⚡ electrical engineering

Semi-physical Gamma-Process Degradation Modeling and Performance-Driven Opportunistic Maintenance Optimization for LED Lighting Systems

This paper proposes a performance-driven, simulation-in-the-loop framework that integrates semi-physical Gamma-process degradation modeling with ray-tracing-based illuminance mapping and surrogate-assisted optimization to determine optimal opportunistic maintenance strategies for large-scale LED lighting systems under uncertainty.

Original authors: Haohao Shi, Huy Truong-Ba, Michael E. Cholette, Brenden Harris, Juan Montes, Tommy Chan

Published 2026-01-15

📖 5 min read🧠 Deep dive

CC BY 4.0

Original authors: Haohao Shi, Huy Truong-Ba, Michael E. Cholette, Brenden Harris, Juan Montes, Tommy Chan

Original paper licensed under CC BY 4.0 (http://creativecommons.org/licenses/by/4.0/). ✨ This is an AI-generated explanation of the paper below. It is not written or endorsed by the authors. For technical accuracy, refer to the original paper. Read full disclaimer

Imagine a large office building with hundreds of LED light fixtures. Over time, these lights don't just suddenly stop working; they slowly get dimmer (like a fading sunset) or, occasionally, a specific part inside them (the driver) suddenly blows out, turning the light off completely.

The paper by Haohao Shi and colleagues is like a smart, futuristic maintenance planner for these lights. Instead of waiting for lights to go dark or changing them all on a fixed calendar schedule (which might be wasteful), this system figures out the perfect time to fix them based on how the light actually feels to the people working in the room.

Here is how the paper breaks down, using simple analogies:

1. The "Crystal Ball" for Dying Lights (Modeling Degradation)

The authors needed a way to predict how lights age. They didn't just guess; they used a "crystal ball" built from real data.

The Slow Fade: They modeled the gradual dimming of the LED bulbs using a "Gamma Process." Think of this like a runner who gets tired. You can't say exactly when they will stop, but you can predict the trend of their slowing down. They used data from "stress tests" (heating the lights up in a lab) to predict how they will age in a normal office.
The Sudden Crash: They also modeled the "drivers" (the power supply) which can fail suddenly, like a car engine stalling.
The Uncertainty: Since they can't know the future perfectly, they used "Bayesian calibration." Imagine a weather forecaster who doesn't just say "it will rain," but says, "There's a 70% chance of rain, and here's the range of how hard it might pour." This helps them account for uncertainty.

2. The "Room Feel" vs. The "Light Bulb" (Performance Mapping)

Most maintenance plans look at individual light bulbs: "Is this bulb broken?"
This paper looks at the room: "Can I read my paper on this desk?"

The Ray-Tracing: They used a sophisticated computer simulation (called Radiance) to see how light bounces off walls, ceilings, and desks. Even if a bulb is still working, if it's too dim or uneven, the room fails the standard.
The "Deficiency Ratio": Instead of just counting broken bulbs, they created a new metric called the "Deficiency Ratio." Imagine a timer that starts ticking every time the light on your desk drops below the required brightness. The goal is to keep this timer from running too long over the next 50 years.

3. The "Speeding Up" Trick (Surrogate Modeling)

Running the detailed light simulation (Radiance) is like running a marathon; it takes a long time. If you have to do it thousands of times to test different maintenance plans, it would take decades.

The Shortcut: The authors built a "surrogate model." Think of this as a cheat sheet or a trained assistant. They ran the slow, detailed simulation a few thousand times to teach the assistant the rules. After that, the assistant can predict the room's lighting in milliseconds instead of minutes. This allowed them to run millions of "what-if" scenarios instantly.

4. The "Opportunistic" Strategy (Maintenance Optimization)

The core of the paper is about Opportunistic Maintenance.

The Old Way: Fix a light only when it breaks (too late) or change all lights every 5 years (too early/wasteful).
The New Way: Imagine a maintenance crew is already in the building to fix one broken light (a "Corrective" visit). The system asks: "Hey, while you're here, are there any other lights that are getting close to being dim? Let's swap those out too."
The Trade-off: The paper finds the "Pareto Frontier." This is a fancy way of saying the "Goldilocks Zone." It shows the best balance between:
1. Keeping the lights bright (Low Deficiency).
2. Making fewer trips to the building (Low Site Visits).
3. Buying fewer new bulbs (Low Replacements).

