Application of an artificial neural network (ANN) simulator to increase the operational efficiency of a roadheader

Abstract

Mining machine simulators involve an IT system based on dedicated software to represent a specific piece of hardware in the working environment of operators, service technicians, and people supervising the operation. In this study, a proprietary roadheader simulator was used to simulate the machine’s operating parameters and its dynamic behavior during the mining process in changing conditions. The information collected from the simulation was subsequently fed to a model and analyzed using artificial neural networks (ANN) to enable learning and predictive features regarding the simulated roadheader. This article presents the findings that led to the development of an ANN structure to determine the values of 15 parameters based on four input signals. The ANN models are multilayer perceptron (MLP) networks with one hidden layer. The ANN learning process was carried out using the backpropagation method based on a dataset consisting of 1029 samples/cases generated by computer simulation. Experimentally verified mathematical models were used to prepare the data, which was subsequently divided into training, testing, and validation sets. Three network variants were considered, for which the effectiveness of predicting the values of targeted parameters was assessed. The test set evaluation was carried out on a separate data set. The results indicated that neural networks with a single neuron in the output layer yield the best results. However, the results of the studies do not offer a clear statement as to which of the analyzed ANN structures yields the best results for all the parameters considered. The simulator-generated parameters were compared with the operating parameters of a virtually controlled roadheader in a known operational condition for verification, and also compared with the measured parameters while operating an actual roadheader manually by the operator. The developed predictive model of the roadheader’s operating parameters, which was implemented in the {RH-Sim} simulator, allows for tracking the machine condition during the implementation of various automatic control strategies to ensure high efficiency and minimizing its dynamic load. This approach offers new opportunities for the development of roadheader automation in construction and mining applications.

Supplementary Information

The online version contains supplementary material available at 10.1038/s41598-025-33449-x.

Introduction

Equipment and vehicle simulators are devices that combine an IT system with hardware (operator’s cabin), which is a human–machine interface (HMI) that reproduces the actual working conditions for machine operators. The simulators operate based on virtual reality (VR) or augmented reality (AR). These systems involve advanced computer software to reproduce the actual behavior of the simulated machine and the operating environment on a computer-generated virtual platform. Advanced algorithms implemented in the simulator software ensure high situational realism, among others, thanks to the use of high-performance graphical engines supporting spatial graphics. The virtual scene is usually displayed on large- projection screens – flat or spatial (providing depth), in VR goggles, or on sets of LCD monitors reproducing the view from the windows of the operator’s cabin.

An important functional feature of the simulator software is the ability to simulate the actual behavior of a machine during operation, predict the actual load status of its drives, the dynamic load of key structural nodes, and the machine’s operating parameters, displayed on indicators located on the control panel in the operator’s cabin. Many simulators also allow the operator’s cabin to move during the simulated operation of the machine or vehicle. Stimuli acting on human vision, hearing, and balance receptors provide the operator with a sense of great realism in the operation of the virtual machine he/she operates. This effect is, even more, intensified when active suspension of the simulator’s operator cabin or the operator’s seat itself is used, ensuring the possibility of limited movement and vibrations of the cabin accompanying the operation of the real machine. Such possibilities are provided, among others, by robots with parallel kinematics, for example, in the form of the Gough-Stewart platform. Such solutions are commonly used in simulators of aircraft¹, floating vessels³, vehicles^4,5, human locomotion functions⁶, mining machines⁷, and even ground behavior during earthquakes⁸.

The values of operating parameters during the simulated implementation of the work process, visualized on indicators and monitors, as in a real machine, are determined using mathematical models describing the kinematics, and often also the dynamics, of the simulated object. During the numerical solution of these models, the machine’s response to input signals from the operator station given by the operator, in the case of manual control by the industrial controller or semi-automatic or automatic control, is collected. The results of numerical calculations performed during simulated machine operation may also constitute input data for controlling the movement of the robot positioning the operator’s cabin. However, this requires adaptive control in the task space, adjusted to changing input signals⁹. Moving the robot according to the predicted motion of the simulated machine requires solving inverse kinematics and inverse dynamics in real-time. Especially in the field of dynamics, this is a difficult task due to the complexity of the mathematical models⁷.

When control is in manual mode, the operator provides control signals by deflecting the control sticks and pedals, activating and deactivating various machine functions using buttons, or entering numerical values from the keyboard. On this basis, the simulator software develops the response of the simulated unit, which is visualized in its virtual environment and is possibly used to control the platform positioning of the operator station.

Machine simulators are mainly used in the staff training process. Exercises in simulators (trainers) are an important element of the education and professional development of operators and people involved in the technical maintenance of machines, civil and military vehicles, as well as robots and manipulators (teleoperators) used to remotely perform precise or dangerous activities by humans. They enable operators to acquire appropriate habits during routine activities, as well as in accidents and emergencies.

Working machines used in various industries, including mining and tunnel construction, are characterized by increasingly complex construction, often at high purchase and operating costs. The need to use simulators to train operators of these machines and services has long been recognized^10,11. Manufacturers of mining machines and mining companies themselves also see the need to use simulators in the process of training mining crews. Hence, a wide range of different solutions in this area have been adapted to the characteristics of machines produced by individual manufacturers¹².

In the virtual environment, the control and operation of mining equipment, as well as their service and repair procedures, are practiced. In the progressive robotization of mining, semi-autonomous robots, partly controlled by operators, are increasingly used. Examples of such machines are autonomous mining loaders and drilling rigs. Loaders move independently through mine openings between stopes, faces, and unloading points. However, the process of extracting fragmented rock from the mine face is carried out manually by a remote operator^13,14, although automation is also being sought using artificial intelligence algorithms¹⁵. In turn, in the case of drilling rigs, the operator remotely controls and usually manually sets drilling parameters¹⁶. Controlling such machines from a long distance requires high skills from the operators because the only source of information about the controlled machine is the image from the cameras installed on the unit and readings from the sensors.

