## 1 Introduction  
As one of the most widely used energy sources, coal has been known as \"black gold\" and \"industrial food\" for a long time. Although the global environmental degradation made the demand to reduce CO2 emissions from fossil fuel combustion more and more urgent, coal still takes up a prominent role in global energy systems, and the switching from a traditional energy system to a renewable one requires a long time and every government's effort in the world. At present, the practical way to reduce CO2 emission is improving the combustion efficiency of boilers in power stations and other industrial plants. The properties of coal, such as carbon content, ash content, volatile matter, and calorific value, etc., have a close relationship with the safety and economy of boiler operation. Although the traditional off-line analysis method has high analysis accuracy, it has the shortcomings of tedious sample pretreatment, complex analysis procedure, long analysis time and the poor timeliness of the detection results, which is not conducive to the real-time control and optimization of the boiler combustion. Low combustion efficiency of the boiler leads to the increase in cost of power generation and delayed guidance of the boiler unit, resulting in the energy waste. Therefore, the demand for the development of rapid detection technology for on-site coal analysis is urgent to build an adaptation to the combustion instability and parameter fluctuation caused by complex coal quality. The routine coal quality analysis methods in a coal-fired power plant are based on national standards of coal quality analysis, such as GB/T 213-2008 [1], GB/T 214-2007 [2] and GB/T 30732-2014 [3], which require a long time and tedious procedure to obtain the value of ash, volatile and calorific value for a single sample. The lag in test results makes it impossible to guarantee real-time coal quality control and boiler efficiency adjustment. Laser-induced breakdown spectroscopy (LIBS) [4] is a rapid spectral detection technology developed rapidly in recent years, which has the advantages of small sample demand, simple sample preparation, simultaneous measurement of multiple elements, and safety [5]. At present, it has been widely used in industrial analysis [6; 7], environmental monitoring [8], medical analysis [9], agriculture [10], etc., and its application potential in the rapid detection of coal quality has been widely recognized. The working principle of LIBS follows: a high-energy pulsed laser strikes the substance to be measured, causing high temperature and high-density plasma formed on the sample surface. The laser plasma radiates photons of a specific frequency that come from the characteristic spectral lines of elements that existed in the coal constituent, whose frequency and intensity contain the information of element type and concentration of the analyzed object. The spectral data coupled with a variety of chemometrics algorithms can realize the qualitative and quantitative analysis of the sample. In industrial production, the ash content, the volatile matter, and the calorific value of coal are directly related to the pricing of coal, the efficiency of power generation and the slagging of boilers. Therefore, the rapid detection of these three indicators is the most concerned issue in on-site detection. Coal ash content is mainly composed of minerals, usually in the form of oxides, such as Al\({}_{2}\)O\({}_{3}\), SiO\({}_{2}\), Na\({}_{2}\)O, K\({}_{2}\)O, CaO, MgO and Fe\({}_{2}\)O\({}_{3}\). The volatile matter of coal is mainly from water, carbon, hydrogen oxides, hydrocarbons, and some easily ionized mineral decomposition, like Si, Al, Ca, Fe, Mg, etc. Calorific value is closely related to the concentration of elements releasing heat during coal combustion, especially C, H, O, N and other elements. All in all, these three indicators are all related to the elemental constituent of coal.