2.1 EIT images and their reconstructed boundary voltage values
One EIT image was selected from each of the three rose cultivars at different temperatures at each sampling time (Fig. 1). During the period of external temperature change, the EIT image accurately displayed the location, shape, and size of the rose stem as well as the distribution of resistivity. The darker the blue color, the smaller the resistivity and the corresponding reconstructed boundary voltage value. In EIT images, the pure blue color corresponds to the maximum value of the reconstructed result. Over the course of the dehardening period, the blue parts of the EIT images of the stems of the three rose cultivars gradually darkened. Figure 2 shows the change of the reconstructed EIT boundary voltage value of the stems of the three rose cultivars during the dehardening period. As shown in Fig. 2, the reconstructed boundary voltage values of the stems of the three rose cultivars showed a significant downward trend. The slopes of the curves of 'Red Cap', 'Tender and Soft as Water', and 'Carefree Wonder' were − 8.84, -8.89, and − 0.92 respectively. Of these, the downward trend of 'Carefree Wonder' was the most significant and the reconstructed boundary voltage value of 'Carefree Wonder' was between 0.078 and 0.036 (Fig. 1). There were no significant differences in the reconstructed boundary voltage values between the three cultivars (P < 0.05).
2.2 Changes in soluble sugar and starch contents
During the dehardening period, the soluble sugar content in the stems of the three rose cultivars showed an overall downward trend. The soluble sugar contents all increased slightly on April 25, and then continuously decreased, with the lowest values observed on May 16 when the last sampling was performed (Fig. 3A). The soluble sugar contents of each of the three rose cultivars were significantly lower on May 16 than at the other four sampling times (P < 0.01). The soluble sugar contents of 'Red Cap', 'Tender and Soft as Water', and 'Carefree Wonder' on May 16 were 41.99%, 45.38%, and 41.35% lower, respectively, than on February 22. However, there were no significant differences in the soluble sugar contents of the same cultivar between the March 14, April 4, and April 25 samples. Furthermore, there were no significant differences in the soluble sugar contents of the different cultivars at each sampling time.
During the dehardening period, the starch content of the stems of all three rose cultivars showed an increasing trend (Fig. 3B). The overall rate of increase in starch content of 'Carefree Wonder' was higher than that of the other two cultivars. The starch content of all three cultivars obviously increased during the period from February 22 to March 14, but the rate of increase was lower for the rest of the sampling period. The starch content of all three cultivars was significantly higher on May 16 than on the four other sampling dates (P < 0.05). The starch contents in the stems of 'Red Cap', 'Tender and Soft as Water', and 'Carefree Wonder' were 41.42%, 44.51%, and 58.93% higher on May 16 than on February 22. The starch content of the stem of 'Carefree Wonder' significantly differed between the five sampling times (P < 0.05). The starch contents of 'Red Cap' and 'Tender and Soft as Water' significantly differed between February 22 and the four other sampling times (P < 0.05); there were no significant differences in sugar content between those four sampling times. There was no significant difference in the starch content between different cultivars at each sampling time.
2.3 Establishment of the regression models for starch and soluble sugar contents as functions of reconstructed EIT boundary voltage values
The soluble sugar and starch contents and the corresponding reconstructed EIT boundary voltage values of the two cultivars 'Red Cap' and 'Carefree Wonder' were used to establish a regression model. The measured EIT boundary voltage values ranged from 0.036 to 0.089. These values were 100 times smaller than the values of starch and soluble sugar contents. Therefore, the measured boundary voltage values were multiplied by 100. These amplified values were used together with the soluble sugar and starch contents in linear and nonlinear regression analyses. The regression model with the greatest R2 was preferentially selected as the best model. The results are shown in Table 1. The R2 values of the established linear, logarithmic, and quadratic regression models for soluble sugar content as a function of reconstructed EIT boundary voltage value, were 0.863, 0.811, and 0.897, respectively (P < 0.001). Thus, for soluble sugar, the quadratic regression model had the greatest R2. The R2 values of the established linear, logarithmic, and quadratic regression models for the starch content as a function of reconstructed EIT boundary voltage value, were 0.894, 0.959, and 0.935, respectively (P < 0.001). Thus, for starch, the logarithmic regression model had the greatest R2.
