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During exercise, heart rate has proven to be a good measure in planning workouts. It is not only simple to measure but also well understood and has been used for many years for workout planning. To use heart rate to control physical exercise, a model which predicts future heart rate dependent on a given strain can be utilized. In this paper, we present a mathematical model based on convolution for predicting the heart rate response to strain with four physiologically explainable parameters. This model is based on the general idea of the Fitness-Fatigue model for performance analysis, but is revised here for heart rate analysis. Comparisons show that the Convolution model can compete with other known heart rate models. Furthermore, this new model can be improved by reducing the number of parameters. The remaining parameter seems to be a promising indicator of the actual subject’s fitness.
Analyzing training performance in sport is usually based on standardized test protocols and needs laboratory equipment, e.g., for measuring blood lactate concentration or other physiological body parameters. Avoiding special equipment and standardized test protocols, we show that it is possible to reach a quality of performance simulation comparable to the results of laboratory studies using training models with nothing but training data. For this purpose, we introduce a fitting concept for a performance model that takes the peculiarities of using training data for the task of performance diagnostics into account. With a specific way of data preprocessing, accuracy of laboratory studies can be achieved for about 50% of the tested subjects, while lower correlation of the other 50% can be explained.
The Fitness-Fatigue model (Calvert et al. 1976) is widely used for performance analysis. This antagonistic model is based on a fitness-term, a fatigue-term, and an initial basic level of performance. Instead of generic parameter values, individualizing the model needs a fitting of parameters. With fitted parameters, the model adapts to account for individual responses to strain. Even though in most cases fitting of recorded training data shows useful results, without modification the model cannot be simply used for prediction.
The MAP-Elites algorithm produces a set of high-performing solutions that vary according to features defined by the user. This technique to 'illuminate' the problem space through the lens of chosen features has the potential to be a powerful tool for exploring design spaces, but is limited by the need for numerous evaluations. The Surrogate-Assisted Illumination (SAIL) algorithm, introduced here, integrates approximative models and intelligent sampling of the objective function to minimize the number of evaluations required by MAP-Elites.
The ability of SAIL to efficiently produce both accurate models and diverse high-performing solutions is illustrated on a 2D airfoil design problem. The search space is divided into bins, each holding a design with a different combination of features. In each bin SAIL produces a better performing solution than MAP-Elites, and requires several orders of magnitude fewer evaluations. The CMA-ES algorithm was used to produce an optimal design in each bin: with the same number of evaluations required by CMA-ES to find a near-optimal solution in a single bin, SAIL finds solutions of similar quality in every bin.
A new method for design space exploration and optimization, Surrogate-Assisted Illumination (SAIL), is presented. Inspired by robotics techniques designed to produce diverse repertoires of behaviors for use in damage recovery, SAIL produces diverse designs that vary according to features specified by the designer. By producing high-performing designs with varied combinations of user-defined features a map of the design space is created. This map illuminates the relationship between the chosen features and performance, and can aid designers in identifying promising design concepts. SAIL is designed for use with compu-tationally expensive design problems, such as fluid or structural dynamics, and integrates approximative models and intelligent sampling of the objective function to minimize the number of function evaluations required. On a 2D airfoil optimization problem SAIL is shown to produce hundreds of diverse designs which perform competitively with those found by state-of-the-art black box optimization. Its capabilities are further illustrated in a more expensive 3D aerodynamic optimization task.
The MAP-Elites algorithm produces a set of high-performing solutions that vary according to features defined by the user. This technique has the potential to be a powerful tool for design space exploration, but is limited by the need for numerous evaluations. The Surrogate-Assisted Illumination algorithm (SAIL), introduced here, integrates approximative models and intelligent sampling of the objective function to minimize the number of evaluations required by MAP-Elites.
The ability of SAIL to efficiently produce both accurate models and diverse high performing solutions is illustrated on a 2D airfoil design problem. The search space is divided into bins, each holding a design with a different combination of features. In each bin SAIL produces a better performing solution than MAP-Elites, and requires several orders of magnitude fewer evaluations. The CMA-ES algorithm was used to produce an optimal design in each bin: with the same number of evaluations required by CMA-ES to find a near-optimal solution in a single bin, SAIL finds solutions of similar quality in every bin.
