Laser induced spectroscopy-based estimation of soil unconfined compressive strength: a machine learning approach

doi:10.21203/rs.3.rs-2644039/v1

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Research Article

Laser induced spectroscopy-based estimation of soil unconfined compressive strength: a machine learning approach

https://doi.org/10.21203/rs.3.rs-2644039/v1

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published 29 Feb, 2024

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Laser-induced breakdown spectroscopy (LIBS) is an outstanding elemental detection and quantification technique employed in various fields such as engineering, science, and medicine. Machine learning techniques have generated a vast interest owing to their ability to predict unknown quantities based on previously trained algorithms. The soil unconfined compressive strength (UCS) is a critical quantity that aids engineers in auditing and designing fundamental geotechnical and environmental structures. It is a direct measure of the soil’s compaction strength. The traditional means of obtaining such a quantity is via the unconfined compression test in the laboratory. Nevertheless, the technique is time-consuming and costly, and the accuracy depends strongly on the equipment quality and expertise of the operator. Herein, we propose a pioneering method of estimating the soil UCS using machine learning algorithms based on the emission intensities of the constituent elements obtained from the LIBS system. Support vector regression (SVR) and Random Forest (RF) regression algorithms were used in modeling the soil UCS. The models’ performance was measured based on standard metric performance indicators such as mean absolute error (MAE), root mean square error (RMSE), R²-value, and the correlation coefficient (CC) between the predicted and experimental UCS values. Our results showed that the SVR outperformed the RF model with a CC of 97.9% and R²-value of 95.7% during the testing phase. The developed models were validated by investigating the UCS of lime and cement-stabilized soils whose input datasets were not considered during the model training, thus, indicating the accuracy and generalization strength of the models.

Laser-induced breakdown spectroscopy

Machine learning

Soil Unconfined Compressive Strength

Random Forest

Support Vector Regression

Laser-induced breakdown spectroscopy (LIBS) is a robust technique employed in various fields for elemental detection and quantification purposes [1]. The technique has been used to study materials’ compositions to investigate the constituent elements for different applications. For example, food processing industries have employed LIBS to detect radioactive and heavy elements that may be hazardous to human health [2]. Similarly, building and construction industries have utilized the method to detect chloride concentrations in concrete materials, which are the major cause of corrosion of metallic constituents [3]. Furthermore, LIBS has found crucial applications in medicine, where patients’ specimens are investigated to identify elements present together with their respective concentrations [4]. The operation of LIBS requires the sample under consideration to be subjected to a concentrated, high-energy laser pulse. The laser-material interaction generates a high-temperature plasma that contains the emission signatures of the constituent atoms. The atomic emission intensities are then collected via an advanced optical device called a spectrometer and processed, after which the output is generated as spectra [5]. In principle, the spectrometer simply captures light of varying intensities and wavelengths. Noteworthy, as the LIBS operate based on matching elements with their wavelength, the elements may not have a unique wavelength since the electrons can be excited from the same or varying energy levels during the plasma formation phase [6, 7].

Soil science is a remarkable field that consists of soil biology, soil physics, and soil chemistry [8]. The soil unconfined compressive strength is a critical engineering quantity that is employed during the design and audit of fundamental geotechnical and environmental structures like pavements, buildings [9], tunnels, railways, road foundations, bridges, and dams [10]. The UCS is a direct measure of the soil’s compaction strength. The traditional means of obtaining such a quantity is via the unconfined compression test in the laboratory [11]. Nevertheless, the technique is time-consuming and costly, thus raising the overall cost of the construction work. In addition, the accuracy of the measurements is significantly affected by the equipment quality and the level of technical expertise of the device operator. Therefore, it will be imperative to devise a facile, low-cost, and more reliable way method of estimating the soil unconfined compressive strength.

