Study and Design of a Machine Learning-Enabled Laser-Based Sensor for Pure and Sea Water Determination Using COMSOL Multiphysics

Abstract

Accurate detection of salt in water is crucial in many applications. Numerous techniques, using direct and indirect methods, have been employed to design seawater sensors. Among the indirect sensing methods, optical sensors are known to be the most accurate, easy to implement, and suitable for application where the chemical properties of the solution to be tested should stay unchanged. This research presents a novel method for real-time label-free biochemical detection of salty water combining various optics concepts with a machine learning system. COMSOL Multiphysics has been employed to design and simulate the proposed sensor. The designed device uses a laser light emitted from the top of a water container, with a sensing part located on the bottom surface. The laser light initially propagates in the air portion, then refracts when it comes into contact with the air-water interface. Different parameters, including the laser beam wavelength $\lambda$ and its incident angles${\theta }_i$, the temperature, and the air-water levels are employed to generate a set of data and the multilayer perceptron classifier (MLP) to model prediction. The obtained results validated the concept of the proposed sensor using machine learning. The sensor’s prediction precision under various temperature conditions is R² = 0.844, the equivalent of an MSE of 0.155.

1. Introduction

Technology using intelligent sensors is increasingly influencing our everyday lives, particularly in the environmental field. Some sensor types have been investigated for detecting humidity, displacement, micro-cavities, and other parameters [1,2,3]. Further research studies focused on real-time water quality monitoring [4,5,6]. Researchers have long recognized that accurately detecting seawater salinity has significant academic and practical implications in marine environment monitoring, mineral exploration, and industrial research [7].

Numerous sensor technologies have been employed to determine pure and salt water. These sensors either use direct or indirect measurement techniques. Direct methods usually require the usage of different chemicals to perform the reading. Despite the fact that they are fast and easy to implement, direct measurement methods could be irrelevant to many applications where the solution’s properties should stay unchanged. On the other hand, indirect measurement techniques are widely used. They employ different methods depending on the applications’ requirements, including acoustic, density, conductivity, and optics-based methods.

Different simulation tools have been used to study the function and performance of different sensors. COMSOL Multiphysics is considered as a powerful tool that can be employed for sensors’ design and function analysis. Numerous research works have employed COMSOL to prove the concept of different seawater sensors. However, using a combination of COMSOL Multiphysics and a machine learning approach to develop seawater sensors is not fully explored. In reference [8], hybrid machine learning algorithms are used to predict chlorophyll sensor parameters located in the upper ocean through the sea ice buoy. Nonetheless, another process should be used to convert data to relevant ocean parameters. Reference [9] presents a new methodology for seawater concentration estimation using generalized radial basis function neural networks method. Although all of the existing techniques developed new methods, approaches, and fabrication techniques for seawater sensors, it is still necessary to develop a simple, effective, economical, and high-performance sensors for detecting the nature of the water (pure water or saltwater), as well as its temperature, among other applications.

In this paper, we present a novel approach to seawater sensors that combines machine learning and optics concepts. This technique is a low-cost technology with label-free biochemical detection, real-time monitoring, and high sensing performance that allows recognition of water type under various temperature conditions. The designed sensor can pave the way for the development of a multi-parameter sensor with a wide range of applications in water pollution and environmental monitoring, among other future applications.

The paper is organized as follows. Section 1 introduces the scope and importance of the research. Section 2 provides a brief overview of the different methods used for pure and salty water sensing. Several research-based devices are listed. Section 3 elaborates the concept and methodology used to design the proposed sensor. Furthermore, COMSOL Multiphysics simulation results are presented, and the machine learning process and obtained data are provided and analyzed. Section 4 describes the obtained sensor’s performance. Section 5 is dedicated for conclusions.

2. Literature Review

Various techniques have been utilized to detect pure and salty water. They could be classified into direct and indirect.

2.1. Direct Measurement Techniques

Among direct seawater salinity measurement techniques, chemo-resistive sensors are widely used [10,11,12]. A recent study in [13] investigated the sensitivity and selectivity of an ITO (Indium-Tin-Oxide) nanoparticle-based sensor for detecting liquid chemicals diluted in brine. This eco-friendly sensor performance is investigated using representative analytes such as methanol (MeOH), ethanol (EtOH), and isopropyl alcohol (IPA) diluted in brine (NaCl 3.5 wt.%). Direct measurement techniques are usually based on different chemical reactions, which could result in changing the chemical properties of the solution to be tested. Although direct measurement techniques could be very simple to implement, they would not be suitable to many applications where the chemical properties of the solution to be tested should stay unchanged.

