OCReP: An Optimally Conditioned Regularization for Pseudoinversion Based Neural Training

In this paper we consider the training of single hidden layer neural networks by pseudoinversion, which, in spite of its popularity, is sometimes affected by numerical instability issues. Regularization is known to be effective in such cases, so that we introduce, in the framework of Tikhonov regularization, a matricial reformulation of the problem which allows us to use the condition number as a diagnostic tool for identification of instability. By imposing well-conditioning requirements on the relevant matrices, our theoretical analysis allows the identification of an optimal value for the regularization parameter from the standpoint of stability. We compare with the value derived by cross-validation for overfitting control and optimisation of the generalization performance. We test our method for both regression and classification tasks. The proposed method is quite effective in terms of predictivity, often with some improvement on performance with respect to the reference cases considered. This approach, due to analytical determination of the regularization parameter, dramatically reduces the computational load required by many other techniques.Comment: Published on Neural Network

Comparative studies of computation tools for moving force

Existing techniques to identify moving forces based on traditional finite element method (TFEM) is subject to a large number of elements with detailed description of a structure, which makes modeling complicated. A new modeling method for a vehicle-bridge system called wavelet finite element method (WFEM) is presented in this paper. It makes use of a multi-scale analysis whereby detailed description can be achieved to overcome this problem. The shape function of WFEM is formed by a scale function in a wavelet space and by a transformation matrix to connect the wavelet space to the physical one. To evaluate the properties of WFEM, simulations of two moving forces on a simply supported and a continuous bridge are conducted with subsequent comparison with TFEM. To smooth the noise and large fluctuations on the boundaries of the identified results in the time history, the first-order Tikhonov regularizations combined with the dynamic programming technique are adapted and compared with the zeroth-order Tikhonov regularization. White noise is added to the simulated dynamic responses. Some parameter effects, such as vehicle bridge parameters, measurement parameters are also considered. Numerical results demonstrate the WFEM method and the first-order Tikhonov regularization method to be effective for moving force identification. The first-order Tikhonov regularization has the property of smoothing noise and avoiding large fluctuations on the boundaries. Meanwhile, the parameters analyzed affect the identified results to some extent

On the interpretation and identification of dynamic Takagi-Sugenofuzzy models

Dynamic Takagi-Sugeno fuzzy models are not always easy to interpret, in particular when they are identified from experimental data. It is shown that there exists a close relationship between dynamic Takagi-Sugeno fuzzy models and dynamic linearization when using affine local model structures, which suggests that a solution to the multiobjective identification problem exists. However, it is also shown that the affine local model structure is a highly sensitive parametrization when applied in transient operating regimes. Due to the multiobjective nature of the identification problem studied here, special considerations must be made during model structure selection, experiment design, and identification in order to meet both objectives. Some guidelines for experiment design are suggested and some robust nonlinear identification algorithms are studied. These include constrained and regularized identification and locally weighted identification. Their usefulness in the present context is illustrated by examples

A PERSPECTIVE ON STRUCTURAL HEALTH AND USAGE MONITORING IN AEROSPACE APPLICATIONS

There is great interest in the benefits of Structural Health and Usage Monitoring in the Aerospace Industry both from a safety point of view and because of the possibility of extending the life of aerospace structural components. Although fail-safe and damage tolerance approaches to design are extensively used and have great advantages, there are never the less components and circumstances where a safe life approach remains appropriate. This leads to an approach to fatigue clearance whereby a component will be taken out of service after a certain number of hours usage irrespective of the environment it has experienced having been cleared based on very conservative loading assumptions. If the actual loads experienced by critical parts of a structure can be derived from a Structural Health and Usage Monitoring System (SHUMS), this then leads to the possibility of extending the time for which the component can remain in service with consequent cost savings. In this paper, a number of fundamental approaches to loads prediction using data available from a Structural Health and Usage Monitoring Systems are reviewed, with the particular application in mind being that of an air-carried guided weapon. Approaches considered will include time-domain and frequency-domain based methods making use of a structural model, together with machine learning based approaches. Their different strengths, weaknesses and pitfalls will be highlighted together with ways to overcome them. Practical aspects of their possible implementation will also be addressed.Non peer reviewe

Ill-posedness of time-dependent inverse problems in Lebesgue-Bochner spaces

We consider time-dependent inverse problems in a mathematical setting using Lebesgue-Bochner spaces. Such problems arise when one aims to recover parameters from given observations where the parameters or the data depend on time. There are various important applications being subject of current research that belong to this class of problems. Typically inverse problems are ill-posed in the sense that already small noise in the data causes tremendous errors in the solution. In this article we present two different concepts of ill-posedness: temporally (pointwise) ill-posedness and uniform ill-posedness with respect to the Lebesgue-Bochner setting. We investigate the two concepts by means of a typical setting consisting of a time-depending observation operator composed by a compact operator. Furthermore we develop regularization methods that are adapted to the respective class of ill-posedness.Comment: 21 pages, no figure

Aircraft turbulence and gust identification using simulated in-flight data

Gust and turbulence events are of primary importance for the analysis of flight incidents, for the design of gust load alleviation systems and for the calculation of loads in the airframe. Gust and turbulence events cannot be measured directly but they can be obtained through direct or optimisation-based methods. In the direct method the discretisation of the Fredholm Integral equation is associated with an ill conditioned matrix. In this work the effects of regularisation methods including Tikhonov regularisation, Truncated Single Value Decomposition (TSVD), Damped Single Value Decomposition (DSVD) and a recently proposed method using cubic B-spline functions are evaluated for aeroelastic gust identification using in flight measured data. The gust identification methods are tested in the detailed aeroelastic model of FFAST and an equivalent low-fidelity aeroelastic model developed by the authors. In addition, the accuracy required in the model for a reliable identification is discussed. Finally, the identification method based on B-spline functions is tested by simultaneously using both low-fidelity and FFAST aeroelastic models so that the response from the FFAST model is used as measurement data and the equivalent low-fidelity model is used in the identification process