Recently, the area of soil mechanics has recorded a significant advancement, particularly with respect to testing methodologies [12]. Multiple in-situ mechanisms and laboratory tests were improvised and strengthened yielding extraordinary progress in the geotechnical investigation of soil [13–15]. These techniques provide quantitative properties of soil materials that can be used for analysis and assessments. However, the majority of these methods are costly, time-consuming, and demand intensive physical efforts. Due to the limitations of the existing techniques used in measuring soil properties and considering the importance of such engineering parameters in construction industries, several empirical methods were proposed to estimate soil properties [16, 17]. It is worth highlighting the complexity involved in using empirical techniques to model the indirect relationship between the soil unconfined compressive strength, which is a physical property, and the soil’s chemical properties. Hence, such empirical methods are limited in the accuracy of their predictions. This calls for the deployment of more advanced tools like machine learning algorithms to estimate the soil UCS based on certain properties extracted from the samples such as laser-induced breakdown spectroscopic emission intensities of the constituent elements.

Machine learning is a powerful and intelligent tool that can be used to predict unknown variables from available input data –based on initially trained models [18]. The desired parameter is called the target variable while the rest of the input features are termed descriptors of the model. The descriptors are generally certain quantities that define the properties of the material under investigation and have some reasonable degree of correlation with the unknown quantity [19]. However, they do not have an explicit relationship with the target variable. The model is initially trained using an available dataset comprising both the descriptors and the target variable. It starts by mapping the descriptors unto the target variable using a high-dimensional feature space, after which it can predict the target based on input descriptors only. The potential of machine learning techniques to create a relationship between the input descriptors and target variable in a complex problem using a high-dimensional feature space, without leveraging on their explicit relationship, makes them suitable for advanced scientific research works [20]. Several research works have been reported where machine learning techniques were utilized to solve multiple problems in business, construction, sciences, engineering, medicine, and energy, to mention some [20–24]. Furthermore, many researchers have employed machine learning tools to conduct calibration-free LIBS investigations [25, 26]. This is possible owing to the ability of LIBS to generate enough data and the potential of machine learning algorithms to create the appropriate pattern between the descriptors and the target parameter. In general, LIBS can only provide information relating to the chemical properties of the material such as the elemental intensities and concentration. However, with sophisticated machine learning tools, the physical properties like soil UCS can be extrapolated based on the well-mapped pattern produced by the machine learning tools, as carried out in the present study.

Herein, multiple types of soil samples were collected across different regions of the Kingdom of Saudi Arabia and investigated under the laser-induced breakdown spectroscopy device. Thereafter, the samples were taken for physical properties measurements in the laboratory to obtain their bulk density, soil unconfined compressive strength, and moisture content. The LIBS-generated intensities of the constituent elements, soil’s bulk density, and moisture content were used as input features to train two different machine learning algorithms to predict the soil unconfined compressive strength. The developed models were further validated by investigating the UCS of soil samples stabilized with lime and cement. The two models exhibited excellent prediction accuracy based on the employed metric performance indicators.

The remaining sections of the article are organized as follows: section 2 provides a brief mathematical description of the proposed models. Section 3 highlights the statistics of the dataset utilized in this work as well as the optimization strategies adopted to achieve high prediction accuracy. The results of the predictions and model performance evaluation mechanisms are presented in section 4. Moreover, the applications of the model in studying cement and lime-treated samples are also presented in section 4.

This section introduces a brief mathematical framework of the random forest regression and support vector regression models used in this work. The modeling was executed using the Sci-Kit learn library [27] as implemented in the Python environment. Figure 1 represents the flow of the machine learning algorithms used in the estimation of the soil UCS from the initial to the final phase. The train-test-split feature was employed to train the UCS estimator using 80% of the total dataset and then tested using the remaining 20% of the data.

Random Forest and Support vector regression learners are among the most powerful machine learning algorithms that do not require an extremely large amount of input data [28, 29]. Unlike many other computational intelligence tools, random forest regression requires only two hyperparameters for accurate prediction of the target variable: the number of evidential features used at each node to grow the regression trees, and the total number of the regression trees [30]. It was demonstrated elsewhere that a higher number of trees minimizes the generalization error of the model, thus overtraining is not a major cause of concern [31]. Meanwhile, reducing the number of evidential features increases the performance of the model. On the other hand, the SVR model possesses the ability to transform non-linear input features into a high-dimensional space where they can be classified linearly by the hyper-planes. SVR hyperparameters include the Kernel function, regularization parameter, epsilon, and gamma. The optimum set of these hyperparameters depends on the volume and type of the data under investigation [32]. Therefore, to obtain a highly generalized model, they must neither underfit nor overfit the dataset.