2.2. Indirect Measurement Techniques

Common indirect pure and salt water detection measurement techniques mainly employ acoustic, density, conductivity, and optics methods. These methods are outlined in the following subsections.

2.2.1. Acoustic Method

Pure and salt water detection using the acoustic method employs sonar technology. The sound velocity in pure water and in salty water is different. The measurement can be obtained according to the return time of the ultrasonic wave [14]. This method is suitable for pure and seawater detection. However, it has a high cost and a poor anti-interference ability [15].

2.2.2. Density Method

Usually, the determination of salty water using the density method employs a precision vibrating tube densimeter. Schmidt et al. [16] proposed a method for measuring seawater density using a vibrating flow densitometer. The vibration tube is made of magnetic material. It should be attached to the object to be tested. The electromagnetic driving coil and detection coil are installed next to the vibration tube. As soon as a pulse exciting current is supplied to the driving coil, the vibrating tube vibrates under the magnetic force of the coil and a current with the same vibration frequency is generated in the detection coil. The density of the liquid could then be calculated using the vibration frequency of the vibration tube, and therefore the liquid/water could be classified as either pure or salty [17].

2.2.3. Conductivity Method

Conductivity measurement is a common method to identify pure and salty water. This method is known by its simple structure, easy implementation, fast response, and low cost, which makes it widely employed in various industrial applications [18,19,20]. Typically, conductivity sensors are classified into two types: electromagnetic induction conductivity and electrode conductivity. Usually, the probe of an electromagnetic induction conductivity sensor contains two metal coils, which are the excitation coil and the induction coil. First, an alternating current excitation signal is applied to the excitation coil of the sensor probe in order to induce an electric field. The induced electric field is then transmitted to the induction coil through the water/liquid to be determined. Therefore, an alternating current output voltage forms on the induction coil. The output voltage and conductivity of the solution form a nonlinear function that can be used to identify different type of solutions, particularly salty water and pure water. Ramos et al. [21] proposed a four-electrode conductivity sensor. It includes two electrodes which are placed in a uniform electric field, and the other two are measured. This configuration is proven to help avoid the measurement errors caused by the polarization effect. Huang et al. [22] employed four electrodes in a measuring board with a conductivity accuracy of 0.03 mS/cm to classify different liquid solutions including seawater and pure water. Some other commercial salinity sensors such as the famous Sea-Bird CTD (Conductivity, Temperature, Depth) profiler are based on conductivity ratio measurement [23]. These sensors need a highly reliable pump to flush water through the conductivity cell at a constant rate and can then be applied to the underway monitoring. It is sensitive to the water velocity, and makes the system complicated and difficult to miniaturize [24]. Furthermore, the non-conductive part of dissolved material in seawater cannot be taken into account by the conductivity CTD [25].

2.2.4. Optics Method

Several research papers proposed various types of sensors based on the surface plasmon resonance (SPR) optical phenomenon in a variety of fields such as medical diagnostics, biochemical sensing, and water pollution monitoring [26,27,28]. Based on the same technique (SPR) [29,30,31,32,33], other works proposed a novel method for multi-parameter sensors’ realization for simultaneous detection of seawater salinity and temperature. Many other studies used Raman spectroscopy for seawater salinity detection [34,35]. The authors in [36,37] proposed a salinity sensor with fiber grating. Gentleman and Booksh [38] employed a multimode optical fiber that uses the principle of surface plasmon resonance to measure the salinity of a liquid. Furthermore, Lee et al. [39] proposed a salinity sensor based on photonic crystal fiber.

Numerous sensor types based on the interferometer method have been deployed, including the Fabry–Perot interferometer structure, the rectangular optical microfiber Sagnac interferometer structure, and the tapered structure [40,41,42]. The fiber interferometer structure has the benefit of high sensitivity, but it is inadaptable in harsh field measurement conditions and is mostly used in laboratories [43].

The refractive index (RI) measurement technique is an optical technique-based salinity sensor as it is correlated to the density according to the relation of Lorentz-Lorenz and thus can be related to the absolute salinity [44,45]. Over the past years, many optical salinity sensors based on refractive index measurements have been developed using optics concepts such as the Fraunhofer method, total internal reflection, critical angle, etc. [46,47,48,49,50,51].

