Analysis of bilinear hysteretic structures with nonlinear fluid viscous dampers using modified stochastic linearization technique

Optimal tracking control for blast furnace molten iron quality based on subspace identification and Krotov's method

“…Problem 1. For the given system Equation ( 23) and the output Equation (24), design a controller that can ensure that the output of the system follows the given reference trajectory (25) and minimize the performance index (26).…”

“…Therefore, bilinear system is widely used in various fields of industrial engineering. [22][23][24] In consideration of the fact that blast furnace ironmaking is a complex nonlinear dynamic system, a bilinear system model can be introduced to improve the accuracy of modeling blast furnace ironmaking process. Moreover, Krotov's method has received special attention in recent years.…”

“…Bilinear system is a kind of simple nonlinear system with special variable structure characteristics of both linearity and nonlinearity, which achieves a good balance between the accuracy of general nonlinear systems and the mathematical tractability of linear systems, and can be used to provide a better approximation for a class of practical processes. Therefore, bilinear system is widely used in various fields of industrial engineering 22‐24 . In consideration of the fact that blast furnace ironmaking is a complex nonlinear dynamic system, a bilinear system model can be introduced to improve the accuracy of modeling blast furnace ironmaking process.…”

A novel stochastic linearization technique for structures with nonlinear fluid viscous dampers including soil-structure interaction

“…Among the different alternatives proposed in the literature, stochastic linearization techniques (SLTs) have proven very efficient to linearize the force-velocity relationship of FVDs. SLTs are practical and convenient because they: a) linearize the nonlinear behavior of viscous dampers using a response spectrum analysis, and b) employ random earthquake simulations, contrary to the common assumption that earthquakes are harmonic [13][14][15][16][17][18]. Probabilistic SLTs also take into account the evolutionary characteristics of the earthquake input.…”

“…More recently, Asadpour et al [17][18] proposed a new modified SLT to analyze structures with nonlinear FVDs. The new SLT reduces the computational errors by using optimized non-Gaussian probability density functions (PDFs), which leads to more accurate results when applied to SDOF and MDOF systems.…”