Data-driven and uncertainty-aware robust airstrip surface estimation

Neural Computing and Applications (2023) 35:19565–19580 https://doi.org/10.1007/s00521-023-08779-4 (0123456789().,-volV)(0123456789(). ,- volV) ORIGINAL ARTICLE Data-driven and uncertainty-aware robust airstrip surface estimation Francesco Crocetti1 • Mario Luca Fravolini1 • Gabriele Costante1 • Paolo Valigi1 Received: 24 May 2022 / Accepted: 12 June 2023 / Published online: 29 June 2023 Ó The Author(s) 2023 Abstract The performances of aircraft braking control systems are strongly influenced by the tire friction force experienced during the braking phase. The availability of an accurate estimate of the current airstrip characteristics is a recognized issue for developing optimized braking control schemes. The study presented in this paper is focused on the robust online estimation of the airstrip characteristics from sensory data usually available on an aircraft. In order to capture the nonlinear dependency of the current best slip on sequential slip-friction measurements acquired during the braking maneuver, multilayer perceptron (MLP) approximators have been proposed. The MLP training is based on a synthetic data set derived from a widely used tire–road friction model. In order to achieve robust predictions, MLP architectures based on the drop-out mechanism have been applied not only in the offline training phase but also during the braking. This allowed to online compute a confidence interval measure for best friction estimate that has been exploited to refine the estimation via Kalman Filtering. Open loop and closed loop simulation studies in 15 representative airstrip scenarios (with multiple surface transitions) have been performed to evaluate the performance of the proposed robust estimation method in terms of estimation error, aircraft braking distance, and time, together with a quantitative comparison with a state-of-the-art benchmark approach. Keywords Braking control  Surface estimation  Dropout neural networks  Kalman filtering 1 Introduction Brake controllers are designed to guarantee the minimum braking time while simultaneously preventing wheel slippage. This is possible by designing Electro-Mechanically Actuated (EMA) anti-skid systems that maximize the tire– road friction coefficient [4]. For this purpose, however, the knowledge of the actual surface characteristics is required to allow the braking controller to track the maximum friction point in the current slip-friction curve. Under the & Francesco Crocetti Mario Luca Fravolini 1.1 Related work and main contribution Gabriele Costante The problem of estimating the tire–road friction coefficient has been extensively investigated in the literature over the last years. In this paper, we focus on ‘‘slip-oriented’’ methods, which exploit the functional dependence of friction l on slip k (i.e., the normalized difference between longitudinal and tangent velocities) to estimate the actual Paolo Valigi 1 circumstances of sudden changes in surface conditions, a reliable estimation of the tire–road friction coefficient would lead to relevant benefits in braking efficiency and passenger safety [30]. In this context, the accuracy, reliability, and velocity of the estimation play a crucial role. In case the road surface characteristics are unknown, these have to be inferred from sensory data. Due to the strongly nonlinear and uncertain physical phenomena involved, the underlined estimation process is challenging and still an open problem. This is particularly relevant in the aeronautical context, where the aircraft’s high speed and the potential fast-changing conditions on the runway make the inference process even more tricky. Department of Engineering, University of Perugia, Via G. Duranti, 93, 06125 Perugia, Italy 123 19566 tire–road conditions. In such a framework, it is common practice to model the longitudinal tire-force Fx as Fx :¼ lFz , where l is the normalized friction coefficient. It can be described, among others, by the Pacejka [2] and the Burckhardt models [5, 19], which assume a nonlinear dependence of l on the slip signal k. An extended Kalman filter (EKF) has been used in [26] to estimate a piece-wise constant friction coefficient l, without any specific relation to the slip. Later [1, 15, 21] proposed other simplified ðk; lÞ models to estimate the actual road friction coefficient. In [34, 35], a least square and maximum likelihood approach has been proposed, to estimate the parameters of a linearly parametrized approximation of the Burckhardt model, based on a sequence of ðk; lÞ pairs as input, and using a Quarter Car Model (QCM) for the system dynamics. In [10], Recursive Least Square is used to online estimate the parameters of a linearized approximation of the Burckhardt model, and in [11], an enhanced constrained version of the same algorithm is proposed. A detailed and accurate discussion on model-based and black-box approaches to slip estimation is given in [24]. Optimal slip estimation has also been addressed by using data-driven approaches; [27, 36], respectively, employ a Support Vector Machine (SVM) and a General Regression Neural Network (GRNN) to solve the estimation problem. In [17], neural network and fuzzy approaches are discussed jointly with a sliding mode controller. The deep learning paradigm has, instead, been explored in [31], although with the assumption of having access to a considerable amount of different input measurements, which does not apply to most braking systems. More recently, the authors of [8] proposed a multilayer perceptron (MLP) to predict the best slip value by processing sequences of slipfriction pairs computed online from the onboard sensor readings. Although all the abovementioned data-driven methods, including Neural Networks, SVM and Fuzzy models, are undoubtedly effective in mapping the uncertain and nonlinear relation between slip and friction, they do not provide confidence measures about their estimates. To overcome this limitation, in this study, we propose an approach derived from [7], which provides, in addition to the MLP-based estimation, a confidence interval for the estimate. Specifically, in order to provide a robust prediction, the Neural Network (NN) has been trained using the stochastic weights dropout method [32]. This mechanism was employed not only in the offline training phase but also at inference time, during the braking. This modification makes available online a confidence interval measure for the MLP estimate of the best friction coefficient. This information has been exploited to further refine the MLP best slip estimate by filtering it via a Kalman Filter whose 123 Neural Computing and Applications (2023) 35:19565–19580 measurement covariance is made proportional to the estimated confidence interval provided by the dropout MLP. We believe that such online confidence information may be useful also for other purposes within an advanced braking control scheme. For example, it may be possible to schedu (...truncated)