 |
Eigensystem Realization Algorithm
The Eigensystem realization algorithm (ERA) is a system identification technique popular in civil engineering, in particular in structural health monitoring. ERA can be used as a modal analysis technique and generates a system realization using the time domain response (multi-)input and (multi-)output data. The ERA was proposed by Juang and Pappa and has been used for system identification of aerospace structures such as the Galileo spacecraft, turbines,Sanchez-Gasca, J. J. "Computation of turbine-generator subsynchronous torsional modes from measured data using the eigensystem realization algorithm." Power Engineering Society Winter Meeting, 2001. IEEE. Vol. 3. IEEE, 2001. civil structures and many other type of systems. Uses in structural engineering In structural engineering the ERA is used to identify natural frequencies, mode shapes and damping ratios. The ERA is commonly used in conjunction with the Natural Excitation Technique (NExT) to identify modal parameters fro ... [...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 of experiments for efficiently generating informative data for 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 system identification. Overview A dynamical 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 processes such as the movement of a falling body under the influence of gravity; * economic processes such as stock markets that react to external influences. One o ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
|
 |
Vibration
Vibration is a mechanical phenomenon whereby oscillations occur about an equilibrium point. The word comes from Latin ''vibrationem'' ("shaking, brandishing"). The oscillations may be periodic, such as the motion of a pendulum—or random, such as the movement of a tire on a gravel road. Vibration can be desirable: for example, the motion of a tuning fork, the reed in a woodwind instrument or harmonica, a mobile phone, or the cone of a loudspeaker. In many cases, however, vibration is undesirable, wasting energy and creating unwanted sound. For example, the vibrational motions of engines, electric motors, or any mechanical device in operation are typically unwanted. Such vibrations could be caused by imbalances in the rotating parts, uneven friction, or the meshing of gear teeth. Careful designs usually minimize unwanted vibrations. The studies of sound and vibration are closely related. Sound, or pressure waves, are generated by vibrating structures (e.g. vocal cords); ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
|
Stochastic Subspace Identification
In mathematics, specifically in control theory, subspace identification (SID) aims at identifying linear time invariant (LTI) state space models from input-output data. SID does not require that the user parametrizes the system matrices before solving a parametric optimization problem and, as a consequence, SID methods do not suffer from problems related to local minima that often lead to unsatisfactory identification results. History SID methods are rooted in the work by the German mathematician Leopold Kronecker (1823–1891). Kronecker showed that a power series can be written as a rational function when the rank of the Hankel operator that has the power series as its symbol is finite. The rank determines the order of the polynomials of the rational function. In the 1960s the work of Kronecker inspired a number of researchers in the area of Systems and Control, like Ho and Kalman, Silverman and Youla and Tissi, to store the Markov parameters of an LTI system into a finite di ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
|
|
Frequency Domain Decomposition
The frequency domain decomposition (FDD) is an output-only system identification technique popular in civil engineering, in particular in structural health monitoring. As an output-only algorithm, it is useful when the input data is unknown. FDD is a modal analysis technique which generates a system realization using the frequency response given (multi-)output data. Algorithm # Estimate the power spectral density matrix \hat_(j\omega) at discrete frequencies \omega = \omega_i. # Do a singular value decomposition of the power spectral density, i.e. \hat_(j \omega_i) = U_i S_i U_i^H where U_i = _,u_,...,u_/math> is a unitary matrix holding the singular value In mathematics, in particular functional analysis, the singular values, or ''s''-numbers of a compact operator T: X \rightarrow Y acting between Hilbert spaces X and Y, are the square roots of the (necessarily non-negative) eigenvalues of the se ...s u_, S_i is the diagonal matrix holding the singular values s_. # For an ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
|
|
State-space Representation
In control engineering, a state-space representation is a mathematical model of a physical system as a set of input, output and state variables related by first-order differential equations or difference equations. State variables are variables whose values evolve over time in a way that depends on the values they have at any given time and on the externally imposed values of input variables. Output variables’ values depend on the values of the state variables. The "state space" is the Euclidean space in which the variables on the axes are the state variables. The state of the system can be represented as a ''state vector'' within that space. To abstract from the number of inputs, outputs and states, these variables are expressed as vectors. If the dynamical system is linear, time-invariant, and finite-dimensional, then the differential and algebraic equations may be written in matrix form. The state-space method is characterized by significant algebraization of general system ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
|
 |
Equation Of Motion
In physics, equations of motion are equations that describe the behavior of a physical system in terms of its motion as a function of time.''Encyclopaedia of Physics'' (second Edition), R.G. Lerner, G.L. Trigg, VHC Publishers, 1991, ISBN (Verlagsgesellschaft) 3-527-26954-1 (VHC Inc.) 0-89573-752-3 More specifically, the equations of motion describe the behavior of a physical system as a set of mathematical functions in terms of dynamic variables. These variables are usually spatial coordinates and time, but may include momentum components. The most general choice are generalized coordinates which can be any convenient variables characteristic of the physical system.''Analytical Mechanics'', L.N. Hand, J.D. Finch, Cambridge University Press, 2008, The functions are defined in a Euclidean space in classical mechanics, but are replaced by curved spaces in relativity. If the dynamics of a system is known, the equations are the solutions for the differential equations describing ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
