Deep Learning Neural Network (DNN) Coupled Laser Induced Breakdown Spectroscopy for Quantitative Analysis of Copper Alloys

Conventional Laser Induced Breakdown Spectroscopy (LIBS) quantitative analysis, employing both calibration and calibration-free techniques, is challenged by spectral overlapping, self-absorption, and spectral broadening effects, leading to decreased accuracy. Recently, integration of machine learning (ML) algorithms with LIBS has been increasingly employed to tackle these challenges. This article explores the augmentation of LIBS with deep learning neural networks (DNN) to enhance accuracy of quantitative analysis of multi-elemental copper alloys. Sufficient training data was acquired by simulating optical emission spectra for bronze (Cu-Sn) and admiralty brass (Cu-Zn-Sn) alloys under standard laser produced plasmas conditions, encompassing different alloy concentrations, electron temperatures, and densities. We designed a regularized DNN structure, fine-tuned using a validation dataset to optimize quantitative results. The model’s accuracy was assessed with test dataset. The quantitative results demonstrated reduced loss as training spectra increased from 500 to 5000 for both alloys. The decline in mean squared error, from 2.793×10−3 to 4.283×10−5 for bronze and from 3.245×10−2 to 5.598×10−4 for admiralty brass alloys, as training data increased from 500 to 5000, underscores the proposed DNN model’s potential for metallurgical alloy quantification.


Introduction
Laser-Induced Breakdown Spectroscopy (LIBS) was swiftly introduced and suggested as a powerful analytical tool shortly after the advent of laser technology in 1960.LIBS functions by directing an intense pulsed laser beam onto a sample's surface, initiating material breakdown and generating microplasma [1].The resulting emission lines signify specific atomic, ionic, or molecular transitions, uniquely identifying and characterizing the sample's composition.
LIBS quantitative analysis can be approached through two primary methods: the standard calibration approach and the calibration-free methods [1][2][3].The most commonly used method involves constructing a calibration curve, which establishes a link between integrated line intensity and known concentrations, enabling the determination of unknown concentrations [1].The calibration-free Laser Induced Breakdown Spectroscopy (CF-LIBS) as an alternative method, is based on a physical model assuming Local Thermodynamic Equilibrium (LTE) and utilizes intensities of lines to initially estimate plasma parameters, which in turn facilitates the determination of chemical compositions [2,3].CF-LIBS depends upon the intensity of emitted spectral lines, and any deviation in this intensity leads to errors in the estimations of analyte concentrations.In most practical situations, the spectral line intensity exhibits fluctuations departing from the actual value, predominantly due to self-absorption, detector 1300 (2024) 012006 IOP Publishing doi:10.1088/1757-899X/1300/1/012006 2 inefficiencies, and variations in laser pulse energy.Consequently, the accuracy of CF-LIBS is often not up to the expectation.
The above-mentioned drawbacks can be minimized by using machine learning (ML) methods that consider the complete measured spectrum as input.Recently, there has been widespread use of these ML techniques to speed up both the qualitative and quantitative analysis of LIBS spectra [4][5][6][7][8].The utilization of these models, coupled with feature engineering techniques has demonstrated remarkable proficiency in precisely identifying materials of comparable chemical compositions.Sun et al. [4] developed a multivariate calibration model using machine learning algorithms and used SelectKBest algorithm for feature selection, aiming to determine trace elements in soil samples.Tian et al. [5] proposed a non-linear support vector machine (SVM) model for the phosphorus determination in seafood.Zhang et al. [6] determined the minor metal elements like Mn, Cr, and Ni in steel by employing multivariate models rooted in back-propagation neural networks (BPNN).Additional regression algorithms, such as random forest regression (RFR), have seen extensive utilization as well [7,8].
In all these examples, machine learning techniques require manual feature selection as part of the regression process.Deep learning, as a subfield within machine learning, has the inherent ability to automatically extract vital feature representations, streamlining machine learning workflows considerably, and it holds the potential to provide a more accurate and efficient approach.Eynde et al. [9] introduced deep learning regression technique to estimate the concentrations of alloying elements in aluminium reference samples and post-consumer scrap pieces.It is noteworthy that deep learning is an emerging procedure for spectral analysis, offering the advantage of avoiding self-absorption and matrix effects, and although there is relatively less work reported in this area, it holds promise for advancing spectral analysis methodologies [9].
LIBS is a key tool for alloy analysis in quality control.Copper-tin-zinc alloys are versatile materials used across industries, demanding precise element quantification for material quality assessment.In this study, a deep learning neural network (DNN) model was designed and employed in combination with LIBS for the efficient quantitative analysis of multielemental copper-tin-zinc alloys for metallurgical purposes.The methodology described in this paper marks a vital starting point for forthcoming endeavors aimed at examining LIBS experimental data.

Deep Learning Neural Network Approach
As an initial step, we simulated optical emission spectra (OES) of bronze and admiralty brass alloys at typical laser produced plasma (LPP) conditions to acquire a sufficient volume of data for training the models.The process of simulating the optical emission spectrum consists of four distinct stages.Initially, we compute the concentration of each ionization state within the plasma, then apply the Boltzmann distribution law to determine the intensity of individual emission lines.Following this, we gave gaussian broadening to each line, and finally, graphed the spectrum based on this broadening [10].A comprehensive explanation of these various stages in the simulation can be found in our prior research work [11].

