Big Data Acquisition and Management Solution for Digital Transition with Prof. Gilles Courret

Big data acquisition and management solution for the digital transition Prof. Gilles Courret, HEIG-VD, gilles.courret@heig-vd.ch Yverdon-les-Bains, March 2023

Acquisition system Analog signal variable Digital signal Acquisition Sensor Amplification & filter Sampling, ADC Band width User settings Filter band width and gain

Chronologic storage ?? ?0 ?0 ?1 ?0 ?2 ?3 ?1 ?4 ?2 . . . ?0 1/??

Stochastic signals Analog signal Digital signal Generation Stochastic signal Acquisition system

Acquisition 1 Acquisition 2 Sampling frequency : 50 Hz Range: [ -20 , 20 ] Sampling frequency : 50 Hz Range: [ -20 , 20 ]

Acquisition 3 Acquisition 4 Sampling frequency : 500 Hz Range : [ -20 , 20 ] Sampling frequency : 500 Hz Range : [ -30 , 30 ] One has to estimate the amplitude and the maximum frequency of the signal

Detecting for furtive events Buffer memory

Nyquist-Shannon theorem ??> 2 ???? Lossless reconstruction condition:

Localisation of variations ??1 ??2 ??1 ???? Spectra Fourier Transform

Spectrum 80.0 Spectral power density 60.0 40.0 ?2 ? ??= 20.0 0.0 ???? 50.0 10.0 40.0 0.0 20.0 30.0 Frequency The reconstituted signal should be more faithful in spectral bands that contain more energy Favor the points corresponding to variations of large amplitudes 1 2??? ?? ??? ?? = 2 ? 0

Groupes of same quantity of information s ?????? s ?????? s ?????? In a record, not all points have as the same relevance It is more acceptable to suppress the points that are less relevant Compression

Assigning a relevance to points Values attribution algorithms Specific methods Generic method Favor a time band Favor a band of values, high, low values ... Favor the corresponding points to big variations s(?1,?2,...) = ???(?1,?2,...)

Favor points corresponding to large variations Arbre de stockage s(?1,?2,...) = (?1,?2,...) ?

Example Time [s]

Example Number of suppressed levels = 1 1 Time [s]

Example Number of suppressed levels = 2 2 Time [s]

Example Number of points Number of suppressed levels

Example Mean error Number of suppressed levels

Compression progressive des donnes Volume of archive [%] Continues compression Temps [an] Constant frequency sampling Chronologic storage Abrupt total loss

Exploration tool Exploration in chronological order Exploration in a random order Navigation in the ladder tree: more relevant and faster. Response time for smooth navigation <0.5s

Multi-scale exploration tool Level n 3 Son n 1 Statistical parameters (1) Time-frequency analysis (2) Rolling bearings health monitoring (3) - - - frequency Local FFT (1): root mean square, kurtosis, crest factor, correlations, variance, zero crossing rate, complexity, entropy, weak periodic signals, Mahalanobis distance, cumulative sum control chart, etc. (2): fast Fourier transform, wavelet transform, discrete wavelet transform, symbolic dynamics filtering, local mean decomposition, empirical mode decomposition, etc. (3): remaining useful life, multi-scale signature, intrinsic characteristic-scale decomposition, etc.

Data acquisition Riemann s concept Time

Acquisition de donnes Lebesgue s concept Time

?0 ?1 ?2 ?5 ?6 ?7 ?2 ?3 ?0 ?4 ?1 ?0 ?0 ?1 ?0 ?1 ?2 ?1 ?2

Asynchronous Sigma Delta Modulator (ASDM) b b 1 ? ?? x(t) - +- -b -b b > max |? ? |

Conclusion Non uniforme sampling Simple design Clockless system Higher resolution, SNR Off-grid wireless sensors Storage in a ladder tree Unstable signals Gain of productivity in data analysis Continues compression Archive management

Thanks for your attention