1. Investigación

The present paper aims at analyzing the topological content of the complex trajectories that weeder-autonomous robots follow in operation. We will prove that the topological descriptors of these trajectories are affected by the robot environment as well as by the robot state, with respect to maintenance operations. Most of existing methodologies enabling efficient diagnosis are based on the data analysis, and in particular on some statistical quantities derived from the data. The present work explores the use of an original approach that instead of analyzing quantities derived from the data, analyzes the “shape” of the data, that is, the time series topology based on the homology persistence. We will prove that this procedure is able to extract valuable patterns able to discriminate the trajectories that the robot follows depending on the particular patch in which it operates, as well as to differentiate the robot behavior before and after undergoing a maintenance operation. Even if it is a preliminary work, and it does not pretend to compare its performances with respect to other existing technologies, this work opens new perspectives in considering quite natural and simple descriptors based on the intrinsic information that data contains, with the aim of performing efficient diagnosis and prognosis.

Modal analysis is widely used for addressing NVH—Noise, Vibration, and Hardness—in automotive engineering. The so-called principal modes constitute an orthogonal basis, obtained from the eigenvectors related to the dynamical problem. When this basis is used for expressing the displacement field of a dynamical problem, the model equations become uncoupled. Moreover, a reduced basis can be defined according to the eigenvalues magnitude, leading to an uncoupled reduced model, especially appealing when solving large dynamical systems. However, engineering looks for optimal designs and therefore it focuses on parametric designs needing the efficient solution of parametric dynamical models. Solving parametrized eigenproblems remains a tricky issue, and, therefore, nonintrusive approaches are privileged. In that framework, a reduced basis consisting of the most significant eigenmodes is retained for each choice of the model parameters under consideration. Then, one is tempted to create a parametric reduced basis, by simply expressing the reduced basis parametrically by using an appropriate regression technique. However, an issue remains that limits the direct application of the just referred approach, the one related to the basis ordering. In order to order the modes before interpolating them, different techniques were proposed in the past, being the Modal Assurance Criterion—MAC—one of the most widely used. In the present paper, we proposed an alternative technique that, instead of operating at the eigenmodes level, classify the modes with respect to the deformed structure shapes that the eigenmodes induce, by invoking the so-called Topological Data Analysis—TDA—that ensures the invariance properties that topology ensure.

We are interested in evaluating the state of drivers to determine whether they are attentive to the road or not by using motion sensor data collected from car driving experiments. That is, our goal is to design a predictive model that can estimate the state of drivers given the data collected from motion sensors. For that purpose, we leverage recent developments in topological data analysis (TDA) to analyze and transform the data coming from sensor time series and build a machine learning model based on the topological features extracted with the TDA. We provide some experiments showing that our model proves to be accurate in the identification of the state of the user, predicting whether they are relaxed or tense.

The aim of this paper is to leverage the main surface topological descriptors to classify tape surface profiles, through the modelling of the evolution of the degree of intimate contact along the consolidation of pre-impregnated preforms associated to a composite forming process. It is well-known at an experimental level that the consolidation degree strongly depends on the surface characteristics (roughness). In particular, same process parameters applied to di erent surfaces produce very di erent degrees of intimate contact. It allows us to think that the surface topology plays an important role along this process. However, solving the physics-based models for simulating the roughness squeezing occurring at the tapes interface represents a computational e ort incompatible with online process control purposes. An alternative approach consists of taking a population of di erent tapes, with di erent surfaces, and simulating the consolidation for evaluating for each one the progression of the degree of intimate contact –DIC– while compressing the heated tapes, until reaching its final value at the end of the compression. The final goal is creating a regression able to assign a final value of the DIC to any surface, enabling online process control. The main issue of such an approach is the rough surface description, that is, the most precise and compact way of describing it from some appropriate parameters easy to extract experimentally, to be included in the just referred regression. In the present paper we consider a novel, powerful and very promising technique based on the topological data analysis –TDA– that considers an adequate metrics to describe, compare and classify rough surfaces.