⚡ electrical engineering

Research on the life assessment of the insulating rod of a fast mechanical switch based on the Weibull distribution and the firefly algorithm

This study proposes a hybrid life assessment method for fast mechanical switch insulating rods that integrates multi-physics finite element modeling, stress-life analysis, and firefly algorithm-optimized three-parameter Weibull distribution to overcome the limitations of pure simulation and testing, thereby enabling reliable reliability prediction under various operating conditions.

Original authors: Yang Kuangbiao, Li Guoli, Sun Zehui, Xu Jiazi, Ding Shuo

Published 2026-06-30

📖 5 min read🧠 Deep dive

CC BY 4.0

Original authors: Yang Kuangbiao, Li Guoli, Sun Zehui, Xu Jiazi, Ding Shuo

Original paper licensed under CC BY 4.0 (https://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

The Big Picture: Predicting When a "Muscle" Will Give Out

Imagine a fast mechanical switch in a power grid as a high-speed gatekeeper. Its job is to slam shut or fly open in milliseconds to stop electrical faults. The "muscle" that makes this happen is a glass-fiber rod (the insulating rod).

The problem? Just like a human muscle that gets tired after lifting heavy weights repeatedly, this rod can eventually snap due to fatigue. If it breaks, the gatekeeper fails, and the power grid could go dark or catch fire.

The researchers wanted to answer a simple question: How many times can this rod open and close before it breaks?

The Problem with Old Methods

Previously, engineers had two bad options to find the answer:

The "Break-It-All" Test: They would build a machine, run it until the rods broke, and count the cycles.
- The Catch: This is incredibly expensive, takes months, and destroys the rods. You can't test every single rod this way.
The "Computer Guess" Test: They would build a virtual model in a computer and simulate the stress.
- The Catch: Computers aren't perfect. Without real-world proof, the numbers might be just a fantasy.

The New Solution: A "Hybrid" Approach

This paper proposes a clever three-step recipe that mixes the best of both worlds: Real Testing + Computer Simulation + Smart Math.

Step 1: The "Stress Test" (Real World)

The team took a few actual rods and subjected them to real electrical shocks (voltages) to see how much they bent and stretched. They used special sensors (strain gauges) and high-speed cameras to record exactly what happened.

The Analogy: Think of this as a coach timing a sprinter with a stopwatch and a camera to get the "ground truth" of their speed.

Step 2: The "Virtual Gym" (Simulation)

Once they knew the real numbers, they built a digital twin of the switch in a computer. They checked the computer's math against the real stopwatch data.

The Result: The computer was 97% accurate (less than 3% error).
The Analogy: Now that the coach knows the stopwatch is accurate, they can use a video game to simulate the sprinter running 1,000 different races under different weather conditions without ever leaving the gym. This saves time and money.

Step 3: The "Smart Predictor" (The Firefly Algorithm & Weibull Distribution)

The computer generated data for 14 different voltage scenarios. Now, they needed to turn this messy pile of numbers into a clear prediction.

The Weibull Distribution (The "Weather Forecast"):
This is a specific type of math curve used to predict when things break. The researchers found that a three-parameter version of this curve fit their data best.
- The Analogy: Imagine trying to predict when a tire will blow out. A simple guess might say "50,000 miles." The Weibull curve is like a sophisticated weather forecast that says, "There's a 10% chance of a blowout at 40,000 miles, a 50% chance at 50,000 miles, and it's almost guaranteed by 60,000 miles." It accounts for the fact that some tires are just luckier than others.
The Firefly Algorithm (The "Smart Searchlight"):
To make the "Weather Forecast" (Weibull curve) as accurate as possible, they needed to find the perfect numbers for the formula. They used an algorithm inspired by fireflies.
- The Analogy: Imagine a swarm of fireflies in a dark forest looking for the brightest light (the perfect answer). Each firefly moves toward the brightest one it sees. If a firefly finds a brighter spot, the others follow. This "swarm intelligence" quickly finds the best mathematical settings without getting stuck in a "local" bright spot that isn't the best one.

What They Found

By combining the real tests, the virtual simulations, and the "firefly" math, they created a reliable life guide for the rod:

The "Safe Zone": If you use the rod for about 6,820 cycles, there is a 90% chance it will still be working. (Great for critical power lines).
The "Warning Zone": At 7,516 cycles, the risk of failure starts to get higher (80% chance of survival). This is when you should plan to replace it.
The "Half-Life": At 10,344 cycles, half of the rods will have broken, and half will still be working.
The Failure Type: The math showed the rods don't break randomly; they break because of wear and tear (like an old shoe sole wearing thin), which confirms they need to be replaced before they get too old.

The Bottom Line

This research didn't just guess or just test. It built a trustworthy bridge between reality and simulation. By using a "Firefly" search to fine-tune a "Weather Forecast" math model, they gave engineers a precise map to know exactly when to replace these critical rods, keeping the power grid safe without wasting money on unnecessary tests.

