Nonlinear Autoregressive Exogenous Research Articles

Transient modeling of a solid oxide fuel cell using an efficient deep learning HY-CNN-NARX paradigm

Control and monitoring systems are crucial for ensuring optimal performance, efficiency, and longevity of Solid Oxide Fuel Cells (SOFC). Developing a model to accurately capture the transient behavior of the SOFC under dynamic operation is essential for these applications. As electrochemical, mass-transfer, and thermal equations are involved in SOFCs’ dynamic, physics-based approaches to capture all the complexity of SOFC systems are often too computationally expensive for real-time implementation. In this paper, an innovative multi-input neural network is developed to build an accurate model of SOFC that is computationally efficient. The proposed algorithm uses experimental data and is a modified nonlinear autoregressive exogenous (NARX) network. An optimal sequence of the most recent observations (output voltages) that characterize the SOFC dynamics is passed through stacked 1D convolutional layers (CNN) to extract latent spatial/temporal information. Then the output is concatenated with current and past exogenous inputs. The fusion of learned features, representing the internal dynamics and the effect of exogenous inputs, is then fed to a fully connected network for one-step ahead performance prediction. This hybrid structure, called HY-CNN-NARX, is capable of identifying the transient dynamics of the SOFCs by unrolling information from historical outputs and inputs within a feedforward framework. To evaluate the model performance, lab-scale tubular SOFCs are experimentally tested at 650–750 °C under various dynamic operations and initial conditions, and the transient and steady-state responses of the SOFC are collected. Once the model is validated using a wide operating range of data, the generalization and prediction performance of the proposed network is compared with a conventional NARX and a recurrent stacked Long short-term memory (LSTM) model. The comparative results demonstrate that the proposed HY-CNN-NARX model outperforms the NARX model on unseen data with an accuracy improvement of 59.2% for root mean square error and 53.7% for mean absolute percentage error. In addition, the prediction performance of the HY-CNN-NARX is comparable to its recurrent counterpart, the LSTM model, but with a 39.3% faster execution time.

Novel design of nonlinear autoregressive with exogenous noise-based intelligent networks for dynamics of MHD Casson–Williamson models involving heat generation and viscous dissipation

In the current arena, the role of artificial intelligence (AI) has gained immense impact in the field of computational fluid dynamics (CFD) due to mesh improvement efficiency, optimal manual intervention, reliable forecasting, comprehending data analytic decisions, and utilization of machine automation. The study under investigation treatise on CFD problem representing the flow of Casson and Williamson fluids (CWFs) model with heat generation and viscous dissipation by using AI-based knacks through nonlinear autoregressive exogenous (NARX) networks backpropagated with Bayesian regularization technique (BRT), i.e. NARX-BRT. The design NARX-BRT procedure implemented on data generated with Adams numerical scheme for CWFs by carefully altering parameters i.e. Darcy number, Casson fluid, mass convective Williamson, mixed convection, thermal conductivity, thermal convective, and Eckert number, with fixed values Prandtl and Schmidt numbers. Results invariably matched with the reference/standard numerical solutions for the CWF model having significantly reduced magnitude of error for each anticipated CWF scenario. The effectiveness of projected CWF is portrayed exhaustively through mean square error (MSE) based iterative learning curves, analysis of adaptive controlling factors, error histogram plots, and regression metrics for variants of nonlinear differential order systems of CWF-based CFD.

A robust microgrid using an inverter with CCS-MPC control and resilient operation

Modern generation trend through renewable energy-based distributed energy resources has made microgrids an important part of the power system. Robust control of the inverter providing quality power has become an essential microgrid (MG) requirement. This paper proposes continuous control set model predictive control (CCS-MPC) on inverter for dynamic voltage regulation supplying reactive power to the load for a MG. The proposed method uses the terminal voltage magnitude, which reduces calculation time, sensor per phase, and the engagement burden of the controller. This paper applies a nonlinear VSI model and a series parallel structure nonlinear autoregressive exogenous (NARX) model of artificial neural network (ANN) to predict future output which CCS-MPC optimizes. The proposed VSI with CCS MPC is applied to a case study of a real system as a plug-and-play device. Simulation shows the satisfactory result of the proposed controller. The inverter control system has been made resilient to protect itself and automatically recover from faults on the DC and AC side, providing quality power to its local load when the fault has been removed.

