Optimization of Lightning Strike Intervals
When performing lightning induced transient testing, exposing the UUT (unit under test) to multiple transients over a short period of time can cause overheating, excessive stress on components, and potential failures. On the other hand, waiting too long between strikes unnecessarily extends the testing time, increasing costs and reducing efficiency. By using an optimization strategy, and considering constraint factors, the ideal wait time between strikes can be preemptively determined. This article aims to investigate potential constraint considerations, and offer a theoretical, optimized ideal objective function through mixed integer non-linear programming (MINLP).
Understanding Lightning Induced Transient Testing
Lightning induced transient testing is a critical part of electromagnetic compatibility (EMC) testing, ensuring that electronic devices can withstand electrical surges. DO-160G Section 22 (1), a commonly used standard, specifies how the equipment should be tested against transient lightning-induced effects. The purpose of these tests is to simulate the induced effects of lightning by applying high voltage/high current transients. Of these tests, varying waveforms will be applied in a positive and negative polarity, directly to the pins or coupled onto the cables of the UUT, refer to table 22-2 and 22-3
Optimization of Lightning Strike Intervals Using MINLP
Mixed-Integer Non-Linear Programming (MINLP) is a prominent choice for optimizing this problem as it allows for a combination of continuous variables such as wait time between strikes, discrete time intervals and binary decision variables (2). The objective function would minimize the total test time
where is the binary decision variable, is the wait time corresponding to a predetermined interval, and N is the number of lightning strikes.
The constraints ensure the device has enough recovery time to stay within predefined safe limits. MINLP could be solved using optimization solvers like MATLAB, CPLEX, or other alternatives such as GLPK (4). Mixed Integer Linear Programming (MILP) could be used in place of MINLP as an approximation when thermal recovery or component recovery times are unknown, however, this would lead to less accurate results of the optimization strategy and assume Newtons law of cooling to be linear.
Key Constraints in Lightning Strike Interval Optimization
Thermal Recovery constraint – Thermal dissipation of internal components is the most important constraint to consider, which is focused on in this paper, however; other constraints such as energy storage/discharge, and dielectric recovery, can be considered depending on the specifications of the UUT. After each strike, the UUT must dissipate the heat generated, with the cooling time being influenced by the device’s thermal resistance, capacity, and how much energy it absorbs from each strike. If the UUT does not have enough time to dissipate the heat, its temperature can accumulate over multiple strikes, leading to overheating and failure. The non-linearity of heat dissipation can be observed when applying Newton’s law of cooling with arbitrary dissipation coefficients, see figure 1.
Figure 1 depicts Newton’s law of cooling with arbitrary k values, assuming ambient
temperature at 22C and an initial temperature of 100C
Consider the base form of Newton’s law of cooling,
we can then derive an equation for the time it takes for the UUT to reach safe operating conditions,
Time Intervals Constrain – While we aim to reduce test time, there must be an upper and lower bound on the total testing duration. The lower bound, , prevents unsafe rapid testing, while the upper bound, , ensures the process remains efficient. DO-160G (1) defines as 60 seconds for pin injection and single stroke testing, with being limited by the lightning generator used for testing. This constraint balances safety with time optimization by preventing the algorithm from choosing short or unnecessarily long wait times.
By introducing , this assumes discrete time interval steps from 10s to 60s with being specific wait times, if the time interval is selected, otherwise.
Our generalized objective function and constraints then collectively become, 
This setup allows for the testing of discrete values in the range of {10, 20,…60}, however, by removing the binary constraint and introducing a factor of 10, the equations simplify to, 
Which assumes the wait time between each strike will be identical across the 10 total strikes.
Figure 2 shows the total test duration versus time between strikes, based off hypothetical values of the UUT.
Using MATLAB (5), I was able to represent a hypothetical optimal wait time for a device using an arbitrary value, with an initial temperature of 80°C after a single strike, see figure 2. MATLAB’s optimization was implemented using fmincon, which minimizes while also adhering to the constraints, providing an optimal solution for the wait time across 10 strikes.
Conclusion: The Importance of Lightning Strike Interval Optimization
Optimizing the time between lightning strikes in testing is essential to maintaining the safety, efficiency, and cost-effectiveness of the process. If wait times are too short, devices risk heat related degradation and failure. If they are too long, testing becomes inefficient and costly. By applying optimization techniques such as Mixed-Integer Linear Programming, test engineers can determine the ideal balance between component safety and overall test duration. A properly optimized strategy not only ensures compliance with standards like DO-160G but also improves reliability, reduces costs, and enhances the EMC.
References:
(1) (2010). Environmental conditions and test procedures for airborne equipment (DO-160G). RTCA, Inc.
(2) Tang, B., Khalil, E. B., & Drgoňa, J. (2024). Learning to optimize for mixed-integer non-linear programming. arXiv. https://arxiv.org/abs/2410.11061
(3) (2023, August 28). Newton’s law of cooling – derivation, formulas, solved examples. BYJUS. https://byjus.com/jee/newtons-law-of-cooling/
(4) Chong, E. K. P., & Zak, S. H. (2013). An introduction to optimization Edwin K.P. chong. John Wiley & Sons.
(5) The MathWorks, Inc. (2024). MATLAB (Version R2024a) [Software]. The MathWorks, Inc. https://www.mathworks.com
Article Written by
Reid Shillingburg
CKC EMC Test Engineer
