This article shows a new Te-transform and its periodogram for applications that mainly exhibit stochastic behavior with a signal-to-noise ratio lower than −30 dB. The Te-transform is a dyadic transform that combines the properties of the dyadic Wavelet transform and the Fourier transform. This paper also provides another contribution, a corollary on the energy relationship between the untransformed signal and the transformed one using the Te-transform. This transform is compared with other methods used for the analysis in the frequency domain, reported in literature. To perform the validation, the authors created two synthetic scenarios: a noise-free signal scenario and another signal scenario with a signal-to-noise ratio equal to −69 dB. The results show that the Te-transform improves the sensitivity in the frequency spectrum with respect to previously reported methods.

The architecture design of industrial data analytics system addresses industrial process challenges and the design phase of the industrial Big Data management drivers that consider the novel paradigm in integrating Big Data technologies into industrial cyber-physical systems (iCPS). The goal of this paper is to support the design of analytics Big Data solutions for iCPS for the modeling of data elements, predictive analysis, inference of the key performance indicators, and real-time analytics, through the proposal of an architecture that will support the integration from IIoT environment, communications, and the cloud in the iCPS. An attribute driven design (ADD) approach has been adopted for architectural design gathering requirements from smart production planning, manufacturing process monitoring, and active preventive maintenance, repair, and overhaul (MRO) scenarios. Data management drivers presented consider new Big Data modeling analytics techniques that show data is an invaluable asset in iCPS. An architectural design reference for a Big Data analytics architecture is proposed. The before-mentioned architecture supports the Industrial Internet of Things (IIoT) environment, communications, and the cloud in the iCPS context. A fault diagnosis case study illustrates how the reference architecture is applied to meet the functional and quality requirements for Big Data analytics in iCPS.

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This article solves the problem of detecting water leaks with a minimum size of down to 1 mm in diameter. Two new mathematical tools are used to solve this problem: the first one is the Te cross-spectral density and the second is Te coherence. These mathematical tools provide the possibility of discriminating spurious frequency components, making use of the property of multi-sensitivity. This advantage makes it possible to maximize the sensitivity of the frequency spectrum. The wavelet function used was Daubechies 45, because it provides an attenuation of 150 dB in the rejection band. The tools were validated with two scenarios. For the first scenario, a synthetic signal was analyzed. In the second scenario, two types of background leakage were analyzed: the first one has a diameter of 1 mm with a signal-to-noise ratio of 2.82 dB and flow rate of 33.7 mL/s, and the second one has a diameter of 4 mm with a signal-to-noise ratio of 9.73 dB with a flow rate of 125.0 mL/s. The results reported in this paper show that both the Te cross-spectral density and Te coherence are higher than those reported in scientific literature.

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