Ergebnisse

Modern sensor technology for GPS signals, heart rate, oxygen uptake, and cycling power has made it possible to monitor and quantify road cycling performance in the lab, during training, and even in competitions. In this project we contributed to modeling, prediction, and optimization of road cycling performance by designing, calibrating, and validating mathematical physiological models that provide the means to analyze and predict cycling performance, and methods to compute optimal pacing strategies for cycling time trials based on these models. The research project was interdisciplinary including computer science and sports/exercise science, and it combined method development with implementations and validations in laboratory and field tests. A time trial in road cycling refers to a competition in which each cyclist individually races against the clock on a fixed course. A pacing strategy for such a race informs the athlete about how to expend his or her power to achieve the best result, i.e., the minimal time to reach the finish line. In the literature and in current practice, pacing is qualitative and rule-based. For example, a coach may recommend to generally ride at a certain power output and to increase the effort by 20–40 Watts on uphill road segments. The main goal of this research was a more specific pacing strategy that prescribes for any point along the track precisely the power output in Watts that the athlete should deliver for propulsion. In practice, such a strategy must be communicated to the rider during the course by an instrument like a handlebar mounted, programmable smartphone or a commercial bike computer. In order to compute such optimal pacing strategies, two mathematical models are required. The first one is a mechanical model that relates the pedal power to the speed along the entire track that must be given as a geometric model. There are numerous parameters that need to be calibrated such as rolling and aerial resistance, total system weight, and frictional loss in the drive chain. The second model is required to quantify the performance limits and remaining energy resources of the rider during the exercise, in particular the point of exhaustion. For an optimal performance, complete exhaustion must occur precisely at the finish line of the track. Again, the model must be adapted to the athlete by calibration of its parameters, among them so-called critical power and total anaerobic energy. These mathematical models must be given in a suitable form such that numerical algorithms of optimal control can be applied. This project contributed to all of these components, starting with the development of methods for parameter calibration and design and selection of the physiological model. In particular, the state-of-the-art for modeling oxygen consumption as a function of power and time was generalized from the constant work-rate case to a dynamic model allowing for variable power output. Several variations of the basic critical power model for performance were analyzed. The resulting equations do not easily lend themselves for numerical solution, and required researching suitable reparametrization and regularization methods for implementation in a number of computing packages for numerical optimal control. Besides this basic work, the optimal strategies and their visual feedback to the athlete were implemented in a custom made Android based smart phone application, as well as for application in a commercial bike computer. An adaptation of the optimal strategy was also developed based on current state-of-the-art engineering practice. Such an adaptation should be made when deviations of riding conditions from the ones used in the computation or deviations of the applied pacing from the optimal one occur. Our optimal pacing strategies were tested in severals experiments. The first one was a lab test on a simulator providing the advantage over field rides that the simulated riding conditions could be strictly controlled. We have developed a testing methodology that separates the contribution of the optimal pacing from the effect of just using a pacemaker. It clearly confirmed the potential of the optimal strategies to improve cycling performance. A second series of trials was carried out in the field using smartphones with our app for visual feedback of the pacing. The results show that our app can guide cyclists on precomputed optimal pacing strategies using adaptation algorithms and improve their finish time. For the future, we are planning to modify the technology to be applicable in a broad sense for hobby and amateur riders without requiring elaborate testing for parameter settings. This can be achieved by making use of recorded rides on a social media platform for GPS based activities for calibration, by minimizing the required energy to reach the finish line of an uphill time trial in a desired time specified by the user, and by using a common bike computer giving feedback in the form of time ahead resp. behind the optimal pacing strategy. We have applied optimization also for the cases of systems of two cooperating respectively competing riders, by modeling and incorporating the slipstream effect. The method for cooperating riders can show how often the lead position of the riders should be swapped for optimal performance of the team. The one for competing riders can show, when the drafting rider should overtake the leading one for the final sprint.

Zusammenfassung

Das interdisziplinäre Projekt verbindet mathematische Modellierung, Numerik und Systementwicklung mit Sportwissenschaft und kann somit der Sportinformatik zugerechnet werden. Für den Ausdauersport Rennradfahren werden Methoden zur Modell-basierten Optimierung entwickelt, nämlich für- das Design, die Kalibrierung und die Validierung mathematischer, physiologischer Performanz-Modelle und- die Berechnung optimaler Steuerung für Zeitfahrrennen.Neben einem mechanischen Modell für die wirkenden Kräfte und deren Effekte wird ein individuelles physiologisches Model für jeden Athleten benötigt, das die zu jedem Zeitpunkt verfügbare Leistung sowie die restlichen Energiereserven angibt. Das letztere ist eine offene, schwierige Forschungsfrage. Es ist nicht möglich, alle relevanten physiologischen Aspekte zu modellieren. Der menschliche Organismus mit seinen vielen Subsystemen ist dazu zu komplex. Es gilt, einen Kompromiss für den Tradeoff zwischen notwendiger Abstraktion und Modelltreue zu finden.Zu diesem Zweck werden wir `semi-physical modelling´ einsetzen. Das heißt, die aktuellen Modelle des state-of-the-art bilden die Basis für erweiterte Ansätze, wobei Details und Parameterschätzung auf der Grundlage von gemessenen Input-Output Paaren mit Methoden der System Identification bestimmt werden. Inputs sind geeignet gewählte Belastungsprotokolle zu Ergometertests. Outputs sind die zugehörigen Messreihen von Sauerstoff-Aufnahme, Kohlendioxyd-Abgabe, Puls bzw. Pulsvariabilität und Laktat-Blutwerte.Die mechanischen und physiologischen Modelle ergeben Systeme von Differentialgleichungen mit Nebenbedingungen in der Form von Ungleichungen die als Grundlage für die Berechnung der optimalen Steuerung für Zeitfahrrennen eingesetzt werden. Obwohl effiziente neuere numerische Verfahren und entsprechende, frei verfügbare Programmpakete zur Lösung allgemeiner Probleme der optmalen Steuerung vorhanden sind, erfordern bestimmte Eigenschaften des vorliegenden Problems spezielle Anpassungen und Erweiterungen um verlässliche Konvergenz zu erhalten.Ein Teil des Projektes besteht aus der Evaluierung der Modelle und der Ergebnisse der optimalen Fahrstrategien. Die Genauigkeit der Modellvorhersagen ergibt sich aus den Methoden zur Kalibrierung. Die optimalen Strategien werden zunächst an einem vorhandenen wissenschaftlichen Fahrsimulator und dann auch in Feldversuchen evaluiert. Dazu ist ein gps-fähiges mobiles Endgerät zu entwickeln, dass dem Fahrer an jedem Ort die optimale Leistung und eventuell auch Trittfrequenz vermittelt. Idealerweise soll dieses mobile Gerät die optimale Steuerung an gegebene Abweichungen von der vorgeschriebenen Strategie in Echtzeit anpassen können.
(DFG- Projektnummer 247721022)