5. The Real-World Test

They tested this on a real office at Queensland University of Technology.

They simulated 50 years of operation.
They found that there isn't one "perfect" answer. Instead, there is a menu of options.
- Option A: Change bulbs very often to keep the light perfect, but it costs a lot in labor and materials.
- Option B: Change bulbs rarely to save money, but the light will be dim for longer periods.
- Option C (The Sweet Spot): A strategy where you wait for a light to fail, and then use that visit to "sweep up" and fix a few others that are getting close to failing. This saves a lot of trips without making the room too dark.

Summary

This paper provides a smart, data-driven rulebook for building managers. It moves away from "fixing broken things" to "managing the quality of light." By combining physics-based predictions with a "cheat sheet" for fast calculations, it helps managers decide exactly when to send a crew to the building to get the best balance between saving money and keeping the lights bright.

Technical Summary: Semi-physical Gamma-Process Degradation Modeling and Performance-Driven Opportunistic Maintenance Optimization for LED Lighting Systems

1. Problem Statement

Large-scale LED lighting systems degrade through two competing mechanisms: gradual light-output loss from LED package degradation and abrupt outages caused by driver failures. While traditional maintenance strategies often rely on component-level reliability or static commissioning indices (e.g., initial average illuminance and uniformity), these approaches fail to capture the spatio-temporal evolution of system performance over long operational horizons.

The core challenge addressed is the lack of a framework that:

Integrates stochastic component degradation and failure models with physics-based spatial lighting simulations.
Defines system-level "failure" not merely as a component breakdown, but as a violation of working-plane illuminance requirements (average illuminance and uniformity) over time.
Optimizes opportunistic maintenance (OM) policies under uncertainty, balancing performance compliance against maintenance resource constraints (site visits and replacements) without relying on arbitrary cost assumptions.

2. Methodology

The paper proposes a performance-driven, simulation-in-the-loop framework comprising four main components:

A. Component-Level Modeling and Calibration

LED Package Degradation: Modeled using a semi-physical non-homogeneous Gamma process. The mean trajectory follows an exponential lumen-maintenance trend (consistent with IES TM-21), while the stochastic nature captures path uncertainty. The shape function is time-dependent ( $\alpha(t) = A \exp(bt)$ ).
Driver Failures: Modeled as abrupt failures following a Weibull lifetime distribution.
Competing Failure Integration: A luminaire is considered failed if either the driver fails (state = 1) or the package degradation exceeds the $L_{70}$ threshold (state = 1).
Bayesian Calibration: Parameters for the Gamma process and Weibull distribution are inferred from LM-80 accelerated degradation test (ADT) data across multiple stress temperatures. A linear acceleration model (Arrhenius relationship) extrapolates these parameters to operating conditions, while Bayesian inference quantifies epistemic uncertainty, which is propagated through the system simulation.

B. System-Level Performance Mapping

Physics-Based Simulation: A Radiance ray-tracing engine maps luminaire states (degradation levels and outage status) to working-plane illuminance distributions, accounting for room geometry, surface reflectances, and photometric data.
Dynamic Deficiency Metric: Static indices (average illuminance $E_{avg}$ and uniformity $U$ ) are converted into a long-term Deficiency Ratio (DR). This metric calculates the fraction of the operational horizon where the system violates at least one standard requirement ( $E_{avg} < S_E$ or $U < S_U$ ), based on the duration of violations between event intervals.

C. Surrogate-Based Acceleration

To overcome the computational intractability of running thousands of Radiance simulations for Monte Carlo policy evaluation, a linear surrogate model is developed.
Based on the superposition principle of light transport, illuminance is modeled as an affine function of the luminaire output scaling vector.
The surrogate is trained on a dataset generated by a limited number of Radiance runs (using Sobol sequences for sampling) and achieves high fidelity ( $R^2 = 0.9999$ ), reducing evaluation time from minutes per snapshot to milliseconds.

