Optimizing Lettuce Crop Yield Prediction in an Indoor Aeroponic Vertical Farming System Using IoT-Integrated Machine Learning Regression Models

The increasing population, climate change, and food constraints have led to a growing interest in alternative farming methods like hydroponics and aeroponics. These methods offer year-round harvests, weather protection, easy transportation, support for various crop cultivars, and disease-free practices, making them crucial for addressing food security concerns in the global economy. Aeroponics, a soilless method with an innovative tower structure, has shown significant improvements in crop yields ranging from 7% to 65%, accelerated crop maturation rates, and optimized water, pesticide and fertilizer consumption patterns when compared to the traditional farming techniques [1, 2].

Soil-free cultivation uses hydroponic or aeroponic systems to grow plants without soil. Hydroponics involves submerging roots in nutrient solutions, while aeroponics aerosolizes the solution. These systems offer a controlled environment and easy nutrient manipulation, making them ideal for genetic studies and screening mutant phenotypes. Aeroponic systems are more efficient due to their ability to suspend roots in mist, improve oxygen exposure, and produce fine particles [3-5].

Artificial Intelligence (AI) has shown potential for improving crop yield predictions in fields like healthcare, robotics, and meteorology. It can enhance efficiency and accuracy in agricultural yield prediction by optimizing parameters like light exposure, nutrient supply, and temperature [2, 6-8]. In aeroponic systems, the utilization of AI techniques like machine learning algorithms plays a vital role, especially in data analysis, real-time growth monitoring, resource management and predictive modeling. 

The study stresses how important it is to accurately predict aeroponic crop yields in modern farming. This lets farmers use advanced machine learning algorithms to make the best use of their resources, come up with effective farming strategies, and cut down on losses [9, 10]. Accurate yield prediction in aeroponic systems is crucial for food production and resource management. It optimizes factors like yields, crop appearance, nutritional content, quality, and taste while minimizing resource usage like nutrients, water, and energy, leading to effective cost utilization and optimized resource utilization.

Real-time aeroponics systems require improved decision-making processes and accuracy in yield prediction models to address the aforementioned factors, which have been elaborated on in this research work. The structure of this document comprises four sections: Section 2 provides an overview of existing works, while Section 3 details the methods used to collect and analyze data, including the implementation of machine learning models and interpretability techniques. Section 4 presents the findings and their implications, while Section 5 summarizes key takeaways and potential areas for further research.

3.1 Predicting the yield of aeroponic lettuce-manual and technology-driven methods

The basic comparison of predicting yield using manual and with the help of technology is presented in the form of Table 1.

3.2 Machine learning in lettuce yield prediction

With their advanced analytical ability to cope with the complexity of agricultural systems, machine learning (ML) algorithms have become a potent tool in the prediction of lettuce crop yields. Here, in this work, we have utilized different machine-learning regression models that provide a greater impact on the yield prediction of the lettuce crop.

3.2.1 Utilized machine learning models

Linear Regression. Linear regression is the fundamental and interpretable machine learning regression model used for predicting numerical values with the help of the linear equation. In an aeroponic lettuce crop yield prediction system, the model estimates the linear relationship between the one input variable and the output variable. It is mathematically represented as:

$y=m x+b$       (1)

where, y is the dependent variable (crop yield), x is the independent variable (input parameters), m is the slope and b is the intercept term.

Multiple Linear Regression Model. Linear regression models are simple approaches used to find the relationships between two variables, the input, and the output variable. But for more complex relationships that require more consideration, the multiple linear regression models were highly utilized to find the relationships between the multiple input variables and the output variable i.e. the situation where multiple independent variables are used to estimate the outcome of the single dependent variable.  There are two main uses of this regression analysis: 1) to determine the dependent variable based on the multiple independent variables and 2) to determine how strong the relationship is between the variables.

Multiple linear regression is often used when forecasting more complex relationships. In an aeroponic lettuce crop yield prediction system, multiple regression models can make effective predictions on the new and unseen data. The coefficients of the feature variables are determined which allows the growers to make informed decisions about the crop behavior and yields. Equation 2 is the mathematical representation of the MLR:

$y=b_0+b_1 x_1+b_2 x_2+\cdots+b_n x_n$      (2)

where, $y$ is the dependent variable (crop yield), $\left[x_1, x_2, \ldots, x_n\right]$ is the independent variable (input parameters) and $\left[b_0, b_1, b\right.$ $\left.2, \ldots, b_{\mathrm{n}}\right]$ are the coefficients.

