Optimized Spectral Fault Receptive Fields for Diagnosis-Informed Prognosis (Poster)

Optimized Spectral Fault Receptive Fields for Diagnosis-Informed Prognosis Stan Mu˜noz Guti´errez, and Franz Wotawa Software Engineering and Artificial Intelligence Institute, Graz University of Technology Research Objective and Contributions Our primary objective is to engineer health perception systems capable of actively tracking the degradation state of bearings enabling accurate estimation of their Remaining Useful Life (RUL). Our contributions can be summarized as: Formalization of Spectral Fault Receptive Fields (SFRFs). Efficient computational pipeline for SFRFS. Qualitative analysis of the suitability of SFRFs for condition monitoring and prognosis. Optimization of parameters via a Multi-objective Genetic Algorithm (NSGA-II). Summary of Results Qualitative demonstration of the suitability of SFRFs for capturing degradation trends in run-to-failure vibration data. Optimization of SFRFs parameters via NSGA-II enhances condition monitoring and prognosis performance. Pareto optimal solutions exhibit a strong contrast component, supporting the Difference of Guassians (DoG) model. Higher order SFRFs reduce RUL prediction error. Bearing Fault Frequencies Figure: Bearing parameters. Table: Characteristic frequencies related to bearing faults. BPFO = Ball Pass Frequency Outer Race; BPFI = Ball Pass Frequency Inner Race; BSF = Ball Spin Frequency; FTF = Fundamental Train Frequency (Cage). NB: number of rolling elements; DB: ball diameter; Dp=DI+DO 2: pitch diameter ; ϕ: contact angle; fr: shaft rotational frequency. Acronym Equation BPFO fBPFO =frNB 2h1−DB DP cos ϕi BPFI fBPFI =frNB 2h1 + DB DP cos ϕi BSF fBSF =frDP 2DB1−DB DP cos ϕ2 FTF fFTF =fr 2h1−DB DP cos ϕi Harmonics and Sidebands 0 50 100 150 200 250 300 350 Frequency Fault Frequency Bands 1Fo 2Fo 1Fi 2Fi 1Fb 2Fb 1Fc 2Fc Figure: Fault Frequency Bands for the first and second harmonics. Notation: nF: the n-th harmonic for frequency F, F∈ {Fo,Fi,Fc,Fb}. Frequencies are Fo: BPFO (107.91 Hz), Fi: BPFI (172.09 Hz), Fc: FTF (13.4884 Hz), and Fb: BSF (72.33) Table: Characteristic frequencies for bearing faults including harmonics and sidebands. Notation Nh: number of harmonics, and Ns: number of sidebands. Characteristic Frequencies FO={nfBPFO |n= 1..Nh} FI={nfBPFI +sfr|n= 1..Nh, s =−Ns..Ns} FB={nfBSF +sfFTF |n= 1..Nh, s =−Ns..Ns} FC={nfFTF |n= 1..Nh} Receptive Fields in Primate Retina Figure: Receptive field formation in primate retinal midget (P) ganglion cells. Insets: (A) eye anatomy highlighting retina, fovea, and image formation; (B) micrograph of peri-papillary retina layers (modified from (librepath 2015)); (C) ONand OFF-MG network in parafovea showing LC and MC cone synapses, H1 horizontal cells, flat and invaginating midget bipolar cells; (D) spectral sensitivity of cone types; (E) foveal cone mosaic depicting green-center red-surround receptive field; (F) DoG model illustrating center-surround color contrast. Spectral Fault Receptive Fields Processing Pipeline Figure: SFRFs’ processing pipeline. Top: vibration signals from two accelerometers; snapshots indexed by k. Bottom: pipeline computes FFT and SFRFs per channel, stores vectors in a buffer, and stacks channels to form CIs. SFRFs as Condition Indicators Figure: Empirical CIs (blue filled circles) versus the best RUL-predicting Pareto-optimal solution (open red circles). Promising Prognostic Performance Figure: Remaining Useful Life (RUL) prediction by a bagging regression ensemble. Left. Training MSE RUL prediction error with increasing orders. Right. Comparison of RUL predictions between 0th and 10th order SFRFs. Supplementary Material The MATLAB notebook supporting this paper is available at doi:10.5281/zenodo.15660819. Spectral Fault Receptive Fields (SFRFs) Figure: Parameters of the Difference of Gaussians (DoG) model. Left: Illustration of a DoG model centered at a fault characteristic frequency. For the receptive field gain functions (RFGFs), these are defined for the applicable harmonics and sidebands. Right: Effect of varying sigma rule kσand inhibition factor κH. SFRF Computation Example Figure: Computation of DoG for snapshot Sk=0 vand fault type Ball, and effect of speed on receptive field gain function (RFGF). Left, bottom to top: amplitude spectrum, spectrum filtered by center RFGF GσC F, and spectrum filtered by surround RFGF GσS F. Numeric integrals and final DoG computation included. Right: Effect of shaft speed fron DoG RFGF, GσC F−κHGσS F. https://www.tugraz.at/institute/sai/home {munozgutierrez,wotawa}@tugraz.at