**3.3 Estimation**

In this section, we complement the detection of oil spills (functionality #1) with a new approach targeting the estimation of the oil slick thickness (functionality #2). We present Maximum Likelihood single-, dual-, and multi-frequency estimators. The reflectivity values evaluated at one, two, or multiple frequencies over all possible thickness values form the constellation set that is used for the estimation. The estimator uses the Minimum-Euclidean distance algorithm, in predefined 1-D, 2-D, or K-D constellation sets, on radar reflectivities to estimate the thickness of the oil slick. Every constellation set is divided into different mapping regions that are bounded optimally between all the theoretical reflectivity values constituting the constellation. Any reflectivity value R obtained in one region is mapped by the estimator to the thickness that provides theoretically the nearest reflectivity value.

The derived algorithms are the following:


Using a single-frequency estimator in C-band (4–8 GHz), the mapping regions at low thickness values will be close to each other as shown in detail in [67, 73]. A small noise power may shift the reflectivity values from one region to another. If so, this will be considered an error in the estimation process. At higher frequency values in Xband (8–12 GHz), many thickness values will give the same reflectivity due to its cyclic behavior. Therefore, even in an ideal case when no noise is introduced during the measurements, the estimator is not capable to provide a correct estimation. *This highlights the need to use the combination of reflectivity measurements (2-D or 3-D estimators) to achieve accurate thickness estimation.* Using dual- and tri-frequency estimators, one question will rise: which combination of frequencies is to be used? The best frequency pairs and triads, for each possible thickness between 1 and 10 mm, are derived in [67, 74] respectively. Daou et al. [74] also proposes an advanced iterative procedure to use the 2D estimator for accurate and reliable thickness estimations.

**Figure 6** shows the histograms of the thicknesses estimated by K-D estimators when the actual thickness d is 5 mm with single and multiple (M = 3) scans. The single-frequency (1-D) estimator uses f1 = 4 GHz, and f2 = 12 GHz. The dualfrequency (2-D) estimator uses both f1 and f2. The 3-D estimator uses an additional frequency f3 = 7 GHz. The 4-D estimator uses f1, f2, f3 in addition to f4 = 10 GHz. The 2-D estimator with three scans still provides thickness values from all possible values. The 4-D estimator with three scans decreases the error in the estimation to 4 mm with a probability of correctness of 80%. The percentage error obtained by all estimators under different scenarios is presented in **Table 2**. To check the distribution of the histograms of errors in estimation, refer to Appendix A in [67].

#### **Figure 6.**

*Histograms of the thicknesses estimated by 1-D, 2-D, 3-D, and 4-D estimators with single and multiple scans M = 3. The actual thickness d is 5 mm. Retrieved from [67].*

*Recent Advances in Oil-Spill Monitoring Using Drone-Based Radar Remote Sensing DOI: http://dx.doi.org/10.5772/intechopen.106942*


#### **Table 2.**

*Percentage error obtained by different estimators for different slick thicknesses. Adapted from [67].*

Although some estimators provide a good probability of correctness, it is not sufficient to have a definite decision. We should rather look at the error distribution in the estimation to ensure that the estimations are reliable. Therefore, we should always increase the number of frequencies or scans done to make sure that good and enough estimation information is provided.

We developed an experimental setup to collect radar reflectivity measurements from an oil-spill lab experiment with calm water surface conditions for very low wind speeds with no wave action. The experimental setup includes details about the system model with the multi-layer structure, the radar calibration technique, and other setup parameters [77, 78]. We applied the estimation algorithm to these experimental values. **Figure 7** shows the histograms of estimated thicknesses by 1D, 2D, 3D, and 4D estimators based on experimental reflectivity values with a single scan (M = 1), when the actual thickness is 3 mm. As expected, 1D estimators using a single frequency are not providing very good results. Using f1, the highest estimations are for 4 mm, the probability of error is 72%, and the maximum deviation from the correct value is 7 mm. Using f2, the deviation is decreased to 1 mm with a probability of error of 47%. However, single-frequency estimators are never used alone, therefore, including f2 in the 2D estimator again increases the probability of error to 68% but provides the advantage of decreasing the maximum deviation to 1 mm. For the higher-order 3D estimator, the probability of error decreases to 28% with the same maximum deviation. For the 4D estimator, the performance is further improved, and the probability of error is reduced to 6%. Thus, the results shown validate the proposed higher-order estimators on in-lab experimental data.