In addition to the trainer function, large-scale real-time simulators of working machines are also used in scientific research to support the reasoning process and in diagnostics, to simulate various machine operating states. Therefore, they help analyze, for example, the causes of failures and other events involved with operating this equipment, including accidents. These simulations make it possible to study the behavior of the machine during the implementation of various control strategies¹⁷, which is of key importance from the point of view of automation of the work process and robotization. The possibility of recording the operating parameters of these machines on a virtual platform and assessing their behavior during the work process is particularly important when the machine is subject to stochastic disturbances. Operators encounter such situations in mining and tunneling, especially in the case of rock-cutting machines. The geological structure of the rock mass in which mine openings, roadways, and tunnels are excavated is usually poorly understood and highly variable. Geological disturbances resulting from the rock formation process and the heterogeneity of the rock mass significantly affect the operation of mining machines, as well as their efficiency and reliability. This translates into impacts on costs of mining and production rates, and completion time of the projects. Simulation of the rock excavation process for a given geological and mining conditions makes it possible to select the technology and operating parameters of the mining equipment to obtain the best operating conditions and minimum cost. An example of a solution that provides such possibilities is the research simulator of a boom-type roadheader {RH-Sim} developed at the Department of Mining Mechanization and Robotization of the Silesian University of Technology in Gliwice (Poland) in cooperation with the Colorado School of Mines, Mining Engineering Department (USA). Roadheaders are commonly used for excavating roadways in underground mines, especially coal mines, and in tunnel and underground construction.

This article focuses on predicting the operating parameters of a roadheader during a simulated mining cycle at the heading of a roadway or tunnel. In the earlier development phase of the simulator, approximate dynamic characteristics recorded in the operating conditions of the roadheader were used, which provided only limited possibilities for predicting the parameters of interest. The results of mathematical models describing the kinematics and dynamics of the roadheader in the simulator were not reasonable for manually controlling the roadheader on the virtual platform. The time-consuming numerical calculations (generating breakout graphics and numerical integration of motion equations) could not produce realistic estimates in real-time conditions of the unit, especially for changing parameters characterizing the conditions of the mining process and control signals. To study the machine’s behavior during the implementation of various manual, semi-automatic, and automatic control strategies, it was necessary to use mechanisms enabling real-time determination of the machine’s response (the roadheader’s operating parameters and dynamic load). For this reason, an artificial neural network was selected to predict the operating parameters.

Artificial neural networks (ANN) are a subcategory of artificial intelligence^18,19. Neural networks are widely used due to their ability to easily adapt and solve various computational problems in science and technology. They constitute a universal approximation system mapping multidimensional datasets. They can also generalize and adapt to changing conditions²⁰. They are used, among others, to solve the problem of predicting the values of output parameters based on input data^21–23.

ANN is also used to solve prediction and optimization problems in various mining and civil engineering applications. One such area is the blasting technique that, apart from mechanical cutting, is widely used in mining and tunnel construction in rock. Previous work²⁴ presents the possibility of using an ANN to design blasting works to increase the efficiency of using the energy of detonation of explosives, improve safety, and minimize the impact on the environment. ANNs are used to search for and estimate deposit resources in mining geophysics, rock mechanics, and processing of minerals and raw materials^25,26. The mathematical tools discussed here have been used in mining for many years, and also for the following:

• Selection of deposit exploitation methods^27,28,

• Process optimization^2,29,

• Selection of equipment, and prediction of its durability and work efficiency³⁰,

• Analyzes in the field of miners’ occupational health and safety^31,32.

ANN can also be an element of automatic control systems for mining machines such as roadheaders, which is explored in this and similar studies^33,34.

This article presents the results of the study on artificial neural networks with various configurations to provide the ability to predict the operating parameters of the roadheader based on the ground conditions and the operator’s control commands. The best results obtained from the ANN algorithms are implemented in the roadheader simulator {RH-Sim}.

Brief characteristics of the roadheader research simulator {RH-Sim}

A detailed description of the simulator {RH-Sim} and its functional properties can be found in ref.³⁵. The {RH-Sim} simulator consists of a hardware part – simulating the roadheader operator console and the work environment – and dedicated computer software (Fig. 1). The main program responsible for generating 3D graphics and managing the simulation process of the roadheader’s operation is installed on workstation #1 (central unit) – Fig. S1 (in the appendix). The software installed on workstation #2 is responsible for managing the operator panel, while data collection and processing are carried out via workstation #3 using dedicated software. These computers communicate with each other using the TCP/IP protocol in the client–server architecture. The operator station is equipped with a seat with two joysticks to control the driving mechanism and the movement of the roadheader boom on the virtual stage. The operator station also includes an operator panel with buttons for initiating individual functions of the roadheader, including switching on its drives, under the control logic used in a real machine. The operator panel also includes a set of virtual indicators to visualize the roadheader’s operating status, dynamic load, and operating parameters. Similar to many modern roadheaders, the operator panel displays the outline of the roadway or tunnel being excavated with the geological structure of the rock mass in which the roadway or tunnel is located. In the example shown, the rock mass is composed of three layers: a coal seam, a layer of roof rocks, and a layer of floor rocks (Fig. S2). These layers are inclined transversely to the floor of the excavation, which results in the workability of the rocks changing as the cutter heads move. The cutter head is displayed against the background of the excavation outline in a place corresponding to the current position on the surface of the virtual face. The simulator can also control the operation of a virtual roadheader from a radio console. A remote control is a solution often used in currently manufactured roadheaders.

Fig. 1.

Research simulator of a roadheader {RH-Sim}: (a) general view, (b) view from the operator’s seat, and (c) during manual control of the roadheader on a virtual scene.

To generate 3D graphics of the face of an excavated roadway or tunnel, the Autodesk Inventor Professional 2023 graphics engine (OLE server) is used. In this environment, a model of the R-130 roadheader (manufactured by Famur S.A.) supported by haulage equipment, the rock mass surrounding the excavation being mined, elements of the roadway support, and other equipment at the heading (including a ventilation duct) were constructed. The virtual model in the Autodesk Inventor environment is controlled from the main program (OLE client), thanks to the Inventor software providing access to its functions and parameters through external applications (API). The graphics of cuts made with the cutter head of a roadheader are processed using a script written in the Microsoft Visual Basic for Applications (VBA) environment. In this script, for the current position of the cutter head and the shape of the face surface, the volume of the “mined” rock is determined, constituting one of the input signals based on which the prediction of the roadheader’s operating parameters and its dynamic loading is made.

Prediction of roadheader’s operating parameters

Formulation of the research problem

Real-time prediction of the operating parameters of the roadheader and its dynamic load can be made by an artificial neural network. The structure and parameters of the network are intended to enable the determination of the values of fifteen parameters (i.e., the output signals) visualized on the operator panel in the roadheader simulator (Fig. 2). These include:

1. Parameters characterizing the load on the roadheader drive responsible for the mining process, i.e.:

2. Torque on the motor shaft in the drive of the cutter heads (T_M),

3. The rotational speed of the engine rotor (RPM),

4. Power (P),

5. Load on the boom arcing and lifting actuators (F_SO, F_SP),

6. Vibration acceleration components of the roadheader body (index B), boom (index A), and operator’s seat (index S) (),

7. Parameters characterizing the efficiency of the mining process:

8. Movement speed of cutter heads (v_OW),

9. Instantaneous cutting rate (ICR),

10. Cutting energy consumption (SEC).

Fig. 2.