2.3. Our Proposed Solution

A performance comparison of several techniques used for pure and salt water salinity measurement is detailed in the

Table 1. Comparison table detailing the advantages and limitations of techniques used for pure and salty water salinity measurement.

Reference	Method/Technique	Advantages	Disadvantages/Limitations
[10,11,12,13]	Chemicals (lucigenin, luminophores membranes…)	Fast and easy implementation technique. Chloride measurement over a wide range of salinities. Dynamic range can be adjusted.	Accuracy is not perfect. A dramatic shift of the working range of immobilized lucigenin is required. Lucigenin fluorescence is quenched by chloride, bromide, salicylate, thiocyanate, and iodide. The sensor calibration changed with sensing fluorophores photo bleach at different rates. Not suitable to many applications that require unchanged solution properties.
[14,15]	Acoustic/density	Suitable for pure and seawater detection. - Simple concept.	High cost and a poor anti-interference ability. Design is not perfect (not easy to implement).
[18,19,20,21,22,23,24,25]	Conductivity	Simple and easy implementation. Fast response and low cost. - Widely employed in various industrial applications.	Highly reliable pump is needed to flush water through the conductivity cell at a constant rate. Water velocity dependent technique which makes the system complicated and difficult to miniaturize. All dissolved material in seawater should be conductive.
[29,32,33]	Surface Plasmon Resonance	Achievement of highest wavelength interrogation sensitivity among fiber-based SPR sensors. Simultaneous measurement of seawater salinity and temperature. Possibility of avoiding metal coating in the fiber holes.	The gold layer thickness affected the sensing performance. The noise captured complicated the detection process. The holes filled with the fluid limited the performance of the sensor design. Number of holes in the sensor design limited the light propagation and reduce the core-guided light.
[34,35]	Raman scattering	Verified technique in real ocean water under normal solar illumination.	Raman scattering is neglected in the blue region of the ocean water. Pigment concentration data missing to confirm the technique hypothesis.
[40,41,42,43,44,45,46,47,48,49,50,51]	Interferometer/refractive index	High sensitivity.	Inadaptable in harsh field measurement conditions. Mostly used in laboratories.
[8,9]	Machine learning	Label-free biochemical (chemical properties conservation). - Accurate. Fast response, low cost.	Difficulty of collecting real data to tune the model. Another process should be used to convert data to relevant parameters.

.

Indirect measurement techniques are the most commonly used, especially for applications where the chemical properties of solutions should stay unchanged. Among the indirect measurement techniques, optics methods are the most accurate, cost effective, and easy to implement, especially the refractive index measurement technique that provides an advantageous alternative solution [44] as it is correlated to the density and thus to the absolute salinity, pressure, temperature, and wavelength of light used [45,46,47,48,49,50,51,52,53,54,55]. When it comes to machine learning, a common challenge facing researchers is the difficulty of collecting real data and the filtering process to tune the model.

Our proposed solution combines the optics concept and the machine learning technique. It is based on a simple physics law (Snell’s law) for calculation and avoids the experimental complication of the real time data collection for the machine learning model. We applied a laser-based measuring method in a compact structure to propose a sensor for pure and seawater classification. This novel method uses COMSOL Multiphysics, a solid simulation tool, to design the sensor and define the refractive index of the water sample to be tested. Data collected from simulation are thus implemented in the machine learning as inputs to model whether the water sample is clean or salty under different temperatures as output. The proposed method used for real-time label-free biochemical detection is a low-cost technique, with high sensing performance, and is simple and easy to implement. However, it is important to mention that this research work is a proof of concept determining a new way of water classification combining optics concepts with the machine learning model, and it is not related to any experimental demonstration. The details of this study are explored and analyzed in the following section.

3. Concept and Methodology

In the first part of this section, the sensor concept and design are presented showing the different parameters and equations to be defined in the study. The physics interfaces employed in the simulation study using COMSOL Multiphysics are provided in the second part. The data collected from the simulation study are explored and defined to be used as inputs in the machine learning study that is developed in the third part of this section.

3.1. Sensor Concept and Design

The sensor design is divided into three main parts: a cap to house the laser, a tank to hold the water sample, and a bottom sensing zone where the sensor is located (Figure 1).

