The proposed smart agriculture system integrates agricultural consumer electronics, machine learning models and the sensor data processing to optimize crop yield for sustainable agriculture. The data flow of the proposed model is shown in Fig. 2.

Stages involved in the projected technique to achieve Sustainable agriculture using consumer electronics.

Step 1 The Initial data are processed related to Rainfall (R), Temp as (T), Soil moisture as (S_moi), Soil type as (S_t), humidity as H, Soil as S and y as Yield in Irrigation process, Location as l to sustainable agriculture as (SA) and consumer electronics as (CEd) where 1 < y < SA.

Step 2 Data Preprocessing layer works to normalize the numeric values in T, encode categorical value in S_moi, and finally to ensure T = S_moi.L where y/S_t (CEd).The primary activities on the dataset like removal of missing values, handling of inconsistent values and feature selection are done in this layer.

Step 3 The model is trained with historical environmental data and irrigation methods using machine learning classifier RF (random forest) to rank the feature for 1 < y < SA.

Step 4 The intelligent decision making with RF ensures optimal water utilization and reduces the waste with entropy towards y/S_t (CEd).

Step 5 The trained model is implemented in the agricultural consumer electronics like smart devices related to y = L. A dashboard visualization method is prepared to check the performance of the system like irrigation status and other environmental impacts through CEd.

Step 6 Finally, the yield distribution and sustainable agriculture are achieved with the deployment and monitoring through consumer electronics with y/S_t (CEd).

System model

Let us assume, X is the feature set and y is the target irrigation class. Then, the dataset will be expressed as follows (1).

where R is rainfall precipitation intensity, \(T_{emp}\) is temperature recorded daily for analysing crop-based farming, \(S_{moi} ,\) is soil moisture to analyse the water content in the farm land, \(S_{t} ,\) is soil type , \(H\) is humidity in atmospheric condition, \(S\) is the season for the kind of crops to perform plantation like rabi, kharif , \(A\) is Area cultivated total plot size and finally, I is Irrigation type with different class drip, basin and spray .

The linear operator which includes the dataset is defined as follows (2).

where \(R_{i}\) is the average rainfall index for water availability measure, \(x_{i}\) is the weight factor for normalization and \(R,\) is the Aggregator operator.

Since the dataset collection is an analogue process, the continuous setting integral operator kernel transformation can be defined as (3).

where \(k_{a} \left( {p,q} \right)\) is Gaussian kernel, \(m\) is the window size for some days and \(p,q\) are Spatial analyses with latitude and longitude.

As the dataset is classified into subsets, there is a condition for measures. All measurable subsets include T_emp of S_moi, and H and A as in Eq. (4). It can also be referred as group invariant measure to get the desired output. As this function follows the covariance, this Eq. (4) can be modified as follows (5) and (6).

where \(\mu_{m}\) is covariance Feature for probability measure, \(T_{emp}\) is temperature recorded daily for analysing crop-based farming, \(S_{moi} ,\) is soil moisture to analyse the water content in the farm land, \(H\) refers to the humidity in atmospheric condition, \(A\) represents Area cultivated total plot size, \(\mu \left( H \right)\) is the humidity distribution and \(\mu \left( A \right)\) refers to area distribution.

As the dataset contains both categorical and numerical data fields, equivalent linear operators are required to collect the majority of the decisions from various sub trees (7).

where H is the Decision tree class hierarchy, \(g\) is the feature subspace projection and \(f\) is the predictor function.

The decisions of the sub trees are based on the influencing parameters like temperature, soil moisture, humidity, location and etc.³⁸. It is assumed that the temperature of the location will affect the soil moisture and hence, the equivalent linear operator is expressed as follows (8).

where \(X_{m}\) is the critical threshold for irrigation demand identification and capture non-linear temperature.

The model is trained with 100 estimators, and its performances are evaluated based on accuracy, feature importance and confusion matrix analysis. The random forest function is given as (9).

where n is an optimized decision for out of bag error handling and \(h_{i}\) is an individual tree for some depth.

where n represents the number of decision trees, and gini (X) is the decision of each subtree. Based on this, gini impurity value is calculated ³⁹. It is the criteria where the decision trees use splitting threshold less than 0.2 (10).

where pi is the probability of class i in the dataset X, and c represents the number of classes.

Like Gini index, the Entropy value is also calculated to understand the non-homogeneity of the data ⁴⁰. It is the measure of homogeneity of the dataset and it returns the information about the impurity of the dataset. The entropy is expressed as follows (11).

where P is the number of positive or correct samples and N is the number of negative or wrong samples.

From the entropy value, the information gain is calculated as follows (12).

where Sv is the subset of S with minimum gain 0.01bits.

Finally, the accuracy score and the confusion matrix are used to assess the performance of the model. Feature importance is plotted to determine the most influential factors in irrigation prediction (13).

where TP is the True positive, TN denotes True negative, FP denotes Falso positive and FN denotes False negative.

Algorithm for the proposed model

The following algorithm depicts the proposed model of random forest classifier.

Intelligent irrigation prediction.

Class imbalance handling

The dataset used in this research contains the basic environmental factors like location, rainfall (R), temperature (temp), soil moisture (Smoi), humidity (H), season (S) and the area (A). The class imbalance is addressed through irrigation type identification, including drip, spray, and basin. Three functions are used to handle the class imbalance. The first one is stratified sampling and it is used to split the dataset as 70:30 for testing and training. After the class distribution is processed, second-class weighted RF is assigned for higher weights to split the minority classes and it is proportional to the weights and irrigation class frequencies. Finally, the third method, synthetic minority oversampling, is used to prevent data leakage with different irrigation samples, such as drip, spray, and basin. All these methods improve the irrigation class accuracy score by handling class imbalance in the agricultural dataset for minority crop yield distribution classes. The proposed model inverse frequency weighting increases irrigation detection by reducing false negatives in precision water management in high-temperature areas.