Schematic diagram of the system for predicting operating parameters and dynamic load of a roadheader in the {RH-Sim} research simulator.

The predictors (input signals) of the neural network use the following parameters (Fig. 2):

• Average uniaxial compressive strength of the rock where the cutting head is currently located (σ_c),

• The average brittleness factor of the mined rock, understood as the ratio of its compressive strength to its tensile strength (κ = UCS/BTS),

• Opening coefficient of the hydraulic valve in the power supply system for the boom swinging cylinders (k_do ∈ <0, 1>) – in the case of proportional control, the maximum boom swinging speed depends on the joystick deflection at the operator station,

• The volume of rock mined by the head in its successive rotations (V).

It was assumed that the prediction of the parameters is averaged per revolution of the cutter heads (and, in the case of vibration acceleration, the RMS values) would be carried out as follows:

• Using a one-way, multilayer perceptron network MLP with one hidden layer (it is assumed that one or many such networks will be used),

• The input layer will be composed of four neurons (four inputs: σ_c, κ, k_do, and V),

• The output layer will be composed of neurons in the number resulting from the assumed number of output signals (from 1 to 12),

• All neurons are activated in a sigmoidal activation function,

• The learning process will be carried out using the backpropagation method based on minimizing the sum of squares of learning errors (MSE).

It should be explained here that, out of the fifteen parameters whose values were included in the prediction, the values of twelve of them are to be determined with the help of the ANN. The values of three parameters, i.e., instantaneous cutting rate (mining efficiency) (ICR), mining power (P), and Specific Energy consumption (SEC), are determined from the following formulas^36–38:

1

2

3

where V denotes the volume of rock per revolution of the cutter head [m³], RPM represents the rotational speed of the motor rotor [r/min], i_C is the total gear ratio of the gearbox in the drive of the cutter heads, and T_M is the torque on the motor shaft in the drive of the cutter heads [Nm].

As can be seen, to determine the values of these parameters, it is sufficient to know the current value of the volume of mined rocks (set value), the torque on the drive motor shaft, and the rotational speed of its rotor (predicted values using a neural network).

Current values of the input parameters of the artificial neural network are available in the operating environment of the {RH-Sim} simulator. Information on the real-time value of the hydraulic valve opening (k_do) is read from the operator station and control panel. The current values of the strength parameters of the mined rock and the volume of the mined rock are obtained from the graphic environment, in which the 3D visualization of the roadheader operation is performed.

Since in the real operating conditions of boom-type roadheaders, the cross-section of the excavated headings is composed of rock layers with different (often very different) mechanical properties, the values of the strength parameters σ_c and κ, taken into account at the stage of predicting the roadheader’s operating parameters, are determined as weighted averages, where the weight is the volume fraction rocks with given mechanical parameters in the total volume of rock mined by mining heads in a given revolution, i.e.,

4

5

where σ_{c Roof}, σ_{c Rock}, and σ_{c Floor} are the uniaxial compressive strength of the formations (i.e., roof rocks, mineral resource (e.g., coal seam), and floor rocks, respectively, while κ_Roof, κ_Rock, and κ_Floor) are the corresponding brittleness factors, and (i.e., V_Roof, V_Rock, and V_Floor) V values are the corresponding volume of mined rock.

Otherwise, the values of the mechanical parameters of the rock being mined are taken.

Research method

Figure S3 presents the algorithm for the research procedure. The process of selecting the ANN structure and parameters began with generating data, a set of parameter values characterizing the mining process under various conditions, and the dynamic state of the roadheader. This was accomplished through computer simulations using the simulation system SIMCUT. Considering the widest possible range of parameter values describing the mechanical properties of the mined rocks and the operating parameters of the roadheader allowed us to obtain a large dataset. From this dataset, after normalization, training, and validation test data were selected, and various combinations of input data values resulting from the scope of application of the roadheader under consideration were considered.

An ANN consisting of one input layer, a single hidden layer, and an output layer was built. Three variants were considered, differing in the number of neurons in the output layer (Variant I, II, and III). In each variant, ANNs with varying numbers of neurons in the hidden layer were tested. In each case, the ANN was trained, validated, and tested. Based on the adopted evaluation criteria, the best-performing network was selected for each variant. The final selection of the ANN structure and parameters was based on a comparison of the values of the prediction quality index W, introduced for this purpose.

In the final phase of the study, the selected ANNs were implemented in the simulator software {RH-Sim}, and tests were conducted to determine their effectiveness in predicting the desired operating parameters of the roadheader. These results were compared with the values recorded on the actual roadheader at the experimental stand in the laboratory.

Computer simulation-generated dataset for ANN analysis

To carry out the process of training a neural network with an assumed set of input parameters, a set of training data was developed. The input data and results of computer simulations of the dynamics of a boom-type roadheader were compiled in this dataset. Extensive simulation studies were carried out using mathematical models implemented in the SIMCUT simulation system. These models were verified experimentally based on dynamic characteristics recorded during actual mining with an R-130 roadheader on a test stand in laboratory conditions (Fig. 3a). The dynamic load and vibrations were recorded on the full-scale laboratory roadheader during the mining of a cemented-sand block with a layered structure. For this purpose, the R-130 roadheader was equipped with nearly 70 measurement sensors connected to the National Instruments system for recording, archiving, and processing measurement data. The measurement program was written in the LabVIEW software. While making cuts, the measured parameters were recorded parallel to the floor and averaged over 1/3 of the period of rotation of the cutter heads (this is because the picks were arranged on the cutter head along three spirals). At the stage of processing measurement data, the values of the roadheader’s operating parameters, including power, instantaneous cutting rate, and specific energy, were determined.

Fig. 3.

Experimental stand in the laboratory (a), physical model of (b) the drive system⁴¹ and (c) the body of the R-130 roadheader⁴².

In the next stage of the investigations, to predict the values of the operating parameters of the roadheader, based on the developed ANN, the simulation results of the mining process were compared with the measurements made at the experimental station.

Due to the high degree of complexity of mathematical models, the roadheader dynamics simulation system has a distributed form. It ensures interoperability of the developed simulation models in the MATLAB/Simulink and RAD Studio software, solving mathematical models of separate subsystems of the roadheader, the model of the rock mining process, and the model of the cutter head movement control system.

SIMCUT roadheader simulation system

The SIMCUT simulation system creates several computer modules (programs) enabling numerical simulation³⁹:

• The process of mining the surface of the heading with the transverse cutter heads of a roadheader,

• Dynamics of the converter drive system of cutter heads,

• Dynamics of the roadheader body, which includes hydraulic boom swinging mechanisms,

• Vibrational characteristics of the system as a whole.