The light with an angle of incidence ${\theta }_i$ is emitted from the point of incidence O from the laser in the cap, towards the tank partially filled with the water sample. This incident angle can be controlled by a mirror-servo motor concept as shown in Figure 1. The light bends at the air-water interface while traveling from air medium (refractive index $n_{air}$) to water sample medium (refractive index $n_w$), making an angle of refraction ${\theta }_t$ with the normal to the boundary. The relation between$n_{air}$, $n_w$, ${\theta }_i$, and ${\theta }_t$ is given by the law of refraction or Snell’s law (Equation (1)).

$$n_{air}\sin {\theta }_i=n_w\sin {\theta }_t$$

(1)

The transmitted light propagates with an angle ${\theta }_t$ until it reaches the bottom sensing zone at a location d from the corresponding point of incidence O′ (reference point). This distance d varies with the incident light wavelength λ, angle of incidence${\theta }_i$, water sample refractive index $n_w$, water temperature T, and air/water concentration $W_{air}/W_{water}$.

The value of $n_{air}$ is set to one. Different works have been developed to define the refractive index $n_w$ of the salty water. Reference [56] presented an empirical equation based on references [57] and [58], used to compute $n_w$ up to 3–4 decimal places, as a function of the wavelength λ, water salinity S (S = 0 (pure water) and S = 35% (salt water)), and temperature T. Reference [46] experimented with a new method for measuring the refractive index of salt water based on Fraunhofer’s method. The experimental values obtained were used to generate mathematical equations relating $n_w$ to the temperature and concentration of the water sample. The values of $n_w$ are calculated for S = 0, S = 35%, and λ = 450 nm, using each of the equations presented in references [46,56]. Results comparing $n_w$ are presented in Figure 2 for S = 0 and S = 35% at different temperatures (0, 30, 40, 50, 60, and 90 °C, respectively). The same tendency can be seen between the two curves, with a 0.4% average error, allowing us to assume that both equations used in references [56] and [46] have the same conversion and can be used in our study. In what follows, we are using the equation used in reference [56] (Equation (2)).

$$n_w=a{T}^2+b{\lambda }^2+cT+d\lambda +e$$

(2)

where a, b, c, d are the coefficients defined by $a=-1.50156\times {10}^{-6}$, $b=1.07085\times {10}^{-7}$, $c=-4.27594\times {10}^{-5}$, $d=-1.60476\times {10}^{-4}$, $e=1.39807$ for salt water (S = 35%) and by $a=-1.97812\times {10}^{-6}$, $b=1.03223\times {10}^{-7}$, $c=8.58125\times {10}^{-6}$, $d=-1.54834\times {10}^{-4}$, $e=1.38919$ for pure water ($S=0$).

As mentioned above, the distance d depends on the parameters λ,${\theta }_i$, $n_w$, T, and $W_{air}/W_{water}$. However, $n_w$ depends on only λ, S, and T. The COMSOL Multiphysics simulation tool is used to calculate the distance d, taking into account all these parameters as variables. Data collected from simulation studies will be defined as input parameters for machine learning. The latter, therefore, provides recognition of the nature of the water sample as an output, whether pure water ($S=0$) or salt water ($S=35\%$). The input data can be rearranged in such a way that the temperature is also an output. This study will be developed in a different research paper.

3.2. COMSOL Multiphysics Simulation

As previously stated, COMSOL Multiphysics is used to validate the concept and obtain the necessary data. The 2D sensor model geometry consists of a rectangular design divided into two domains, air (domain one) and water (domain two). The design width and length are fixed to 20 cm and 30 cm, respectively. However, the air depth $W_{air}$ and water depth $W_{water}$ are variable ($W_{air}+W_{water}=20 \mathrm{cm}$). The refractive indices of domains one and two are defined by one and$n_w$, respectively.

The “Geometrical optics” physics interface with a time-dependent study is implemented for modeling the electromagnetic wave propagation, where the wavelength to be used is much smaller than the smallest geometric entity in the model. Diffraction and reflection at edges and corners in the geometry are neglected in the study, and wall boundary conditions are defined as “disappear” options for perfect absorption. An optical path length step is set to 0.01 cm to ensure accurate refraction at the ray-boundary interaction (air-water interface), and the time taken by the ray to reach the sensing part (source-to-target) is calculated by COMSOL. However, the ray is propagated with the speed of light and time taken is measured in the nanosecond-Angstrom scale. In practice, it is difficult to find a time sensor capable of accurately measuring a nanoscale time difference between rays once they reach the sensing part. Therefore, studying the source-to-target time collected by COMSOL is pointless, and the distance d will be the only investigated parameter in this study.

