4.2. Experiment Results
The proposed calibration models were developed for each device. The size of available data points was small. To comprehensively verify the efficacy of the proposed methods on the entire data set, the cross-validation technique was applied to implement the proposed methods using the following steps:
(Step 1) The entire data set D is randomly partitioned into k folds, D = {D1, …, Dk};
(Step 2) Train a MARS/GPR model with data set Pi = D\Di, which is the complementary data set of Di, for I = 1, …, k;
(Step 3) Apply the MARS/GPR model in Step 2 to predict the soil moisture content on the data set Di for I = 1, …, k;
(Step 4) Calculate modeling errors on the entire data set D.
Table 4 illustrates one set of GPR model parameters for test sensors, while the prediction equations of MARS model are given in Equations (14)–(17).
In Equations (14)–(17), the basis function is defined in Functions (18) and (19), where
x is the input variable being either
r (moisture sensor reading) or
T (temperature):
with:
To illustrate the effectiveness of the proposed calibration methods considering the impacts of temperature, the performance of the proposed methods was compared with the sensor reading as well as data-driven methods developed only using information from the original sensor reading.
The comparison of modeling performances by different methods are provided in
Table 5. It is observed from
Table 5 that large differences exist between the measured and actual soil moisture data. More accurate soil moisture was obtained by using the data-driven calibration methods in terms of MBE, MAE, and RMSE. Moreover, the consideration of temperature impacts highly improved the modeling accuracy with the data-driven models. Therefore, the MARS model and the GPR model are effective for developing the data-driven calibration method for soil moisture sensors considering temperature impacts. Between the MARS model and the GPR model, neither dominated the other for all three metrics and four sensors.
Table 6 illustrates an example of the modeling performance at various temperatures. It is observable that at the extremely high and low temperature, the improvement of modeling accuracy by incorporating the temperature information was much greater than by only using the sensor reading. In China, the ambient temperature can be around 0 °C during the growth period of winter wheat, while the ambient temperature can be greater than 35 °C during the growth period of summer corn. Hence, the improvement of measurement accuracy at high/low temperatures can be of great importance to the arrangement of irrigation during the growth period of crops in different seasons.
The boxplot of the bias error is illustrated in
Figure 3. It is further demonstrated that the proposed methods highly improved the accuracy compared to the sensor reading, while the variation of the bias errors was also reduced.
To further demonstrate the performance of the proposed methods, the calibrated and actual soil moisture at temperature 30 °C is depicted in
Figure 4. It is observable that the modeling soil moisture by the proposed data-driven calibration methods agreed well the actual soil moisture.
From the above analysis, the proposed data-driven calibration of soil moisture sensors considering the impact of temperature can greatly improve the accuracy of soil moisture content measurement. The MARS and GPR model were used due to their strong capability in nonlinear modeling with a limited training dataset. The MARS model can be more efficiently implemented on embedded devices compared to the GPR model in terms of model complexity, while the latter achieved better performance for most cases in this study. Hence, the trade-off between the modeling accuracy and the ease of model implementation should be considered when selecting calibration models in practice. In the future, more machine learning algorithms such as boosted regression trees and neural networks [
20] can also be applied to sensor calibration with rich data.