System Identification from Operational Data
Extracting mathematical models from measured behavior when physics-based derivation falls short
Multi-Objective Optimization: Navigating the Pareto Frontier
When objectives conflict irreconcilably, the Pareto frontier maps the territory of genuine engineering trade-offs.
Requirements Decomposition: From System Need to Component Specification
Systematic methods for transforming stakeholder needs into verifiable specifications while preserving intent and traceability.
State Estimation in Noisy Environments: Beyond Kalman
When linear Gaussian assumptions fail, advanced filtering architectures maintain estimation integrity through principled mathematical machinery.
Architecture Trade Studies That Actually Inform Decisions
Rigorous methods for trade studies that expose decision structure rather than obscure it with false precision
Optimal Sensor Placement for Complete Observability
Where to measure when you cannot measure everywhere—the mathematics of sensor location decisions
Stability Margins: What They Really Tell You
Classical margins measure robustness along axes; real failures occur diagonally in perturbation space.
System Degradation: Designing for Graceful Performance Loss
How sophisticated architectures maintain useful operation through systematic capability shedding and intelligent mode transitions.
Emergent Behavior Prediction in Complex Integrations
Systematic methods for anticipating system-level behaviors that component specifications cannot predict, from classification frameworks to simulation architectures.
The Constraint Propagation Problem in Large System Design
Master the mathematical structure of constraint networks to navigate complex system design from infeasibility to optimized solutions.
The Hidden Mathematics of Requirements Traceability
Transform requirements management from documentation exercise into mathematical analysis that reveals hidden gaps and proves verification completeness.
Why Your System Architecture Fails at Scale
Structural principles that determine whether your architecture enables graceful growth or guarantees eventual collapse under scaling pressure.
Why Redundancy Architecture Often Reduces Reliability
Understanding why adding backup systems can paradoxically increase failure risk—and the rigorous methods that achieve genuine reliability improvement.
Control Loop Interaction: When Independent Systems Fight
Master the frequency-domain tools and architectural patterns that prevent independently designed controllers from creating destructive feedback conflicts in integrated systems.
Coupled Dynamics: Modal Analysis of Multi-Body Systems
Master the eigenvalue methods that reveal how vibrating bodies interact and discover design principles for preventing destructive resonance in coupled mechanical systems.