Advanced Statistical Techniques in Engineering

🌧️ Rainfall data analysis as a fundamental input for advanced hydrological modelling . Rainfall data is the governing variable in hydrological studies, as it directly affects the estimation of surface runoff, the hydrological response of basins, and the accuracy of mathematical model outputs used in flood risk assessment and water infrastructure design. 📊 The hydrological importance of rainfall analysis Accurate analysis of rainfall data aims to: Describe the statistical characteristics of rainfall (frequency, intensity, variability) Represent the temporal and spatial distribution of precipitation Identify design storms Reduce uncertainty in hydrological models. 🧠 Advanced statistical analysis of rainfall The choice of statistical method depends on the nature of the data and the length of the time series. The most prominent methods are: 🔹 Frequency Analysis Application of probability distributions such as: Gumbel Extreme Value Type I Log-Pearson Type III Generalised Extreme Value (GEV) Goodness of Fit test using: Kolmogorov–Smirnov Chi-Square Anderson–Darling. 🔹 Intensity-Duration-Frequency (IDF) Curves Derivation of mathematical relationships between intensity (I), duration (D), and frequency (T) Form the basis for the design of stormwater drainage networks and urban infrastructure. ⏱️ Temporal Analysis Time series analysis to detect: Long-term trends (Trend Analysis) Climate changes and their impact on precipitation patterns Use of tests: Mann–Kendall Sen’s Slope Estimator. 🌍 Spatial Rainfall Analysis Due to the heterogeneity of precipitation, rainfall is spatially represented using: Thiessen Polygons Inverse Distance Weighting (IDW) Kriging (Geostatistical Methods) Integration with geographic information systems (GIS) is an essential step in improving rainfall representation at the catchment level. 💧 Linking rainfall and hydrological models Rainfall analysis results are used directly in: Rational Method (for small basins with rapid response) SCS Curve Number Method for estimating loss and surface runoff Rainfall–Runoff Models such as: HEC-HMS WMS SWMM ⚠️ Technical challenges Incomplete or irregular rainfall records High spatial variability of storms The impact of climate change on the stability of statistical assumptions (Stationarity). Any hydrological model, regardless of its computational accuracy, remains dependent on the quality of the rainfall data analysis input into it. Rainfall analysis is not a preliminary step, but rather the essence of the entire hydrological process.

🤔 Ever wondered you get hard core scientific proof that your correlations and model results aren't just spurious ❓ 🥇 The example here is the gold standard. Let's take the #Tech sector #XLK We have produced a factor model, where XLK returns are a function of macro factor returns like real GDP Nowcasting, inflation, real/nominal rates, credit spreads, the US Dollar. 12 factors in total (with the data all normalized and "de-correlated" using a Partial Least Squares Regression PLSR) 👉 We ran a Null Hypothesis test: A statistical method for determining if a REAL relationship exists in a population, or if an observed relationship in a sample is just due to chance It involves assuming that a “null hypothesis” of “no effect” is true and then using sample data to decide if there is enough evidence to reject it in favour of an alternative hypothesis The test’s outcome helps researchers make inferences about the larger population based on sample data, ensuring statistical rigour and managing the risk of false conclusions For a particular day, given that one has the (historical) factors mean return and their CoVar matrix (125 trading days, 90 half-life) ..and assuming the factor return jointly follows a multivariate Gaussian distribution (or any other distribution like an alpha-stable) ..it is possible to generate (simulate) multivariate random draws of our factor returns that follow that distribution (correlations included). We generate 125 of these simulated random draws in each step (the same as the historical window) Then we take these random generated factor returns and we regress them against the target (e.g. XLK) For this operation (PLSR), we also get the value for the macro exposures. ❗ These exposures were obtained from a random sample, therefore they are the result of chance. 🤖 We repeat the above process 10,000 times and we record those 10,000 exposures (and the R^2) and we do a histogram (in blue) with them This histogram give us the "range" of exposure values one can get from a pure chance process Then we do one extra PLSR this time with the REAL factor return data We plot the real exposures over the previous histograms (red line) ❓ And the question is: Are the red lines (real exposures) well inside the histograms of the random samples or not ? If they are, then those exposures (or R^2) are NOT significant because they could have been obtained just by chance However, when we look at these plots we see that the R^2 are every time very far from the histograms , and many of the model exposures are on the distribution tails (> 95% tail) or much further away One can only conclude that: 1️⃣ Macro is driving XLK: Significant R^2 (outside of the histograms by over 40 std deviations) 2️⃣ Many macro exposures also are significant (outside the histograms), because they couldn't have been the result of chance 👉 A null hypothesis test on your model is a very rigorous way to test for spuriousness #equities #factorinvesting