Support Vector Regression. Support Vector regression is a type of supervised machine learning algorithm that works similarly to that of the SVM algorithm. The model aims to minimize the errors in the actual and predicted values which fit the hyper plane into the data points. In an aeroponic lettuce yield prediction system, the dependent variable lettuce yield is predicted using the independent variables which are the environmental factors for growing the lettuce crop with the help of different kernel functions to fix the non-linearities into linear problems. It deals with the complex relationship between the environmental factors and the yield.  SVR allows hyper-parameter tuning which improves the accuracy of the prediction model to better fit into the dataset. Like other regression models, SVR can be iteratively improved by incorporating the new and the unseen data.

The mathematical formulation of the SVR objective function involves defining a hyperplane that finds the relationship between the input parameters and the output (yield). The data points n concerning the input parameters X_i and the corresponding output (yields) y_i, where, i=1, 2, 3, …, n the SVR objective function could be written as two different equations as represented below.

i) In the case of linear kernel

$min _{w, b, \zeta, \zeta^*} \frac{1}{2} w^T w+C \sum_{i=1}^n\left(\zeta_i+\zeta_i^*\right)$   (3)

subject to the constraints $=\left(y_i-w^T X_i-b \leq \varepsilon+\zeta_i\right)\left(w^T X_i+\right.$ $\left.b-y_i \leq \varepsilon+\zeta_i^*\right)$ where, $\zeta_i, \zeta_i^* \geq 0$.

ii) In the case of a non-linear kernel

$min _{w, b, \zeta, \zeta^*} \frac{1}{2} w^T w+C \sum_{i=1}^n\left(\zeta_i+\zeta_i^*\right)$  (4)

subject to the constraints $=\left(y_i-\phi\left(X_i\right)^T w-b \leq \varepsilon+\right.$ $\left.\zeta_i\right)\left(\phi\left(X_i\right)^T w+b-y_i \leq \varepsilon+\zeta_i^*\right)$ where, $\zeta_j, \zeta_i^* \geq 0$.

where, $\phi\left(X_i\right)$ is the transformation of $X_i$ into a highdimensional space.

In these equations, $w$ and $b$ are the parameters to be learned from the training data, $\zeta_{\mathrm{i}}$ and $\zeta_i^*$ are slack variables allowing for deviations from the actual output and $C$ is a regularization parameter controlling the trade-off between model simplicity and accuracy.

Random Forest Regression. The Random Forest (RF) is the collection and utilization of multiple decision trees for output predictions. It is the ensemble learning approach that combines the output of multiple weak learners to improve the accuracy and robustness of the model. Each decision tree deals with the subset of random features that promotes the diversity leading to the chances of better predictions. It has the capability of handling missing values which does not require any external preprocessing techniques. Also, the model could effectively handle larger datasets.  In an aeroponic vertical farming system, the RF supports the complex interaction between the dependent and the independent features. One of the main advantages of RF regression is that it handles the overfitting problem due to the randomness in the feature selection. With the help of feature importance, the growers were able to gain insights into the input parameters that have the most significant impact on the lettuce yield.

It is represented as the average of individual tree predictions which is given below:

$\hat{y}(X)=\frac{1}{N} \sum_{i=1}^N F_i(X)$    (5)

where, $\hat{y}(X)$ is the predicted output (yield) for the given set of input parameters $(X), N$ is the number of trees in the random forest, $F_i(X)$ is the prediction output from $i^{\text {th }}$ decision tree.

Here, each tree $F_i(X)$ is constructed based on the random subset of features at each split. The final prediction is an average of these individual tree predictions.

XGBoost Regression. The Extreme Gradient Boosting-XGBoost model is a powerful machine learning algorithm that excels in real-world prediction tasks. It uses a decision-tree-based ensemble model to reduce errors and improve accuracy. The learning rate is used to control the behavior of each decision tree, affecting the overall model's accuracy. The model is effective in aeroponic lettuce crop yield prediction, handling missing values, non-linearities, and complex relationships, and preventing overfitting. It also focuses on feature importance, identifying environmental factors, and ensuring sufficient resource allocation and decision-making by growers. The model learns patterns and predicts outcomes effectively with new data.

Assuming the dataset with n observations and m features and predicting a continuous output variable y based on the input features X, the XGBoost regression model is given by:

$\widehat{y}_l=\phi\left(x_i\right)=\sum_{k=1}^K f_k\left(x_i\right)$   (6)

where, $\widehat{y}_l$ is the predicted output for observation $i$, $\phi\left(x_i\right)=$ $\sum_{k=1}^K f_k\left(x_i\right)$ is the ensemble prediction for observation $i$, $f_k\left(x_i\right)$ is the prediction of the $k^{\text {th }}$ regression tree.

