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Bouc–Wen Model Of Hysteresis
In structural engineering, the Bouc–Wen model of hysteresis is a hysteretic model typically employed to describe non-linear hysteretic systems. It was introduced by Robert Bouc and extended by Yi-Kwei Wen, who demonstrated its versatility by producing a variety of hysteretic patterns. This model is able to capture, in analytical form, a range of hysteretic cycle shapes matching the behaviour of a wide class of hysteretical systems. Due to its versatility and mathematical tractability, the Bouc–Wen model has gained popularity. It has been extended and applied to a wide variety of engineering problems, including multi-degree-of-freedom (MDOF) systems, buildings, frames, bidirectional and torsional response of hysteretic systems, two- and three-dimensional continua, soil liquefaction and base isolation systems. The Bouc–Wen model, its variants and extensions have been used in structural control—in particular, in the modeling of behaviour of magneto-rheological dampers, base-i ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Structural Engineering
Structural engineering is a sub-discipline of civil engineering in which structural engineers are trained to design the 'bones and joints' that create the form and shape of human-made Structure#Load-bearing, structures. Structural engineers also must understand and calculate the structural stability, stability, strength, structural rigidity, rigidity and earthquake-susceptibility of built structures for buildings and nonbuilding structures. The structural designs are integrated with those of other designers such as architects and Building services engineering, building services engineer and often supervise the construction of projects by contractors on site. They can also be involved in the design of machinery, medical equipment, and vehicles where structural integrity affects functioning and safety. See glossary of structural engineering. Structural engineering theory is based upon applied physics, physical laws and empirical knowledge of the structural performance of different ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Rosenbrock Methods
Rosenbrock methods refers to either of two distinct ideas in numerical computation, both named for Howard H. Rosenbrock. Numerical solution of differential equations Rosenbrock methods for stiff differential equations are a family of single-step methods for solving ordinary differential equations. They are related to the implicit Runge–Kutta methods and are also known as Kaps–Rentrop methods. Search method Rosenbrock search is a numerical optimization algorithm applicable to optimization problems in which the objective function is inexpensive to compute and the derivative either does not exist or cannot be computed efficiently. The idea of Rosenbrock search is also used to initialize some root-finding routines, such as fzero (based on Brent's method) in Matlab MATLAB (an abbreviation of "MATrix LABoratory") is a proprietary multi-paradigm programming language and numeric computing environment developed by MathWorks. MATLAB allows matrix manipulations, plotting of ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Solid Mechanics
Solid mechanics (also known as mechanics of solids) is the branch of continuum mechanics that studies the behavior of solid materials, especially their motion and deformation (mechanics), deformation under the action of forces, temperature changes, phase (chemistry), phase changes, and other external or internal agents. Solid mechanics is fundamental for civil engineering, civil, Aerospace engineering, aerospace, nuclear engineering, nuclear, Biomedical engineering, biomedical and mechanical engineering, for geology, and for many branches of physics and chemistry such as materials science. It has specific applications in many other areas, such as understanding the anatomy of living beings, and the design of dental prosthesis, dental prostheses and surgical implants. One of the most common practical applications of solid mechanics is the Euler–Bernoulli beam theory, Euler–Bernoulli beam equation. Solid mechanics extensively uses tensors to describe stresses, strains, and the r ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Materials Science
Materials science is an interdisciplinary field of researching and discovering materials. Materials engineering is an engineering field of finding uses for materials in other fields and industries. The intellectual origins of materials science stem from the Age of Enlightenment, when researchers began to use analytical thinking from chemistry, physics, and engineering to understand ancient, phenomenological observations in metallurgy and mineralogy. Materials science still incorporates elements of physics, chemistry, and engineering. As such, the field was long considered by academic institutions as a sub-field of these related fields. Beginning in the 1940s, materials science began to be more widely recognized as a specific and distinct field of science and engineering, and major technical universities around the world created dedicated schools for its study. Materials scientists emphasize understanding how the history of a material (''processing'') influences its struc ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Particle Swarm Optimization
In computational science, particle swarm optimization (PSO) is a computational method that Mathematical optimization, optimizes a problem by iterative method, iteratively trying to improve a candidate solution with regard to a given measure of quality. It solves a problem by having a population of candidate solutions, here dubbed Point particle, particles, and moving these particles around in the Optimization (mathematics)#Concepts and notation, search-space according to simple formula, mathematical formulae over the particle's Position (vector), position and velocity. Each particle's movement is influenced by its local best known position, but is also guided toward the best known positions in the search-space, which are updated as better positions are found by other particles. This is expected to move the swarm toward the best solutions. PSO is originally attributed to James Kennedy (social psychologist), Kennedy, Russell C. Eberhart, Eberhart and Yuhui Shi, Shi and was first int ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Genetic Algorithms