D. Optimization Framework

Policy Formulation: An opportunistic maintenance policy is defined by two decision variables: the Preventive Maintenance (PM) interval ( $T_{PM}$ ) and an OM threshold ( $H_{OM}$ ). When a maintenance event (PM or Corrective Maintenance) occurs, other luminaires are replaced if their remaining time to the next scheduled PM falls within the $H_{OM}$ window.
Multi-Objective Optimization: The framework seeks Pareto-optimal solutions for three objectives:
1. Minimize the long-term Deficiency Ratio ( $R_{DR}$ ).
2. Minimize the total number of site visits ( $N_{tv}$ ).
3. Minimize the total number of replacements ( $N_{tr}$ ).
Evaluation: A discrete-event Monte Carlo simulator evaluates candidate policies over a 50-year horizon, incorporating stochastic degradation trajectories and the surrogate-based performance mapping.

3. Key Contributions

The paper claims the following specific contributions:

Dynamic System-Level Metric: Extends static commissioning indices to a long-term dynamic deficiency metric that quantifies the duration of requirement violations, enabling explicit quantification of system-level performance failure.
Programmatic Pipeline: Establishes an automated degradation–simulation–metric workflow that propagates stochastic luminaire-state trajectories through a physics-based lighting model for Monte Carlo evaluation.
Uncertainty-Aware Modeling: Integrates a semi-physical non-homogeneous Gamma process for packages and a Weibull model for drivers, calibrated via Bayesian inference from ADT data to quantify parameter uncertainty for downstream simulation.
Scalable Policy Evaluation: Introduces a surrogate-based performance mapping that replaces repeated ray-tracing, enabling large-scale Monte Carlo policy search with negligible loss of fidelity.
Multi-Objective Trade-off Analysis: Demonstrates a simulation-in-the-loop optimization that identifies Pareto-optimal maintenance policies balancing performance deficiency against resource proxies (visits and replacements) without requiring specific cost data.

4. Results

The framework was applied to a case study of a large office zone (Zone 1) at Queensland University of Technology, featuring 76 LED luminaires.

Calibration: Bayesian inference successfully fitted the Gamma process parameters to LM-80 data at 55°C, 85°C, and 105°C, with posterior-predictive trajectories matching observed data. The model was extrapolated to a 45°C operating condition.
Pareto Front Analysis: The optimization identified 36 statistically robust, non-dominated policies.
- Trade-offs: A clear trade-off exists between the number of replacements and site visits. Aggressive opportunistic policies (low $T_{OM}$ ) reduce replacements but may increase site visits if not coordinated well, while conservative policies (high $T_{OM}$ ) reduce replacements but significantly increase the deficiency ratio and site visits due to delayed corrective actions.
- Policy Types: The analysis distinguished between "PM-driven" policies (where scheduled maintenance dominates) and "CM-driven" policies (where failure-triggered maintenance dominates).
Sensitivity Analysis: Variations in driver reliability (scenarios where drivers fail earlier or later than packages) significantly shifted the Pareto front. Early driver failures (Scenario S3) led to a pronounced increase in total replacements and site visits, highlighting the critical impact of component reliability assumptions on maintenance planning.
Computational Performance: The surrogate model reduced the computational time for 10,000 simulations from an estimated ~700 days (using direct Radiance) to approximately 20 seconds, making the optimization feasible.

5. Significance and Claims

The paper asserts that its primary significance lies in shifting the paradigm of lighting system maintenance from component-centric or static-commissioning-centric approaches to a performance-driven, dynamic framework.

Decision Support: By providing a Pareto front of solutions, the framework offers facility managers a range of options to balance lighting quality (deficiency ratio) against operational effort (visits and replacements), tailored to their specific priorities.
Uncertainty Propagation: The explicit handling of parameter uncertainty via Bayesian calibration ensures that maintenance decisions are robust against the inherent variability in degradation and failure processes.
Scalability: The surrogate-based acceleration makes it computationally feasible to optimize maintenance for large-scale systems over long horizons, a task previously hindered by the high cost of physics-based lighting simulations.
Practicality: The use of resource proxies (visits and replacements) rather than specific monetary costs allows the framework to be applied even when detailed cost data is unavailable, while still capturing the essential trade-offs of maintenance planning.

The authors conclude that while the current framework uses resource proxies, future work could integrate richer cost models and spatial heterogeneity (location-dependent criticality) to further enhance field applicability.