Non-iterative simulation methods for virtual analog modelling

The simulation of nonlinear components is central to virtual analog simulation. In audio effects, circuits often include devices such as diodes and transistors, mostly operating in a strongly nonlinear regime. Mathematical models are in the form of systems of nonlinear ordinary differential equations (ODEs), and traditional integrators, such as the trapezoid and midpoint methods, can be employed as solvers. These methods are fully implicit and require the solution of a nonlinear algebraic system at each time step, introducing further complications regarding the existence and uniqueness of the solution, as well as the choice of halting conditions for the iterative root finder. On the other hand, fast explicit methods such as Forward Euler, are prone to unstable behaviour at standard audio sample rates. For these reasons, in this work, a family of linearly-implicit schemes is presented. These schemes take the form of a perturbation expansion, making the construction of higher-order schemes possible. Compared with classic implicit designs, the proposed methods have the advantage of efficiency, since the update is computed in a single iteration. Furthermore, the existence and uniqueness of the update are proven by simple inspection of the update matrix. Compared to classic explicit designs, the proposed schemes display stable behaviour at standard audio sample rates. In the case of a single scalar ODE, sufficient conditions for numerical stability can be derived, imposing constraints on the choice of the sampling rate. Several theoretical results are provided, as well as numerical examples for typical stiff equations used in virtual analog modelling

An effective simulation model to predict and optimize the performance of single and double glaze flat-plate solar collector designs

This paper outlines and formulates a compact and effective simulation model, which predicts the performance of single and double glaze flat-plate collector. The model uses an elaborated iterative simulation algorithm and provides the collector top losses, the glass covers temperatures, the collector absorber temperature, the collector fluid outlet temperature, the system efficiency, and the thermal gain for any operational and environmental conditions. It is a numerical approach based on simultaneous guesses for the three temperatures, Tp plate collector temperature and the temperatures of the two glass covers Tg1, Tg2. A set of energy balance equations is developed which allows for structured iteration modes whose results converge very fast and provide the values of any quantity which concerns the steady state performance profile of any flat-plate collector design. Comparison of the results obtained by this model for flat-plate collectors, single or double glaze, with those obtained by using the Klein formula, as well as the results provided by other researchers, is presented

An Adaptive Retraining Method for the Exchange Rate Forecasting

The paper advances an original artificial intelligence-based mechanism for specific economic predictions. The time series under discussion are non-stationary; therefore the distribution of the time series changes over time. The algorithm establishes how a viable structure of an artificial neural network (ANN) at a previous moment of time could be retrained in an efficient manner, in order to support modifications in a complex input-output function of financial forecasting. A "remembering process" for the former knowledge achieved in the previous learning phase is used to enhance the accuracy of the predictions. The results show that the first training (which includes the searching phase for the optimal architecture) always takes a relatively long time, but then the system can be very easily retrained, as there are no changes in the structure. The advantage of the retraining procedure is that some relevant aspects are preserved (remembered) not only from the immediate previous training phase, but also from the previous but one phase, and so on. A kind of slow forgetting process also occurs; thus it is much easier for the ANN to remember specific aspects of the previous training instead of the first training. The experiments reveal the high importance of the retraining phase as an upgrading/updating process and the effect of ignoring it, as well. There has been a decrease in the test error when successive retraining phases were performed.Neural Networks, Exchange Rate, Adaptive Retraining, Delay Vectors, Iterative Simulation

Segment assembly, structure alignment and iterative simulation in protein structure prediction

http://deepblue.lib.umich.edu/bitstream/2027.42/112917/1/12915_2013_Article_660.pd

P5_9 The Daredevil on Mars

This paper analyses the dynamics of the Daredevil, Felix Baumgartner’s Red Bull Stratos freefall if he were to perform the event in Mars’ atmosphere. We used an iterative simulation to calculate the trajectory taken under the effects of balancing drag and acceleration. We found that Felix would reach terminal velocity only a few hundred metres above the surface of Mars