Abstract: Stochastic modeling concerns the use of probability
to model real-world situations in which uncertainty is present.
Therefore, the purpose of stochastic modeling is to estimate the
probability of outcomes within a forecast, i.e. to be able to predict
what conditions or decisions might happen under different situations.
In the present study, we present a model of a stochastic diffusion
process based on the bi-Weibull distribution function (its trend
is proportional to the bi-Weibull probability density function). In
general, the Weibull distribution has the ability to assume the
characteristics of many different types of distributions. This has
made it very popular among engineers and quality practitioners, who
have considered it the most commonly used distribution for studying
problems such as modeling reliability data, accelerated life testing,
and maintainability modeling and analysis. In this work, we start
by obtaining the probabilistic characteristics of this model, as the
explicit expression of the process, its trends, and its distribution by
transforming the diffusion process in a Wiener process as shown in
the Ricciaardi theorem. Then, we develop the statistical inference of
this model using the maximum likelihood methodology. Finally, we
analyse with simulated data the computational problems associated
with the parameters, an issue of great importance in its application to
real data with the use of the convergence analysis methods. Overall,
the use of a stochastic model reflects only a pragmatic decision on
the part of the modeler. According to the data that is available and
the universe of models known to the modeler, this model represents
the best currently available description of the phenomenon under
consideration.
Abstract: Probabilistic characteristics of seismic responses of the
Partially Restrained connection rotation (PRCR) and panel zone
deformation (PZD) installed in older steel moment frames were
investigated in accordance with statistical inference in
decision-making process. The 4, 6 and 8 story older steel moment
frames with clip angle and T-stub connections were designed and
analyzed using 2%/50yrs ground motions in four cities of the
Mid-America earthquake region. The probability density function and
cumulative distribution function of PRCR and PZD were determined
by the goodness-of-fit tests based on probabilistic parameters
measured from the results of the nonlinear time-history analyses. The
obtained probabilistic parameters and distributions can be used to find
out what performance level mainly PR connections and panel zones
satisfy and how many PR connections and panel zones experience a
serious damage under the Mid-America ground motions.