The starting point is a simulation of the mining process of the heading face of an excavated tunnel for the given parameters of the mining process and the mechanical properties of the rock layers. Due to the natural conditions of tunnels, the layered structure of the rock mass is considered at the stage of simulation of the mining process and, consequently, the current position of the cutter heads on the surface of the face. Based on the generated breakout pattern (cut projection), the following parameters are determined in real-time⁴⁰:

• Depth of cuts made with individual picks of the cutter head,

• Variability of rock strength parameters for individual picks,

• Cutting forces acting on individual picks from mining,

• Torque of the cutter head,

• Loads or resultant forces on the boom swinging mechanisms,

• Efficiency, average power demand, and specific energy consumption of mining.

The time characteristics of the mining process determined in this way, with a multi-pick cutter head for the current values of the mining process implementation parameters, constitute vibration in the dynamic model of the cutter head drive and the dynamic model of the roadheader’s body. Due to the feedback occurring between the mining process and the response of the tested object, simulations are run in a loop until the solution converges. In each calculation cycle, the input data of the mining process simulation are corrected, resulting from the behavior of the roadheader drives.

The dynamic characteristics of the cutter head drive are determined by solving (numerical integration) the differential equations of mass motion in the physical model (Fig. 3b). A discrete physical model with 15 degrees of freedom, a converter drive equipped with an electric motor powered by a frequency converter, and a three-stage gear transmission was used⁴¹. As a result of solving the numerical model of the equations of motion, time characteristics are obtained in the form of the angular position and velocities of individual rotating masses, as well as the course of the torque on the drive motor shaft.

The time steps of the dynamic load on the boom swinging actuator mechanisms and the key structural nodes of the roadheader’s body, the reactions at the roadheader support points on the floor, and the vibration acceleration components are determined during the solution of a numerical mathematical model describing the movement of masses in the physical model of the roadheader’s body (Fig. 3c). It is a discrete model with 19 degrees of freedom⁴². Similar to the drive of the cutter head, the equations of motion were derived based on the Lagrange equation of the second type.

Computer simulations

Simulation tests on the dynamics of the roadheader included a wide range of input data corresponding to the use of the R-130 roadheader, for which the operating parameters and dynamic load are predicted in the {RH-Sim} simulator. The input data for the simulation considered the technical characteristics of the roadheader, including the possible speeds of moving the cutter heads and the permissible load of the roadheader’s drives responsible for mining. Table S1 (in the appendix) lists the ranges of parameter values constituting input data for the simulation of the dynamics of the R-130 roadheader. This data included the following groups of parameters:

1. Mechanical properties of mined rocks:

   • Uniaxial compressive strength σ_c,
   • Brittleness factor κ,
2. Cutting process parameters:

   • Depth of cut or sump z,
   • Cut height h,
   • Hydraulic pressure and hence the acting force of the boom swinging cylinders k_do,
3. Location of the cutter heads on the face:

   • Boom angle in the horizontal plane (parallel to the floor) α_H,
   • Boom angle in the vertical plane α_V.

Various combinations of mining process parameters were considered. After eliminating cases that were impossible to implement in practice (for example, overload of drives, jamming or stalling of cutter heads, going over max swing force, reaching the limit for the speed of the boom), the training set contained 1029 data sets (samples) of data. Due to the extensive scope of simulations for the preparation of training data for network training, they were limited to one revolution of the cutter heads at a given boom position. This dataset was used for the subsequent ANN analysis.

ANN structure and to predict the operating parameters of a roadheader

Following the assumptions formulated in Sect. “Prediction of roadheader’s operating parameters” of this paper, the prediction of parameters characterizing the mining process and the dynamics of the roadheader in the {RH-Sim} research simulator was made using a multilayer perceptron network (MLP) with a sigmoidal neuron activation function. To select the structure of the neural network and its parameters, i.e., weights and bias, three approaches (variants) were considered.

First, it was assumed that the values of each target parameter are predicted using a separate neural network with four neurons in the input layer and only one neuron in the output layer. According to the literature⁴³, this is the approach that should provide optimal results, but it requires building as many as twelve separate neural networks. From the point of view of software implementation, this is a cumbersome solution.

In the second variant, the possibility of using two artificial neural networks was considered, separately for two groups of parameters. They were divided in such a way that the first one consisted of parameters characterizing the load of the roadheader drives responsible for mining (T_M, RPM, F_SO, F_SP, v_OW), power P, instantaneous cutting rate ICR, and specific energy consumption SEC (calculated parameters). The second group of parameters characterizes the vibration intensity of the roadheader (). The first neural network consists of an input layer of four neurons and an output layer of five neurons. In turn, the second network will be created by four neurons in the input layer and seven neurons in the output layer.

The third solution assumes the use of one neural network with four neurons in the input layer and twelve neurons in the output layer. If such a network operates correctly and its output was acceptable in the validation process, it will be the most convenient way to solve the formulated problem.

Variant I – use of many neural networks with one output

Research on the structure of the neural network was carried out in MATLAB environment with the Deep Learning Toolbox library, using the solver built into this software. These studies were aimed at selecting the number of neurons in the hidden layer that would provide optimal results in predicting the values of individual parameters. According to Kolmogorov’s theory, a sufficient number of neurons in the hidden layer is expressed by the formula²⁰:

6

where n signifies the number of hidden layer neurons and N denotes the number of input layer neurons.

Another way to determine the initial number of hidden layer neurons is to assume a number equal to the geometric mean number of inputs and outputs²⁰, i.e.,

7

where n represents the number of hidden layer neurons, N is the number of input layer neurons, and M is the number of output layer neurons.

The number of hidden layer neurons pre-calculated from formulas (6) and (7) is 9 and 2, respectively (N = 4 and M = 1). Due to the large discrepancy in the number of hidden layer neurons determined from these formulas, tests were carried out on the effectiveness of predicting the roadheader’s operating parameters and its dynamic load using an artificial neural network with a hidden layer composed of neurons ranging from 2 to 11.

The neural network configuration process consisted of the following stages:

• Normalization of input data and parameters searched for in the training set,

• Conducting the neural network training process,

• Assessment of network performance on the control set.

The learning process was based on a set of samples consisting of various configurations of input parameter values and the response of the roadheader to the mining process with these parameters. This set was subjected to the data normalization process in the range <–1, 1>. It was then divided into the subsets training, validating, and testing in the proportions of 70%, 15%, and 15% of the total population, respectively. The classification of individual samples into the mentioned subsets was undertaken by a randomization algorithm. Since the selection of the composition of the training subset has a significant impact on the result of training the network, the training process was repeated ten times for each of the above-mentioned subsets. The optimal learning result was taken – the smallest value of the minimized mean squared error: min{MSE} (delta rule)⁴⁴.

