Development of hybrid extreme learning machine based chemo-metrics for precise quantitative analysis of LIBS spectra using internal reference pre-processing method

Highlights: • Development of extreme learning machine for quantitative analysis of LIBS spectra. • Development of homogeniously hybridized ELM for performance improvement. • Enhancement of ELM performance using internal reference preprocessing method. • Enhancement of HELM performance using internal reference preprocessing method. - Abstract: Laser induced breakdown spectroscopy (LIBS) is a versatile spectroscopic technique that requires little or no sample preparation and capable of simultaneous elemental sample analysis. Quantitative analysis of its spectra has been a major challenge due to self-absorption of the emitted radiation during plasma cooling and inadequate description of non-linear complex interactions taking place in the laser induced plasma. This work presents a novel chemo-metric tool, extreme learning machine (ELM) and its hybrid HHELM (homogenously hybridized ELM), for the first time in modeling the complex interactions of laser induced plasma and quantification of LIBS spectra. Internal reference preprocessing (IRP) method is also proposed as a novel method of enhancing the performance of ELM based chemo-metrics. Since the proposed chemo-metrics (ELM and HHELM) determine their input weights as well as their hidden biases in a random manner, ELM and HHELM are respectively hybridized with gravitational search algorithm (GSA) for optimization of the number of hidden neurons. Effect of IRP, obtained by normalizing the emission spectra intensities with the emission intensity that has highest upper level excitation energy and lowest transition probability, on the performance of the proposed GSA-ELM and GSA-HHELM chemo-metrics is investigated. The proposed models are implemented using spectra of seven bronze standard samples. Chemo-metrics with IRP (GSA-ELM-IRP and GSA-HHELM-IRP) show better generalization performance than those without IRP (GSA-ELM-WIRP and GSA-HHELM-WIRP) while GSA-HHELM based chemo-metrics perform better than their counterparts. The outstanding performance demonstrated by the proposed chemo-metrics and their self-absorption correction ability would definitely widen the applicability of LIBS and improve its precision for the quantitative analysis.