Solar air heater with underground latent heat storage system for greenhouse heating: Performance analysis and machine learning prediction

The increasing demand for renewable energy sources in greenhouse heating, driven by the high cost of fossil fuels, has prompted the exploration of various alternatives, such as solar collectors, heat pumps, biomass, and cogeneration systems. This study aimed to establish an optimal environment for plant growth by employing a unique solar air heater and an underground latent heat storage system with a packed bed of phase change material unit (CaCl2-6H2O). Conducted in a double-span greenhouse in Ghardaia, Algeria, characterized by a semi-arid climate, the research utilized two distinct machine learning algorithms to predict the heating system's thermal behavior accurately. An experimental assessment of climatic parameters revealed that the greenhouse equipped with the heating system maintained an air temperature 57 % higher than that of a conventional greenhouse during the nighttime. The use of phase change materials resulted in the release of only 20 kJ of energy at night, indicating the potential to meet 30 % of the greenhouse's energy requirements during nighttime. Utilizing artificial neural networks, this study accurately predicted internal greenhouse parameters with and without LTES. The Nonlinear Autoregressive Exogenous (NARX) model exhibited high accuracy in prediction, with an R2 value of 0.9986 in both cases, while the Recurrent Neural Network (RNN) model showed acceptable performance, achieving an R2 value of 0.9893. These results underscore the potential of ANN models in advancing thermal energy storage technologies and their applicability in sustainable agriculture. This research significantly contributes to thermal energy storage systems and their benefits for sustainable agriculture.

Vehicle Dynamics in Electric Cars Development Using MSC Adams and Artificial Neural Network

Recently, there has been renewed interest in lightweight structures; however, a small structure change can strongly affect vehicle dynamic behavior. Therefore, this study provides new insights into non-parametric modeling based on artificial neural networks (ANNs). This work is then motivated by the requirement for a reliable substitute for virtual instrumentation in electric car development to enable the prediction of the current value of the vehicle slip from a given time history of the vehicle (input) and previous values of synthetic data (feedback). The training data are generated from a multi-body simulation using MSC Adams Car; the simulation involves a double lane-change maneuver. This test is commonly used to evaluate vehicle stability. Based on dynamic considerations, this study implements the nonlinear autoregressive exogenous (NARX) identification scheme used in time-series modeling. This work presents an ANN that is able to predict the side slip angle from simulated training data generated employing MSC Adams Car. This work is a specific solution to overtake maneuvers, avoiding the loss of vehicle control and increasing driving safety.

Novel knacks of chaotic maps with Archimedes optimization paradigm for nonlinear ARX model identification with key term separation

Archimedes' optimization algorithm (AOA) is a recently proposed physics-based optimization algorithm inspired by Archimedes' Principle. However, for optimization of complex engineering problems, it shows slow convergence and can easily fall into local minima. Chaotic maps have non-repeatability properties they can effectively scan the search space with fast convergence in optimization algorithms. In this study, knacks of physics-based optimization along with chaotic maps are exploited for the parameter estimation of autoregressive exogenous (ARX), nonlinear input ARX (NI-ARX), LD-Didactic temperature process plant models and electrically stimulated muscle model. Ten chaotic maps have been applied to AOA. The fitness function of both models is constructed based on the square error between true and estimated response. The chaotic variants indicate that AOA with a chaotic Circle map (CAOA2) gives the best performance in terms of accuracy and convergence against reptile search heuristics, sine cosine optimization approach, harris hawks optimizer (HHO) and whale optimization algorithm (WOA) for different variations of generation and noise levels. Statistics based on mean square error, convergence plots, statistical plots, Taguchi test, average fitness, t-test, and Friedman test for repeated measures approve the reliability of CAOA2 for parameter estimation of ARX, NI-ARX, LD-Didactic temperature process plant models and electrically stimulated muscle model.

