Effects of distributed delays on the stability of structures under seismic excitation and multiplicative noise

The effects of seismic excitation and multiplicative noise (arising from environmental fluctuations) on the stability of a single degree of freedom system with distributed delays are investigated. The system is modelled in the form of a stochastic integro-differential equation interpreted in Stratonovich sense. Both deterministic stability and stochastic moment stability are examined for the system in the absence of seismic excitation. The model is also extended to incorporate effects of symmetric nonlinearity. The simulation of stochastic linear and nonlinear systems are carried out by resorting to numerical techniques for the solution of stochastic differential equations

Stochastic stability of structures under active control with distributed time delays

The pathwise behaviour of a single degree of freedom (SDOF) system with symmetric nonlinearity and distributed delays is investigated under the presence of seismic excitation and multiplicative noise. Besides distributed time delays and finite build-up time of control force are taken into consideration. The system is modelled as stochastic integro-differential equation with exponential type kernels. Interpreting stochastic equations in Stratonovich sense, stochastic stability is analyzed in terms of Lyapunov exponents. Estimates of frequencies with which sample paths of displacement of SDOF system cross certain critical values are also obtained. Studies of stochastic linear and nonlinear systems are carried out by resorting to numerical techniques for the solution of (ordinary) stochastic differential equations

Performance comparison of optimal fractional order hybrid fuzzy PID controllers for handling oscillatory fractional order processes with dead time

This is the author accepted manuscript. The final version is available from Elsevier via the DOI in this record.Fuzzy logic based PID controllers have been studied in this paper, considering several combinations of hybrid controllers by grouping the proportional, integral and derivative actions with fuzzy inferencing in different forms. Fractional order (FO) rate of error signal and FO integral of control signal have been used in the design of a family of decomposed hybrid FO fuzzy PID controllers. The input and output scaling factors (SF) along with the integro-differential operators are tuned with real coded genetic algorithm (GA) to produce optimum closed loop performance by simultaneous consideration of the control loop error index and the control signal. Three different classes of fractional order oscillatory processes with various levels of relative dominance between time constant and time delay have been used to test the comparative merits of the proposed family of hybrid fractional order fuzzy PID controllers. Performance comparison of the different FO fuzzy PID controller structures has been done in terms of optimal set-point tracking, load disturbance rejection and minimal variation of manipulated variable or smaller actuator requirement etc. In addition, multi-objective Non-dominated Sorting Genetic Algorithm (NSGA-II) has been used to study the Pareto optimal trade-offs between the set point tracking and control signal, and the set point tracking and load disturbance performance for each of the controller structure to handle the three different types of processes

Profitability of time series momentum

© 2015 Elsevier B.V. We propose a continuous-time heterogeneous agent model consisting of fundamental, momentum, and contrarian traders to explain the significant time series momentum. We show that the performance of momentum strategy is determined by both time horizon and the market dominance of momentum traders. Specifically, when momentum traders are more active in the market, momentum strategies with short (long) time horizons stabilize (destabilize) the market, and meanwhile the market under-reacts (over-reacts) in short-run (long-run). This provides profit opportunity for time series momentum strategies with short horizons and reversal with long horizons. When momentum traders are less active in the market, they always lose. The results provide an insight into the profitability of time series momentum documented in recent empirical studies

Dynamics and simulations of stochastic COVID-19 epidemic model using Legendre spectral collocation method

The aim of this study is to investigate the dynamics of epidemic transmission of COVID-19 SEIR stochastic model with generalized saturated incidence rate. We assume that the random perturbations depends on white noises, which implies that it is directly proportional to the steady states. The existence and uniqueness of the positive solution along with the stability analysis is provided under disease-free and endemic equilibrium conditions for asymptotically stable transmission dynamics of the model. An epidemiological metric based on the ratio of basic reproduction is used to describe the transmission of an infectious disease using different parameters values involve in the proposed model. A higher order scheme based on Legendre spectral collocation method is used for the numerical simulations. For the better understanding of the proposed scheme, a comparison is made with the deterministic counterpart. In order to confirm the theoretical analysis, we provide a number of numerical examples