Statistical and Stochastic Methods for MDS-Rely Satish Iyengar Statistics Department University of Pittsburgh Pittsburgh, PA April 12, 2022 Email: ssi@pitt.edu Overview Learning from existing data Optimization methods for designing experiments Stochastic modeling Analysis of Existing Data: Degradation Models Long history: Statistical Modeling for Degradation Data (2017) by Chen, Lio, Ng, Tsai Brownian motion model for time to failure. Fatigue grows according to a Brownian motion (random walk) B t with drift μ > 0 and diffusion σ 2 . Failure occurs when fatigue reaches critical threshold θ dF t = μ dt + σ dB t , F 0 = f 0 , T = inf { t : F t = f 0 + μ t + σ B t = θ } T has inverse Gaussian distribution; inference very well developed. R software available (it’s an example of a GLM). Methods have been extended to other diffusion models. Optimization: Response Surface Methods (RSM) Simple case: one outcome (lifetime, L ) that we want to optimize; several inputs (temperature T , pressure P ) that we want to optimize over. Start with L = f ( T , P ) or L = f ( T , P ) + E If we knew f , could optimize it and use arg max f ( T , P ). In practice, use low-degree polynomial or spline to and use hill-climbing algorithms decide which values of ( T , P ) to test. Small-data problem; often experiments expensive (time, money). For design of experiments, choose next feature to optimize what we learn: maximize Fisher information, minimize parameter’s variance estimate; early work on linear models, but now computation allows us to work with more complex models. Practical challenges Data acquisition Models nice, good data often better than models Digging up data from records can be tedious, expensive Big data, small data Both can be useful Large data sets usually heterogeneous Specific questions may be addressed by much smaller subsets Small data sets need more input (constraints, regularization) Must combine statistics with engineering Each can guide the other Stochastic Modeling: Two-Photon Laser Scanning Microscopy (TPLSM) It is used to get high-resolution 3-d images TPLSM data comes from ∼ 100 10 − 15 s pulses N : number of photons detectable/pulse; Poisson( α ). α ˆ : estimate of α ; determines intensity of pixel. W : emission waiting time; exponential. δ : dead period ( = ∆ / τ , τ is time constant for W ). D : observed photon count Imaging requires counts of photons emitted, but counter has a dead period. So undercount D , lower signal-to-noise ratio (SNR). Easy estimate: use p 0 = P ( N = 0) = e −α , α ˆ = − ln( p ˆ 0 ). Distribution of D is considerably harder. Note: Of ∼ 10 8 photons at focus, detected counts are about 1 X 1 X 2 X 3 X 4 X 5 X 6 t 1 t 2 t 3 t 4 t 5 t 6 photon arrivals X 1 X 2 X 3 X 4 X 5 X 6 t 1 1 t +δ t 3 3 6 6 t +δ t t +δ photon arrival with dead time Comparison of methods Improvement in Fisher information [0, 01, 012] Proprietary to MDS-Rely Faculty Name: Chris Wirth, PhD Chemical and Biomolecular Engineering Case Western Reserve University Training/Experience BS, ChemE, Univ. at Buffalo PhD, ChemE, Carnegie Mellon Univ. Postdoc, PPG/KU Leuven (Belgium) Team Complex Fluids and Suspensions, Particle Interactions, Chemical Product Manufacturing Coatings (NSF, PPG) Defect formation and rheology Adhesion ( NSF ) Particle interactions and sticking Research Support Sag Orange Peel Lubricants ( Lubrizol ) Evaluating emulsion stability Imaging for All Projects • Feature extraction and tracking • Interpretation of dynamics • Software and hardware development for manufacturing environments Email: wirth@case.edu Department of Mechanical Engineering and Material Science Functional Materials for Energy Applications Jung-Kun