced, and identifying weak images. The WPD decomposes a coefficient of each layer continually. Both discrete and continuous transform are present in the WPD. The mother wavelet transform function ) (t  adopts the continuous wavelet transform for a signal ) (t F ( Zhitong et al. 2001) The scale coefficient and translation coefficient are denoted as c and d . The complex conjugates are denoted as  . The following equation describes a WPD process of decomposition.
Therefore, the time index and the wavelet packet levels are denoted as t and k j Q . The low and high pass filters are denoted as H and G . The single branch reconstructions reconstruct each packet atthe last decomposition level to the original level. The other packet values of similar levels are expressed to be zero if the construction is an inverse of the decomposition process.

Long short-term memory networks:
Enhancement of Recurrent Neural Network (RNN) is called long short-term memory (LSTM). Instead of conventional RNN units, the LSTM accomplishes memory blocks to solve exploding gradient and vanishing problems (Hochreiter et al. 1998). The network of LSTM memorizes and links the existing data to information received in the current stage (Zhang et al. 2012). Three gates such as input, forget and output gates are combined to form the LSTM. The current input is considered as j x the new and previous cell states are denoted as The sigmoid layer is used to pass  (7) executes the forget-based data from an existing cell with a certain probability. The sigmoid function, offset and weight matrix are denoted as  , j a and j W .
According to equations (8) and (9), the inputs 1  j h are j y determined by the LSTM output gates. The tanh layer The LSTM, output gates weighted matrices are denoted as o W and o a .

Archimedes optimization algorithm (AOA) for multiple single LSTM networks:
In the first step, the original image is decomposed by applying WPD and various reconstruction models are taken up. The performance of bean disease classification is improved by incorporating the combined multiple single LSTM network strength . The classification results are obtained from every LSTM network after inputting the decomposed images. The final classification results are obtained by summing this LSTM network. Instead of summing, apply the Archimedes optimization algorithm (AOA) to enhance the classification accuracy. The AOA is used to evaluating the weight coefficient of each model. The mean absolute percentage error (MAPE) minimization determines the optimized weight coefficient. The image series minimizing standards and the error values determines it ). The MAPE minimization calculates a weight coefficient of the combined classification model. TheArchimedes optimization algorithm is mainly based on the Archimedes principle which is an interesting law of physics. The immersed objects are considered as a population of individuals in AOA. The accelerations, densities, random volumes with the initial population of objects are commenced in AOA (Li et al. 2021). Both exploitation and exploration processes are encompassed in AOA, which is considered a global optimization algorithm. The AOA updates the volume and density of every object in different iterations. The mathematical formulation of AOA stages are delineated as follows:

Initialization:
Equation (1) The j th population of M objects is j OB . The upper and lower limits of a search space are denoted as j U and j L . Equation (11) and (12) is used to update the density (D) and volume (V).

random D j 
The D-dimensional vector creates the random interval as 0 to 1 and is denoted as random. Equation (13) updates the acceleration (A) of j th objects (Zhitong et al. 2001).
The best fitness value with the objects is selected there also an initial population is evaluated. Assign best A , best V , best D and best y . The fitness function of this work is optimal accuracy.

Density and volume update:
Equation (15) is used to update the volume and density of j th objects for the t+1 iteration (Hashim et al. 2020 Here, the best volume and density are 1  t j V and 1  t j D connected to the best objects.

Density factor and transfer operator:
The collision between objects occurs at first and the objects try to reach an equilibrium state after some time. The transfer operator Tf with AOA implements this. Equation (17) transforms search space from exploration to exploitation.
Here, the number of iteration and the maximum number of iteration are denoted as t and max t . Where Dd is denoted as the density decreasing factor.

Exploration stage:
The collision between objects occurs if 5 . 0  Tf , then selects the random material RM. Equation (19) updates theacceleration of the object for the t+1 iteration.
Hence, the volume, density, and acceleration of random material are expressed as Rm V ,

Rm D and
Rm A . During one-third of iterations, the Tfguarantees an exploration.

Exploitation stage:
There is no collision between the objects if 5 . 0  Tf . Equation (20) updates the acceleration of the object for the t+1 iteration.
Here, the best object acceleration is best A .

 
Where the normalization range is denoted as and  .

Validation:
The objective function evaluates each object. Assign best A , best V , best D and best y . The steps involved in AOA for multiple single LSTM networks are depicted in algorithm 1.
Algorithm 1: AOA steps for multiple single LSTM networks Initialization of AOA population,D, input, forget, and output gatesof LSTM with the maximum number of iterations max t Initialize AOA acceleration, density, and volume with random position Compute the fitness function using equation (14) and choose the excellent fitness Set t=1 While max t t  do For every j object do Equation (15) and (16) is used to update the volume and density Use equation (17) and (18) (20) and (21) to update the acceleration and normalization Use equation (22) (21) and (22) to update the acceleration and normalization Use equation (24) to update the direction flag

End If End If End for
Select the best fitness and compute each object Set t=t+1 End While Obtain the optimalclassification accuracy Return to object with the optimal fitness value End

