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Wave-like differential equations occur in many engineering applications. Here the engineering setup is embedded into the framework of functional analysis of modern mathematical physics. After an overview, the –Hilbert space approach to free Euler–Bernoulli bending vibrations of a beam in one spatial dimension is investigated. We analyze in detail the corresponding positive, selfadjoint differential operators of 4-th order associated to the boundary conditions in statics. A comparison with free string wave swinging is outlined.
We propose a method for recognizing dynamic gestures using a 3D sensor. New aspects of the developed system include problem-adapted data conversion and compression as well as automatic detection of different variants of the same gesture via clustering with a suitable metric inspired by Jaccard metric. The combination of Hidden Markov Models and clustering leads to robust detection of different executions based on a small set of training data. We achieved an increase of 5% recognition rate compared to regular Hidden Markov Models. The system has been used for human-machine interaction and might serve as an assistive system in physiotherapy and neurological or orthopedic diagnosis.
Due to the large interindividual variances and the poor optical accessibility of the ear, the specificity of hearing diagnostics today is severely restricted to a certain clinical picture and quantitative assessment. Often only a yes or no decision is possible, which depends strongly on the subjective assessment of the ENT physician. A novel approach, in which objectively obtainable, non invasive audiometric measurements are evaluated using a numerical middle ear model, makes it possible to make the hidden middle ear properties visible and quantifiable. The central topic of this paper is a novel parameter identification algorithm that combines inverse fuzzy arithmetic with an artificial neural network in order to achieve a coherent diagnostic overall picture in the comparison of model and measurement. Its usage is shown at a pathological pattern called malleus fixation where the upper ligament of the malleus is pathologically stiffened.
We present a new method for detecting gait disorders according to their stadium using cluster methods for sensor data. 21 healthy and 18 Parkinson subjects performed the time up and go test. The time series were segmented into separate steps. For the analysis the horizontal acceleration measured by a mobile sensor system was considered. We used dynamic time warping and hierarchical custering to distinguish the stadiums. A specificity of 92% was achieved.