## 2 State of the Art
In the case of accurate NOx emissions prediction tool development (a soft sensor), the overall performance of the ventilation system can be optimized and the working atmosphere improved in the underground mine. Due to the characteristics of NOx and its negative effects on human health, a lot of research is being conducted to improve occupational safety by reducing emissions. Currently, many researchers are working to develop an innovative method to control and predict dangerous gases from diesel engine emissions in underground mines [41; 42]. To predict the concentration of dangerous gases in underground mines, air monitoring systems can be installed to continuously monitor the concentrations of various gases in the mine atmosphere. Real-time monitoring of gas concentrations can help to identify potential hazards and enable mine operators to take appropriate measures to control the release of dangerous gases [43; 44; 45]. In addition, mathematical models can be developed to predict the concentration of dangerous gases in the mine atmosphere. These models take into account various factors such as ventilation rates, engine emissions, and the physical characteristics of the mine and can help mine operators anticipate dangerous levels of gases and take appropriate measures to mitigate risks [46]. The operation of LHD vehicles is characterized by reverse motion with frequent changes from acceleration to deceleration and repeating cycles, as well as quick transitions from one level of engine load to another [47]. Although the powertrain of these vehicles usually contains a hydraulic torque converter, which reduces torque peaks [48] and smooths torque demand to the engine, there is a big challenge to meet the environmental legislation because of inertia in the flow rate and temperature in exhaust gas recirculation (EGR) systems [49]. To tackle this problem, different models for NOx prediction have been developed and tested both in the lab and real conditions. A simplified physics-based model of the engine is proposed in [50] to predict NOx emissions by narrow-range inputs. However, fuel combustion in diesel engines is a significantly nonlinear process. Physics-based models cannot account for all influencing parameters due to certain assumptions and simplifications. Therefore, data-driven approaches are also widely used in this domain. The Hammerstein-Wiener model is applied in [51] but for a small region of operation parameters. In work [52], NOx emissions from a diesel engine are modelled with a nonlinear autoregressive with exogenous input (NARX) model. Experimental results show that NOx emissions can be estimated with a reduced set of regressors in order to be more stable and robust. In [53], the authors proposed a combined grey-box modelling approach with numerical identification of static maps, while the main factors are accounted for by physical assumptions. This model showed a wide range of validity and high accuracy, but the fitting performance in highly dynamic conditions is insufficient. To capture memory effects, Volterra polynomials were employed in [54] for identification of nonlinear models of diesel engine emissions. An increasing number of inputs and the degree of polynomials increases the set of estimated parameters and makes this approach difficult for practical application. In work [55], the authors give a model for NOx and soot emissions in the form of local linear regression models where the parameters are represented in tables. Then, using the \(\beta\)-spline function, they find the parameters of a globally optimal model by solving a linear least-squares problem. However, this work is evaluated only for steady-state engine operations. The authors of work [56] estimated NOx emissions of a heavy-duty diesel engine with engine speed and pressure measurements. Principal component analysis (PCA) and L2 regularization techniques are used to derive a simple and reliable estimator.