Intelligent Analog Beam Selection and Beamspace Channel Tracking in THz Massive MIMO With Lens Antenna Array

Beamspace multiple-input-multiple-output (MIMO) as a green technology can efficiently substitute for the conventional massive MIMO, provided that the beamspace channel is acquired precisely. The prior efforts in this area of study, especially the learning-driven ones, however, indicate remarkable performance losses owing to a lack of generalization. In this paper, we propose a modified non-linear auto-regressive exogenous (NARX) model for tracking and predicting the beamspace channel over the sequences of time. Benefiting from bounded generalization error, fast convergence, limited prediction variance, and negligible performance loss, the proposed scheme achieves up to 15% spectral efficiency (SE) gain over its counterparts. We further improve this performance by means of an ensemble learning technique for simultaneously training multiple NARX modules in parallel, thus leading to a 23% SE gain. Relying on the predicted beamspace channel, we propose a beamspace analog beam selection technique through fine-tuning the architecture of a pre-trained off-the-shelf GoogleNet, which brings up to 21% SE gain over similar baselines. With the aid of an ensemble learning technique, it is further indicated numerically that up to 34% SE improvement can be achieved, as compared to the counterparts.

Predictions of solar activity cycles 25 and 26 using non-linear autoregressive exogenous neural networks

ABSTRACT This study presents new prediction models of the 11-yr solar activity cycles (SC) 25 and 26 based on multiple activity indicator parameters. The developed models are based on the use of non-linear autoregressive exogenous (NARX) neural network approach. The training period of the NARX model is from July 1749 to December 2019. The considered activity indicator parameters are the monthly sunspot number time series (SSN), the flare occurence frequency, the 10.7-cm solar radio flux, and the total solar irradiance (TSI). The neural network models are fed by these parameters independently and the prediction results are compared and verified. The obtained training, validation, and prediction results show that our models are accurate with an accuracy of about 90 per cent in the prediction of peak activity values. The current models produce the dual-peak maximum (Gnevyshev gap) very well. Based on the obtained results, the expected solar peaks in terms of SSN (monthly averaged smoothed) of the solar cycles 25 and 26 are RSSN = 116.6 (February 2025) and RSSN = 113.25 (October 2036), respectively. The expected time durations of SC 25 and SC 26 cycles are 9.2 and 11 yr, respectively. The activity levels of SC 25 and 26 are expected to be very close and similar to or weaker than SC 24. This suggests that these two cycles are at the minimum level of the Gleissberg cycle. A comparison with other reported studies shows that our results based on the NARX model are in good agreement.

Wear prediction of 3D-printed acrylonitrile butadiene styrene-carbon nanotube nanocomposites at elevated temperatures

Abstract In this study, multi-wall carbon nanotube (MWCNT) reinforced acrylonitrile butadiene styrene (ABS) nanocomposite filaments are produced. Filaments are examined through thermogravimetric analysis (TGA) and definitive scanning calorimetry (DSC) analysis. Produced nanocomposite filaments are used in the fused deposition modeling (FDM) process to manufacture parts. Wear tests are conducted on 3D-printed parts using wear test apparatus with an attached heating module under different ambient temperatures. Hence, the influence of CNT reinforcement, along with different FDM process parameters and varying test conditions on the wear behavior of 3D-printed ABS-CNT parts, are examined. Worn surfaces of the specimens are examined by scanning electron microscopy (SEM). Nonlinear autoregressive exogenous (NARX) models are proposed for the prediction of the wear behavior of 3D-printed ABS-CNT nanocomposites. While wear rate is taken as output, ambient temperature and amount of nanofiller are accounted as input parameters along with the variation of coefficient of friction (COF) which is obtained from measured frictional force and three input-one output model structure is proposed for NARX. The use of multiple input-single output (MISO) model structure and examining the wear behavior of 3D-printed ABS-CNT samples under different wear test conditions with different FDM process parameters are the novelties in this work.

Time-series clustering and forecasting household electricity demand using smart meter data

This study forecasts electricity consumption in a smart grid environment. We present a bottom-up prediction method using a combination of forecasting values based on time-series clustering using advanced metering infrastructure (AMI) data, one of the core smart grid technologies. Remote data metering every 15 min to 1 h is possible with real-time communication on power generation information, consumption, and AMI development. Hence, its prediction is more challenging due to the large variation of each household’s electricity. These issues were solved by time-series clustering methods using Euclidean distances and Dynamic Time Warping distance. The auto-regressive integrated moving average (ARIMA), ARIMA exogenous (ARIMAX), double seasonal Holt–Winters (DSHW), trigonometric, Box–Cox transform, autoregressive moving average errors, trend and seasonal components (TBATS), neural network nonlinear autoregressive (NNAR), and nonlinear autoregressive exogenous (NARX) models were used for demand forecasting based on clustering. The result showed that the time-series clustering method performed better than that using the total amount of electricity demand regarding the mean absolute percentage error and root mean squared error.Hence, various exogenous variables were considered to improve model accuracy. The model considering exogenous variables—cooling degree day, humidity, insolation, indicator variables, and generation power consumption performed better than that without exogenous variables.

