2.1.

Experimental materials

The data for model building were collected during the experiment of Pn measurement. This experiment was conducted at College of Mechanical and Electronic Engineering, Northwest A&F University, from December 1, 2019 to January 10, 2020. The cucumber for experiment was “Bonai 14-3”. The cucumber seeds were soaked in a petri dish for a week to make them swell and germinate, and then they were planted in 50-hole trays. After these cucumber seedlings grew three weeks, they were planted into flowerpots with size of 15×15×10cm. These seedlings were grown in a growth chamber (MD1400, Sinde, Netherlands). The environment of climate chamber was set as follows: the light period of day and night was 14 and 10 hours; the temperature of day and night was 25 and 16°C; the relative humidity of day and night was 60% and 50%; the [CO₂] was 400 μmol·m^-2·s^-1. When cucumber seedlings grew five leaves, the fluorescence detection and Pn collection were carried out on the third leaf. Before the experiment, the F_v/F_m of cucumbers were detected by MINI-PAM-II Portable Fluorometer (WALZ company, Germany) to choose leaves with similar chlorophyll fluorescence. And then, the Pn of these leaves under different environment were determined by a portable photosynthesis system (LI-6800, USA). The data collection processes were in Figure 1.

Figure 1.

Methods and data collection processes.

2.2.

Experimental methods

The chlorophyll fluorescence parameter F_v/F_m of leaves were measured to determine the leaf state, and 90 cucumber seedlings with the same or similar F_v/F_m of the third leaf were selected to measure Pn. The test leaves should be fully dark adapted for 20 minutes by dark blade clamp at the position of Pn data to be collected. Then, the dark blade clamp was opened, and the minimum fluorescence parameter F_o of the test sample was measured under the measurement light (wavelength of 470 nm, LI of 0.05 μmol·m^-2·s^-1). After that, the sample was irradiated with saturated pulsed light (wavelength of 470 nm, LI of 6000 μmol·m^-2·s^-1) for 300 ms to obtain the maximum fluorescence parameter F_m. F_v/F_m could be calculated by:

Air temperature, [CO₂], LI and LQ were selected to design a nested experiment to measure the Pn of the living third leaves of cucumber seedlings. The experiment was carried out from 9:00 to 17:30 every day, and the data was measured by using LI-6800 to control many environmental factors, such as temperature, [CO₂], and light of leaves. During the nested experiment, the flow rate was set to 500 μmol·s⁻¹ in flow control module, the fan speed was set to 1000 r/min in fan control module, and the moisture control module was used to set the relative humidity of 50%. The gradients of the temperature parameter are set to 18, 21, 24, 27, 30, 33 °C. The gradients of the [CO₂] parameter are set to 300, 700, 1000 μmol·mol⁻¹. The gradients of the LQ parameter are set to 0.1, 0.3, 0.4, 0.5, 0.6, 0.7, 0.9. The gradients of the LI parameter are set to 0, 30, 75, 150, 200, 300, 500, 600, 700, 800, 1000, 1200, 1400, 1600, 1800 μmol·m^-2·s^-1. In the experiment, Pn was collected by the light response program of LI-6800. Before the measurement, the temperature, [CO₂], and LQ should be set by respective modules, and the LI of chamber was set to 1800 μmol·m^-2·s^-1 to make leaves be adapted to light. After the Pn was stable, the light response program was started to record photosynthetic data. 1890 groups (15×3×6×7) of experimental data were obtained.

2.3.

Predictive model of photosynthetic rate

In the study of predictive model of Pn, SVR algorithm were widely used. In this paper, the data obtained from the experiment were combined with SVR algorithm to create a predictive model of Pn for cucumber. Temperature, [CO₂], LI, and LQ were taken as input, and Pn was taken as output. The process of model building was shown in Figure 2.

Figure 2.

The process of model building.

First of all, it was necessary to normalize the data of different dimensions to make them in the same order of magnitude. 70% of the normalized data was randomly selected as training set, and 30% of the normalized data was randomly selected as prediction set. The inputs of the i^th sample were , and the output was Pn_i. , and were [CO₂], temperature, LQ and LI. And Pn_i was the Pn of the i^th sample.

In parameters selection, radial basis function (RBF) has the feature that its complexity would not change with the change of parameters. As a kernel function, RBF could convert the data to a higher dimensional space. Then, some nonlinear problem that could not be solved in low dimensional space can be linear problem in high dimensional space. The support vector could be easy to obtained using RBF kernel. Finally, the final regression hyperplane was determined by the support vector. For SVR algorithm, it would be coupled to affect the model performance that the kernel parameter g and penalty coefficient c changed. According to the results of multiple training of the grid validation method, it could be obtained that the generalization ability of the model was the best with the parameter c of 40 and g of 5. The final predictive model of Pn was as follows:

where , which is RBF kernel function; X is the original data;X^p is the support vector; , 𝛼_i are Lagrange Multiplier in solving process; b is the bias of model.

3.1.

Photosynthetic rate results

The partial results of Pn test of temperature, [CO₂], LI and LQ coupling are shown in Figure 3. Pn is directly affected by light, and also affected by temperature and [CO₂].

Figure 3.

The partial results of experiment.

3.2.

Prediction results

To verify the performance of SVR model, the other machine learning algorithm of random forest (RF) and a nonlinear regression (NLR) algorithm of quartic cubic polynomial regression are selected to fit the same training set data. The results are shown in Table 1. Among them, SVR model had the highest coefficient of determination (DC), which was 0.9990. Meanwhile, the maximum absolute error (MAE) of 0.6214 μmol·m^-2·s^-1and root mean square error (RMSE) of 0.0478 μmol·m^-2·s^-1 were all the lowest in these three models. Accordingly, SVR algorithm had advantages in building photosynthetic model.

Table 1.

Comparison of the performance of three models.

To further verify the generalization ability of the predictive model of Pn for unknown data, the model validation was used to calculate the DC and RMSE from the prediction set data. As shown from Table 1, the largest DC of 0.9974 and the smallest RMSE of 0.1294 μmol·m^-2·s^-1 shows the best performance of SVR model. The fitting results between the predicted value and the real value of the model are shown in Figure 4. The slope of SVR model is 1.0015, which is the nearest of 1, and the intercept is 0.0223, which is the closest to 0. This indicated that the model had accurate results and strong generalization ability.

Figure 4.

Fitting results of the models: (a), (b) and (c) are fitting graphs of real Pn and predictive Pn of SVR, RF and NLR algorithm respectively.