Algorithms for Constructing the Confidence Interval for the Mathematical Expectation of the Noise and their Application in the Control of the Dynamics of Accident Development

The paper deals with the development of algorithms for constructing the confidence interval for the mathematical expectation of the noise of a noisy signal. It is noted that the noise characteristics can be used as informative attributes of the beginning of the initiation of a defect in a technical object. It is also indicated that the problem of determining the dynamics of changes in the technical condition  of an  object is more important than the control of the onset of a malfunction. This is based on the fact that with a slight development of a malfunction or lack of development, there is no need to stop the object’s operation for repair. In contrast, strong dynamics of development of a defect requires urgent action. It is noted that a timely solution to this problem is especially relevant for oil and gas production facilities and other similar facilities. It is shown that confidence intervals for the noise characteristics of a noisy signal can be used as informative attributes of determining the dynamics of a malfunction. Algorithms for determining the confidence interval for the mathematical expectation of the noise are developed. Technologies are proposed for determining the latent period of the initiation of the malfunction of  technical  objects  and  the  dynamics  of  its  development  using  the  confidence  interval  for  the  mathematical  expectation of the noise. To this end, at the instant of time when the object is in a normal state, a confidence interval is constructed for the mathematical expectation of the noise, and a set of possible values that fall into this interval is compiled. After a certain period of time, this procedure is repeated. It is noted that when a malfunction occurs, the width of the confidence  interval increases. Therefore, the difference between the sets of possible values of the mathematical expectation of the noise at the previous and current instants is found. A correspondence is established between the value of this difference and the degree of damage development. By determining each time the differences of the sets of possible values of the mathematical expectation of the noise, the dynamics of the development of the malfunction in time is revealed. Then the corresponding conclusions are made, such as "the malfunction develops with uniform intensity", "the malfunction develops intensively", "the malfunction develops very intensively", etc. Depending on the degree of malfunction development, appropriate preventive or repair work is carried out with or without stopping the operation of the control object. To verify the reliability of the developed algorithm for constructing the confidence interval for the mathematical expectation of the noise of a noisy signal and the technology for determining the latent period of initiation of malfunction of technical objects and the dynamics of its development, computational experiments are carried out using the MATLAB computing environment.

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