Difference between revisions of "Team:NCTU Formosa/Dry Lab/Productivity Model"

     The core nutrients nitrogen, phosphorus and potassium directly impact the productivity of crops. To predict how our fertilizers affect crop yield, we generate a model that relates cumulative N, P and K application to final curcumin concentration. Using neural networks is a popular method of deriving connection between a combination of factors and a final value, in this case a combination of N, P and K values and a productivity value. Constructing the following neural network with back-propagating methods results in a non-linear regression model that predicts productivity from cumulative fertilization.

     We use simple three layer ANN (Artificial Neural Network) design to build up our productivity model, including one input layer, one hidden layer, and one output layer. Input layer contains the data of nitrogen, phosphate, and potassium, three nutrients added to soil respectively. Hidden layer contains three neuron (more details will be explained below). Finally, output layer contains one predicted productivity.

     Set all the weights and threshold levels of the network to random numbers uniformly distributed inside a small range (Haykin, 2008): $$\left ( -\frac{1}{Fi},+\frac{1}{Fi} \right )$$ where Fi is the total number of inputs of neuron i in the network. The weight initialization is done on a neuron-by-neuron basis.

     Activate the back-propagation neural network by applying our inputs (N,P,K value) and outputs (productivity)

Update the weights in the back-propagation network propagating.
( Backward the errors associated with output neurons.)

$$\delta _{k}(p)=y_{k}(p)\times\left [ 1-y_{k}(p) \right ]\times e_{k}(p)$$      where $$e_{k}(p)=y_{d,k}(p)-y_{k}(p)$$      Calculate the weight corrections: $$\Delta w_{jk}(p)=\alpha\times y_{j}(p)\times \delta_{k}(p)$$      Update the weights at the output neurons: $$w_{jk}(p+1)=w_{jk}(p)+\Delta w_{jk}(p)$$

$$\delta_{j}(p)=y_{j}(p)\times\left [ 1-y_{j}(p) \right ]\times\sum_{k=1}^{l}\delta_{k}\times w_{jk}(p)$$      Calculate the weight corrections: $$\Delta w_{ij}(p)=\alpha\times x_{i}(p)\times\delta_{j}(p)$$      Update the weights at the hidden neurons: $$w_{ij}(p+1)=w_{ij}(p)+\Delta w_{ij}(p)$$

Increase iteration p by one, go back to Step 2(Activation) and repeat the process until the selected error criterion is satisfied.

     Using the neural net fitting tool from MATLAB, can help us easily build up the whole neural network. Furthermore, we use MATLAB API, which can be used to connect MATLAB with Python, to integrate all the model we built.
     The training result of our nueral network was shown below. The accuracy can be expressed through “Performance” and “Regression” figure below.

     With every iteration, the error will decrease, and maxize the performance of our neural network. The training and test mean square errors was shown in the following figure.

     Regression model shows how well our model had been trained and how accurate our model predicted. The training accuracy result of our model was shown below through the regression model.

     All the training results including weights and bias values, parameters, and equations were shown in the code below. If you're really interesting in the detail of our results, please click the button below to see more!