## Periodic Reporting for period 1 - ANALYST (EM compatibility ANALYsis Statistical Techniques in aeronautics)

Reporting period: 2018-11-01 to 2019-10-31

The large density of cables transporting various signals due to the introduction of composite materials and the transition to a More Electrical Aircraft is nowadays increasing the complexity of the design from an EMC point of view. So that the evolution of regulations makes safety analysis mandatory for the EWIS, leading to the necessity to estimate the reliability of the wiring system together with the functions which are committed to it.

Onboard equipment is supposed to sustain Electromagnetic (EM) susceptibility current and voltage levels, either imposed by standards or measured at the connector pinout of equipment pieces. For a given constitution of an EWIS prototype, EM cross-coupling functions strongly depend on the distance between cables to such an extent that the safest way to avoid cross-coupling is to increase the distance between cables. In EWIS designs, electric cables are grouped together in “cable bundles” for which the EM compatibility of all cables is guaranteed. However, if two cables are in two different cable-bundles, the question is to determine the minimum distance acceptable between bundles in order to avoid overcoming the EM susceptibility thresholds of equipment.

At the design stage of EWIS, the constitution of cables-bundles is generally known but the distance to be applied between bundles remains unknown. Of course, the smallest distance is pursued since it minimizes the EWIS footprint in the aircraft. However it increases the possibility of unacceptable EM cross-coupling. The EWIS installer must thereby have some tools to evaluate the distances making acceptable cross-coupling and justify them. Particularly, if this distance is lower that the distances provided by the airframer rules, such a tool must help justifying derogation.

In the Analyst project addresses the EM Compatibility problem of EM cross-coupling existing between the electric cables of an EWIS (Interconnected Wiring System), the phenomenon can be summarized as follows: if an electric wire (source wire) carries a source that drives an electrical signal (a current or a voltage), this signal will induce a signal on close-by wires. This induced signal is likely to produce an EM interference signal (current or voltage) higher than EM susceptibility levels of equipment.

This problem is a complex problem and the approach carried out in ANALYST is a first step of a long research activity. It consists in simplifying the problem by studying two bundles of the same length, running in parallel or with a crossing angle. This problem must thereby cope with all ranges of variations of relevant cable-bundle geometrical parameters. The random variables of this problem are the heights of the two bundles, the length of the bundles, the angle in case the bundles are not parallel. Therefore, the ANALYST tool must manage uncertainty. The mathematical problem to solve is thereby formulated as the determination of the optimum distance between two parallel bundles in order not to trigger a susceptibility level with a given level of confidence (being aware of the probability of occurrence).

In addition, even if the problem is restricted to two bundles, those bundles remain complex especially in terms of number of conductors which implies large calculation times and possibly large calculation resources. Hopefully, the project may rely on validated calculation modules existing in the consortium and capable to handle this calculation weight. Nevertheless, speed-up techniques must be investigated to make possible the statistical analysis in reasonable times.

Finally, even simplified, this approach is very close to EWIS engineer expectations and it is worth being validated when tested to real EWIS installation. The project will thereby define a real EWIS, apply distance segregation rules between bundles and observe the compatibility with the EM susceptibility levels.

Onboard equipment is supposed to sustain Electromagnetic (EM) susceptibility current and voltage levels, either imposed by standards or measured at the connector pinout of equipment pieces. For a given constitution of an EWIS prototype, EM cross-coupling functions strongly depend on the distance between cables to such an extent that the safest way to avoid cross-coupling is to increase the distance between cables. In EWIS designs, electric cables are grouped together in “cable bundles” for which the EM compatibility of all cables is guaranteed. However, if two cables are in two different cable-bundles, the question is to determine the minimum distance acceptable between bundles in order to avoid overcoming the EM susceptibility thresholds of equipment.

At the design stage of EWIS, the constitution of cables-bundles is generally known but the distance to be applied between bundles remains unknown. Of course, the smallest distance is pursued since it minimizes the EWIS footprint in the aircraft. However it increases the possibility of unacceptable EM cross-coupling. The EWIS installer must thereby have some tools to evaluate the distances making acceptable cross-coupling and justify them. Particularly, if this distance is lower that the distances provided by the airframer rules, such a tool must help justifying derogation.

In the Analyst project addresses the EM Compatibility problem of EM cross-coupling existing between the electric cables of an EWIS (Interconnected Wiring System), the phenomenon can be summarized as follows: if an electric wire (source wire) carries a source that drives an electrical signal (a current or a voltage), this signal will induce a signal on close-by wires. This induced signal is likely to produce an EM interference signal (current or voltage) higher than EM susceptibility levels of equipment.

This problem is a complex problem and the approach carried out in ANALYST is a first step of a long research activity. It consists in simplifying the problem by studying two bundles of the same length, running in parallel or with a crossing angle. This problem must thereby cope with all ranges of variations of relevant cable-bundle geometrical parameters. The random variables of this problem are the heights of the two bundles, the length of the bundles, the angle in case the bundles are not parallel. Therefore, the ANALYST tool must manage uncertainty. The mathematical problem to solve is thereby formulated as the determination of the optimum distance between two parallel bundles in order not to trigger a susceptibility level with a given level of confidence (being aware of the probability of occurrence).