2.1. Random forest regression

Random Forest regression employs multiple decision tree learners to predict an unknown quantity based on a prior trained model. When RF get an input vector (x) consisting of different values of evidential features for a particular training set, it develops K regression trees and compiles their resultant average. Thus, ${\left\{T\left(x\right)\right\}}_{1}^{k}$ learners are grown after K trees. The predictor for the RF regression then becomes [29]:

$${\widehat{\text{f}}}_{\text{r}\text{f}}^{\text{K}}\left(\text{x}\right)=\frac{1}{\text{K}}\sum _{\text{k}=1}^{\text{K}}\text{T}\left(\text{x}\right)$$

To circumvent the issue of correlating different trees, the random forest learner improves the diversity of the trees by nurturing them from various subsets of the training set created via bagging. When RF nurtures a tree, it utilizes the superior split point among the subset of evidential features chosen at random from the total features. In a way, this decreases the strength of the individual trees, however, it lowers the correlation between the trees which in turn decreases the generalization error. Interestingly, the RF-nurtured trees grow without pruning, making them computationally lighter.

2.2. Support vector regression

The SVR is a reliable regression tool that shares the same concept with the support vector machine (SVM) i.e., the concept of Vapnik’s support vectors. However, what differentiates them is that epsilon is applied as tolerance in SVM, while it is to be generated from the problem in SVR. The main goal is to minimize the error and widen the margin using a hyperplane. The model’s generalization optimization is guaranteed using the epsilon which ensures a global minimum.

The SVR utilizes a non-linear transformation function to map the input features into high-dimensional feature space and apply linear regression in the high-dimensional space. The model’s priority is set not to penalize errors less than $\epsilon$ which means that an insensitive loss function $\epsilon >0$ has to be introduced when it comes to the implementation of the SVR model. A summarized mathematical illustration of the models is given below [33]:

$${\left|\left({k}_{r}-{f(X}_{i}\right)\right|}_{\epsilon }=\text{m}\text{a}\text{x}(0,{\left|\left({k}_{r}-{f(X}_{i}\right)\right|}_{\epsilon }-\epsilon )$$

The algorithms in SVR select a function that optimally estimates the target variable with an accuracy $\epsilon$ that sets the maximum accepted deviation of the predicted variable from the target variable for the training dataset. Subsequently, the input parameters were mapped onto an n-dimensional feature space using a radial basis kernel mapping function

$$g\left(x\right)=\tilde{\omega }\phi \left(x\right)+C$$

Where the input dataset pattern is contained in R^N and $\tilde{\omega }$ is a weight factor based on the training data $\{{x}_{i},{k}_{ei}\}$, $i=1, 2, 3 . . . n$. In addition, $\tilde{\omega }, \phi \in {R}^{N}$ and $b \in R$. Minimizing the regularized risk is enabled to achieve a small error test in Eq. (3).

$$\frac{1}{2}\parallel \tilde{\omega }{\parallel }^{2}+C.{R}_{emp}\left(f\right)$$

The complexity of the model is guided by $\parallel \tilde{\omega }{\parallel }^{2}$ and Eq. (4) denotes the empirical risk factor.

$${R}_{emp}\left(f\right)= \frac{1}{n}\sum _{i=1}^{n}{\left|\left({k}_{e}-{f(X}_{i}\right)\right|}_{\epsilon }$$

A small risk is obtained using a simple model to describe the data which controlled both the model complexity and training error demanded by the statistical learning theory. The minimizing of $\parallel \tilde{\omega }{\parallel }^{2}$ is accomplished by the SVR through obtaining the deviation above $\epsilon$ of the training data with non-negative slack parameters. Hence, the optimization problem is now:

Minimize:

$$\theta \left(\tilde{\omega },\xi , \tilde{\xi }\right)=\frac{1}{2}\parallel \tilde{\omega }{\parallel }^{2}+C\sum _{i=1}^{n}\left({\xi }_{i}+{\tilde{\xi }}_{i}\right)$$

Subject to

$$\left\{\begin{array}{c}{k}_{e}-(\tilde{\omega }\phi \left(x\right)+C )\le \epsilon +\xi \\ \tilde{\omega }\phi \left(x\right)+C- {k}_{r}\le \epsilon +\tilde{\xi }\\ \xi ,\tilde{\xi }\ge 0, i=1, . . . n\end{array}\right.$$