What is a Corner Model? A Corner Model represents the extreme boundaries of process, voltage, and temperature (#PVT) variations. We don't just care if a #chip works at room temperature; we care if it works when the manufacturing process is "slow," the battery is low, and the device is sitting in a car in the Sahara. We typically track three primary variables: #Process (P): Variations in doping concentrations, oxide thickness, and lithography. This is categorized as Fast (F) or Slow (S). #Voltage (V): Fluctuations in the power supply. Lower voltage typically leads to slower carrier mobility. #Temperature (T): High heat increases scattering and reduces mobility (slowing logic), while extreme cold can lead to "hot carrier" effects or timing violations in fast paths. The Engineering Trade-off: Performance vs. Yield ◾Design for SS (Slow-Slow): If your critical path meets timing here, it will likely work everywhere. However, over-designing for the absolute worst-case SS corner at high temperatures can lead to massive area and power penalties. ◾Design for FF (Fast-Fast): This is where we validate Hold Time. If the clock is slow but the logic is too fast, data hits the flip-flop before the previous cycle is finished. This results in functional failure that no amount of software patching can fix. Beyond the Basics: The Move to Statistical Models In advanced nodes (7nm, 5nm, and below), fixed corners are often too pessimistic. The industry has shifted toward Global Corners + Local Variation (Monte Carlo). We now use Advanced OCV (AOCV) or Statistical Static Timing Analysis (SSTA) because, at 3nm, the random variation between two transistors sitting right next to each other (mismatch) can be as significant as the global process shift. #VLSI #Semiconductor #SiliconDesign #ICDesign #EngineeringExcellence #HardwareEngineering #Analog #Analogdesign #Analoglayout

Excited to share some recent advancements in the area of multifidelity uncertainty quantification (MFUQ) from collaborations with our colleagues at University of Michigan and Sandia National Labs! 🤝📈 MFUQ approaches combine predictions from a high-fidelity (but expensive) model with faster, lower-fidelity models to produce UQ estimators with improved efficiency and precision 🎯. My team at NASA has been collaborating for several years with leading researchers in this area from UMich and Sandia, using entry, descent, and landing (EDL) problems to assess the performance of new techniques we develop together. I’m sharing three papers below that we’ve released over the past month or so. Many thanks to Thomas Dixon (UMich) in particular for leading the charge on two of them 💪. 1) 𝗔 𝗠𝘂𝗹𝘁𝗶-𝗙𝗶𝗱𝗲𝗹𝗶𝘁𝘆 𝗔𝗽𝗽𝗿𝗼𝗮𝗰𝗵 𝘁𝗼 𝗗𝗶𝘀𝘁𝗿𝗶𝗯𝘂𝘁𝗶𝗼𝗻 𝗘𝘀𝘁𝗶𝗺𝗮𝘁𝗶𝗼𝗻 𝗔𝗽𝗽𝗹𝗶𝗲𝗱 𝘁𝗼 𝗔𝗲𝗿𝗼𝘀𝗽𝗮𝗰𝗲 𝗔𝗽𝗽𝗹𝗶𝗰𝗮𝘁𝗶𝗼𝗻𝘀   💡Most MFUQ approaches are limited to estimating statistical moments (e.g., mean and variance). In this paper, we present a novel extension of MFUQ for estimating full cumulative distribution functions, and demonstrate its performance on EDL and additive manufacturing applications.  🔗 Paper: https://lnkd.in/e6RaztCe 2) 𝗔𝘂𝘁𝗼𝗺𝗮𝘁𝗲𝗱 𝗠𝗼𝗱𝗲𝗹 𝗧𝘂𝗻𝗶𝗻𝗴 𝗳𝗼𝗿 𝗠𝘂𝗹𝘁𝗶𝗳𝗶𝗱𝗲𝗹𝗶𝘁𝘆 𝗨𝗻𝗰𝗲𝗿𝘁𝗮𝗶𝗻𝘁𝘆 𝗣𝗿𝗼𝗽𝗮𝗴𝗮𝘁𝗶𝗼𝗻 𝗶𝗻 𝗧𝗿𝗮𝗷𝗲𝗰𝘁𝗼𝗿𝘆 𝗦𝗶𝗺𝘂𝗹𝗮𝘁𝗶𝗼𝗻 💡The performance of MFUQ methods depends crucially on the computational cost of, and correlations among, the available models. In addition, low-fidelity models often have hyperparameters (e.g., those controlling spatial/temporal discretization) that govern their cost-accuracy tradeoff. In this paper, we introduce an approach to automatically tune these hyperparameters on-the-fly to maximize MFUQ performance, with application to EDL problems. 🔗 Paper: https://lnkd.in/eDsjarf8 3) 𝗕𝗜𝗦𝗧𝗥𝗢 -- 𝗔 𝗕𝗶-𝗙𝗶𝗱𝗲𝗹𝗶𝘁𝘆 𝗦𝘁𝗼𝗰𝗵𝗮𝘀𝘁𝗶𝗰 𝗚𝗿𝗮𝗱𝗶𝗲𝗻𝘁 𝗙𝗿𝗮𝗺𝗲𝘄𝗼𝗿𝗸 𝘂𝘀𝗶𝗻𝗴 𝗧𝗿𝘂𝘀𝘁-𝗥𝗲𝗴𝗶𝗼𝗻𝘀 𝗳𝗼𝗿 𝗢𝗽𝘁𝗶𝗺𝗶𝘇𝗮𝘁𝗶𝗼𝗻 𝗨𝗻𝗱𝗲𝗿 𝗨𝗻𝗰𝗲𝗿𝘁𝗮𝗶𝗻𝘁𝘆 💡Optimization under uncertainty in engineering systems is often intractable due to repeated evaluations of an expensive, high-fidelity simulation. In this paper, we present a new bi-fidelity stochastic optimization framework that leverages both design-space curvature information and random-space correlations from a low-fidelity model. We demonstrate significant performance improvements over existing methods on benchmark problems and a 20-dimensional space shuttle reentry test case.  🔗 Paper: https://lnkd.in/eFByQswH Collaborators: Geoffrey Bomarito (NASA), Joshua Pribe (AMA/NASA), Thomas Dixon (UMich), Alex Gorodetsky (UMich), Gianluca Geraci (Sandia), Michael Eldred (Sandia)