The initialization of the weights was also performed randomly using the Nguyen-Widrow method. In each repetition of the learning process, the initial values of the weights were drawn anew. Two learning methods were considered in the learning process: Levenberg–Marquardt (LM) optimization (a gradient method combining the features of the steepest descent method and the Gauss–Newton method) and Bayes (BR) with default learning parameters set in the MATLAB solver. In the latter case, the LM optimization process is further extended by minimizing the combination of squared errors and weights to determine the combination that ensures the generalization ability of the network. This process is called Bayesian regularization⁴⁵. The LM learning algorithm is fast, but the BR algorithm grants the network a greater ability to generalize. Network training was carried out using the backpropagation algorithm.

Figure 4 shows an analysis of the training process of an example network for predicting the torque value on the motor shaft in the drive T_M of the cutter heads. As can be seen, the objective function was achieved in the 41st generation (Fig. 4a). Prediction errors dominated in the range from –0.015 to + 0.024 (normalized values) as shown in Fig. 4c. The predicted values are relatively close to the straight line, reflecting a good correlation with the target values (Fig. 4d).

Fig. 4.

Effects of teaching the network for predicting the torque on the motor shaft T_M in the drive of cutter heads: (a) course of the learning process, (b) network training status, (c) prediction error histogram (normalized data), and (d) regression charts: predicted values-expected values for the training set, testing set, and the entire training data population.

The effectiveness of the ANN algorithm was assessed based on the prediction results of individual roadheader operating parameters for the data included in the control set. This set consisted of 10 samples obtained from a computer simulation of the dynamic behavior of a roadheader, for data not previously used in the development of the training set (from the scope given in Table S1). The values of the following prediction quality indicators obtained for the control set were assessed:

• Root mean square error (RMSE) – markers in the form of orange triangles,

• Mean percentage prediction error (MPE) – markers in the form of blue dots,

• Range of prediction error values (R) – markers in the form of whiskers.

Figure 5 shows the values of the above-mentioned indicators for the tested number of neurons in the hidden layer. There is a large variation in the values of the analyzed parameters depending on the number of hidden neurons. The lowest RMSE value was recorded for a network with four hidden neurons (200 Nm), as listed in Tables 1 and 2. The average percentage error MPE was + 18%. Similarly, the R range of 89% is one of the smallest in the considered set of results. For one-third of the control set, the percentage error in torque prediction was within ± 5%. This demonstrates a very good representation of the load on the cutter heads’ drive system under randomly changing operating conditions. In as many as 90% of the control set cases, the percentage error in torque prediction did not exceed 25%. This is an acceptable level, considering the complex nature of excavations in rock with possible variability in properties in mixed face conditions.

Fig. 5.

The influence of the number of neurons in the hidden layer on the effectiveness of the network for predicting the torque on the motor shaft in the drive of cutter heads (Variant I).

Table 1.

Summary of the values of quality indicators for predicting the operating parameters of a roadheader using neural networks (Variant I).

Parameter	RMSE [*]	MPE [%]	R [%]	Parameter	RMSE [m/s2]	MPE [%]	R [%]
TM [Nm]	200	+ 18	89		0.27	−10	60
RPM [r/min]	10.5	+ 0.4	2.2		1.2	−11	105
vOW [m/s]	0.009	−3	13		1.2	+ 16	108
FSO [kN]	30	+ 3	38		1.3	−42	78
FSP [kN]	58	−9	337		1.6	−33	98
P [kW]	31	+ 18	88		1.2	−5	110
ICR [m3/h]	0.2	+ 0.5	2.5		2.2	+ 8	116
SEC [kWh/m3]	4.3	+ 18	88

* – units depending on the type of parameter.

Table 2.

List of the number of neurons in the hidden layer of neural networks for predicting individual operating parameters of a roadheader delivering the best result (Variant I).

Parameter	n	Parameter	n
TM	4		3
RPM	7		3
vOW	4		11
FSO	10		4
FSP	10		3
P	–		4
ICR	–		6
SEC	–

An equally good result was obtained for six hidden neurons. In this case, the average percentage error was 20% smaller, but the root mean square error was larger. This is due to the greater share of larger error values in the considered population of control set samples (Fig. 6). For this reason, a network with four neurons in the hidden layer was considered superior for torque predictions. The points reflecting the predicted values relative to the expected values are located around a straight line with a slope coefficient of 1 (dashed line in red) – see Fig. 7. This indicates the correct operation of the neural network with the selected structure, although points that deviate significantly from the trend line are also visible.

Fig. 6.

Distribution of errors in the prediction of the torque on the motor shaft in the drive of the cutter heads on individual samples of the control set for the tested range of the number of neurons in the hidden layer (Variant I).

Fig. 7.

Comparison of the results of predicting the torque on the motor shaft in the drive of the cutter heads using a neural network (PRED) with the expected values (TARGET) (Variant I).

To compare network training methods, a numerical experiment was carried out in which a neural network composed of neurons with the number 4–4-1 (input layer-hidden layer-output layer) was subjected to a 10-time learning process using the LM and BR algorithms. The effects of training with both methods are shown in Fig. 8 using the example of the control set. The RMSE in the case of the LM algorithm was 35% higher than the value obtained for the tested population of samples in the case of network training using the BR method. In the case of using the LM learning method, for most of the ten samples considered, the prediction error was larger compared to the prediction error provided by the network trained with the BR method. For this reason, the BR learning method was selected to proceed with the analysis. The extension of the network training time with this method compared to the LM method is negligible.

Fig. 8.

Comparison of errors in predicting the torque on the motor shaft in the drive of the cutter heads for individual samples of the control set using the LM and BR learning methods.

Analyses were performed for the remaining eleven parameters of interest. The results of these analyses are shown in Figs. S4 and S5 (in the appendix). For example, each examined neural network structure (the number of neurons in the hidden layer) correctly predicts the values of the rotational velocity of the cutter head. However, the best solution was considered to be a network with seven neurons in the hidden layer (lower RMSE) (Fig. S4a). In the case of predicting the boom swinging speed v_OW, the result of the operation of a neural network with four neurons in the hidden layer was considered the best result (Tables 1 and 2).

The prediction results of vibration acceleration components for the training population are shown in Fig. S5. For all considered vibration acceleration components, the trend lines (black) deviate downwards compared to the theoretical lines (red). In the upper ranges of vibration acceleration values. This could indicate that neural networks underestimated the result. There is quite a large dispersion of the results of predicting the values of all vibration acceleration components in the considered structural nodes of the roadheader. This translates into the values of the error range R (Table 1).

