Fitting Jump Models

We describe a new framework for fitting jump models to a sequence of data. The key idea is to alternate between minimizing a loss function to fit multiple model parameters, and minimizing a discrete loss function to determine which set of model parameters is active at each data point. The framework is quite general and encompasses popular classes of models, such as hidden Markov models and piecewise affine models. The shape of the chosen loss functions to minimize determine the shape of the resulting jump model.Comment: Accepted for publication in Automatic

Data driven discovery of cyber physical systems

Cyber-physical systems embed software into the physical world. They appear in a wide range of applications such as smart grids, robotics, and intelligent manufacturing. Cyber-physical systems have proved resistant to modeling due to their intrinsic complexity arising from the combination of physical and cyber components and the interaction between them. This study proposes a general framework for discovering cyber-physical systems directly from data. The framework involves the identification of physical systems as well as the inference of transition logics. It has been applied successfully to a number of real-world examples. The novel framework seeks to understand the underlying mechanism of cyber-physical systems as well as make predictions concerning their state trajectories based on the discovered models. Such information has been proven essential for the assessment of the performance of cyber- physical systems; it can potentially help debug in the implementation procedure and guide the redesign to achieve the required performance

Diabetes Mellitus Glucose Prediction by Linear and Bayesian Ensemble Modeling

Diabetes Mellitus is a chronic disease of impaired blood glucose control due to degraded or absent bodily-specific insulin production, or utilization. To the affected, this in many cases implies relying on insulin injections and blood glucose measurements, in order to keep the blood glucose level within acceptable limits. Risks of developing short- and long-term complications, due to both too high and too low blood glucose concentrations are severalfold, and, generally, the glucose dynamics are not easy too fully comprehend for the affected individual—resulting in poor glucose control. To reduce the burden this implies to the patient and society, in terms of physiological and monetary costs, different technical solutions, based on closed or semi-closed loop blood glucose control, have been suggested. To this end, this thesis investigates simplified linear and merged models of glucose dynamics for the purpose of short-term prediction, developed within the EU FP7 DIAdvisor project. These models could, e.g., be used, in a decision support system, to alert the user of future low and high glucose levels, and, when implemented in a control framework, to suggest proactive actions. The simplified models were evaluated on 47 patient data records from the first DIAdvisor trial. Qualitatively physiological correct responses were imposed, and model-based prediction, up to two hours ahead, and specifically for low blood glucose detection, was evaluated. The glucose raising, and lowering effect of meals and insulin were estimated, together with the clinically relevant carbohydrate-to-insulin ratio. The model was further expanded to include the blood-to-interstitial lag, and tested for one patient data set. Finally, a novel algorithm for merging of multiple prediction models was developed and validated on both artificial data and 12 datasets from the second DIAdvisor trial

Physiological Control of Human Heart Rate and Oxygen Consumption during Rhythmic Exercises

Physical exercise has significant benefits for humans in improving the health and quality of their lives, by improving the functional performance of their cardiovascular and respiratory systems. However, it is very important to control the workload, e.g. the frequency of body movements, within the capability of the individual to maximise the efficiency of the exercise. The workload is generally represented in terms of heart rate (HR) and oxygen consumption VO2. We focus particularly on the control of HR and VO2 using the workload of an individual body movement, also known as the exercise rate (ER), in this research. The first part of this report deals with the modelling and control of HR during an unknown type of rhythmic exercise. A novel feature of the developed system is to control HR via manipulating ER as a control input. The relation between ER and HR is modelled using a simple autoregressive model with unknown parameters. The parameters of the model are estimated using a Kalman filter and an indirect adaptive H1 controller is designed. The performance of the system is tested and validated on six subjects during rowing and cycling exercise. The results demonstrate that the designed control system can regulate HR to a predefined profile. The second part of this report deals with the problem of estimating VO2 during rhythmic exercise, as the direct measurement of VO2 is not realisable in these environments. Therefore, non-invasive sensors are used to measure HR, RespR, and ER to estimate VO2. The developed approach for cycling and rowing exercise predicts the percentage change in maximum VO2 from the resting to the exercising phases, using a Hammerstein model.. Results show that the average quality of fit in both exercises is improved as the intensity of exercise is increased

Computational driver behavior models for vehicle safety applications

The aim of this thesis is to investigate how human driving behaviors can be formally described in mathematical models intended for online personalization of advanced driver assistance systems (ADAS) or offline virtual safety evaluations. Both longitudinal (braking) and lateral (steering) behaviors in routine driving and emergencies are addressed. Special attention is paid to driver glance behavior in critical situations and the role of peripheral vision.First, a hybrid framework based on autoregressive models with exogenous input (ARX-models) is employed to predict and classify driver control in real time. Two models are suggested, one targeting steering behavior and the other longitudinal control behavior. Although the predictive performance is unsatisfactory, both models can distinguish between different driving styles.Moreover, a basic model for drivers\u27 brake initiation and modulation in critical longitudinal situations (specifically for rear-end conflicts) is constructed. The model is based on a conceptual framework of noisy evidence accumulation and predictive processing. Several model extensions related to gaze behavior are also proposed and successfully fitted to real-world crashes and near-crashes. The influence of gaze direction is further explored in a driving simulator study, showing glance response times to be independent of the glance\u27s visual eccentricity, while brake response times increase for larger gaze angles, as does the rate of missed target detections.Finally, the potential of a set of metrics to quantify subjectively perceived risk in lane departure situations to explain drivers\u27 recovery steering maneuvers was investigated. The most influential factors were the relative yaw angle and splay angle error at steering initiation. Surprisingly, it was observed that drivers often initiated the recovery steering maneuver while looking off-road.To sum up, the proposed models in this thesis facilitate the development of personalized ADASs and contribute to trustworthy virtual evaluations of current, future, and conceptual safety systems. The insights and ideas contribute to an enhanced, human-centric system development, verification, and validation process. In the long term, this will likely lead to improved vehicle safety and a reduced number of severe injuries and fatalities in traffic