Temperature prediction of solar greenhouse based on NARX regression neural network

Temperature has an important influence on plant growth and development. In protected agriculture production, accurate prediction of temperature environment is of great significance. However, due to the time series, nonlinear and multi coupling characteristics of temperature, it is difficult to achieve accurate prediction. We proposed a method for building a solar greenhouse temperature prediction model based on a timeseries analysis, that considers the time series characteristics and dynamic temperature changes in the greenhouse system. The method would predict the temperature of greenhouse, and provide reference for the temperature change law in protected agriculture. A parameter analysis was performed on the nonlinear autoregressive exogenous (NARX) neural network, and a solar greenhouse temperature time series prediction model was established using the NARX regression neural network. The results showed that the proposed model depicted a maximum absolute error of 0.67 °C, and model correlation coefficient of 0.9996. Compared with the wavelet and BP neural networks, the NARX regression neural network accurately predicted and significantly outperformed in the solar greenhouse temperature prediction model. Moreover, the prediction model can accurately predict temperature trends within the solar greenhouse and is pivotal to obtaining precise control of solar greenhouse temperature.

Storm surge level prediction based on improved NARX neural network

The northern Gulf of Mexico coast is affected by the North Atlantic hurricane season, which causes storm surge disasters every year and brings serious economic losses to the southern USA; therefore, it is necessary to make an accurate advance prediction of storm surge level. In this paper, a model with simple structure, fast computation speed, and accurate prediction results has been constructed based on nonlinear auto-regressive exogenous (NARX) neural network. Five types of data collected from observation stations are selected as the input factors of the model. To improve the model's computational efficiency, a neuron pruning strategy based on sensitivity analysis is introduced. By analyzing the output weights of the neurons in the hidden layer on the sensitivity of the model prediction output, the model structure can be adjusted accordingly. Moreover, a modular prediction method is introduced based on the tide harmonic analysis data so as to make the model prediction results more accurate. At last, a complete storm surge level prediction model, pruned modular (PM)-NARX, is constructed. In this paper, the model is trained by using historical data and used for storm surge level prediction along the northern Gulf of Mexico coast in 2020. The simulation test results show that the correlation between the predicted data and the observed data is stable above 0.99 at 12 h in advance and the model is able to produce the results within one minute. The prediction speed, accuracy, and stability are higher than those of conventional models. In addition, two sets of follow-up tests show that the prediction accuracy of the model can still maintain a high level. The above can prove that the pruned modular (PM)-NARX model can effectively provide early warning before the storm surge to avoid property damage and human casualties.

Development of an artificial intelligence-based framework for biogas generation from a micro anaerobic digestion plant

Despite the advantages of the Anaerobic Digestion (AD) technology for organic waste management, low system performance in biogas production negatively affects the wide spread of this technology. This paper develops a new artificial intelligence-based framework to predict and optimise the biogas generated from a micro-AD plant. The framework comprises some main steps including data collection and imputation, recurrent neural network/ Non-Linear Autoregressive Exogenous (NARX) model, shuffled frog leaping algorithm (SFLA) optimisation model and sensitivity analysis. The suggested framework was demonstrated by its application on a real micro-AD plant in London. The NARX model was developed for predicting yielded biogas based on the feeding data over preceding days in which their lag times were fine-tuned using the SFLA. The optimal daily feeding pattern to obtain maximum biogas generation was determined using the SFLA. The results show that the developed framework can improve the productivity of biogas in optimal operation strategy by 43 % compared to business as usual and the average biogas produced can raise from 3.26 to 4.34 m3/day. The optimal feeding pattern during a four-day cycle is to feed over the last two days and thereby reducing the operational costs related to the labour for feeding the plant in the first two days. The results of the sensitivity analysis show the optimised biogas generation is strongly influenced by the content of oats and catering waste as well as the optimal allocated day for adding feed to the main digester compared to other feed variables e.g., added water and soaked liner.