Table 2 lists the network configurations with a 4-n-1 structure for all considered parameters characterizing the operation of the roadheader and its dynamic load that provides the best results (where n is the number of neurons in the hidden layer). The structures of individual neural networks are shown in Fig. 9.

Fig. 9.

Configurations of artificial neural networks with the structure (Diagrams generated using a Matlab script: Fabricio Castro (2023). Artificial Neural Network Architecture Generator https://www.mathworks.com/matlabcentral/fileexchange/102734-artificial-neural-network-architecture-generator), MATLAB Central File Exchange. Retrieved November 1, 2023). (a) 4-3-1, (b) 4-4-1, (c) 4-6-1, (d) 4-7-1, (e) 4-10-1, and (f) 4-11-1 (I is an input layer, H is a hidden layer, and O is an output layer) (Variant I).

Variant II – use of two neural networks with multiple outputs

In the second variant, an assumption was made that the prediction of the roadheader’s operating parameters was carried out using two multilayer neural networks (MLP). The first one (marked SSN-1) will be small and responsible for predicting the values of T_M, RPM, F_SO, F_SP, and v_OW. On this basis, the following would be calculated: P, ICR, and SEC. The second network (marked SSN-2) would predict the values of the vibration acceleration components of the roadheader . Similar to Variant I, the influence of the number of neurons in the hidden layer on the prediction result for the control set (ten data samples) was examined. The learning process was carried out using the Bayesian method (BR). Each training epoch was repeated ten times, for each of which, subsets from the training set and initial values of the weights were drawn. The influence of the number of neurons of the SSN-1 network on the prediction quality indicators RMSE, the mean value of the MPE prediction error, and the error range R for the control set samples are shown in Figs. 10 (and S6). The ANN structure that was rated the best was determined.

Fig. 10.

The influence of the number of neurons in the hidden layer on the effectiveness of the SSN-1 network for predicting the torque on the motor shaft in the drive of cutter heads (Variant II).

Of the five parameters whose values are generated by the SSN-1 network, and three parameters whose values are calculated on this basis the optimal results were achieved by the network with five neurons in the hidden layer. These parameters are T_M, F_SO, F_SP, P, and SEC (Table 3). In the case of the rotational velocity of the cutter head (RPM) and the boom deflection speed (v_OW), the best result was achieved by a network with ten hidden neurons, while for cutting efficiency (ICR), the optimal result was obtained for four hidden neurons. Table 4 lists the values of the analyzed indicators of the quality of prediction of the values of individual parameters using the SSN-1 network with the numbers of hidden neurons specified in Table 3. These results were deemed satisfactory. The exception was the prediction of the load of the boom lifting actuators, for which the RMSE is 73 kN (for the control set), the average MPE prediction error was + 28%, and the R range is as much as 356%. The prediction of the F_SP load value in Variant II was similarly poor, as was the case for Variant I.

Table 3.

List of the number of neurons in the hidden layer of the SSN-1 and SSN-2 networks for predicting individual operating parameters of the roadheader, providing the best result (Variant II).

SSN-1		SSN-2
Parameter	n	Parameter	n
TM	5		10
RPM	10		10
vOW	10		2
FSO	5		2
FSP	5		6
P	5		5
ICR	4		2
SEC	5

Table 4.

Summary of the values of the quality indicators for predicting the roadheader operating parameters with the SSN-1 and SSN-2 networks (Variant II).

SSN−1				SSN−2
Parameter	RMSE [*]	MPE [%]	R [%]	Parameter	RMSE [m/s2]	MPE [%]	R [%]
TM [Nm]	134	−10	51		1.0	−92	5
RPM [r/min]	4.8	−0.06	1.0		1.8	−49	33
vOW [m/s]	0.006	−3.4	17		1.2	−6	90
FSO [kN]	15	~ 0	25		1.4	−48	48
FSP [kN]	73	+ 28	356		0.8	+ 40	106
P [kW]	20	−10	51		6.7	−40	58
ICR [m3/h]	0.18	~ 0	~ 3		4.3	+ 43	175
SEC [kWh/m3]	3	−10	53

* – units depending on the type of parameter.

The results of predicting the values of vibration acceleration components in key structural nodes of the roadheader using the SSN-2 network from two to eleven neurons in the hidden layer, and the best result was obtained for the 4–2-7 structure (i.e., two neurons in the hidden layer) – Fig. S7. Table 3 shows the summary result of the prediction.

Analyzing the effects of training the SSN-1 and SSN-2 networks and the results on the control set, it was decided that the first network would have five neurons in the hidden layer, and the second one would have two neurons in the hidden layer. The structures of these networks are shown in Fig. 11.

Fig. 11.

Structures of the SSN-1 and SSN-2 networks selected to predict the operating parameters of the roadheader and its dynamic load (Diagrams generated using a Matlab script: Fabricio Castro (2023). Artificial Neural Network Architecture Generator https://www.mathworks.com/matlabcentral/fileexchange/102734-artificial-neural-network-architecture-generator), MATLAB Central File Exchange. Retrieved November 1, 2023). (Variant II).

To check the effectiveness of the neural network with a 4–5-5 structure, prediction of the roadheader operating parameters was carried out on the control set (Fig. 12a). As can be seen, the MPE (blue points) ranged from –10% to + 30% for all predicted parameters, and the R ranges (whiskers) did not exceed 60%. The root mean square error RMSE (orange markers) did not generally exceed 20%. The exception was the result of predicting the torque of the cutting heads (T_M) and the boom-lifting actuators (F_SP). The prediction of these parameters for data collected in the control set was characterized by a significantly higher RMSE value.

Fig. 12.

Network operation efficiency: (a) SSN-1 for a 4-5-5 network configuration and (b) SSN-2 for a 4-2-7 network configuration (Variant II).

Figure 12b shows the result of predicting the acceleration components of the roadheader vibrations for the control set made using the SSN-2 network with a 4–2-7 structure, which is the selected configuration due to the best results.

Variant III – use of one neural network with multiple outputs

In the last tested variant, it was assumed that the prediction of the values of all 12 parameters (plus three calculated from formulas (1)–(3)) would be made using one neural network (designated SSN). The advantage of this variant would be to greatly simplify the implementation of the network in the simulator software. A neural network with a different number of neurons in the hidden layer was tested, this time ranging from 2 to 12.