Dataset Preparation
Using simulation approach, we generated datasets that exhibited characteristics aligned with the underlying assumptions: i. 500 and 5000 normalised spectral datasets were generated separately for both bronze and admiralty brass alloys.ii.The spectral range was 200-1100 nm and resolution (resolution refers to the ability to distinguish and separate closely spaced spectral lines in a spectrum) used was 0.7 nm.iii.To determine the elemental composition for each bronze spectrum, we initiated the process by selecting a random uniform value for the copper (Cu) concentration ranging from 0% to 100%.Subsequently, the tin (Sn) concentration was adjusted to complete the total concentrations to 100%.The same method was applied to generate datasets for admiralty brass alloy.iv.The electron temperature (Te) was then selected randomly within the range of 0.5 to 1.5 eV, and the electron number density (Ne) was chosen between 1.0×10 16 and 1.0×10 18 cm -3 .These Te and Ne values are typical for laser induced plasmas.

Data Preprocessing
As part of the preprocessing step, the input feature (intensities) is scaled to fall within the [0,1] range, ensuring that all emission lines are placed on a uniform intensity scale.With the goal in mind, we adjust each input value using the max-min formula as described in equation (1), where I represent the original intensity,   is the normalized intensity, and   and   denote the highest and lowest possible values of emission intensity, respectively.

Deep Learning Neural Network Model Development
Here, we introduced a deep learning neural network (DNN) approach for dealing with the problem of finding out the composition of the elements present in the simulated spectra of Bronze (Cu-Sn) and Admiralty brass (Cu-Zn-Sn) alloys used in metallurgical field without using the time-consuming calibration curve approach.Scikit-learn, a python library for machine learning available as open-source and Keras, a deep learning framework, make the process of data analysis more accessible and efficient [12].A deep neural network involves two key stages: firstly, the feed-forward.Secondly, there is the backpropagation step, where the model parameters are updated by assessing the disparity between the target and predicted values.The proposed deep feed-forward neural network model consists of two hidden layers, with 128 and 180 hidden neurons in each hidden layer for bronze and admiralty brass alloys respectively, to implement the fitting model.The deep neural network has the spectral lines as input and two and three outputs (elements and their corresponding concentrations as output) for bronze and admiralty brass alloys respectively.As outlined in table 1, the activation functions for hidden neurons and output neurons are the ReLU function (Rectified Linear Unit) and the Softmax function, respectively.The proposed DNN model (figure 1) was used for training 500 and 5000 simulated spectra of both bronze and admiralty brass alloys separately for quantitative analysis.The network model that was created is trained using 60% of the available data, validated with 20%, and tested with the remaining 20%.Transfer Functions ReLU (Hidden Layers), Softmax (Output Layer)

Results and Discussion
The proposed DNN model was used for predicting the composition of simulated bronze and admiralty brass alloy samples.The DNN data are represented as a matrix during the input process, as depicted in figure 1.The input tensor undergoes fully connected dense layers, and activation functions to generate prediction results.The model parameters are subsequently fine-tuned iteratively using stochastic gradient descent in the backpropagation step.While constructing the network model, we ascertain the most effective regression by adjusting DNN parameters and structure and evaluating model performance on the verification dataset.In each iteration, we evaluated the network's performance by computing the Mean Square Error (MSE) on the test dataset following the formula provided in equation (2).
where   and  0 (vectors) represent the desired and estimated concentration values for spectrum i and N is the number of test spectra included in the evaluation.As the training dataset size grew from 500 to 5000 spectra, the mean square error value for bronze alloy decreased from 2.793×10 −3 to 4.283×10 −5 .Likewise, the MSE for admiralty brass exhibited a similar trend, decreasing from 3.245×10 −2 to 5.598×10 −4 as the training dataset expanded from 500 to 5000 spectra.As the spectral data used for training increased, the proposed deep neural network model, tend to exhibit improved accuracy and robustness in the alloy quantification.This observation strongly indicates an enhanced predictive capacity of the proposed model for determining the elemental composition within bronze and admiralty brass alloys as the training dataset size increases.The accuracy and loss rate of the proposed DNN model tend to converge after 1000 training epochs of 500 and 5000 number of spectra which clearly indicates the increase in the accuracy of the proposed model for efficient quantitative analysis of bronze and admiralty brass alloy samples.The prediction (predicted wt% values) versus ground truth (true wt% values) and loss function graphs corresponding to 500 and 5000 number of spectra for bronze and admiralty brass alloys respectively, are depicted in figure 2.
The findings demonstrate the robustness and benefits of utilizing DNN models.Clearly, the proposed DNN model demonstrates a strong ability in accurately determining the elemental composition of simulated Cu-Zn-Sn alloys.Although the models did well with simulated data, future research should aim to create DNN models using real experimental data.

Conclusion
We illustrated an effective approach that leverages a combination of laser-induced breakdown spectroscopy and deep neural networks for efficient multi-elemental quantitative analysis of alloys used in metallurgical purposes.This approach is utilized to ascertain the composition of copper alloys by analysing simulated datasets generated through computational methods.The proposed deep neural network model is a feed-forward deep neural network with spectral line data as input neurons, two hidden layers, and two and three output neurons for bronze and admiralty brass alloys respectively.To utilize network for alloy composition analysis, we used 60% of the simulated spectra for training the neural network, 20% for validation and the remaining 20% for testing.The decrease in MSE values for both the alloys, as the number of alloy spectra used for training increased from 500 to 5000 clearly demonstrates that regression accuracy improves with a larger dataset.This indicates that the proposed DNN model is highly effective in determining the composition of alloys employed in the metallurgical industry.

Figure 1 .
Figure 1.Schematic representation of the deep learning neural network model (DNN) coupled LIBS for quantitative analysis of bronze alloy.

Figure 2 .
Figure 2. True wt% values vs. Predicted wt% values for 500 and 5000 spectra of bronze alloy (a,b) and admiralty brass alloy (e,f) respectively.The loss function curve of learning process for 500 and 5000 spectra of bronze alloy (c,d) and admiralty brass alloy (g,h) respectively.

Table 1 .
Parameters used for deep neural network model.