In computer science and operations research, a genetic algorithm (GA) is a metaheuristic inspired by the process of natural selection that belongs to the larger class of evolutionary algorithms (EA). Genetic algorithms are commonly used to generate high-quality solutions to optimization and search problems via biologically inspired operators such as selection, crossover, and mutation. Some examples of GA applications include optimizing decision trees for better performance, solving sudoku puzzles, hyperparameter optimization, and causal inference. Methodology Optimization problems In a genetic algorithm, a population of candidate solutions (called individuals, creatures, organisms, or phenotypes) to an optimization problem is evolved toward better solutions. Each candidate solution has a set of properties (its chromosomes or genotype) which can be mutated and altered; traditionally, solutions are represented in binary as strings of 0s and 1s, but other encodi ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Differential Evolution
Differential evolution (DE) is an evolutionary algorithm to optimize a problem by iteratively trying to improve a candidate solution with regard to a given measure of quality. Such methods are commonly known as metaheuristics as they make few or no assumptions about the optimized problem and can search very large spaces of candidate solutions. However, metaheuristics such as DE do not guarantee an optimal solution is ever found. DE is used for multidimensional real-valued functions but does not use the gradient of the problem being optimized, which means DE does not require the optimization problem to be differentiable, as is required by classic optimization methods such as gradient descent and quasi-newton methods. DE can therefore also be used on optimization problems that are not even continuous, are noisy, change over time, etc. DE optimizes a problem by maintaining a population of candidate solutions and creating new candidate solutions by combining existing ones accor ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Particle Filter
Particle filters, also known as sequential Monte Carlo methods, are a set of Monte Carlo algorithms used to find approximate solutions for filtering problems for nonlinear state-space systems, such as signal processing and Bayesian statistical inference. The filtering problem consists of estimating the internal states in dynamical systems when partial observations are made and random perturbations are present in the sensors as well as in the dynamical system. The objective is to compute the posterior distributions of the states of a Markov process, given the noisy and partial observations. The term "particle filters" was first coined in 1996 by Pierre Del Moral about mean-field interacting particle methods used in fluid mechanics since the beginning of the 1960s. The term "Sequential Monte Carlo" was coined by Jun S. Liu and Rong Chen in 1998. Particle filtering uses a set of particles (also called samples) to represent the posterior distribution of a stochastic process giv ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Kalman Filter
In statistics and control theory, Kalman filtering (also known as linear quadratic estimation) is an algorithm that uses a series of measurements observed over time, including statistical noise and other inaccuracies, to produce estimates of unknown variables that tend to be more accurate than those based on a single measurement, by estimating a joint probability distribution over the variables for each time-step. The filter is constructed as a mean squared error minimiser, but an alternative derivation of the filter is also provided showing how the filter relates to maximum likelihood statistics. The filter is named after Rudolf E. Kálmán. Kalman filtering has numerous technological applications. A common application is for guidance, navigation, and control of vehicles, particularly aircraft, spacecraft and ships Dynamic positioning, positioned dynamically. Furthermore, Kalman filtering is much applied in time series analysis tasks such as signal processing and econometrics. K ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
System Identification
The field of system identification uses statistical methods to build mathematical models of dynamical systems from measured data. System identification also includes the optimal design#System identification and stochastic approximation, optimal design of experiments for efficiently generating informative data for regression analysis, fitting such models as well as model reduction. A common approach is to start from measurements of the behavior of the system and the external influences (inputs to the system) and try to determine a mathematical relation between them without going into many details of what is actually happening inside the system; this approach is called Black box (systems), black box system identification. Overview A dynamic mathematical model in this context is a mathematical description of the dynamic behavior of a system or process in either the time or frequency domain. Examples include: * physical system, physical processes such as the movement of a falling bo ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Brent Method
In numerical analysis, Brent's method is a hybrid root-finding algorithm combining the bisection method, the secant method and inverse quadratic interpolation. It has the reliability of bisection but it can be as quick as some of the less-reliable methods. The algorithm tries to use the potentially fast-converging secant method or inverse quadratic interpolation if possible, but it falls back to the more robust bisection method if necessary. Brent's method is due to Richard Brent and builds on an earlier algorithm by Theodorus Dekker. Consequently, the method is also known as the Brent–Dekker method. Modern improvements on Brent's method include Chandrupatla's method, which is simpler and faster for functions that are flat around their roots; Ridders' method, which performs exponential interpolations instead of quadratic providing a simpler closed formula for the iterations; and the ITP method which is a hybrid between regula-falsi and bisection that achieves optimal worst-c ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Gauss Hypergeometric Function
In mathematics, the Gaussian or ordinary hypergeometric function 2''F''1(''a'',''b'';''c'';''z'') is a special function represented by the hypergeometric series, that includes many other special functions as specific or limiting cases. It is a solution of a second-order linear ordinary differential equation (ODE). Every second-order linear ODE with three regular singular points can be transformed into this equation. For systematic lists of some of the many thousands of published identities involving the hypergeometric function, see the reference works by and . There is no known system for organizing all of the identities; indeed, there is no known algorithm that can generate all identities; a number of different algorithms are known that generate different series of identities. The theory of the algorithmic discovery of identities remains an active research topic. History The term "hypergeometric series" was first used by John Wallis in his 1655 book ''Arithmetica Infinitoru ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