Classical methods often lean on linearity and convenient distributional assumptions. Linearity should be a pleasant surprise, not a prerequisite. #NNS uses partial moments, the elements of variance, to handle: Core Analytics: → Nonlinear correlation & dependence (beyond Pearson) → Clustering without distance metrics → Causality detection from observational data Modeling & Prediction: → Nonlinear regression with strong extrapolation → Classification without parametric assumptions → Time-series forecasting (seasonality + nonparametric ARMA) Advanced Tools: → Numerical integration & differentiation → Copula estimation → Stochastic dominance for portfolio optimization → Maximum entropy bootstrap with controllable drift/correlation All while maintaining equivalence to traditional statistics when data is linear. It's a complete rethink of the statistical toolkit. Video walkthrough + quantitative finance applications: ovvolabs.com/media

What Monte Carlo REALLY means for engineers 🎯 If you’ve never heard of Monte Carlo, don’t worry — it’s not a casino trick. It’s one of the most powerful ideas in engineering and science. Here’s the intuition 👇 🔹 You have a problem that’s hard (or impossible) to solve analytically Closed-form equations either don’t exist or are too complex. 🔹 So you use randomness on purpose You generate many random samples and let statistics do the heavy lifting. 🔹 The answer emerges from repetition More samples → better approximation And the uncertainty can be quantified. I created an animation to estimate π using Monte Carlo. 🟦 Step 1: Draw a square 🔵 Step 2: Inscribe a circle 🎯 Step 3: Randomly throw points into the square Some points land inside the circle, some outside. The ratio (points inside the circle) / (total points) → converges to π / 4 Multiply by 4 → π Now the key Monte Carlo ideas become visible 👀 ✅ Each run uses a different random seed ✅ Each run gives a slightly different answer ✅ As the number of samples increases, all runs converge to the same value ✅ The spread between runs tells you the uncertainty This is why Monte Carlo is everywhere in engineering. Monte Carlo isn’t about randomness. It’s about extracting order from randomness. #MonteCarlo #Engineering #Simulation #NumericalMethods #UncertaintyQuantification #Probability #Statistics #ScientificComputing #ComputationalEngineering #DataDriven #MachineLearning #STEM #EngineeringLife