Training models have been proposed to model the effect of physical strain on fitness. In this work we explore their use not only for analysis but also to generate training plans to achieve a given fitness goal. These plans have to include side constraints such as, e.g., maximal training loads. Therefore plan generation can be treated as a constraint satisfaction problem and thus can be solved by classical CSP solvers. We show that evolutionary algorithms such as differential evolution or CMA-ES produce comparable results while allowing for more flexibility and requiring less computational resources. Due to this flexibility, it is possible to include well known principles of training science during plan generation, resulting in reasonable training plans.
The positive influence of physical activity for people at all life stages is well known. Exercising has a proven therapeutic effect on the cardiovascular system and can counteract the increase of cardiovascular diseases in our aging society. An easy and good measure of the cardiovascular feedback is the heart rate. Being able to model and predict the response of a subject’s heart rate on work load input allows the development of more advanced smart devices and analytic tools. These tools can monitor and control the subject’s activity and thus avoid overstrain which would eliminate the positive effect on the cardiovascular system. Current heart rate models were developed for a specific scenario and evaluated on unique data sets only. Additionally, most of these models were tested in indoor environments, e.g. on treadmills and bicycle ergometers. However, many people prefer to do sports in outdoors environments and use their smart phone to record their training data. In this paper, we present an evaluation of existing heart rate models and compare their prediction performance for indoor as well as for outdoor running exercises. For this purpose, we investigate analytical models as well as machine learning approaches in two training sets: one indoor exercise set recorded on a treadmill and one outdoor exercise set recorded by a smart phone.
With the increasing average age of the population in many developed countries, afflictions like cardiovascular diseases have also increased. Exercising has a proven therapeutic effect on the cardiovascular system and can counteract this development. To avoid overstrain, determining an optimal training dose is crucial. In previous research, heart rate has been shown to be a good measure for cardiovascular behavior. Hence, prediction of the heart rate from work load information is an essential part in models used for training control. Most heart-rate-based models are described in the context of specific scenarios, and have been evaluated on unique datasets only. In this paper, we conduct a joint evaluation of existing approaches to model the cardiovascular system under a certain strain, and compare their predictive performance. For this purpose, we investigated some analytical models as well as some machine learning approaches in two scenarios: prediction over a certain time horizon into the future, and estimation of the relation between work load and heart rate over a whole training session.
Microcontroller-based sensor systems offer great opportunities for the implementation of safety features for potentially dangerous machinery. However, in general they are difficult to assess with regard to their reliability and failure rate. This paper describes the safety assessment of hardware and software of a new and innovative sensor system. The hardware is assessed by standardized methods according to norm EN ISO 13849-1, while the use of model checking is presented as an approach to solve the problem of validating the software.
The Fitness Fatigue model is often used for performance analysis. It uses an initial basic level of performance and two antagonistic terms: a fitness-term and a fatigue-term. By fitting the models parameters, we adapt the model to the subject’s individual physical response to strain. Even though in most cases fitting of recorded training data shows useful results, without modification the model cannot be simply used for prediction.
This paper describes the development of a Pedelec controller whose performance level (PL) conforms to European standard on safety of machinery [9] and whose soft- ware is verified to conform to EPAC standard [6] by means of a software verification technique called model checking. In compliance with the standard [9] the hardware needs to implement the required properties corresponding to categories “C” and “D”. The latter is used if the breaks are not able to bring the velomobile with a broken motor controller to a full stop. Therefore the controller needs to implement a test unit, which verifies the functionality of the components and, in case of an emergency, shuts the whole hardware down to prevent injuries of the cyclist. The MTTFd can be measured through a failure graph, which is the result of a FMEA analysis, and can be used to proof that the Pedelec controller meets the regulations of the system specification. The analysis of the system in compliance with [9] usually treats the software as a black box thus ignoring its inner workings and validating its correctness by means of testing. In this paper we present a temporal logic specification according to [6], based on which the software for the Pedelec controller is implemented, and verify instead of only testing its functionality. By means of model checking [1] we proof that the software fulfills all requirements which are regulated by its specification.