Another proposed estimation algorithm is based on a machine learning approach [75]. For this, a support vector regression (SVR) model that is following a supervised learning approach is trained on reflectivities calculated for three radio-wave frequencies to predict oil thicknesses between 1 and 10 mm. The input features to the SVR model are the power reflection coefficients (reflectivities) evaluated at f1 = 4.39 GHz, f2 = 6.98 GHz, and f3 = 9.07 GHz. After training the model using 80% of the simulated data, it is validated on the remaining 20% of the simulated and on in-lab experimental data. The model yielded an R2 score of 0.992 on the simulated data, which is very close to 1 indicating that the regression predictions are very close to the actual oil thicknesses. The model is supposed to predict a continuous value of the thickness as the predicted output. But by rounding the estimated thickness to the closest integer, we

#### **Figure 7.**

*Histograms of the thicknesses estimated by 1D, 2D, 3D, and 4D estimators based on experimental data with single scan M = 1. The actual thickness is 3 mm. Retrieved from [67].*

get the following percentages of estimating the correct value in the confusion matrix: [62.4, 95.5, 99.7, 97.7, 97.7, 99.6, 99.4, 95.4, 80.5, 89.6%] for the thicknesses [1, 2, 3, 4, 5, 6, 7, 8, 9, 10 mm] respectively. The R<sup>2</sup> score obtained on the experimental data is 0.86 indicating that the experimental thickness values and the predicted thicknesses are close even though the model is only trained on simulated data and is not exposed to any experimental reflectivity. For further validation, even though the model is trained on calm surface data, it is tested with rough surfaces in two scenarios for slick thicknesses: 5 mm and 8 mm. The model's predictions are mostly concentrated at 6 mm for the 5 mm spill. Similarly, for the 8 mm spill, the predictions are mostly at 7 and 8 mm. This shows that using a machine learning algorithm for oil thickness estimation is an attractive approach. Another algorithm is developed in [76], but for convenience, we will discuss it in the following section. This concept can be further developed by using larger and more complex machine learning models and more diversified training data to achieve better thickness estimations in varied environments.

#### **3.4 Classification**

An important task to perform during oil spills is to specify the oil type to predict the environmental damage to maritime life. The oil type classification could be qualitatively similar to what is proposed by [60, 79–81]. Another way for classification is by analyzing the physical characteristics of the oil material, namely the relative dielectric constant, as we proposed in [76]. In this work, we use an artificial neural network (ANN)-based model to estimate the relative permittivity of oil slicks for

### *Recent Advances in Oil-Spill Monitoring Using Drone-Based Radar Remote Sensing DOI: http://dx.doi.org/10.5772/intechopen.106942*

different oil-types classification. In addition, the model can predict the thicknesses of such oil slicks at the same time. The input features to the model are nine radar reflectivity values measured simultaneously and selected uniformly from C- (4–8 GHz) and X- (8–12 GHz) bands. The ANN-model post-process these measurements to extract the implicit information about the thickness and the relative permittivity of the thick oil layer covering the sea surface, even though the reflectivities and the estimated parameters have a highly nonlinear relationship. To further improve the model's accuracy, we also incorporate multiple observations to boost the estimator's performance. Results show that by jointly analyzing the reflectivity behavior at multiple frequencies, the model explores their dependence over the full plausible range of thicknesses. The predicted thicknesses are accurate to +/ 0.5 mm in most cases. For example, testing the model at 5.5 mm would still lead to estimations between 5 and 6.1 mm. Similarly, relative permittivity values 2.9, 3, and 3.1 are approximated accurately where the shift in estimations' mean is smaller than 0.05. The error in estimations for the remaining values 2.8, 3.2, and 3.3 is higher. To test the performance of the model, we simulate an oil spill scenario when the thickness of the oil slick that is close to the source is 10 mm, and it decreases gradually going away from the source to 1 mm. The trained ANN model shows that it can perfectly reconstruct the spill environment with accurate estimations of the thicknesses and the relative permittivity, where the error of the average estimate for the latter over the full map is 3% only. To further validate the performance of the model, it is applied to in-lab experimental data when the actual thickness is 7 mm. After collecting 13 measurements, the estimated thickness is 7.65 mm compared with 8.2 with a single scan measurement. Unfortunately, we are not able to compare the estimated permittivity with the actual value since the latter has not been measured during the in-lab experimental procedure.