Artificial neural networks based harmonics estimation for real university microgrids using hourly solar irradiation and temperature data

The need for renewable energy is increasing day by day due to different factors such as increasing energy demand, environmental considerations as well as the will to decrease the share of fossil fuel-based generation. Due to their relative low-cost and ease of installation, PV systems are leading the way for renewable energy deployments around the globe. However, there are meticulous studies that need to be undertaken for realization of such projects. Studying local weather and load patterns for proper panel sizing or considering grid components to determine cable and transformer sizing can be named as some examples for pre-installation studies. In addition to these, post-installation impact studies, e.g. accurate harmonic analysis contribution, is more important to ensure safe and secure operation of the overall system. These steps need to be taken for all PV installation projects. The aim of this study is to show a step-by-step analysis of the effect of a real PV system on the network and to improve the prediction and give a new perspective to the harmonic estimation by using the hourly temperature and radiation data together. At the first phase of the study, a detail real-time 250 kW PV system was modeled for real university campus, and then harmonic estimation based on hourly solar irradiation and hourly temperature was performed with artificial neural networks (ANN) and nonlinear autoregressive exogenous (NARX). The accuracy of the prediction made with ANN was 0.98, and the accuracy of the prediction made with NARX was 0.96.Researchers in PV sizing and control field as well as engineers in power quality area would find these findings beneficial and useful. Use of ANNs and NARX for such analysis indicates the trend in this field that can be targeted by new research projects.

Solar PV Power Estimation and Upscaling Forecast Using Different Artificial Neural Networks Types: Assessment, Validation, and Comparison

According to its various features, the solar photovoltaics (PV) system is realized as a significant promising energy source to cope with energy shortcomings and environmental impacts like contamination. Therefore, it is mandatory to estimate and predict the output power for prediction intervals to avoid any power outage or urgent disturbances in the utility grid. These are challenging tasks as the solar PV output power depends on the weather variables data such as temperature and solar radiation. In this article, the estimation and forecast of solar PV output power are investigated with an upscaling method using three different types of artificial neural networks (ANNs) in order to reduce the estimation errors in current types of ANNs. The multilayer feedforward neural network (MLFFNN), recurrent neural network (RNN), and nonlinear autoregressive exogenous (NARX) model neural network (NARXNN) are applied to estimate and forecast the total output power of four real solar PV substations in Egypt. Hence both the surface temperature and the solar radiation of each PV substation are applied as the inputs of each designed NN, whereas the total output power of the four PV substations is its output. For the training and effectiveness investigation procedures of each applied ANNs, the data of two months (60 days) are attained and collected from these four PV substations. Here, the data of the first 45 days are applied to train the three designed NNs, while the data from the remaining 15 days, which are not applied for the training, are used to check the effectiveness and the generalization capability of the trained NNs. Hence, the estimation process is considered a prior step for the forecast of the output power. Therefore, upscaling method is utilized for assessing and forecasting a regional solar PV output power because of the limited number of monitored plants and applied data. The results provide evidence that the trained NNs are running very well and efficiently to estimate the power correctly. The performance of the MLFFNN is the best compared with the other NNs, whereas the NARXNN’s performance is the lowest one. The MLFFNN achieves the lowest mean squared error (MSE) of 0.27533 and the lowest absolute approximation error of 0.2099 MWh. Finally, the assessment and comparison among the three trained NNs and other techniques in recently published articles are highlighted and presented which reveal the performance superiority of the three trained NNs compared to other ANNs.

An Input-to-State Stable Virtual Sensor for Electric Motor Rotor Temperature

We present a physics-informed neural ordinary differential equation (ODE) based model to determine the temperature in electric motor permanent magnets. The input-to-state stability (ISS) property is ensured by the model's architecture independently of the model's parameters. This improves the model's safety and contributes to easy deployment as a virtual sensor. We train this model on a real-world data set and demonstrate its advantages over a nonlinear autoregressive exogenous (NARX) neural network.