For a fixed $W_{air}$ and $W_{water}$, and a sweep of angle ${\theta }_i$ from 0 to 45° with 0.5° step, the distance d is calculated for both water types (S = 0 and S = 35%). A similar study is repeated with sweeping $W_{water}$ from 5 to 10 cm by 1 cm step (the total width is kept constant at 20 cm). The above simulations are computed for three different wavelengths (450 nm (blue), 520 nm (green), and 660 nm (red)) and three different temperatures, 30, 40, and 50 °C, to obtain the values of the distance d.

As mentioned above, $n_w$ depends only on λ, S, and T. Using Equation (2), the values of the refractive indices for pure water and salt water ($n_w$ (S = 0) and $n_w$ (S = 35%)), for different wavelengths and temperatures, are represented in Figure 3. It should be noted that $n_w$ (S = 0) and $n_w$ (S = 35%) reduce in value as the wavelength increases. This is logical since the phase velocity of light is slower in the material than in air, and waves with different λ travel at different velocities in a medium; short waves travel slower than long waves.

Data collected from COMSOL, for the distance d, can be easily verified using Snell’s law and trigonometry by Equation (3).

$$d=W_{air} tan{\theta }_i+W_{water} tantan (\frac{n_{air} sin{\theta }_i}{n_{water}})$$

(3)

Values for the distance d obtained by COMSOL and Equation (3) are compared for four random examples with different parameters and are shown in

Table 2. Distance d values obtained by COMSOL and Equation (3) for four different examples.

Example	Distance d (cm) Using Equation (3)	Distance d (cm) Using COMSOL	Error
1	3.29951	3.29950	$3.03\times {10}^{-4}$
2	8.56587	8.56588	$1.17\times {10}^{-4}$
3	16.63138	16.63126	$7.22\times {10}^{-4}$
4	13.03546	13.03559	$9.97\times {10}^{-4}$

.

Example 1: $W_{water}=5 \mathrm{cm},$ S = 35, ${\theta }_i=10°$, λ = 520 nm, T = 50 °C,

Example 2: $W_{water}=7 \mathrm{cm}$, S = 35, ${\theta }_i=25.5°$, λ = 450 nm, T = 30 °C,

Example 3: $W_{water}=9 \mathrm{cm}$, S = 0, ${\theta }_i=45°$, λ = 520 nm, T = 40 °C,

Example 4: $W_{water}=10 \mathrm{cm}$, S = 0, ${\theta }_i=38°$, λ = 660 nm, T = 30 °C.

We can notice that the values of d are similar to an average error of $2.2\times {10}^{-5}$, which validates the results obtained using COMSOL.

3.3. Machine Learning and Data

As already stated, COMSOL Multiphysics is used to simulate laser beam refraction for different wavelengths λ (nm), temperatures T (°C), incident angles${\theta }_i$, air-water concentration ($W_{air}/W_{water})$, and for two types of water samples (pure water and salt water). The distance d will therefore be calculated for each parameter, feature, or variable change, after which all are merged to form an input-output data set as seen in

Table 3. Input-output data set sample.

INPUT									OUTPUT
			Configuration 1		Configuration 2		Configuration 3
${\theta }_i$ (°)	Air/water concentration $W_{air}/W_{water}$ (cm)	T (°C)	Distance d (cm)	λ (nm)	Distance d (cm)	λ (nm)	Distance d (cm)	λ (nm)	Water sample
42.5	15/5	30	16.668650	450	16.67984	520	16.69381	660	0
8.5	14/6	30	2.7557548	450	2.757758	520	2.760128	660	1
14.5	13/7	50	4.6986000	450	4.702555	520	4.707375	660	0
18	14/6	50	5.9764883	450	5.980795	520	5.986045	660	0
23	10/10	40	7.2846954	450	7.294368	520	7.306362	660	1

where zero denotes pure water and one denotes salt water.

Table 3 shows a fraction of the full data set defined as input/output data parameters used for training. The total number of rows is 3064. The data set’s variables used in simulation are:

(1)

Incident angle ${\theta }_i$ from 0 to 45° with 0.5° step;

(2)

Air-water concentration $W_{air}/W_{water}$ (cm) with six different configurations (15/5, 14/6, 13/7, 12/8, 11/9, 10/10);

(3)

Temperature T with three different configurations (30, 40, and 50 °C, respectively);

(4)

Wavelength λ with three different configurations (450, 520, and 660 nm, respectively).

