THE DEVELOPMENT OF TRAINING PROCEDURES FOR MODELING THE PROCESSES OF DIAGNOSING TECHNICAL SYSTEMS

This article discusses and improves training methods in constructing models for diagnosing complex technical systems with incomplete and heterogeneous information about inoperative conditions caused by failures of functional elements. The vector Y-<n>(y1, y2, yn) nny. of registered values of diagnostic (informative) parameters yj is the observed state of the system. On the set Y = {Y}, the structure of an n-dimensional Euclidean space is defined in which the domains Yi, 1,im. are allocated. Each of the domains Yi represents the i-th inoperative condition of the system. The model for diagnosing is based on images - a formalized description of inoperative conditions. The image is formed as a vector. 12(,,...,), i i i in iE.e e e E.E, that accumulates the properties of all the observed states of the system from the Yi domain. Images are synthesized on the basis of a training sample {| 1,}i k i iY k.N.Y by means of recurrence relations E-i(k) = E-i(k-1)-1/k[E-i(k - 1) - GY'(k))], i = 1m, allowing to display the image Ei(k) at the current step through the same image Ei(k-1) at the previous step and the next sample element Yi. The indicated relations are derivatives of the stochastic approximation method. The vector function. 1 C2 [pi, pi], represents the orthogonal transformation of the observed condition Y. The coordinate functions gr(Y) are formed on the basis of the orthogonal trigonometric basis, which is contained in the space C2[-p; p] of continuous functions, square integrable in the Riemann, with the domain of definition [- p; p], where p similar to 3,14. Strict pairwise orthogonality of coordinate functions takes place for |yj| = p only. Non-compliance with this stipulation reduces the convergence of the training process. It is proposed in recurrence relations to use a trigonometric basis orthogonal in the space C2[-z; z], where max. | 1,.. jz.y j.n Then the coordinate functions are given in the form This ensures pairwise orthogonality of gr(Y) for any values of yj. As a result, a closed and bounded Euclidean space G(Y) is generated, which contains the set E of the formed images. The metric of this space allows you to compare the convergence of various options for the training process. Let d be the distance in G(Y) between the image vectors at the current and subsequent training steps: (1)) ii. EkEk.... If d1 and d2 are distances when training based on bases in the spaces C2[-p; p] and C2[-z; z] respectively (training options 1 and 2), then in the case of 1 2 1(...)..100.. the convergence is higher for option 2 (where. is the integral relative error of registering diagnostic parameters at the control points of the system). gr(Y)={delta rjsin pi/2lyj, l = (j+1)/2, j-dd; delta rjsin pi/2lyj, l = (j+1)/2, j-dd; An example of image synthesis is given, showing a higher convergence of the training process when an orthogonal trigonometric basis in the space C2[-z; z] is applied. Thus, a more efficient use of statistical information about inoperative conditions of the system is evident.