The regularization factor is denoted by C, which describes the trade-off between the training and testing data.

$$\sum _{i=1}^{n}\left(k-\tilde{k}\right)=0$$

For transforming the dual optimization problem, a Lagrangian multiplier was subsequently applied to Eq. (5) as presented below:

Minimize

$$\theta \left(k,\tilde{k}\right)=-\frac{1}{2}\sum _{i,j=1}^{n}\left({k}_{i}-\tilde{{k}_{i}}\right)\left({k}_{j}-{\tilde{k}}_{j}\right)K\left({x}_{i},{x}_{j}\right)-\epsilon \sum _{i=1}^{n}\left({k}_{i}+{\tilde{k}}_{i}\right)+\sum _{i=1}^{n}{k}_{r}\left({k}_{i}-{\tilde{k}}_{i}\right)=0$$

Subject to

$$\left\{\begin{array}{c}\sum _{i=1}^{n}\left(k-\tilde{k}\right)=0\\ {k}_{i},{\tilde{k}}_{i},{k}_{j},{\tilde{k}}_{j}\in [0,C]\end{array}\right.$$

Where The kernel function guides the non-linear pattern between ${k}_{e} and x$ is $K\left({x}_{i},{x}_{j}\right)=\sum _{i}^{n}\phi \left({x}_{i}\right)\phi \left({x}_{j}\right)$ and $k and \tilde{k}$ are the dual decision variables.

Equation (7) is the result of the solution of the optimization Eq. (6) which provides the dual n-vectors $k,\tilde{k}$ as shown below

$$g\left(x\right)= \sum _{i=1}^{n }\left(k-\tilde{k}\right)K(x,{x}_{i})+C$$

This section summarizes the methodology employed in the optimization of the models’ parameters. It also presents the statistical analysis of the laser-induced breakdown spectroscopy-generated elemental intensities used in building the models as well as the measured soil unconfined compressive strength. The justification for choosing the given descriptors to predict the soil UCS has also been highlighted.

3.1. LIBS experimental details

The excitation source of the LIBS was the state-of-the-art Quantel Nd: YAG laser operating at the fourth harmonic (266 nm) wavelength, with a pulse energy of 50 mJ/pulse, pulse duration of 8 ns, and repetition rate of 20 Hz [34]. A 20 cm quartz lens was employed to focus the laser beam onto the soil sample surface, creating a spot size of 800 µm, and the optical signal from the luminous plasma was collected via a fiber optic cable.

To minimize background noise and enhance LIBS performance, laser energies, delay times, and number of accumulations were carefully optimized. A two-dimensional motorized sample stage was employed to prevent the formation of deep craters on the soil sample surface. The excitation-acquisition time delay was set in the range of 100 to 300 ns, and the gate opening time was kept at 2 µs. The output from the spectrograph was directed to an ICCD camera (Andor-iStar) equipped with 1024 by 1024-pixel size and integrated for 17 ms, with an average of 3 pulses per accumulation [35].

The LIBS spectra of the soil samples were acquired in the wavelength range of 200 to 800 nm, and elements were identified through comparison with the NIST database. Multiple spots on the soil samples were used to record the LIBS spectra and determine the major elements present. The resulting LIBS spectra consisted of various spectral peaks corresponding to the atomic and ionic lines of elements present in the soil samples, thereby providing insight into their elemental composition.

3.2. Sample preparation method

The sample preparation methodology adopted in this study involved the utilization of conventional soil testing methods, in accordance with the principles of non-destructive LIBS analysis. To ensure consistent and reliable results, the soil specimens were prepared following the guidelines outlined by the ASTM D2166 standard [36]. The soil specimens were cylindrical in shape, with an average diameter of 1.5 inches and a height of 3 inches. The preparation of these specimens required the use of stainless-steel molds, which were filled in thirds and compacted using a standardized tamping hammer. The compaction process was performed in such a manner as to ensure uniform density and consistency throughout the specimen.