It is important to note that changing these variables will result in changes in the distance d, and they will all combine to form an input data set for the two possible outputs 0/1 (pure water/salt water).

Data set scaling is a common requirement for machine learning (ML) training. This is typically done by killing the mean and adjusting the difference in units. However, for some data sets, a negative impact on learning/training can be observed. In such cases, the medium and near range always give better results. As aforementioned, the first step is to limit or adhere to the proportional information best suited for controlling the size of the features or variables in the iterative cycle, such as the timeout vector in the background, for example, to avoid numerical risks due to cost variability. The standard scaler (MinMax) pre-processing capability within the sci-kit learn library is used to capture data set scatter to the quintile (min–max) range, by setting each element and simply scaling application insights to the boundaries of the sample information [59]. Centering and scaling are performed independently of each component by calculating the relevant sample statistics in the training set. The mean and standard deviations are stored for use in later conversion data.

The neural network is simply a collection of many general units of neuron management. Each unit in the layer is linked to the next layer, applying the fact that the neural network is fully interconnected. The most important layer is the input layer, and its units capture the advantages of information. The last layer is the resulting layer, which contains one unit for each network output value. When the layers are assembled, each unit has a bias predisposition, and each pair of units in two contiguous layers has a specific weight. Subsequently, the network’s calculations can be written by Equation (4) [60,61].

$$h_i^{\left(1\right)}={\Omega }^{\left(1\right)}\left({\displaystyle \sum }_j{w}_{ij}^{\left(1\right)}{x}_j+b_i^{\left(1\right)}\right) ;h_i^{\left(2\right)}={\Omega }^{\left(2\right)}\left({\displaystyle \sum }_j{w}_{ij}^{\left(2\right)}{x}_j+b_i^{\left(2\right)}\right);y_i={\Omega }^{\left(3\right)}\left({\displaystyle \sum }_j{w}_{ij}^{\left(3\right)}{x}_j+b_i^{\left(3\right)}\right)$$

(4)

where $h_i^{\left(1\right)}$ represents units in the nth hidden layer, $x_j$ input units or features, $b_i^{\left(1\right)}$ bias, ${\displaystyle \sum }_j{w}_{ij}^{\left(1\right)}$ weight, ${\Omega }^{\left(1\right)}$ activation functions, and $y_i$ output unit.

The used (MLP) multilayer perceptron classifier model contains 13 hidden layers and employs the Hyperbolic Tangent activation function with two random states. The input layer has 3054 data samples plus 10 more samples for tuning. Strategies used to forestall over-fitting in MLP are model decision, early consummation, weight decay, and pruning [28]. Because MLPs are universal function approximations, as demonstrated by Cybenk’s theorem, they can be used to construct mathematical models using regression analysis. MLPs produce good classification algorithms because classification is a specific case of change because the response variable is categorical. The multilayer perceptron (MLP) model is an artificial neural network that maps input data sets to a set of corresponding outputs. As previously cited, an MLP consists of several layers of nodes in a directed graph, with each layer being fully interconnected with the others. In addition to the input, each node is a neuron (as a processing element) with a nonlinear activation function. MLP uses a managed learning technique called back-propagation to train the network. MLP is a modification of the standard linear perceptron and identifies nonlinearly separated data.

Figure 4 summarizes all of the mentioned parts of the methodology. Figure 4 is a flowchart that systematically explains the research flow, highlighting all important points involved in data collection or simulation, data set formation, and machine learning modeling. To verify the model results or predictions, a variety of error parameters are determined with the primary focus on the mean absolute error (MAE), root mean squared error (RMSE), and R-squared.

$$\mathrm{MAE}=\frac{1}{m}{\displaystyle \sum }_{k=1}^m\left|y_k-{\yen }_k\right|$$

(5)

where ${\yen }_k$ are the predicted values for interval k and $y_k$ represents the real output. Similarly, the RMSE formula is given as:

$$\mathrm{RMSE}=\sqrt{\frac{1}{m}{\displaystyle \sum }_{k=1}^m{\left(y_k-{\yen }_k\right)}^2}$$

(6)

Both MAE and RMSE describe a typical model assumption, both with the units of the variable of interest, where the two estimates can range from 0 to ∞, and are aloof in regards to the course of bumbles. They are known as conversely organized scores, and they imply that lower scores address a predominant model [60,61].