Technical Summary: Life Assessment of Fast Mechanical Switch Insulating Rods

Problem Statement
The insulating rod is a critical force-transmitting component in fast mechanical switches used for fault isolation and power quality regulation in power systems. These rods, typically made of glass fiber-reinforced epoxy resin, are subjected to complex, time-varying multi-axial stresses during frequent opening and closing cycles. Engineering statistics indicate that approximately 35% of switch faults stem from rod fatigue failure, often manifesting as interlaminar fracture due to stress concentration.

Current life assessment methods face significant limitations:

Pure Testing: Life tests are prohibitively expensive, time-consuming (lasting several months), and restricted to small sample sizes due to the destructive nature of the tests.
Pure Simulation: While efficient, simulation models often lack experimental calibration, leading to virtual data with insufficient credibility for engineering applications.
Parameter Estimation: Existing methods struggle to accurately optimize reliability model parameters when dealing with small-sample failure data.

Methodology
This study proposes a closed-loop framework integrating experimental verification, multi-physics simulation, and intelligent optimization to predict the life of insulating rods under multiple driving voltage conditions.

Multi-Physical Field Modeling and Verification:
- A two-dimensional axisymmetric finite element model of the fast mechanical switch was established using COMSOL software, incorporating electromagnetic, mechanical, and structural interactions.
- Experimental Validation: Actual stress tests were conducted on a prototype using strain gauges (NI-9923 system) and high-speed cameras at three voltage levels (780V, 820V, 867V).
- Results: The simulation model showed a relative error of less than 5% in maximum stress values and less than 10% in overall stress trends compared to experimental data, confirming the model's credibility.
Life Simulation and Damage Calculation:
- Using the validated model, the study simulated 14 distinct voltage conditions (ranging from 775V to 871V) to cover the operational spectrum.
- Fatigue Analysis: The S-N curve of the resin material and the Palmgren-Miner linear cumulative damage theory were applied. The simulation quantified the fatigue damage per opening cycle based on dynamic stress histories.
- Failure Criterion: The total fatigue life for each voltage was determined when the cumulative damage reached the critical value of 1. This generated a dataset of 14 failure life points.
Reliability Modeling and Optimization:
- Distribution Selection: The failure data were analyzed using the Weibull probability paper method. Comparisons between single-parameter, two-parameter, and three-parameter models demonstrated that the three-parameter Weibull distribution provided the best fit (lowest sum of squared residuals).
- Firefly Algorithm Optimization: To overcome the challenges of parameter estimation with small samples, the Firefly Algorithm (a heuristic intelligent optimization algorithm) was employed.
- Objective Function: A four-dimensional weighted objective function was constructed to minimize the residuals between the theoretical Weibull functions (CDF, PDF, Reliability Function, and Hazard Rate Function) and the empirical data. Weights were determined using the Analytic Hierarchy Process (AHP), prioritizing the Cumulative Distribution Function (CDF) and Reliability Function (RF).

Key Results

Optimized Parameters: The Firefly algorithm successfully converged (within ~240 iterations) to optimal parameters for the three-parameter Weibull distribution: Shape parameter ( $\beta$ ) = 1.92, Scale parameter ( $\eta$ ) = 7689.45, and Location parameter ( $\gamma$ ) = 3987.21.
Failure Mode Characterization: The shape parameter $\beta > 1$ confirms that the insulating rod exhibits a "wear-out" failure mode, consistent with progressive damage accumulation under cyclic loading.
Statistical Life Indicators:
- Mean Time To Failure (MTTF): Calculated as 10,807 operations.
- Median Life: 10,344 operations (50% reliability).
- Reliability-Based Thresholds:
  - 90% Reliability: 6,820 operations (suitable for critical main grid circuits).
  - 80% Reliability: 7,516 operations (recommended for preventive replacement in regular circuits).
  - 70% Reliability: 8,050 operations (applicable to general circuits).
Convergence: The optimization process demonstrated rapid convergence and stability, effectively avoiding local optima.

Significance and Claims
The paper claims to provide a universal solution for the reliability design and maintenance decision-making of fast mechanical switches by bridging the gap between pure simulation and pure testing. The proposed framework offers three primary contributions:

Credibility: By verifying the simulation model against actual stress tests, the study ensures the virtual data used for life prediction is engineering-reliable.
Efficiency: The simulation expansion method allows for the assessment of life under multiple voltage conditions without the need for extensive, destructive physical testing.
Accuracy: The integration of the Firefly algorithm with the three-parameter Weibull distribution overcomes the bottleneck of parameter optimization in small-sample scenarios, providing precise statistical indicators for maintenance strategies.

The authors assert that this approach establishes a theoretical and engineering foundation for the life assessment of key components in high-end power equipment, offering a reusable methodology for similar components.