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The Feed Forward Back Propagating Neural Network (FFBPNN) models for crop yield were developed and calibrated in MATLAB environment. During training, the model perceptron’s were trained with 75 of the 100 inputs upto10,000 epochs with 1 to 10 hidden neurons. Four performance indices (coefficient of multiple determination, R²; MAE; RMSE and the average ratio between estimated yield to target crop yield [R_ratio]) were calculated to achieve optimum neural network. Accurate and stable results observed from the model for paddy with highest mean relative error as 6.166% and the lowest relative error as −0.133%. The range of R² values were 0.946 and 0.967 for training and same for testing was 0.936 and 0.950 for paddy in Kharif and Rabi seasons, whereas for sugarcane the values are 0.916 and 0.924 during testing and training, respectively. The highest MAE was 0.178 for Paddy (Rabi). The R_ratio values showed the under crop yield estimation of sugarcane crop. The model’s best performance was observed at [i+1] and [i+2] hidden nodes. The statistical analysis revealed that the reliability of the model in paddy yield estimation. However, slight under estimation of yield of the sugarcane crop indicates sensitivity of yield algorithms to crop input parameters. The results demonstrated the high efficacy of using remote sensing images and NN models to generate accurate crop yield maps and also revealed significant superiority of neural network models over conventional methods.

      Keywords: Crop yield, remote sensing, neural networks, feed forward and back propagation, NDVI, APAR, crop water stress

2.1 Introduction

      Climate change posing serious challenges on fresh water and good soil and are becoming serious limitations for agriculture around the world. Average raise in temperatures was causing more extreme heat throughout the year. Rainfall patterns are also shifted more intense storms of short spells and longer dry periods. Severe droughts tolled heavily on crops, and livestock. On the other hand, increased floods destroy crops and livestock, accelerate erosionof soil, pollute fresh water, and damage roads and bridges. Sea level rise is also the intensity of floods on farms and sea water intrusion in coastal regions. New pests are boosting up and damaging crops [1].

It is also important to know that climate change risks are not constant and not distributed equally neither in space nor in time. In turn, it requires regular crop monitoring and management of resources to get maximum yields. The monitoring of crops at regional level includes crop type mapping, cropping pattern recognition, crop condition estimation, crop yield estimation, estimation of evapotranspiration, irrigation scheduling, monitoring of water resources, uncertainty analysis, Identification of pest attack, soil mapping, and so on [2]. Although agriculture is a complex interlinked phenomenon, clear-cut success has been achieved with the technological interventions in decision-making processes and in shaping adaptation strategies with the changing scenarios. Technological innovations like mechanization, artificial intelligence and robotics, UAVs, sensors, Internet of Things (IoT), remote sensing, machine learning, deep learning, and their combinations in agriculture have the ability to transform food chain of the crops. The integration of local agricultural knowledge with remote sensing depends on the understanding of complex phenomena in agriculture [3].

      Crop yield estimation at regional level plays crucial role in planning for food security of the population. This is of greater important task for some wide applications, including management of land and water management, crop planning, water use efficiency, crop losses, economy calculation, and so on. Traditional ground observation-based methods of yield estimation, such as visual examination and sampling survey, require continuous monitoring, and regular recording of crop parameters [4–6]. Spectral information from remote sensing images gives very accurate crop attributes that can be used for crop mapping and estimation. Further integration of machine learning algorithm with remote sensing provides explicit estimation of yield [7]. The present study focused on ability of machine learning algorithm in integration with remote sensing in crop yield prediction of paddy and sugarcane crops at regional level.

2.2 Introduction to Artificial Neural Networks

      2.2.1 Overview of Artificial Neural Networks

An artificial neural network (ANN) is a wide class of flexible and simple mathematical model. It is capable to identify complex nonlinear relationships between input and output observed datasets. Neural network consists of a large number of “neurons,” nonlinear computational elements, connected internally in a complex way and arranged into layers [7]. Artificial neural network simulates natural neural network in the brain. In the rain, the fundamental neural network is connected to each other by synapses. The neurons are basic components of the human brain are processing unit in the brain. The neurons are responsible for learning and retention of information. The sensory/observed data are the input to the network, processes it, and gave output for other neurons. In ANN, everything is designed to replicate this process. An ANN also consists of a bundle of neurons. Biological axon-dendrite connects each node to other nodes via links. All the data the variable name “X” enters in the system with a weight of “w” for generating a weighted value. Each link weight determines the strength of nodes influence on other node. This denotes the strength of a signal in the brain. An activation function that use the basic mathematical equations to determine input-output relation. The familiar activation functions in NN are logistic function, binary step function, rectified linear units, and hyperbolic tangent function. The ANN models are efficient; particularly in solving the problem in the complex processes, which are difficult to describe using physical equations [8]. The ANN models are capable of modeling the complex nonlinear relationships, compared with a traditional linear regression model approach [9]. The ANN also has excellent fault tolerance and is fast and highly scalable with parallel processing. ANN models are similar to statistical models like generalized linear regression models, polynomial models, nonparametric models and discriminant analysis, principal component analysis, and other models in which the prediction of complicated phenomena is important than the explanation. On the other hand, NN models, like learning vector quantization, counter propagation, and self-organizing maps, are useful for data analysis. Some of the published work that provide insight about relation between statistics and NN are discussed.

      2.2.2 Components of Neural Networks

      The human brain on an average contains 86 billion neurons approximately [10]. A biological neuron consists of thin fibers, and those are known as dendrites. Dendrites receive incoming signals. The cell body, “soma” responsible for processing input signals and to decide firing/nonfiring of neurons to output signal. Processed signals output from neurons received by “axon” and passes it to relevant cells.

Artificial neuron called also as “perceptron” is a fundamental component of neural network, which is a mathematical function of a real-world problem with binary outputs. The neurons are systematically organized into two or more than two layers. One layer of neurons are connected to immediately preceding neurons layer and immediately succeeding neuron layer. The first (input) layer receives the external data, and the last (output) layer ultimately produces result. Each artificial neuron receives input from input layer, process the weights and sums and pass the sum through a nonlinear mathematical relation to produce output. In between them are one or more hidden layers (Figure 2.1). Weights are multiples of respective input values arranged in an array. To achieve a final value of prediction, bias is added to the weighted sum. The size of the correction values to adjust for errors by the model is known as a learning rate. Activation function decides whether or not a neuron is fired [11]. The neural network uses previous step output data values for the network training and minimizes the error between observed and estimated. The process readjusts the weights at each interaction of neuron. The training will stop after reaching the optimal learning rate [12, 13]. The higher learning rate reduces the time for training, and ultimate accuracy is low. Lower learning rate takes longer time and higher accuracy.

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