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The finite element method (FEM) is widely accepted for the steady-state dynamic response analysis of acoustic systems. It exhibits almost no restrictions with respect to the geometrical features of these systems. However, it is limited to the low-frequency range due to the rapidly growing model size for increasing frequencies. An alternative method is the wave based method (WBM), which is based on the indirect Trefftz approach. It exhibits better convergence properties than the FEM and therefore allows accurate predictions at higher frequencies. However, the applicability is limited, since the high computational efficiency only appears for systems of moderate geometrical complexity. In order to benefit from the advantageous features of both methods, i.e. the wide application range of the FEM and the high convergence rate of the WBM, the coupling between both methods is proposed. Only the parts of the problem domain with a complex geometry are modeled using the FEM, while the remaining parts are described with a wave based model. The resulting hybrid model contains less degrees of freedom, which allows a further model refinement. The proposed coupled approach has the potential to cover the mid-frequency range, where it is still difficult to obtain satisfactory prediction results with currently existing deterministic techniques.

Many biological systems are genuinely hybrids consisting of interacting discrete and continuous components and processes that often operate at different time scales. It is therefore desirable to create modeling frameworks capable of combining differently structured processes and permitting their analysis over multiple time horizons. During the past 40 years, Biochemical Systems Theory (BST) has been a very successful approach to elucidating metabolic, gene regulatory, and signaling systems. However, its foundation in ordinary differential equations has precluded BST from directly addressing problems containing switches, delays, and stochastic effects. In this study, we extend BST to hybrid modeling within the framework of Hybrid Functional Petri Nets (HFPN). First, we show how the canonical GMA and S-system models in BST can be directly implemented in a standard Petri Net framework. In a second step we demonstrate how to account for different types of time delays as well as for discrete, stochastic, and switching effects. Using representative test cases, we validate the hybrid modeling approach through comparative analyses and simulations with other approaches and highlight the feasibility, quality, and efficiency of the hybrid method.

Time plays an essential role in many biological systems, especially in cell cycle. Many models of biological systems rely on differential equations, but parameter identification is an obstacle to use differential frameworks. In this paper, we present a new hybrid modeling framework that extends René Thomas’ discrete modeling. The core idea is to associate with each qualitative state “celerities” allowing us to compute the time spent in each state. This hybrid framework is illustrated by building a 5-variable model of the mammalian cell cycle. Its parameters are determined by applying formal methods on the underlying discrete model and by constraining parameters using timing observations on the cell cycle. This first hybrid model presents the most important known behaviors of the cell cycle, including quiescent phase and endoreplication.

This paper proposes a new modeling method for Buck three-level (TL) converter. Based on the equivalent translation principle, the operating conditions of the Buck TL converter in different modes can be transformed into linear inequalities. Then, a new model of Buck TL converter containing matrix inequality is obtained. Compared with other Buck TL converter models, the proposed model of Buck TL converter is more concise. Finally, the proposed model is simulated in MATLAB and its effectiveness is verified by simulation and experimental results. Moreover, the experimental results are consistent with the simulation results.

We propose two methods of analysis of chaotic processes to be applied in sensory analysis. These methods may be used off-line in clinics e.g. for analysis of biosignals registered during sleep, or implemented into new sensor systems e.g. for drivers' vigilance monitoring in real time; they may also be applied in new type of hybrid models of circulatory and respiratory systems.

Goal-oriented measurement following the Goal/Question/Metric (GQM) approach is a well-defined and powerful tool in software management and decision-support. This chapter proposes the integration of GQM with a mature software process simulation approach, System Dynamics, in order to further enhance software managers' analytic, explorative, and decision-making capability. The proposed hybrid approach, which we denote “Dynamic GQM”, overcomes limitations that exist if applying GQM and system dynamics in isolation. It offers a new dimension of support to managers and decisionmakers by integrating traditional goal-oriented measurement and static modeling with the newly emerging paradigm of software process simulation and dynamic modeling. The hybrid approach is holistic by nature, i.e. it takes a global perspective on decision making in contrast to the local perspective advocated by traditional GQM. The proposed approach combines individual GQM plans into one consistent model and adds timedynamic behavior on top of it, thus offering a comprehensive view on what is actually happening in software projects.

Because of the special structure, it's not feasible to instrument pressure transducer, or torque sensor. The method of using strain gauge to measure the trunnion torque of centrifuge suspended basket is proposed. Therefore, torque measurement system is imperative to be founded. The mapping function of input and output is not absolute linear in practice. A neural network (NN) hybrid modeling approach is proposed and applied to torque measurement system calibration. The simulated studies on the calibration of single output system are conducted respectively by use of the developed hybrid modeling scheme. The NN hybrid modeling approach is utilized to calibrate torque measurement system prototype based on the measured data obtained from calibration tests. The simulated and experimental results show that the NN hybrid modeling approach can improve significantly calibration precision in comparison with traditional calibration methods. In addition, the NN hybrid modeling is superior to NN black box modeling because the former possesses smaller network scale, higher convergence speed, higher calibration precision and better generalization performance.