Hybrid deep learning model (WPD-LSTM) for classification model:
The WPD is used to decompose the image series in the proposed model. Mother wavelet utilizes a frequencybased third-order Daubechies type wavelet function (db3). In the classification image series, different frequency bands regularly exist simultaneously. The classification image series are separated in to high and low-frequency components after decomposition through WPD Sahu et al. 2020). Some random output and fast varying image output are represented using high-frequency components and the low-frequency components denote the image output trend. The historical image output is an input model used in the proposed hybrid learning model . the relationship among bean image disease classification will be considered in this way. Fig 2 explains the hybrid deep learning with the AOA model for bean disease classification. Where, From step (i), develop an independent LSM network for each sub-series. The inputs of each LSTM network consider the image data are the input variables of each LSTM. The deep learning model adopts four independent well trained three-layer LSTM networks. The classification result provided these independent LSTM networks.
(iii) A final classification result of bean disease classification is acquired by adopting an Archimedes optimization algorithm (AOA).

Experimental Analysis:
In this work, we have proposed hybrid deep learning with the AOA (HDL-AOA) model for bean disease classification in which the proposed model performances are evaluated using various types of performance evaluation metrics and comparative analysis. The tensorFlow2 on an Intel(R) Core(TM) 17-2.2GHz processor with Python and Keras package implement the proposed HDL-AOA for bean disease classification. Additionally, the 4G and 16 GB RAM with graphical processing unit (GPU) NVIDIA GTX 1050 execute the experiments. (Turkoglu et al. 2019) The experimental investigation in terms of classification performance analysis and comparative analysis are delineated in the following section. Table 2 delineates the parameter used for bean disease classification.

Dataset explanation:
In this work, the dataset images were taken from Soybean (Large) Data Set (Dua et al. 2019) and (Markell et al. 2016) (https://www.ag.ndsu.edu/publications/crops/dry-ediblebean-disease-diagnostic-series#section-12). This dataset consists of 19 classes of attributes. From this, we have selected a single healthy class with four unhealthy classes such as Bean halo blight, Pythium diseases, Rhizoctonia root rot, and Anthracnose (Fig 3). The training and testing image details based on the dataset are delineated in Table 3. Table 4 explains the bean disease symptoms.

Evaluation measures:
The performance efficiency of the proposed model is evaluated using different kinds of evaluation metrics such as accuracy, specificity, sensitivity, precision, recall, F-score, and MAPE. Each measure is delineated as follows: Where the number of instances that belong to the correctly identified class is True Positive (TP). The number of instances that belong to the incorrectly identified class isFalse Negative (FN). The number of instances that do not tend to the class, which are incorrectly identified is called False Positive (FP). Similarly, the number of instances not tends to the class, which are correctly identified are called True Negative (TN). Equation (30) and (31)   Internal brick-red discoloration of pith

Performance Analysis:
The performance analysis with respect to accuracy and loss is depicted in Fig 4. According to the ratio of 70/30 divides both training and testing set. The input images were resized into 224 224  pixels. The training and testing performance in terms of accuracy and loss are depicted in Fig 4 (a) and (b). There are 30 epochs chosen for this experiment . Fig 4 (a) takes 30 epochs with 100% accuracy in which the accuracy levels varying from 0.65% to 0.98% training accuracy and the testing accuracy varies from 0.83% to 0.92%. According to Fig 4 (b), the training loss varies from 0.82% to 1.0%. Similarly, the testing loss varies from 0.45% to 0.23%. The proposed HDL-AOA takes better training accuracy and testing accuracy as well as training loss and testing loss in terms of bean disease classification.
Fig 5 depicts the proposed HDL-AOA performance analysis with respect to each class. We have selected a healthy bean plant with four unhealthy images belongs to Bean halo blight, Pythium diseases, Rhizoctonia root rot, Anthracnose diseases. The accuracy, specificity, and sensitivity performance of each class are evaluated. For a healthy class, we have obtained 84% accuracy, 89% specificity, and 91% sensitivity results. We have obtained 89% accuracy, 81% specificity, and 90% sensitivity results for the bean halo blight class. The Pythium class provided 91% accuracy, 84% specificity, and 81% sensitivity outcomes. For Rhizoctonia root rot, we have attained 91% accuracy, 95% specificity, and 84% sensitivity results. Similarly, 92% accuracy, 88% specificity, and 95% sensitivity results are obtained for Anthracnose. The Confusion matrix with respect to each class is delineated in Fig 6.  Fig 7 illustrates the proposed HDL-AOA performance analysis with respect to ROC. When analyzing the overall performance, the ROC curves plotted among true positive rate (TPR) and false-positive rate (FPR) respectively. Each class varies from 0.1 to 1.0. The area under ROC (AUC) is computed to be 9.9% for HDL-AOA models. Based on the ROC curve, we have obtained better true positive rates in terms of the healthy class, Bean halo blight, Pythium disease class, Rhizoctonia root rot class, Anthracnose class.   proposed HDL-AOA achieves 2% MAPE for healthy class, 2.1% for bean halo blight, 3% for Pythium, 5% for Rhizoctonia, and 2% for Anthracnose. However, the proposed HDL-AOA model accomplishes low errors during bean disease classification.   Proposed HDL-AOA performance analysis with respect to each class Confusion matrix with respect to each class Proposed HDL-AOA performance analysis with respect to ROC Figure 8 Performance evaluation of MAPE with respect to various methods and each class