A comprehensive analysis of cardiovascular control (CVC) patterns with multiple subjects is presented. It became feasible by recent methodological advances. Simple computer models were generated automatically, reproducing only factors of the true model that are relevant to the focus if investigation. These models?named aspect-models?could in turn be used in model individualization, thus reducing the necessary computational amount. The achieved speedup by a factor of more than three thousand and the high numerical stability of the resulting method allows the unsupervised identification of a large body of experimental data. The analysis of tilt table experiments of 18 subjects revealed a remarkable variety of reaction patterns. Closer examination yielded different classes of subjects. Two main groups corresponding to basic types of CVC were observed. Three outliers could be assigned to the specific situation of some subjects.
A detailed analysis of autonomic cardiovascular control (ACVC) may provide a key to a better understanding of the mechanisms underlying postflight orthostatic hypotension. The central substrate of human ACVC is not directly accessible to measurements and observation in space research. Modelling--supporting inference and physiological reasoning--is a valuable tool to disclose its involvement We are currently determining the suitability of artificial neural networks (ANN's) as a model of the central substrate of ACVC. Having conducted a number of experiments with simulated tilt test data to clarify the choice of input coding and of architectural biases in network training we will now report on the approximation of data obtained from human subjects during preparation of the German MIR'97 and D-2 missions.
A concept called model individualization is presented. It is used to modify computer based models to reproduce observed individual behavior. During D2-, MIR97- and Neurolab-missions tilt-table and LBNP-experiments were carried out. Physiological data describing the cardiovascular reactions of the astronauts were recorded. The appropriateness of the rheoretical principles is demonstrated with MIR97 tilt-table experiments. Finally the resulting individualized model is investigated to propose hypotheses on probable alterations in the cardiovascular system induced by microgravity.
In der vorliegenden Arbeit werden Verfahren vorgestellt, die geeignet sind, Modelle des menschlichen kardiovaskulären Systems an individuelle Kreislaufreaktionen anzupassen. Allgemeine Kreislaufmodelle des menschlichen kardiovaskulären Systems sind in der Regel nichtlineare Differentialgleichungssysteme, für die es keine effizienten Optimierungsverfahren gibt. Durch die Einschränkung auf relevante Aspekte (bzgl. der Individualisierungsaufgabe) wird ein solches Modell auf Modelle einfacherer Struktur projiziert, die eine Approximation durch Funktionsapproximatoren erlauben, für welche wiederum effiziente Optimierungsalgorithmen existieren. In Abhängigkeit von der Struktur der Individualisierungsaufgabe kommt zusätzlich ein modifiziertes BFGS-Verfahren zum Einsatz, das Approximationen solcher Modellaspekte verwendet um die Konvergenz der Modellindividualisierung zu verbessern.
We present a model checking algorithm for ∀CTL (and full CTL) which uses an iterative abstraction refinement strategy.
It terminates at least for all transition systems M that have a finite simulation or bisimulation quotient. In contrast to other abstraction refinement algorithms, we always work with abstract models whose sizes depend only on the length of the formula θ (but not on the size of the system, which might be infinite).
An evolved neural network controller is presented to solve the optimal control problem for energy optimal driving. A controller is produced which computes equivalent control commands to traditional graph searching approaches, while able to adapt to varied constraints and conditions. Furthermore, after training, trivial amounts of computation time and memory are required, making the approach applicable for embedded systems and path planning applications.
An evolutionary algorithm is presented to solve the optimal control problem for energy optimal driving. Results show that the algorithm computes equivalent strategies as traditional graph searching approaches like dynamic programming or A*. The algorithm proves to be time efficient while saving multiple orders of magnitude in memory compared to graph searching techniques. Thereby making it applicable in embedded applications such as eco-driving assistants or intelligent route planning.