In addition to standard compaction, the soil specimens were stabilized with chemical agents such as cement and lime, in varying concentrations of 3%, 6%, and 9%. These stabilizing agents were added to the soil specimens to improve certain soil characteristics, such as strength, and to ensure that the specimens would maintain their physical and chemical properties during the testing phase. The prepared samples were placed in air-tight plastic bags to maintain their humidity and protect them from external factors that could affect their stability. The stabilized specimens were then tested at different curing ages, including 7, 14, and 28 days, to evaluate the effects of curing time on their physical and chemical properties.

3.3. Description and statistics of the dataset

The input dataset utilized in this work consists of certain physical and chemical properties of the soil samples. The physical properties such as soil UCS, water content, and bulk density were measured in a laboratory. Meanwhile, the elemental intensities (chemical properties) of the constituent elements used in this work were captured from the laser-induced spectroscopy device. The LIBS-generated spectrum within the given wavelength range showing the constituent elements present in the soil samples is presented in Fig. 2, for both the stabilized and unstabilized samples. The descriptors constitute two physical quantities, i.e., bulk density and moisture content of the soil. Meanwhile, the chemical quantities include the persistent lines of K, O, Ti, In, Zn, Al, Na, Ca, Mg, Fe and Si. To achieve better generalization of the proposed models, the soil samples used in this work were sourced from multiple regions across the Kingdom of Saudi Arabia.

Tables 1a and 1b present the statistical description of the dataset. A total of 448 datapoints were used in building the models. The minimum and maximum values of each input feature have also been highlighted with the average mean deviation. Figures 3 and 4 depict histograms presenting the distribution of the input features over the full spectrum range—scaled to showcase the peak value of each descriptor and the desired target parameter. This provides a better understanding of the relative frequencies of the LIBS-generated emission intensities of the individual elements contained in the soil samples.

Table 1

a. The statistical description of the dataset
	Si-I (a.u)	Fe-I (a.u)	Mg-I (a.u)	Ca-I (a.u)	Na-I (a.u)	Al-I (a.u)	Zn-II (a.u)
Count	448	448	448	448	448	448	448
Mean	1997.903	3475.311	2546.195	4351.785	3058.826	2361.727	2311.644
Std	2287.507	4017.401	2460.807	3693.774	3355.137	2030.786	2524.423
Min	7.12	7.34	7.26	30.51	54.21	8.94	97.38
Max	13569.26	38302.41	20496.91	23850.11	22487.01	12691.91	13182.71

Table 1

b. The statistical description of the dataset (cont.)
	In-II (a.u)	Ti-I (a.u)	O-I (a.u)	K-I (a.u)	bulk-dens (g/cm³)	water-con (%)	UCS (KPa)
Count	448	448	448	448	448	448	448
Mean	818.7336	3346.286	3818.821	774.9583	1.698918	1623.253	40.66735
Std	1026.145	3009.922	3073.8	936.3752	0.271832	15736.48	43.05548
Min	20.2	30.47	10.3	5.01	0	6.73986	0
Max	6067.24	15954.71	24961.51	9455.23	2.165333	166087.1	217.8911

The selection of the domain variables, otherwise known as the descriptors, is a fundamental phase in building an accurate machine learning model [37]. Herein, the Pearson correlation coefficient between each descriptor and the soil UCS was evaluated and those parameters with significant absolute correlation were chosen. The correlation coefficient between the domain variables and the target is presented as a heatmap in Fig. 5. Notably, the dependence of the input features on each other is also highlighted in the map. On the other hand, a brief discussion on the merit of selecting the given features as determinants for the soil UCS is in order. The soil UCS is a physical property of the material which inevitably depends on the material’s chemical contents. Meanwhile, the elemental intensities of the constituent elements subtly dictate the concentration of the constituent elements [12]. Moreover, the bulk density of the soil plus its moisture content would invariably affect its compressive strength. Therefore, based on the evaluated coefficient of correlation and the foregoing arguments, the chosen descriptors are suitable for soil UCS estimation.

It is interesting to note that some of the chosen descriptors like emission intensities of K, Zn, and Na are negatively correlated with the desired target parameter. This simply implies that their presence in the soil samples deteriorates the compression strength of the material. On the other hand, the soil UCS increases with a positive correlation coefficient between the domain variables and the target feature. In summary, the performance of the model is higher with input features having a higher absolute correlation with the target variable.