Lee Department of Mechanical Engineering and Material Science University of Pittsburgh Email: jul37@pitt.edu Department of Mechanical Engineering and Material Science Highly Stable Perovskite Solar cells Stability of perovskite solar cells in humid and hot environment is greatly improved by simple coating of the graphene oxide - polymer composite layer. Department of Mechanical Engineering and Material Science 0.0 0.5 1.0 0.0 0.5 1.0 10 0 10 1 1 0 2 10 3 0.0 0.5 1.0 B endin g C ycle s Normalized PCE ( ) 1 cm 1 cm 1 cm Flexible Perovskite Solar Cells on Metal Plate Strong need for solar cells compatible with flexible electronics Perovskite solar cells on Ti plate possess excellent photovoltaic performance and mechanical strength , which meets this need. Department of Mechanical Engineering and Material Science Surface Plasmon Assisted Light Absorption Plasmonic particles Surface plasmonic solar cells using a unique design of metal- dielectric interface 300 400 500 600 700 800 0 10 20 30 40 Pure TiO 2 TiO 2 - 22vol% core-shell IPCE (%) Wavelength (nm) Embedded SiO 2 core-Au shell particles SiO 2 Core Au shell Department of Mechanical Engineering and Material Science 3.0 3.5 4.0 4.5 5.0 10 18 10 19 10 20 10 22 10 23 Pure Ag film 0.70 vol. % Ag NPs 0.35 vol. % Ag NPs 0.07 vol. % Ag NPs Carrier Concentration (cm -3 ) 1000/T (K -1 ) Pure AZO film (a) 3.0 3.5 4.0 4.5 5.0 10 0 10 1 10 2 0.70 vol.% 0.35 vol.% 0.07 vol.% Mobility (cm 2 /V.s) 1000/T (K -1 ) AZO New transparent conducting oxide (TCO) using the electron emission of metal nanoparticles A novel type of TCO film embedded with metal nanoparticles. Independent control of carrier concentration and mobility, which is different from traditional TCO materials. Department of Mechanical Engineering and Material Science Powder-Bed Ceramics Processing C. Shih, et. al, J. Nuclear Mater. vol . 409, pp. 199 (2011) - Needs for low temperature sintering and exact size ceramics fabrication - Combination of polymer infiltration and pyrolysis and powder bed printing Before the infiltration After the infiltration Department of Mechanical Engineering and Material Science • Interpenetrating polymer networks (IPNs) - nanocomposites - IPNs can provide a great opportunity to have or more polymers with distinguishing properties compared to individual polymers. - By adding nanoparticles in the polymer, water permeation and surface wettability can be further controlled. Schematics (b) interpenetrating polymer networks (IPNs) and (c) IPNs mixed with nano particles hydrophobicity hydrophilicity Topic (I) - Encapsulation Materials for Solar Cells Department of Mechanical Engineering and Material Science • Fast improvement of perovskite solar cell in efficiency Department of Mechanical Engineering and Material Science • Accelerated degradation test (in water at 85 °C) - The degradation of the perovskite can be easily observed by the color change. Yellow color is PbI 2 (bandgap: ~2.3 eV) No color change Bandgap of CH 3 NH 3 PbI 3 : 1.5 eV Water Diffusion in PMMA-PU IPNs with SiO 2 - H 2 O diffusion coefficient at 85 °C is decreased from 8.06 × 10 -8 cm 2 /s of PMMA-PU to 4.03 × 10 -8 cm 2 /s of PMMA-PU/SiO 2 (1.4 vol%). 0.0 0.5 1.0 1.5 4x10 -8 5x10 -8 6x10 -8 7x10 -8 8x10 -8 D(cm 2 /s) Volume % CeO 2 SiO 2 Department of Mechanical Engineering and Material Science • Damp Heat test (85 °C/85 RH (Relative Humidity)) - The 85/85 test for 1000 hrs attempts to simulate 20 years of moisture ingress into a given product. Passivation by Composite - The encapsulated device exhibits dramatically suppressed degradation process even in a standardized damp heat aging condition. 84 % of the initial PCE was maintained.