Acceleration deterministic model

This problem was solved using the Point Estimate technique with the following set of values (after (Kelly 1993)) m=100 t, Wb = 66 t, cos Stt rad/s, cob = 7T rad/s, Vs = 0.02, Vb = 0.1. For the peak ground acceleration Ag a mean value equal to 0.25g was employed. The results for the standard deviation of the base and structural displacements are 0.0676 m and = 0.0135 m. The solution required only six deterministic calculations of the displacement responses. Finally, the standard deviations of these displacements without regard to parameter uncertainties and using their mean values were found to be 0.0614 m and 0.0123 m, respectively. For both cases the error in omitting the uncertainties in model parameters is 10.2%. 

The PDF transport equation (12.4.2-2) is deterministic. Convection appears in closed form. The conditional acceleration term (12.4.2-3) and the conditional diffusion / reaction term (12.4.2-4) are unclosed. In the conditional acceleration term (12.4.2-3), only the first term in the right hand side is actually unclosed. The effects of gravity are dealt with in an exact way. In the conditional diffusion / reaction term (12.4.2-4), the turbulent mixing term is unclosed, but the reaction rate appears in closed form whatever the complexity and nonlinearity of the reaction kinetics. The remaining part of this section focuses on closure models. 

The stop margin is the deterministic runway length minus the operational landing distance, which depends on a number of factors that are modeled as random variables. The model is derived from the equations of motion. The acceleration of the aircraft in x-direction is ... 

For the acceleration and deceleration simulations, the powertrain and/or braking system dynamics are considered in a very approximate manner. Deterministic functions of time are adopted which account for typical time delays involved in these system s responses and the available level of performance for the type of vehicle being modelled. The input quantities will be either driving or braking forces for the linear tyre which assume no slip in the longitudinal motion of the wheels. 

In the simplest case, the effects of xmcertainty can be assumed by the default values of seismic performance of a structure can be used. This enables the use of analytical models for the determination of the target displacement. Parametric studies have shown that the cri depends on the limit state and the type of seismic intensity measure. If the intensities causing collapse are assessed by the spectral acceleration corresponding to the first vibration period, the crin is in the interval between 0.3 and 0.5 (Lazar and Dolsek 2014). The (Tin imLs increases with respect to the period of structure if it is assessed on the basis of peak ground acceleration. It varies between 0.5 and... 

Analytic Fragility and Limit States [P(EDP IM)] Nonlinear Static Procedures, Fig. 3 The limit-state peak ground accelerations and displacements associated with the set of structural models and (a) the deterministic... 

The objective of state estimation is to estimate the system states from a limited number of response measurements (e.g., acceleration measurements) and a system model. The state vector can be determined using a deterministic approach (e.g., least squares estimation of the state vector in the frequency domain) or using a combined deterministic-stochastic approach, which mostly results in recursive time-domain algorithms which can be applied for online state estimation. The best-known recursive state estimation algorithm for linear systems is the Kalman filter algorithm (Kalman 1960), which is outlined next. 

The structural response factor, Frs, is based on the recognition of the fact that in the design analyses, structural response is computed using specific (often cmiservative) deterministic response parameters for the stmcture. Since many of these parameters are nondeterministic (often with wide variability), the actual response may differ substantially from the calculated response for a given peak ground acceleration. Frs is modeled as a product of factors influencing the response bias and variability ... 

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