3.2 Parameter optimization strategy

The parameter optimization phase is one of the most critical stages of any machine learning model development as it determines how accurate the predicted variables will be. For this work, a test-set-cross-validation method was employed to optimize the models’ parameters. Briefly, the cross-validation optimization method sets the model hyperparameters to a certain reasonable value and continues to tune the variables one after the other until the lowest root mean square error is achieved [22]. For the support vector regression, the model hyperparameters include epsilon, gamma, regularization parameter (C), and Kernel function. These hyperparameters influence the model’s accuracy as follows: Epsilon determines the margin of tolerance and the number of support vectors. The Kernel function makes it possible to map a nonlinear function into a high-dimensional feature space so that it can be solved using linear regression techniques. The regularization parameter controls the extent to which the model is penalized for the estimated function. It is important to note that setting large regularization parameter may lead to the overfitting of the model. However, excessively small regularization parameter may not adequately penalize the training data. Therefore, to develop an efficient model, the parameter should be set to create a balance between reducing the training error and minimizing the model’s intricacy. Figure 6 shows a contour plot representing the combined effect of changing the regularization parameter and epsilon on the R² value of the soil unconfined compressive strength predicted using the SVR model. For the Random Forest model, the number of classifying decision trees on different sub-samples of the input dataset determines the predictive power of the model. The hyperparameters used in this work to estimate the soil UCS for both the SVR and RF models are presented in Table 2. In either case, the hyperparameters represent the set of values derived from the cross-validation exercise conducted to identify the optimum parameters.

Table 2

Optimized parameters obtained for the models
	SVR	RF
Kernel	RBF
C	1000
Epsilon	0.1
Gamma	0.01
Max depth		20

This section presents the results of the soil unconfined compressive strength predicted using Support Vector regression and Random Forest regression machine learning algorithms. The role of the models’ hyperparameters on the overall prediction accuracy is also highlighted. To verify the generalization strength of the developed models, some external problems whose data did not form part of the training and testing set were investigated. Specifically, different soil samples were treated with cement and lime as stabilizing agents. The stabilized samples were investigated under the laser-induced breakdown spectroscopy system to collect the elemental intensities similar to the unstabilized samples. Thereafter, their UCS values were measured in the laboratory. The ability of the developed models to predict the soil UCS values of the stabilized soil samples accurately further confirms their suitability for soil unconfined compressive strength measurements.

Figure 7 shows the cross plot between the estimated and actual values of the soil UCS obtained by the SVR model for both the testing and training phases. On the other hand, Fig. 8 presents the cross plot between the experimental and estimated UCS values obtained using the RF model for the testing and training phases.

It is evident from the prediction results that the SVR model outperformed the RF model in mapping the relationship between the LIBS-generated elemental intensities and the soil unconfined compressive strength. For instance, the correlation coefficient between the predicted and experimental soil UCS obtained using the SVR model during the testing phase is 97.9%. Meanwhile, the RF model yielded a 97.0% coefficient of correlation between the estimated and the actual soil UCS value for the same dataset. Even for the training phase where the models have already seen the input data, the SVR model outshined the RF model in terms of the correlation coefficient between the actual and predicted soil UCS. Overall, the high coefficient of correlation and R² values achieved for both the SVR and RF models demonstrate their suitability for the prediction of soil UCS based on LIBS-generated elemental intensities, moisture content, and bulk density. It is worth noting that the models were trained to generate a functional relationship between the descriptors and soil unconfined compressive strength using 80% of the input dataset. This is the reason behind the excellent prediction of the UCS when the remaining 20% of the unseen dataset was provided for the testing phase, further confirming the models’ generalization ability.

The soil unconfined compressive strength estimator provided in this work was built from the soil’s bulk density, moisture content, and LIBS-generated intensities of the constituent elements using the test-set cross-validation method. Tables 3 and 4 summarizes the high R² values and correlation coefficient between the actual and estimated soil UCS values for both the testing and training phases respectively. Interestingly, both the SVR and RF models have exhibited more than a 99% correlation coefficient between the experimental and predicted UCS values during the training phase, thus indicating suitable mapping of the descriptors to the target parameter. The models’ performance during the testing stage signifies their suitability, efficiency, and stability to estimate the compressive strength of the soil samples.

