Laminated Wave Turbulence: Generic Algorithms III

Model of laminated wave turbulence allows to study statistical and discrete layers of turbulence in the frame of the same model. Statistical layer is described by Zakharov-Kolmogorov energy spectra in the case of irrational enough dispersion function. Discrete layer is covered by some system(s) of Diophantine equations while their form is determined by wave dispersion function. This presents a very special computational challenge - to solve Diophantine equations in many variables, usually 6 to 8, in high degrees, say 16, in integers of order $10^{16}$ and more. Generic algorithms for solving this problem in the case of {\it irrational} dispersion function have been presented in our previous papers. In this paper we present a new generic algorithm for the case of {\it rational} dispersion functions. Special importance of this case is due to the fact that in wave systems with rational dispersion the statistical layer does not exist and the general energy transport is governed by the discrete layer alone.Comment: submitted to IJMP

A dynamic prognosis algorithm in distributed fault tolerant model predictive control

This paper presents a dynamic prognosis algorithm in distributed fault tolerant model predictive control (DFTMPC). The dynamic prognosis, which means predicting the trajectories of process variables under distributed model predictive control, is performed when a fault is diagnosed and several candidate reconfigured controls are proposed. Then, the dynamic prognosis is utilized to check whether the candidate reconfigured controls are able to drive the system to the new operating conditions and to evaluate the performance during the transition period. Thus, the most suitable candidate reconfigured controller is selected and its feasibility is ensured without using a Lyapunov function that is difficult to obtain for large-scale systems. On the other hand, the on-line computation burden of the prognosis algorithm is moderate under the assumption that the sets of active constraints in non-faulty subsystems remain the same as they are at the nominal operating conditions. Thus, the dynamic prognosis for DMPC is aimed to improve the applicability of the existing fault tolerant methods to large-scale systems.Peer reviewe

A method for detecting non-stationary oscillations in process plants

This paper proposes a method for detecting oscillations in non-stationary timeseries based on the statistical properties of zero-crossings. The main development presented is atechnique to remove non-stationary trend component from the analysed signals before applyingan oscillation detection procedure. First, the method extracts the signal's baseline that is utilizedto stationarize the signal. Then, an index describing the regularity of the stationarized signal'szero-crossings is computed in order to determine the presence of oscillation. The propertiesand performance of the method are analysed in simulation studies. Furthermore, the methodis comprehensively tested with industrial data in a comparative study in which the proposedmethod is tested against other oscillation detection methods using industrial benchmark dataand in tests on paperboard machine process. Finally, the simulation and industrial results areanalysed and discussed.Peer reviewe

A performance optimization algorithm for controller reconfiguration in fault tolerant distributed model predictive control

This paper presents a performance optimization algorithm for controller reconfiguration in fault tol-erant distributed model predictive control for large-scale systems. After the fault has been detectedand diagnosed, several controller reconfigurations are proposed as candidate corrective actions for faultcompensation. The solution of a set of constrained optimization problems with different actuator andsetpoint reconfigurations is derived by means of an original approach, exploiting the information onthe active constraints in the non-faulty subsystems. Thus, the global optimization problem is split intotwo optimization subproblems, which enable the online computational burden to be greatly reduced.Subsequently, the performances of different candidate controller reconfigurations are compared, andthe better performing one is selected and then implemented to compensate the fault effects. Efficacyof the proposed approach has been shown by applying it to the benzene alkylation process, which is abenchmark process in distributed model predictive control.Peer reviewe