For each parameter covered by the forecast, the case (number of hidden neurons) that was considered optimal was indicated, as can be seen in Table S2, and the performance results of the models are presented in Table S3. Comparing them with analogous values for Variant I, and especially Variant II, there was a slight improvement in the prediction efficiency of the load of the F_SP boom-lifting actuators and vibration acceleration components in the roadheader’s structural nodes. Of the fifteen parameters covered by the prediction (twelve predicted by a given network and three calculated from formulas), for three parameters, the neural network provided the best results when it had nine hidden neurons.

Two neural networks were selected for further analysis, with four (Variant IIIa – Fig. 13a) and eleven (Variant IIIb – Fig. 13b) neurons in the hidden layer. They provided the best results for the largest number of predicted roadheader operating parameters and their dynamic load.

Fig. 13.

Structure of the SSN network (Diagrams generated using a Matlab script: Fabricio Castro (2023). Artificial Neural Network Architecture Generator https://www.mathworks.com/matlabcentral/fileexchange/102734-artificial-neural-network-architecture-generator), MATLAB Central File Exchange. Retrieved November 1, 2023). (a) Variant IIIa (4-4-12) and (b) Variant IIIb (4-11-12).

Figures 14 and S8 show the results of predicting the operating parameters of the roadheader and its dynamic load using both neural networks (Variant IIIa and IIIb). When comparing the values of RMSE, MPE, and R prediction of individual parameters for the control set, it is not possible to directly state which network provides a better result. However, it was found that seven of the roadheader’s operating parameters obtained more favorable values with ANN 4–4-12 (Variant IIIa). These parameters are v_OW, F_SO, F_SP, , , , and . In the case of the 4–11-12 neural network (Variant IIIb), more favorable values of these indicators were recorded in five cases for T_M, P, SEC, and . For three parameters (RPM, ICR, and ), the results were similar.

Fig. 14.

Efficiency of the SSN network for the 4-4-12 network configuration (Variant IIIa).

Selection of the ANN for predicting the operating parameters and dynamic load of a roadheader in a research simulator

To compare the effectiveness of prediction and the selection of the structure of the ANN, an indicator was introduced to assess the quality of prediction of the operating parameters of a roadheader in the following form:

8

where MPE_i represents the average percentage error in predicting the value of the ith parameter [%], R_i is the range of the percentage error in predicting the ith parameter [%], and l_P is the number of parameters covered by the predictor (l_P = 15) for i = 1, 2, …, 15.

The W index represents a normalized distribution of prediction results against the expected values in the control set (containing ten samples obtained from computer simulation) per one predicted parameter. The average value of the prediction error in the examined data set and its dispersion should be as small as possible, which is equivalent to minimizing the value of the W index. Therefore, the lower the value of the W index, the better.

Using the evaluation index W described by Eq. (8), the results of predicting the operating parameters of the roadheader and its dynamic load were compared with four selected variants of artificial neural networks for the control set. The values of this indicator are summarized in Table 5.

Table 5.

Summary of the values of the evaluation index W for selected variants of the artificial neural network structure for predicting the operating parameters of a roadheader.

Variant	W
I	0.13
II	0.20
IIIa	0.18
IIIb	0.20

Significant values are in bold.

The best results were provided by predictions of individual roadheader operating parameters using separate neural networks to estimate only one neuron in the output layer (Variant I). The indicator for assessing the quality of network operation, W, reached the lowest value in this case (W = 0.13). In the case of the remaining three variants tested, the result obtained is less accurate. The highest values of the W index were obtained for Variant II (two neural networks: 4–5-5 and 4–2-7) and Variant IIIb (4–11-15). Neural networks in variants II, IIIa, and IIIb provided similar results.

Unfortunately, this approach (use of many neural networks with one output layer) complicates the simulator software because it requires coding as many as twelve networks (three parameters are calculated from formulas based on parameter prediction using neural networks). On the other hand, it makes it possible to easily modify the prediction algorithm, separately for each of the predicted parameters, without interfering with other prediction models. The structures of the adopted ANNs are shown in Fig. 9.

Implementation of ANN in the roadheader simulator

The developed ANN algorithms were implemented in the RAD Studio Delphi environment. They were included in the Operator Panel software, in which artificial neural networks were recreated for the prediction of individual parameters using the MITOV IntelligenceLab library. Neural networks were built in separate units attached to the program code. An example architecture of an artificial neural network in the RAD Studio Delphi software (OpenWire window) is shown in Fig. 15.

Fig. 15.

Neural network architecture for predicting the torque on the motor shaft in the drive of cutter heads implemented in the software of the operator panel of the research simulator {RH-Sim}.

Reconstruction of the mining process in {RH-Sim}

Figure 16a shows the recorded parameters on the real machine, and Fig. 16b,c show the result of the {RH-Sim} simulator. The results of the comparison of averaged measured values (solid lines) and those obtained during prediction using the developed ANNs (dashed lines) are shown in Fig. 17, indicating a good match between the ANN results and the real excavation by roadheader. Two indicators were used to quantitatively compare the actual and simulated data, including MAE and MAPE. The summary of these indicators is presented in Table 6.

Fig. 16.

Reconstruction of the cutting process in the {RH-Sim} simulator: (a) cutting of a cement-sand block with a real roadheader, (b) virtual heading face before cutting, and (c) virtual heading face after cutting (line red – the trajectory of the cutter heads’ movement).

Fig. 17.

Comparison of the course of the operating parameters of the roadheader obtained from measurement (Measur) and in the {RH-Sim} simulator (Sim): (a) torque on the motor shaft in the drive of the cutter heads and its rotational speed, (b) mining power and speed boom deflection, (c) instantaneous cutting rate and energy consumption, (d) load on the boom rotation actuators, (e) load on the boom lifting actuators, (f) body vibration acceleration components, (g) boom vibration acceleration components, and (h) vertical component of the operator’s seat vibration acceleration.

Table 6.

List of indicators of matching the waveforms obtained in the {RH-Sim} simulator to the measurement results.

Parameter	MAE [*]	MAPE [%]	Parameter	MAE [*]	MAPE [%]
TM [Nm]	89.2	1.1		1.64	38.4
RPM [r/min]	18.1	1.2		0.97	39.8
vOW [m/s]	0.01	2.5		1.28	31.8
FSO [kN]	34.9	48.4		1.91	25.0
FSP [kN]	24.2	169.0		0.95	18.6
P [kW]	24.4	34.8		0.80	14.2
ICR [m3/h]	4.6	26.8		4.50	29.7
SEC [kWh/m3]	0.9	21.4

* – units depending on the type of parameter.