Black-Box Large-Signal Average Modeling of DC-DC Converters Using NARX-ANNs

This paper investigates the use of non-linear autoregressive exogenous (NARX) artificial neural networks (ANNs) to achieve black-box average dynamic models of dc-dc converters capable of capturing the main converter non-linearities. Non-linearities may include, for example, dynamic behavior variations due to changes of operating point or operating mode (e.g., discontinuous conduction mode, continuous conduction mode). This paper presents design guidelines for determining the NARX-ANN architecture and the dataset to be used in the training process. Dataset definition includes the choice of the perturbations for stimulating the aimed system behaviors and optimizations for dataset size reduction. The proposed approach is first derived for a dc-dc boost converter. To verify the generality of the proposed method, the same methodology is also applied to a Ćuk converter. In both cases, the proposed NARX-ANN modeling provided accurate results, with only limited deviations observed in the time-domain responses to step variations of duty-cycle and output current. The proposed model provided accurate small-signal behavior under different operating conditions. The validity of the approach is evaluated experimentally by considering a boost converter prototype.

Comparison of machine learning techniques for reservoir outflow forecasting

Abstract. Reservoirs play a key role in many human societies due to their capability to manage water resources. In addition to their role in water supply and hydropower production, their ability to retain water and control the flow makes them a valuable asset for flood mitigation. This is a key function, since extreme events have increased in the last few decades as a result of climate change, and therefore, the application of mechanisms capable of mitigating flood damage will be key in the coming decades. Having a good estimation of the outflow of a reservoir can be an advantage for water management or early warning systems. When historical data are available, data-driven models have been proven a useful tool for different hydrological applications. In this sense, this study analyzes the efficiency of different machine learning techniques to predict reservoir outflow, namely multivariate linear regression (MLR) and three artificial neural networks: multilayer perceptron (MLP), nonlinear autoregressive exogenous (NARX) and long short-term memory (LSTM). These techniques were applied to forecast the outflow of eight water reservoirs of different characteristics located in the Miño River (northwest of Spain). In general, the results obtained showed that the proposed models provided a good estimation of the outflow of the reservoirs, improving the results obtained with classical approaches such as to consider reservoir outflow equal to that of the previous day. Among the different machine learning techniques analyzed, the NARX approach was the option that provided the best estimations on average.

Use of meta-heuristic approach in the estimation of aquifer's response to climate change under shared socioeconomic pathways

Climate change is one of the main sources of stress on the aquifers. However, few studies have appraised its impact on groundwater systems, especially in Iran with unprecedented groundwater depletion rates. Not influenced by anthropogenic influences, Pali aquifer, southwest Iran, has climate data scarcity. To determine the response of the aquifer, one approach is to utilize a pre-downscaled data set. To this end, WorldClim data set under shared socioeconomic pathways (SSPs), i.e. SSP245 and SSP585, was considered. Furthermore, nonlinear autoregressive exogenous (NARX) and artificial neural networks (ANNs) along with support vector regression (SVR) combined with the meta-heuristic algorithms of wavelet (WSVR) and innovative gunner (AIG-SVR) were applied, regarding 1970–2000 as the base time span, and 2021–2040 and 2041–2060 as the future time periods. Among observational data (2007–2018), 80 and 20% were considered for the network's training and testing, respectively. An increase in temperature, between +1.93 and + 3.7 °C, would occur in the future with the most increment in summer 2041–2060 under SSP585. Additionally, precipitation fluctuate from −0.43 to +1.17 mm/month with a probable rise in fall and most decline in winter 2041–2060 under SSP585. As regards the groundwater modeling, considering that NARX and ANNs were not able to simulate the aquifer altogether, the meta-heuristic approaches demonstrated high proficiencies. With R = 0.995, R2 = 0.989, mean absolute error (MAE) = 0.249 m and Nash-Sutcliffe efficiency (NSE) = 0.982 for the test data, WSVR illustrated the greatest efficacy, which disclosed that the groundwater level would face the utmost reduction from −5.4 to −10.9 m in observation wells, especially in spring 2041–2060. Indeed, this decline in groundwater level is exclusively induced by climate change, emphasizing on proposing groundwater adaptation strategies to address the groundwater issues, like land subsidence, in Iran. Moreover, it is proposed that different modeling approaches be evaluated, such that the outputs of the best model be considered.

Nonlinear UGV Identification Methods via the Gaussian Process Regression Model for Control System Design

In this paper, two identification methods are proposed for a ground robotic system. A Gaussian process regression (GPR) model is presented and adopted for a system identification framework. Its performance and features were compared with a wavelet-based nonlinear autoregressive exogenous (NARX) model. Both algorithms were compared and experimentally validated for a small ground robot. Moreover, data were collected throughout the onboard sensors. The results show better prediction performance in the case of the GPR method, as an estimation algorithm and in providing a measure of uncertainty.