There are several algorithms for analyzing and interpreting cardiorespiratory signals obtained from in-bed based sensors. In sum, these algorithms can be broadly grouped into three categories: time-domain algorithms, frequency-domain algorithms, and wavelet-domain algorithms. A summary of these algorithms is given below to highlight which category of algorithms will be used in our analysis. First, time-domain algorithms are mainly focused on detecting local maxima or local minima using a moving window, and therefore finding the interval between the dominant J-peaks of ballistocardiogram signal. However, this approach has many limitations because of the nonlinear and nonstationary behavior of the ballistocardiogram signal. The implication is that the ballistocardiogram signal does not display consistent J-peaks, which can usually be the case for overnight, in-home monitoring, particularly with frail elderly. Additionally, its accuracy will be undoubtedly affected by motion artifacts. Second, frequency-domain algorithms do not provide information about interbeat intervals. Nevertheless, they can provide information about heart rate variability. This is usually done by taking the fast Fourier transform or the inverse Fourier transform of the logarithm of the estimated spectrum, i.e., cepstrum of the signal using a sliding window. Thereafter, the dominant frequency is obtained in a particular frequency range. The limit of these algorithms is that the peak in the spectrum may get wider and multiple peaks may appear, which might cause a problem in measuring the vital signs. At last, the objective of wavelet-domain algorithms is to decompose the signal into different components, hence the component which shows an agreement with the vital signs can be selected. In other words, the selected component contains only information about the heart cycles or respiratory cycles, respectively. Interbeat intervals can be found easily by applying a simple peak detector. An empirical mode decomposition is an alternative approach to wavelet decomposition, and it is also a very suitable approach to cope with nonlinear and nonstationary signals such as cardiorespiratory signals. Apart from the above-mentioned algorithms, machine learning approaches have been implemented for measuring heartbeats. However, manual labeling of training data is a restricting property. Furthermore, the training step should be repeated whenever the data collection protocol has been changed.

Shape control of beams under general loading conditions is implemented using piezoceramic actuators to provide the control forces. The objective of the shape-control is to minimize the maximum deflection of the beam to obtain a min-max deflection configuration with respect to loading and piezo-actuators. In practice, the loading on a beam is a variable quantity with respect to its magnitude, and this aspect can be handled easily by optimizing the magnitude of the applied voltage to achieve the min-max deflection. This property of the smart materials technology overcomes the problem of one-off conventional optimal designs which become suboptimal when the loading magnitude changes.In addition to the magnitude of the applied voltage, the optimal values for the locations and the lengths of the piezo-actuators are determined to achieve the min-max deflection. Due to the complexity of the governing equations involving finite length piezo patches, the numerical results are obtained by the finite-difference method. The analysis of the problem shows the effect of the actuator locations, lengths and the applied voltage on the maximum deflection. The optimal values for the actuator locations and the voltage are determined as functions of the load locations and load magnitudes, respectively. The effect of the actuator length on the min-max deflection is investigated and it is observed that the optimal length depends on the applied voltage. Finally, it is shown that using multiple actuators are more effective than a single actuator in the cases of complicated loading.

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