Analysis of the Transformation of Random Signals and Noise Using Poly-Gaussian Models

Analysis performed transformation of random signals and noise in linear and nonlinear systems based on the use of poly-Gaussian models and multidimensional PDF of the output paths of information-measuring and radio systems. The classification of elements of these systems, as well as expressions describing the input action and output response of the system are given. It is shown that the analysis of information-measuring and systems can be carried out using poly-Gaussian models. The analysis is carried out with a series connection of a linear system and a nonlinear element, a series connection of a nonlinear element and a linear system, as well as with a parallel connection of the named links. The output response in all cases will be a mixture of a poly-Gaussian distribution with a number of components. An example of the analysis of signal transmission through an intermediate frequency amplifier and a linear detector against a background of non-Gaussian noise is given. The resulting probability density distribution of the sum of the signal and non-Gaussian noise at the output of the detector will be poly-Rice. The multidimensional probability distribution density of the output processes of the nonlinear signal envelope detector is also obtained. The results of modeling the found distribution densities are presented. It is shown that the use of the poly-Gaussian representation of signals and noise, as well as the impulse response of the system, makes it possible to effectively analyze inertial systems in the time domain.

A Setup for Measuring the Centering Error of a Dual-Element Pyroelectric Infrared Sensor Module

This paper presents an experimental setup to measure the horizontal centering error of a pre-built pyroelectric infrared (PIR) sensor module, in which a dual-element PIR sensor is aligned at the focal point of a single-zone Fresnel Lens. In the setup, the sensor module was placed facing a modulated infrared radiating source and turned over a range of horizontal angles. The position of the optical axis of the sensor module was determined based on the analysis of the output response of the sensor at turned angles. Thus, the horizontal centering error of the module is defined as the difference between the mechanical axis of the housing and the found optical axis. For the prebuilt sensor module, with the specific available equipment, the measurement of the centering error of the module achieved a resolution of 0.02 degrees.

Critical Evaluation into the practical utility of the Design of Experiments

The research aims to emphasise the relevance of the Design of Experiments (DOE) technique as a reliable method for ensuring efficient use of statistical methods in routine industrial processes. A case study approach with a deductive strategy was used to assess the effectiveness of different DOE methods to achieve the desired objectives. Screening, mid-resolution and high-resolution DOE methods helped identify, characterise, and optimise an experimental variable against the desired output response. A general framework for effective DOE is provided as part of DOE planning, including defining DOE objectives, selection criteria, noise reduction, and application across industries. Overall, various DOE models proved successful in identifying a complicated relationship between experimental variables and output response. However, when ideal DOE models may not be feasible, reducing test run by choosing lower resolution DOE or fewer replicates can still provide important insights into the experimental variables’ impact on output responses.

Cascaded Nonlinear Mass Fluctuation Stochastic Resonance System and Its Application in Bearing Fault Diagnosis

Stochastic resonance (SR) can realize bearing fault signal diagnosis by transferring noisy energy. In order to enhance the output response of the system and realize effective signal extraction, the nonlinear mass fluctuation SR system caused by nonlinear asymmetric dichotomous noise is cascaded to obtain the cascaded nonlinear mass fluctuation SR system. First, the output amplitude gain of the first-stage of the system is derived, and the influence of different parameters on it is explored; then the effects of different parameters of the cascaded system on the output amplitude gain and the output SNR are studied separately, which proves that the cascaded system can effectively double enhance the output response of the system; finally, the adaptive genetic algorithm is used to solve the difficulty of parameter adjustment, and the cascaded nonlinear mass fluctuation SR system is applied to the bearing fault diagnosis. The system proposed in this paper takes into account the effects of nonlinear asymmetric dichotomous noise and cascaded systems and performs waveform smoothing and double enhancement of the output signal. It can better extract fault signals and has effective engineering value.