distributed fiber-optic measuring system
parallel beam tomography
non-uniform schemes of measuring lines stacking
radial basis function neural network (RBFNN)
Yu. N. Kulchin, E. V. Zakasovskaya
Present day science intensive production cannot do without constant monitoring and control over the behavior dynamics of parameters range of distributed physical fields. The distributed information-measuring systems are called upon to solve this problem. These systems have various topologies and organization, and are constructed, for example, on fiber-optical element base.
One of the fundamental parts of the distributed fiber optical measuring system (DFOMS) is distributed fiber optical measuring network (FOMN) responsible for collecting measuring information regarding the physical field parameters under study. FOMN represents a set of fiber-optical measuring lines (MLs) stacked in accordance with a certain setup on the surface studied. Thus reconstructing distributed physical fields’ parameters against characteristics of optical radiation passing through FOMN assigns this mathematical problem to tomography.
Standard analytical methods are unacceptable for a fiber-optical tomography as direct application of inverse operator does not provide a unique stable solution.
Restoring physical fields’ functions by using FOMN can be broken into several steps:
1. FOMN’s geometry optimization,
2. Special processing with use neural network and algebraic methods,
3. Restoring FOMN’s geometry.
Such FOMN usually have less MLs than the number of areas to be controlled. Appropriate system of linear algebraic equations is also underdetermined. Huge dimension of entrance data requires preprocessing which allows to specify only the most significant parameters and thereby to lower a number of free parameters in system.
The approach whose novelty involves complex of neural networks after the measuring network geometry optimization to restore of the functions studied is presented. An alternative to choose and apply an appropriate neural network from the set of several, previously trained neural networks of radial-basic type is investigated. Thus it is possible to receive additional projections at non-uniform on a corner scanning scheme.
From the represented results it is follows, that preprocessing based on the procedure of area clipping followed by neural networks’ collective processing is very winning in terms of accuracy and speed. In this case mse error for the elements belonging to the training page goes down by 10 times. This can be explained by reduction of dimensions of the data used for training of a neural network.
Further it is possible to apply any of algorithms:
1) classical algorithm FBP,
2) restoration applying NN g from a neural networks complex SN g and at a following stage algebraic algorithm UQC 2 for the projections doubling.