Before elaborating on the machine learning (ML) model results, it is important that we graphically show the data sets and some visible impact of concentration, temperature, wavelengths, and their correlation with changes in the index of refraction or distance d. The following key point is significant because it demonstrates changes in the input layer or data variables that assist the ML model in mapping inputs with outputs or distinguishing and learning from the provided data sets. Therefore, it can correlate inputs to outputs by generating weights and biases. This can be seen in Figure 5, Figure 6, Figure 7 and Figure 8. Figure 5 represents and depicts the effect of water concentration ($W_{water}$), indicating that distance d is changing with water concentration and is more noticeable with higher incident angle values.

Another factor that helps ML to predict and correlate inputs with outputs is temperature dependence, which is clearly shown in Figure 6 by indicating the change in distance d for different temperature values and different incident angles ${\theta }_i$. Refractive index (pure water and salt water) effect on the distance d for different incident angles ${\theta }_i$ is also shown in Figure 7. Finally, Figure 8 denotes changes in the distance d for different wavelengths.

4. Results and Discussion

Figure 5, Figure 6, Figure 7 and Figure 8 show that all the factors used are generating a specific “fingerprint” or change in data input parameters, which is then used to generate a machine learning model based on those points as a variable input parameter. The “fingerprint” term here means that a specific pattern of input-output data is unique, as demonstrated previously by changes in the distance d and its dependence on other input parameters. This assures that the MLP model can fit input to output because no input set is unique.

Table 4. MLP model classification errors.

Coefficient of Determination R2	0.844
Mean Squared Error MSE	0.155
Mean Abs Real Error MARE	0.326
Mean Square Log Error MSLE	0.075
Root Mean Squared Error RMSE	0.395
Mean Absolute Error MAE	0.156
Root Mean Squared Logarithmic Error RMSLE	0.274

and

Table 5. MLP model classification test on new inputs (pure water).

Number of Total Test Data Samples	Data Set Size Angle of Incidence${\mathit{\theta }}_{\mathit{i}}$(0.5–45)	MLP-Multi-Layer Perceptron Classifier
		Correct Classification Count	Wrong Classification Count
90	Pure water (S = 0)	73	17
90	Salt water (S = 35%)	66	24

show the MLP training/testing errors and accuracy parameters.

In Table 4, the error outputs parameters show that the MLP model accuracy is very high with $R^2=0.844$ and the mean absolute error is 0.156. This demonstrates that the proposed MLP model can be used for input-output mapping purposes. To make the data more interesting, Table 4 shows a tabular form of the data with new input parameters and MLP predictions, along with the corresponding error or classification. It is important to mention that the input data in Table 4 are data not used during the training stage ($W_{water}=8 \mathrm{cm}$, T = 40 °C). This table displays the predictions of 90 datasets per sample, each with a final classification. It is obvious that with more correct predictions, water’s final classification will be guaranteed. It is also worth noting that a similar prediction for salty water is observed.

The results presented in Table 5 show the model prediction on the unfamiliar data input which is the key point that describes the model accuracy. In this table, the classification is based on the incident angle ${\theta }_i$ (°) range, considering 90 samples of data. The results show that there are more correct prediction samples than incorrect prediction samples, resulting in a correct overall water sample classification. In combination with Table 4, the overall model results are adaptable. The error parameters shown in Table 4 are based on the training stage with 3054 inputs, from which 70% are used in the training stage and 30% are used to test and calculate the given errors plus an additional 10 inputs used for MLP model calibrations.

This research is a proof of concept of the proposed sensor design. It consists of a new method of water classification combining optics concepts with the machine learning model. Different simulations using COMSOL have been performed, but no prototype has been developed at this time. The obtained COMSOL simulation results have been validated by comparing them to values obtained from experimental work and to analytical equations. Results showed a good agreement.

5. Conclusions

We demonstrated a novel design concept for a laser-based sensor that can detect the nature of water, pure or salty water, under different temperature conditions, without affecting the chemical properties of the water sample. The system combines machine learning and optics-laser concepts. The data set was generated using COMSOL Multiphysics and was used to train the MLP model. Simulation results show that the model prediction is acceptable with an MSE of 0.155 and $R^2$ of 0.844. The proposed method uses low-cost and biochemical-free technology with possible Internet of things (IoT) applications. The designed sensor can pave the way for the development of a multi-parameter sensor and prototyping demonstration for a wide range of applications in water pollution and environmental monitoring, among other future applications.