Table 3

Performance indicators of the models at the testing phase
	SVR	RF
R2	0.95715	0.93661
MAE	1.9844	5.227516
RMSE	7.869398	10.425449
CC	0.97892	0.97001

Table 4

Performance indicators of the models at the training phase
	SVR	RF
R2	0.99999	0.985641
MAE	0.0002	2.972708
RMSE	0.00024	5.19957
CC	0.9999	0.99404

4.1 Model Performance Evaluation

The prediction accuracy of the established SVR and RF models was evaluated based on certain standard metric performance indicators such as root mean square error, mean absolute error, R²-value, and the coefficient of correlation between the predicted and experimental soil UCS. The mathematical illustration of the employed metric performance indicators is summarized in (1)–(3) [38].

$\text{M}\text{A}\text{E}=\frac{1}{\text{N}}\sum _{\text{i}=1}^{\text{N}}|{\text{Y}}_{\text{a}\text{c}\text{t}}-{\text{Y}}_{\text{p}\text{r}\text{e}\text{d}}|$ (1 )

$${\text{R}}^{2}\_\text{v}\text{a}\text{l}\text{u}\text{e}=1-\frac{\text{s}\text{u}\text{m} \text{o}\text{f} \text{s}\text{q}\text{u}\text{a}\text{r}\text{e}\text{d} \text{e}\text{r}\text{r}\text{o}\text{r}}{\text{s}\text{u}\text{m} \text{o}\text{f} \text{s}\text{q}\text{u}\text{a}\text{r}\text{e}\text{d} \text{t}\text{o}\text{t}\text{a}\text{l}}$$

$$\text{M}\text{S}\text{E}=\frac{1}{\text{N}}\sum _{\text{i}=1}^{\text{N}}{({\text{Y}}_{\text{a}\text{c}\text{t}}-{\text{Y}}_{\text{p}\text{r}\text{e}\text{d}})}^{2}$$

Where

$$\text{s}\text{u}\text{m} \text{o}\text{f} \text{s}\text{q}\text{u}\text{a}\text{r}\text{e}\text{d} \text{e}\text{r}\text{r}\text{o}\text{r}= \sum _{\text{i}=1}^{\text{i}=\text{N}}{({\text{Y}}_{\text{a}\text{c}\text{t}}-{\text{Y}}_{\text{p}\text{r}\text{e}\text{d}})}^{2}$$

$$\text{s}\text{u}\text{m} \text{o}\text{f} \text{s}\text{q}\text{u}\text{a}\text{r}\text{e}\text{d} \text{t}\text{o}\text{t}\text{a}\text{l}= \sum _{\text{i}=1}^{\text{i}=\text{N}}{({\text{Y}}_{\text{a}\text{c}\text{t}}-{\text{m}\text{e}\text{a}\text{n}(\text{Y}}_{\text{p}\text{r}\text{e}\text{d}}))}^{2}$$

Y_pred is the predicted soil UCS, Y_act is the experimental soil UCS, MSE represents the mean square error, from which the root mean square error is derived, MAE represents the mean absolute error, and N stands for the total number of the datapoints.

The results of the metric performance indicators used in this work are presented in Tables 3 and 4 for the testing and training phases respectively. Notably, all four metric indicators validate the outcome of one another. For example, during the testing phase, the SVR was characterized by the highest R²-value and coefficient of correlation between predicted and actual soil UCS values compared to the RF regression model as presented in Fig. 9. On the other hand, SVR exhibited the lowest mean absolute errors and root mean square error, as expected. Interestingly, the trend follows a similar pattern during the training phase. This assertion further indicates the edge of the SVR model over the RF regression model in establishing the complex non-linear relationship between the soil UCS on one hand, and the LIBS-generated elemental intensities, soil water content, and soil bulk density on the other hand.

4.2. Model Validation and Applications

Following the successful testing of the models, the developed support vector regression and random forest learners were validated by investigating the UCS of lime and cement-stabilized soil samples whose LIBS-generated emission intensities and other physical properties were not considered during the training phase of the model. Although the models were built based on the unstabilized samples dataset, it was able to predict the unconfined compressive strength of the cement and lime-treated soils with a high degree of accuracy as observed from the coefficient of correlation and R²-value. This further indicates the generalization strength of the developed models and implies that the model can be applied for external applications in the building and construction industries, provided that the LIBS-generated intensities can be obtained.

