Mathematical Models TRIZ Cases

Knowledge-reinforced learning with dual extended Kalman filters improves lithium-ion battery RUL prediction and supports thermal control.

A Dragonnet-VAE approach updates transaction control groups to stay representative, reduce bias, and improve fraud detection accuracy.

Telematics-driven behavior models update transit and carpool routes in real time to cut travel time, fuel cost, and pollution.

Recursive allowed-region analysis across component models helps optimize physical systems under objective and constraint limits.

Time-varying threshold curves allocate randomly arriving jobs in real time, maximizing cumulative reward without known arrival models.

Sensor readings replace unreliable GPS and manual venue labeling to predict user routines and trigger timely mobile assistance.

Historical plant workflows are mined and modeled with generative AI to preserve expert know-how and guide next engineering steps.

Dynamic valve switching routes solar-heated water between electric and gas heaters to match local power availability and avoid costly grid surges.

Aging-model PDFs with EOL boundary conditions and Bayesian updates improve failure prediction and maintenance timing for monitored devices.

Real-time monitoring with reinforcement learning predicts final quality and adjusts each process step to cut waste and improve consistency.

Entropy-based surprisal and conviction measures prune low-value data elements to keep AI reasoning models broad, smaller, and faster to train.

Audio segments are pre-analyzed and stitched with mixing instructions to deliver gapless, customized playback with less manual processing.

Mean field game scheduling spaces UAV human-loop requests to improve cooperative positioning resilience without overloading limited operators.

Gaussian process regression builds speed-based performance curves from limited calibration data to detect mechanical damage with fewer false positives.

Uncertainty-based state selection cuts expert queries while refining a control policy with full trajectory demonstrations for vehicle tasks.

Independent actor-critic agents fuse image and parameter data to keep autonomous vehicles operating when communication is limited or lost.

Flight-data embeddings turn engine ageing into a monotonic state indicator, improving maintenance prediction without engine models.

Multiple AI components process building management data in parallel and merge outputs to produce more accurate building information models.

AI components convert image-based building management system data into accurate information models, reducing manual mapping errors and energy waste.

Transforms uncertain curve and point geometry into covariance-based proximity estimates for more reliable autonomous control in noisy sensing.

MCMC-based steering calibration uses uncertain downhole measurements to stabilize drill-bit position and orientation control during automated drilling.

Particle-updated semantic occupancy grids keep environment categories consistent for automated driving decisions with real-time complexity.

Reinforcement learning penalizes intervention actions so mobile robots avoid collisions with fewer disruptions, shorter travel time, and less environmental stress.

Substring frequency matrices and probability scoring classify non-standard building automation points faster, cutting manual commissioning effort.

Generative AI maps user intents to entities, devices, and action sequences to automate coordinated IoT interactions across real and virtual environments.

Causal analysis of IED disturbance records speeds substation fault diagnosis and pinpoints likely and exact causes from complex data.

IED disturbance records are turned into causal patterns and ML fault predictions to speed substation diagnosis and pinpoint exact causes.

Sensor voting filters faulty pilot-input data in electric aircraft flight control, improving maneuver reliability during failures.

A federated stochastic configuration network predicts product quality across factories while protecting data privacy and avoiding local minima.

Reinforcement learning agents use process graphs to cut excess sensor data while preserving monitoring performance in industrial IoT.

Softmax1 attention regularization and relational encoding improve convergence and interpretability on noisy manufacturing data with missing values.

A perceptron efficiency metric and Gaussian Process model let drilling control explore safely while optimizing multiple real-time performance metrics.

A probabilistic filter updates robotic state and motion models with time-varying Gaussian basis functions while enforcing structural constraints.

Machine learning turns telematics travel patterns into dynamic transit and carpool routes, reducing route obsolescence and improving rider fit.

Reinforcement learning combines local and remote subsystem data to stabilize web tension, cut setup effort, and reduce package defects.

Combines fault trees with Bayesian networks to quantify how environmental conditions and E/E faults drive safety goal violations.

A hybrid fault tree and Bayesian network approach quantifies how component faults and environmental conditions affect safety goal violations.

Monitoring data, multi-agent models, and surrogate analysis help verify resilience scenarios faster and visualize priorities for infrastructure stability.

Bayesian causal models decompose intrinsic and extrinsic variation to pinpoint semiconductor equipment mismatch causes faster and more objectively.

Particle filter updates and Markov health states improve long-horizon asset prognosis when sensor data is intermittent.

A learning model adjusts gas purification to handle fluctuating waste-derived gas composition and enable efficient reuse as industrial raw material.

Maps multivariate covariates into surrogate features to forecast non-stationary extremes with lower computation and real-time updates.

Predictive analysis links each power asset to similar historical assets to estimate remaining life and prevent unplanned outages.

Reinforcement learning coordinates local and remote sub-system data to tune jaw control, improving package formation accuracy and reducing waste.

Multimodal learning from human cues and feedback helps robots build emotional connection while avoiding dangerous, costly trial-and-error.

Time-series preprocessing with ML classification and expert rules pinpoints faulty sequencing subcomponents and avoids incorrect replacement.

Local anomaly detection and remote rule building cut data transfer and privacy risk while improving laboratory instrument maintenance.

Virtual error augmentation helps a single prediction model resist recursive error buildup and keep process simulations accurate over time.

Virtual error data is added to time-series training inputs so a process simulator can limit error propagation and keep predictions reliable over time.

Bayesian optimization cuts laser drilling and welding trials by combining simulated and measured results to converge on high-quality process settings.

A hierarchical neural network classifier identifies entities in unstructured text using sub-classifiers and a combiner.

A neural waveform distinguishing apparatus processes gradient waveforms using an encoder ensemble to extract concatenated feature codes for signal separation.