The best prediction results were obtained in the case of the torque of the cutter heads drive motor (T_M), rotational velocity (RPM) (Fig. 17a), and the boom deflection speed (v_OW) (Fig. 17b). The average absolute error does not exceed 3%. The weakest effect of matching the prediction results to real operation was noted in the case of loading the boom lifting cylinders (F_SP). The MAPE here is close to 170%. Although some consistency of the compared values is visible, such a large error value results from a greater variability of the values of the analyzed parameter predicted using ANN (Fig. 17e). This applies especially to the second half of the analyzed time interval. A MAPE value of nearly ~ 50% was recorded when the boom rotation actuators (F_SO) were loaded. The compared waveforms differ more in the first half of the considered time interval (Fig. 17d). The expected values of power (P), instantaneous cutting rate (ICR), and energy consumption of this process (SEC) vary on average from about 20% to about 35% (Table 6). In the case of power, the theoretical and actual curves are quite similar (the predicted values are, more variable, especially during the first 4 s of the mining process) as shown in Fig. 17b. Determining the actual variability of instantaneous cutting rate in subsequent periods seems to be difficult. Hence, the variability of this parameter is quite smooth as the cutter heads move (Fig. 17c). The actual instantaneous cutting rate was estimated based on the measured depth of cut and the cut height, accounting for the variability of these parameters as a function of the boom rotation angle. However, the variability resulting from the shape of the face surface, resulting from previously made cuts and transverse vibrations of the boom were not considered. Despite this, MAPE did not exceed 27%, which can be considered an acceptable result.

The average error in predicting the vibration components of the roadheader’s body (Fig. 17f), the boom (Fig. 17g), and the operator’s seat (Fig. 17h) ranges from 14% () to nearly 40% ( and ) – see Table 6. In most cases, however, this error does not exceed 30%, which can be considered a satisfactory result.

Simulation of the mining process while manually controlling a roadheader

The results of the {RH-Sim} simulation of an excavation operation while manually controlling the roadheader by the operator from the operator station (Figs. S9 and S10) showed good fidelity and the possibility to mimic the behavior of the operator based on the analysis of their responses to the face conditions. The results show the response of the simulated operator to cutting rocks with different mechanical properties (the layered rock mass). The variability of external conditions and parameters of the mining process selected by the operator follows the variability of the ground conditions and operating parameters of the roadheader selected by the simulator is a good analog to the potential response and machine reaction to the loads.

Conclusions

This article focused on the use of a proprietary simulator of a roadheader {RH-Sim} and the use of an ANN algorithm to predict important operating parameters of the machine and their dynamic load condition. Extensive simulation studies were carried out to select their structure and parameters, the results of which were quantitatively assessed. Three variants of ANN structures were considered in terms of the number of neurons in the output layer and a different number of neurons in the hidden layer. The tested ANN algorithms could offer a good correlation with individual parameters. The best results were obtained in predicting power, rotational speed of the cutter head drive motor rotor, and boom deflection.

Computer research supported by experimental results indicates that:

• The tested ANNs were developed to predict the values of parameters characterizing the roadheader load, vibrations in its key structural nodes, and operating parameters. The trend lines of the dependencies between the predicted and expected values were close to straight lines, representing a good correlation between predicted and measured individual quantities (with a slope of m = 1) of target parameters. However, in the case of the load of the boom oscillation and vibration, the trend showed a tendency to underestimate the upper range of variability of the mentioned parameters.

• For the torque T_M, the rotational speed of the cutter head drive motor rotor RPM, and the boom deflection speed v_OW, the coefficient of determination values reach very high values (close to unity indicating very good predictive capabilities of the selected ANN. In the remaining cases, the coefficients of determination reach lower values. The ANN performs the worst in predicting the value of the boom vibration component, , for which R² = 0.7254 was registered.

• In the case of neural networks with one neuron in the output layer (Variant I) (the value of each parameter is determined using a separate ANN), the number of neurons in the hidden layer is not uniform and ranges from 3 () to 11 (). The selection of the number of these neurons, similarly to the other variants, was based on the evaluation of the RSME, MPE, and R values obtained with different numbers of hidden layer neurons ranging from 2 to 11. For such selected ANN configurations, the mean percentage error (MPE) obtained during the prediction of individual parameters ranged from close to zero (RPM, ICR, v_OW, and F_SO) to over 30% (absolute value), for and . The ranges of the prediction error values (R) ranged from close to zero (RPM, ICR) to approximately 100% (, , , ).

• The degree of agreement between the values of five and seven parameters predicted simultaneously using two ANNs (Variant II) also varies significantly. This is evidenced by the values of both MPE and R. Comparing the values of these indicators with those obtained for Variant I, some improvement in the prediction efficiency was observed for several parameters. This resulted in a reduction of the absolute value of MPE to ~ 10% and the range of R (to ~ 40% for the SSN-1 network, and even to ~ 70% for the SSN-2 network). However, for some parameters, a deterioration in the degree of agreement of the obtained prediction results was observed, especially for some vibration acceleration components (, , i ). As a result of using one ANN network to predict the values of all considered parameters (Variant III), a slight improvement was found, especially in relation to the load of the boom lifting cylinders F_SP (decrease in the R range value by 11%) and the components of vibration acceleration in the road header’s structural nodes (lower RMSE values).

• The results of the study do not allow for a clear distinction between ANN structures for optimal results for all the considered parameters. Index W was introduced to account for all 15 parameters for comparison of the ANN result, and the best results were obtained from the ANN with one neuron in the output layer. In other words, if the target parameters were to be predicted separately.

• Comparison of the prediction results made with the developed ANNs with the results of measurements in an experimental trial using an R-130 roadheader confirmed that the selected neural networks can offer a reasonably accurate prediction of main operating parameters with an average absolute percentage error of less than 3%. Comparison of the prediction results using ANN with measured parameters in experiments confirms the adequacy of the simulation model used in the research with the real object. The differences in the values of prediction results and measured values are related to the simplifying assumptions adopted at the stage of building mathematical models.

Visualizing the operation of the roadheader and prediction of its operating parameters on the {RH-Sim} simulator and related operator panel offers a good solution for the training of the operators and prediction of machine behavior in given ground conditions. The ANN simulator could mimic machine behavior when controlling the roadheader manually, semi-automatically, or automatically.

Author contributions

Writing—original draft preparation, P.C.; Methodology, P.C. and J.R.; Investigation, P.C.; Supervision, P.C.; Funding acquisition, P.C.; Data curation, G.G.; Validation, G.G.; Visualization, G.G.; Writing—review & editing, J.R.; Formal analysis, J.R.

Funding

Publication supported by the Rector’s pro-quality grant. Silesian University of Technology, grant number 06/020/RGJ25/0082.

Data availability

Data will be made available upon request by the corresponding author.

Declarations

Competing interests

The authors declare no competing interests.