In addition, even if the problem is restricted to two bundles, those bundles remain complex especially in terms of number of conductors which implies large calculation times and possibly large calculation resources. Hopefully, the project may rely on validated calculation modules existing in the consortium and capable to handle this calculation weight. Nevertheless, speed-up techniques must be investigated to make possible the statistical analysis in reasonable times.

Finally, even simplified, this approach is very close to EWIS engineer expectations and it is worth being validated when tested to real EWIS installation. The project will thereby define a real EWIS, apply distance segregation rules between bundles and observe the compatibility with the EM susceptibility levels.

At the end of period one, the following project progress can be summarized as follows:

- The optimization has been formulated. For this a normalized G scalar function has been defined in order to cope with either frequency dependent currents or voltages without any consideration of units. This function includes the comparison with the susceptibility levels on each wire of the cable-bundle.

- Investigations of candidate optimization techniques have been made. Because the problem must be formulated as an optimization problem, the straightforward Monte Carlo (MC) still remains the most appropriate technique. However, in order to generate the number of samples required for a good MC assessment, the approach is to generate the samples by an interpolation on preliminarily calculated deterministic samples on a grid. Two techniques have been identified:

o One technique consists in generating the grid samples on a Latin Hypercube Sampling grid and applying Kriging to interpolate the missing sample. When Kriging is sought to be not precise enough, additional deterministic samples are calculated and enrich the existing grid.

o The other technique comes from the Smolyak method. The deterministic samples are calculated on a grid with predefined rules dictated by the method and allowing interpolation of the missing samples. If the grid is pre-calculated with enough samples, the Smolyak interpolation is precise enough not to have to generate additional samples.

- The structure of the tool is well defined in terms of calculation loops (including both optimisation and brute MC approaches) and calculation modules. Those calculation modules are instanced in series in order to calculate the G function. Those calculation modules have been evaluated comparing several of them in terms of computer resources in order to choose the most appropriate one.

- Four Test-cases of increasing complexity have been defined in order to validate the ANALYST tool. Complexity ranges from bundles with tens of cables to bundles with hundreds of cables.

- A specific test-case extracted from the former 4 test-cases has been defined and verified in terms of data consistency. It has been used to program a dedicated calculation suite (calculation “black bock”) to calculate the G function for this specific example. It is used to assess the performance of both Kriging and Smolyak approaches with advantages and drawbacks.

- Conclusions on the perimeter of validity of the approach have been made in order to evaluate them in the fine tuning phase of the tool development that will start at the beginning of the second period (precision of the frequency sampling, limitation on the variation ranges of the possible heights and distances…)

- The optimization has been formulated. For this a normalized G scalar function has been defined in order to cope with either frequency dependent currents or voltages without any consideration of units. This function includes the comparison with the susceptibility levels on each wire of the cable-bundle.

- Investigations of candidate optimization techniques have been made. Because the problem must be formulated as an optimization problem, the straightforward Monte Carlo (MC) still remains the most appropriate technique. However, in order to generate the number of samples required for a good MC assessment, the approach is to generate the samples by an interpolation on preliminarily calculated deterministic samples on a grid. Two techniques have been identified:

o One technique consists in generating the grid samples on a Latin Hypercube Sampling grid and applying Kriging to interpolate the missing sample. When Kriging is sought to be not precise enough, additional deterministic samples are calculated and enrich the existing grid.

o The other technique comes from the Smolyak method. The deterministic samples are calculated on a grid with predefined rules dictated by the method and allowing interpolation of the missing samples. If the grid is pre-calculated with enough samples, the Smolyak interpolation is precise enough not to have to generate additional samples.

- The structure of the tool is well defined in terms of calculation loops (including both optimisation and brute MC approaches) and calculation modules. Those calculation modules are instanced in series in order to calculate the G function. Those calculation modules have been evaluated comparing several of them in terms of computer resources in order to choose the most appropriate one.

- Four Test-cases of increasing complexity have been defined in order to validate the ANALYST tool. Complexity ranges from bundles with tens of cables to bundles with hundreds of cables.

- A specific test-case extracted from the former 4 test-cases has been defined and verified in terms of data consistency. It has been used to program a dedicated calculation suite (calculation “black bock”) to calculate the G function for this specific example. It is used to assess the performance of both Kriging and Smolyak approaches with advantages and drawbacks.

- Conclusions on the perimeter of validity of the approach have been made in order to evaluate them in the fine tuning phase of the tool development that will start at the beginning of the second period (precision of the frequency sampling, limitation on the variation ranges of the possible heights and distances…)

MTLN modelling for EMC applications is now well spread in the community. However applications including management of uncertainties are not frequent and, to our knowledge, not very mature. The formulation of the ANALYST problem allows combining an optimisation problem with uncertainty, which is the essence of EMC. From this point of view, the tools and approaches developed in ANALYST will overcome this strict application and make possible other types of applications.

The impact of the project is also in terms of industrial process since this application addresses installation of cable harnesses in aircraft for which safety must be maintained while optimizing room inside the aircraft. From a societal point of view, the ANALYST application seeks for more confidence in safety assessment.

The impact of the project is also in terms of industrial process since this application addresses installation of cable harnesses in aircraft for which safety must be maintained while optimizing room inside the aircraft. From a societal point of view, the ANALYST application seeks for more confidence in safety assessment.