4.2.1. Effect of stabilization with cement.

To investigate the effects of treating the soil samples with cement, several samples were prepared and stabilized with different cement dosages. They were studied under laser-induced breakdown spectroscopy to acquire the elemental intensities. The samples were then taken to the laboratory for the measurement of the physical properties. At this stage, both the LIBS-generated data and the physical properties have not been sighted by the developed models. Therefore, to validate the models, the generated input parameters were supplied to the model to predict the laboratory-measured unconfined compressive strength to assess the models’ capacity and generalization potentials. Interestingly, both the SVR and RF models have yielded the desired soil UCS for the cement-stabilized soil samples with high correlation coefficients as depicted in Figs. 10 and 11. Such treatment of soils with a stabilizing agent is a common practice in construction works as it improves soil quality, load-bearing, impermeability, and stability. It is therefore worth developing an intelligent tool such as machine learning to estimate the soils’ unconfined compressive strength.

4.2.2. Effects of stabilization with lime

The SVR and RF models were further employed to predict the unconfined compressive strength of lime-stabilized soil samples. Similar to the cement-stabilized samples, the LIBS-generated input dataset for the lime-treated samples was not considered during the training and testing of the models. However, both the RF and SVR models have estimated the soil UCS with a high degree of accuracy as depicted in Figs. 10 and 11. Studying the physical characteristics of lime-stabilized soil samples via intelligent learners is of great importance considering the role of such analysis in designing and construction of fundamental infrastructures such as bridges, domestic buildings, and dams. Lime is one of the building materials used in drying wet soils at construction sites to decrease downtime and enhance the working surface. Soils treated with lime are characteristically impermeable and stable. Therefore, a computational intelligence method of estimating the unconfined compressive strength of lime-treated soils will be of high significance to the building construction community.

In summary, laser-induced breakdown spectroscopy and machine learning algorithms were used to investigate different soil samples collected from multiple locations. After studying the specimens under LIBS, some physical properties of the soil samples such as bulk density, unconfined compressive strength, and moisture content were measured in the laboratory. Subsequently, support vector regression and random forest regression machine learning tools were employed to design a model that can predict the soil UCS based on the LIBS-generated emission intensities of the constituent elements, bulk density, and soil moisture content. The performance of the models was evaluated based on the standard metric performance indicators such as mean absolute error, root mean square error, R²-value, and coefficient of correlation between the experimental and predicted soil UCS. The SVR model exhibited a higher R² value and coefficient of correlation compared to the RF model. For example, the correlation coefficient between the predicted and experimental soil UCS obtained using the SVR model during the testing phase is 97.9%. Meanwhile, the RF model yielded a 97.0% coefficient of correlation between the estimated and the actual soil UCS value for the same dataset. To validate the models for on-site applications, the UCS of soils stabilized with lime and cement was investigated. The ability of the models to predict with high precision, such quantities whose datasets were not involved during the development of the model indicates its accuracy and generalization strength. The soil UCS estimator developed in this work provides a facile, low-cost, and reliable way of calculating the soil unconfined compressive strength for different applications. In the future, the concept of dimensionality reduction may be applied to improve the models’ accuracy and minimize computational costs.

Conflict interest

None

Data availability

The data used in this work is available upon reasonable request.

Acknowledgment

The authors appreciate the financial support from the Interdisciplinary Research Center for Construction & Building Materials (IRC-CBM) at King Fahd University of Petroleum & Minerals (KFUPM), Saudi Arabia, through Project No. INCB2216. We equally appreciate the Physics department and Civil Engineering department for their support.

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Laser induced spectroscopy-based estimation of soil unconfined compressive strength: a machine learning approach

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Abstract

Figures

1. Introduction

2. Brief Description Of The Proposed Models

2.1. Random forest regression

2.2. Support vector regression

3. Experimentation And Empirical Studies

3.1. LIBS experimental details

3.2. Sample preparation method

3.3. Description and statistics of the dataset

3.2 Parameter optimization strategy

4. Results Discussion

4.1 Model Performance Evaluation

4.2. Model Validation and Applications

4.2.1. Effect of stabilization with cement.

4.2.2. Effects of stabilization with lime

5. Conclusion And Future Scope

Declarations

References

Additional Declarations

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