The individual regression tree prediction, f_k(x_i) is constructed based on the sum of predictions from each tree node along with the path that observation i takes down the tree.

$f_k\left(x_i\right)=w_{q_{(i, k)}}$    (7)

where, $w_{q_{(i, k)}}$ is the weight associated with the terminal node $q_{(\mathrm{i}, k)}$ that observation $i$ reaches in the $k^{\text {th }}$ regression tree.

Hence, the overall objective function for the XGBoost regression model is the sum of a regularized training loss and the regularization term:

$\operatorname{obj}(\theta)=\sum_{i=1}^n L\left(y_{i,} \widehat{y}_l\right)+\sum_{k=1}^K \Omega f_k$  (8)

where, $\theta$ represents the parameter of the model; $L\left(y_{i,} \widehat{y}_l\right)$ represents the training loss of the observation $i$ and $\Omega \mathrm{f}_{\mathrm{k}}$ is the regularization term for the $k^{\text {th }}$ regression tree. Here, important to note that is, the training loss is often MSE for the regression trees.

3.3 Systematic representation of lettuce yield prediction

The systematic representation or the workflow diagram is represented in Figure 1. It is the collection of different modules used to describe the stepwise implementation of the proposed system. In other words, it is the encapsulation of the workflow that provides a clear-cut graphical illustration of the implementation procedure. It improves communication and provides an easy understanding of the underlying mechanism.

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From Figure 1, it is clear that the implementation procedure starts with data collection and proceeds with the series of processes towards the yield prediction as the outcome. The detailed description of the various processes is explained below.

3.3.1 Data collection and data visualization

The first and foremost step in the implementation procedure is the data collection. Here, sensors such as pH sensor, EC sensor, temperature sensor, total dissolved salts (TDS) sensor, turbidity sensor, humidity sensor, and light sensor were deployed in the aeroponic lettuce growth tower. The data were collected from the growth tower at regular intervals of time, sample data is represented in the Figure 2. To easily understand the data distributions, data visualization techniques like bar charts (univariate data representation technique), correlogram (bivariate data analysis technique), and Andrews curve were utilized and implemented using the Python packages with the help of Python programming language.

From Figure 2 (a-j), the input parameters are represented individually with the help of bar plots.

Correlogram of the input dataset highlights the correlation between the input variables. Here, in Figure 2(l), the considered lettuce growth parameters were less correlated with the other parameters. This showcases that the parameters are independent of each other i.e. one cultivation parameter will not affect another parameter which is necessary for efficient lettuce growth and yield prediction.

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Figure 2. Sample dataset and dataset visualization techniques

3.3.2 Data preprocessing

One of the most important steps in the machine learning implementation is the pre-processing of the dataset for efficient prediction output. Here, in the aeroponic lettuce crop yield prediction system, the outliers are the major cause of higher error rates and low prediction accuracy. Hence, the removal of the outlier’s mechanism is incorporated for effective prediction by the regression models. The dataset size is represented below before pre-processing as the old shape and after pre-processing as the new shape of the dataset.

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Figure 3. Data preprocessing

The boxplot represents the dataset after pre-processing. The x-axis provides the different features of the lettuce growth dataset i.e. [0-8] is [pH to Yield] collected from the aeroponic vertical farming tower which is highlighted in Figure 3 (a) and (b).

3.3.3 Dataset splitting

Once the data is collected, pre-processed and ready for the implementation process, there is a necessary step called data partitioning or splitting of the data, before the data is fed into the ML model. In the case of the efficient implementation of the classification or regression model, the data has to be split into two: training data and testing data as shown in Figure 4.

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Figure 4. Dataset splitting

3.3.4 Machine learning implementation: Model training and model testing

The actual work of the implementation phase begins now. A structured methodology is used to train and evaluate machine learning regression models for predicting aeroponic lettuce crop yields. The collected, analyzed and pre-processed datasets were fed into all four machine-learning models for training purposes. Once, the training of the models is done, next comes the testing phase. The test dataset is supplied to the trained machine learning models for testing the performance of the models. The testing scores were recorded and based on the produced results, the process called hyper-parameter tuning is carried out to achieve better results further. The detailed description of the results produced by the models was described in the results and discussions section.