Abstract

Peak particle velocity (PPV) prediction remains governed by the empirical scaled-distance law, PPV=K\ast\left(\frac{D}{\sqrt W}\right)^n, wherein residuals are conventionally relegated to diagnostic checking for normality and homoscedasticity. This study re-conceptualizes residuals as exploitable operational assets and proposes the Tripod+ AI framework, a hybrid Diagnose-Mine-Learn (D-M-L) architecture, to use residuals efficiently beyond diagnostics. The hybrid model was considered in three steps. Step 1 (Diagnose) fits the baseline logPPV=a+b\ logSD and extracts residuals e_{i=y_i}-\hat{f}\left(X_i\right)\ via projection ({(I-H)}_y. Step 2 (Mine) models residuals as e_i=g\left(Z_i\right)+\varepsilon_i , where Z = [Bench, Holes, Hole Dia, log W] captures omitted operational signatures, revealing E[e|X]≠0 under misspecification. Step 3 (Learn) constructs the hybrid predictor ŷhybrid = f̂(X) + ĝ(Z), with theoretical improvement condition ove,ĝ>12Var(ĝ). Four instantiations of g(·) are compared on 1,522 production blasts from TEBEREBIE CUT 3, CUT 7, MANTRIEM/TEB CUT 4 and PEPE pits, Tarkwa, Ghana (2019–2022; clean n = 1,424): Polynomial, Random Forest (RF,\ B\ =\ 20,\ d\ =\ 6), XGBoost (K = 50, d = 3, ν = 0.12) and Gaussian Process (GP, RBF kernel, m = 500). Crucially, strict time-ordered validation is employed (70% train: 977 blasts, 2019–2021; 30% test: 419 blasts, 2021–2022) to emulate operational deployment across the lithological transition (Bench −81 m to 0 m). The baseline achieves test {MSE}_{log}= = 0.0304. Poly D-M-L overfits ({MSE}_{log} = 0.0322, −6.0%, R2res = −0.19) and GP-RBF overfits (0.0348, −14.4%, R2res = −0.29), whereas XGBoost retains 0.0281 (+7.6%) and RF achieves 0.0262 (+13.8% gain, R2res = 0.06). Bagging variance Var(gRF) ≈ ρσ2T/B provides regularization against distributional shift. At the same time, GP extends the noisy-input GP (NIGP) formalism with effective variance \sigma2eff\ =\ \sigma2y\ +\ \nabla gT\Sigma z\nabla g\ +\ V[g], enabling 95% prediction intervals essential for 0.5 mm/s community compliance. In-sample random splits overstate gain (41%), underscoring the necessity of temporal validation. The framework is model agnostic, preserves regulatory acceptance of the USBM law, and demonstrates that residuals are predictive assets when mined with regularized learners.