Table 1
Analysis of the regression for soluble sugar and starch contents as functions of reconstructed electrical impedance tomography (EIT) boundary voltage values
Item | Index | Equation | Regression model | R2 | F |
Soluble sugar value | Boundary voltage reconstruction value | Linear | y = 0.868x + 2.125 | 0.863 | 50.527 |
Logarithmic | y = 4.758ln(x) − 1.034 | 0.811 | 34.411 |
Quadratic | y = 0.142x2 − 0.823x + 6.757 | 0.897 | 30.538 |
Starch value | Boundary voltage reconstruction value | Linear | y = − 0.333x + 5.271 | 0.894 | 67.350 |
Logarithmic | y = − 1.917ln(x) + 6.634 | 0.959 | 104.964 |
Quadratic | y = 0.059x2 − 1.032x + 7.189 | 0.935 | 50.132 |
2.4 Testing the accuracy of the regression models for soluble sugar and starch contents as functions of reconstructed EIT boundary voltage values
The measured data from the cultivar ‘Tender and Soft as Water’ was used to test the accuracy of the regression models. The Root Mean Square Error (RMSE), Relative Error (RE), Offset, and the coefficient of determination (R'2) of the fitted linear regression based on measured and predicted values were compared between the established linear, logarithmic, and quadratic models. The RE is the percentage of the absolute error of the measurement divided by the measured value. Generally, the RE can well reflect the reliability of a measurement and was calculated using the Eq. 3. RMSE is used to estimate the deviation between the predicted value and the measured value [24], and is usually used as a standard for assessing the predicted results of a model. The RMSE was calculated using Eq. 4.
where xi refers to the measured reconstructed EIT voltage values of 'Tender and Soft as Water'; f(xi) is the soluble sugar content and starch content calculated by the model; yi is the measured value of soluble sugar and starch content corresponding to xi; and n = 5 represents the five sampling times within the dehardening period.
The validation result of the models is shown in Table 2. The quadratic regression model for soluble sugar content prediction (y = 0.142x2 − 0.823x + 6.757) had the greatest R2 (0.897), and the smallest RMSE (0.811), RE (10.64%), and Offset (1.38). Therefore, it was the best model and the prediction accuracy was 89.36%. The logarithmic regression model for starch content prediction (y = − 1.917ln(x) + 6.634) had the greatest R2 (0.959) and R'2 (0.948), and the smallest Offset (0.022). The RMSE was only 0.010 times greater than that of the linear model. Taking into consideration the R2, RMSE, RE, Offset, and R'2, the logarithmic model was the best model for predicting starch content, with a prediction accuracy of 93.98%.
Table 2
Indexes for assessing the fitting of measured and predicted values of soluble sugar and starch contents
Item | Index | Regression model | RMSE | RE (%) | Offset | R'2 |
Soluble sugar | Boundary voltage | y = 0.868x + 2.125 | 1.060 | 11.56% | 3.294 | 0.923 |
y = 4.758ln(x) − 1.034 | 1.197 | 11.26% | 4.293 | 0.876 |
y = 0.142x2 − 0.823x + 6.757 | 0.811 | 10.64% | 1.380 | 0.977 |
Starch | Boundary voltage | y = − 0.333x + 5.271 | 0.202 | −5.58% | 0.554 | 0.926 |
y = − 1.917ln(x) + 6.634 | 0.212 | −6.02% | 0.022 | 0.948 |
y = 0.059x2 − 1.032x + 7.189 | 0.257 | −5.88% | 0.861 | 0.824 |