China
Africa
Explore chapters and articles related to this topic
Bridge damage detection utilizing dynamic force obtained from moving vehicle acceleration
Published in Joan-Ramon Casas, Dan M. Frangopol, Jose Turmo, Bridge Safety, Maintenance, Management, Life-Cycle, Resilience and Sustainability, 2022
S. Hasegawa, C.W. Kim, K.C. Chang, N. Toshi
The unknown dynamic vehicle force vector can be estimated with utilizing Equation 8 and Equation 12. A regularized least square minimization is used to estimate the dynamic vehicle force, as it is an ill-posed inverse problem in which the slight change in the measured data causes a big difference in the estimated results. In order to deal with the ill-posed problem and obtain the robust solution, Tikhonov regularization is used. The cost function (CF) to be minimized is defined as Equation 13. CF=∑j=1N[(dj−QZj,dj−QZj)+(△fv,j,λ△fv,j)]
Minimization of functionals. Addition
Published in Simon Serovajsky, Optimization and Differentiation, 2017
The analysis of the ill-posed problem can be based on the Tihonov regularization method. Consider the functional Iε(v)=I(v)+ε‖v‖2, $$ \begin{aligned} I_\varepsilon (v)\,=\,I(v)+\varepsilon \Vert v\Vert ^2, \end{aligned} $$
Radial basis function (RBF) neural networks
Published in A. W. Jayawardena, Environmental and Hydrological Systems Modelling, 2013
A well-posed problem should satisfy three conditions: existence of an input x and a corresponding output y, uniqueness implying that every pair of values is different, and continuous implying that mapping is continuous. If any of these conditions is not satisfied, then the problem is ill-posed. An ill-posed problem has a lot of data but not much information. An ill-posed problem can be made well-posed by a process called regularization, which involves perturbing the ill-conditioned matrix ϕ to ϕ + λI, where λ is a regularization parameter and I is the identity matrix. A brief description of the regularization theory, which was first introduced by Tikhonov (1963) and later developed by Poggio and Girosi (1990a) in the context of RBFs for representing a multivariate continuous function by an approximate function having a fixed number of parameters, is given below.
Unknown source identification problem for space-time fractional diffusion equation: optimal error bound analysis and regularization method
Published in Inverse Problems in Science and Engineering, 2021
Fan Yang, Qian-Chao Wang, Xiao-Xiao Li
Nowadays, it is a hot topic in the field of inverse problems to deal with ill-posed problems by regularization method. There are many regularization methods to deal with ill-posed problem. In the early days, most scholars used Tikhonov regularization method [11,12] to deal with inverse problems. It is one of the oldest regularization methods. Later, on the basis of Tikhonov regularization method, some scholars studied the modified Tikhonov regularization method [13], the fractional Tikhonov regularization method [14,15] and the simplified Tikhonov regularization method [16]. In dealing with the inverse problem of bounded domain, the regularization methods are as follows: quasi-boundary regularization method [17–19], the truncation regularization method [20,21], a modified quasi-boundary regularization method [22], a mollification regularization method [23], quasi-reversibility regularization method [24,25], Landweber iterative regularization method [26–28], etc. In solving the inverse problem in unbounded domain, the common regularization methods are Fourier truncation regularization method [29–32]. In [33], Liu and Feng considered a backward problem of spatial fractional diffusion equation, and constructed a regularization method based on the improved ‘kernel’ idea, namely the improved kernel method. The modified kernel method can also deal with more ill-posed problem [34–37].
Simultaneous inversion of shear modulus and traction boundary conditions in biomechanical imaging
Published in Inverse Problems in Science and Engineering, 2020
D. T. Seidl, B. G. van Bloemen Waanders, T. M. Wildey
Inverse problems, both continuous and discrete, are often ill-posed, thus regularization is frequently employed to solve a well-posed problem that is ‘close’ to the original problem. Such terms are typically penalties on smoothness as measured in some norm (e.g. semi-norm). An algorithmic ramification of the use of regularization is the need to determine one or more constants that scale the regularization term(s) so that they are appropriately balanced against the data-match term in the objective function. While several methods for choosing a regularization constant exist, they have been largely developed for and applied to linear inverse problems with Tikhonov regularization [40]. In this work we solve nonlinear inverse problems with single-component full-field and sparse data and non-Tikhonov regularization. Thus, the assumptions that go into many of these approaches may not be applicable.
Performance characteristics of the low-cost Plantower PMS optical sensor
Published in Aerosol Science and Technology, 2020
Meilu He, Nueraili Kuerbanjiang, Suresh Dhaniyala
We use the Tikhonov regularization method (Tikhonov and Arsenin 1977) to solve the ill-posed problem. This regularization method has been widely used for calculation of aerosol size distributions from scanning mobility particle size data (e.g., Wolfenbarger and Seinfeld 1990; Dubey and Dhaniyala 2013). To calculate the transfer function for a selected channel (), a cost function defined as the sum of the accuracy term, the second norm of the residual and a smoothness term, is applied. The transfer function is then determined by minimizing the cost function, expressed mathematically as: where is the Euclidean norm, is a matrix to govern the smoothing method, and regularization parameter controls the relative contribution of the two terms. There are several methods to help choose an optimal regularization parameter and here we use the L-curve method (Hansen 2008).