 |
Mass Spring Damper
Mass is an intrinsic property of a body. It was traditionally believed to be related to the quantity of matter in a physical body, until the discovery of the atom and particle physics. It was found that different atoms and different elementary particles, theoretically with the same amount of matter, have nonetheless different masses. Mass in modern physics has multiple definitions which are conceptually distinct, but physically equivalent. Mass can be experimentally defined as a measure of the body's inertia, meaning the resistance to acceleration (change of velocity) when a net force is applied. The object's mass also determines the strength of its gravitational attraction to other bodies. The SI base unit of mass is the kilogram (kg). In physics, mass is not the same as weight, even though mass is often determined by measuring the object's weight using a spring scale, rather than balance scale comparing it directly with known masses. An object on the Moon would weigh ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
 |
Eigenvectors
In linear algebra, an eigenvector () or characteristic vector of a linear transformation is a nonzero vector that changes at most by a scalar factor when that linear transformation is applied to it. The corresponding eigenvalue, often denoted by \lambda, is the factor by which the eigenvector is scaled. Geometrically, an eigenvector, corresponding to a real nonzero eigenvalue, points in a direction in which it is stretched by the transformation and the eigenvalue is the factor by which it is stretched. If the eigenvalue is negative, the direction is reversed. Loosely speaking, in a multidimensional vector space, the eigenvector is not rotated. Formal definition If is a linear transformation from a vector space over a field into itself and is a nonzero vector in , then is an eigenvector of if is a scalar multiple of . This can be written as T(\mathbf) = \lambda \mathbf, where is a scalar in , known as the eigenvalue, characteristic value, or characteristic root a ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
 |
Singular Value Decomposition
In linear algebra, the singular value decomposition (SVD) is a factorization of a real or complex matrix. It generalizes the eigendecomposition of a square normal matrix with an orthonormal eigenbasis to any \ m \times n\ matrix. It is related to the polar decomposition. Specifically, the singular value decomposition of an \ m \times n\ complex matrix is a factorization of the form \ \mathbf = \mathbf\ , where is an \ m \times m\ complex unitary matrix, \ \mathbf\ is an \ m \times n\ rectangular diagonal matrix with non-negative real numbers on the diagonal, is an n \times n complex unitary matrix, and \ \mathbf\ is the conjugate transpose of . Such decomposition always exists for any complex matrix. If is real, then and can be guaranteed to be real orthogonal matrices; in such contexts, the SVD is often denoted \ \mathbf^\mathsf\ . The diagonal entries \ \sigma_i = \Sigma_\ of \ \mathbf\ are uniquely determined by and are known as the singular values ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
|
Hankel Matrix
In linear algebra, a Hankel matrix (or catalecticant matrix), named after Hermann Hankel, is a square matrix in which each ascending skew-diagonal from left to right is constant, e.g.: \qquad\begin a & b & c & d & e \\ b & c & d & e & f \\ c & d & e & f & g \\ d & e & f & g & h \\ e & f & g & h & i \\ \end. More generally, a Hankel matrix is any n \times n matrix A of the form A = \begin a_ & a_ & a_ & \ldots & \ldots &a_ \\ a_ & a_2 & & & &\vdots \\ a_ & & & & & \vdots \\ \vdots & & & & & a_\\ \vdots & & & & a_& a_ \\ a_ & \ldots & \ldots & a_ & a_ & a_ \end. In terms of the components, if the i,j element of A is denoted with A_, and assuming i\le j, then we have A_ = A_ for all k = 0,...,j-i. Properties * The Hankel matrix is a symmetric matrix. * Let J_n be the n \times n exchange matrix. If H is a m \times n Hankel matrix, then H = T J_n where T is a m \times n Toeplitz matrix. ** If T is real symmetric, then H = T J_n will have the same eigenvalues as T ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
|
|
State-space Representation
In control engineering, a state-space representation is a mathematical model of a physical system as a set of input, output and state variables related by first-order differential equations or difference equations. State variables are variables whose values evolve over time in a way that depends on the values they have at any given time and on the externally imposed values of input variables. Output variables’ values depend on the values of the state variables. The "state space" is the Euclidean space in which the variables on the axes are the state variables. The state of the system can be represented as a ''state vector'' within that space. To abstract from the number of inputs, outputs and states, these variables are expressed as vectors. If the dynamical system is linear, time-invariant, and finite-dimensional, then the differential and algebraic equations may be written in matrix form. The state-space method is characterized by significant algebraization of general system ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
|
 |
Civil Engineering
Civil engineering is a professional engineering discipline that deals with the design, construction, and maintenance of the physical and naturally built environment, including public works such as roads, bridges, canals, dams, airports, sewage systems, pipelines, structural components of buildings, and railways. Civil engineering is traditionally broken into a number of sub-disciplines. It is considered the second-oldest engineering discipline after military engineering, and it is defined to distinguish non-military engineering from military engineering. Civil engineering can take place in the public sector from municipal public works departments through to federal government agencies, and in the private sector from locally based firms to global Fortune 500 companies. History Civil engineering as a discipline Civil engineering is the application of physical and scientific principles for solving the problems of society, and its history is intricately linked to advances in ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |