2.1. Modeling of typical interference scenarios

As shown in Fig 2, the electromagnetic compatibility issues of automation equipment primarily stem from three typical interference scenarios: multi-conductor harness crosstalk, vehicle-mounted antenna coupling conduction, and bearing current conduction path [25]. The multi-conductor transmission line equation precisely describes the electromagnetic energy coupling mechanism between cables, and its frequency domain expression is as follows:

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Fig 2. Typical interference scenario.

https://doi.org/10.1371/journal.pone.0341052.g002

(1)

The impedance matrix and admittance matrix respectively characterize the resistance and inductance effects of conductors, as well as the conductivity and capacitance characteristics of dielectrics. The mutual capacitance of dense wiring harnesses inside industrial robot control cabinets can reach up to 50pF/m, and the mutual inductance is approximately 0.3 μH/m, leading to significantly enhanced crosstalk in frequency bands above 30MHz [26].

The offline interference from pantograph-catenary system threatens the on-board communication system through a radiation-conduction coupling path, and its electromagnetic coupling coefficient can be modeled as follows:

(2)

This formula quantifies the spatial integral correlation between the time-varying radiation field and the antenna pattern function . The transient electric field intensity generated by the pantograph of a high-speed train when it is offline exceeds 120dBμV/m at the 200MHz frequency point, which couples through the GSM-R antenna port to form in-band interference as high as -35dBm, leading to a sharp increase in communication bit error rate [27].

The bearing current conduction path forms a closed interference loop, and its conducted disturbance voltage satisfies a differential equation:

(3)

This model characterizes the conduction characteristics of pulse trains generated by the switching devices of the induction system through the mechanical structure. Actual measurements show that when a frequency converter drives a motor, the peak longitudinal voltage across the bearings exceeds 100V. Pulses with a pulse width of 2μs form mA-level discharge currents through parasitic capacitance, accelerating the electrical erosion damage to the bearings [28].

2.2. Construction of industrial-grade EMC dataset

To ensure sufficient data diversity, the industrial-grade EMC dataset was constructed across multiple representative application scenarios, including high-speed rail traction converters, industrial robot control cabinets, photovoltaic inverters, and motor drive systems. For each scenario, measurements were performed under varied operating conditions, such as different load levels, switching frequencies, modulation strategies, and cable configurations. This design enables the dataset to cover a broad range of conducted and radiated interference characteristics, spanning both low-frequency harmonics and high-frequency transient pulses up to the gigahertz range.

All measurements were conducted on standardized EMC test platforms compliant with IEC 62236-3. Calibrated high-bandwidth current probes and near-field probes were deployed at predefined ports, and waveform acquisition was performed using oscilloscopes with sampling rates up to 5 GS/s and a dynamic range exceeding 80 dB. Environmental parameters, including temperature and supply voltage, were kept within controlled ranges to ensure recording consistency and repeatability across experiments.

To guarantee ground truth integrity, interference sources were isolated using a controlled excitation and sequential activation protocol. During data acquisition, only one dominant noise source—such as inverter switching, bearing discharge, or cable crosstalk—was intentionally excited at a time, while other potential interference paths were physically disconnected or electrically suppressed. As a result, waveform labeling was based on known excitation conditions, circuit topology, and synchronized trigger signals, rather than post hoc statistical inference. This physics-guided acquisition and labeling strategy ensures a clear one-to-one correspondence between recorded waveforms and their originating noise sources, providing reliable ground truth for GAN training and subsequent pulse-based feature extraction.

To ensure physical consistency, the dataset construction was guided by established electromagnetic coupling theory and practical EMC measurement experience. Data acquisition was designed in consultation with EMC engineers to isolate dominant interference paths and to enforce known physical constraints, such as bounded pulse widths, monotonic spectral energy decay, and impedance-consistent coupling behavior. As a result, the recorded waveforms inherently reflect Maxwell-compatible propagation characteristics, providing a physically meaningful foundation for GAN training.

A high-frequency current probe and a 5GS/s sampling rate oscilloscope system are deployed at the DC bus port to capture the broadband noise generated during the switching on and off process of switching devices:

(4)

This model characterizes the damped oscillation waveform excited by the switching events of insulated-gate bipolar transistor (IGBT) modules, which is positively correlated with the rate of change of switching current and determined by parasitic parameter resonance. A total of 1500 sets of effective data have been collected, with a dynamic range of 80dB, covering the frequency band from 0 to 2.5GHz [29].

The generation of adversarial networks for synthesizing bearing fault current waveforms addresses the issue of sample scarcity. The generator network maps Gaussian noise to time-domain waveforms through five layers of transposed convolution, while the discriminator employs a multi-scale feature extraction structure:

(5)

The gradient penalty term is set to 0.3 to stabilize the training process. The generated samples are verified through feature selection, and the global discrepancy with the measured data is less than 0.25, with the pulse width error controlled within 0.1μs [30–32].

The raw signal from the vibration sensor needs to be converted into a sparse pulse sequence to accommodate the neuromorphic computing architecture. Based on the integration-and-firing mechanism, the timing of the trigger pulse for the vibration envelope signal is determined by threshold conditions:

(6)

During setting, the pulse emission rate after encoding the typical bearing vibration signal is approximately 12kHz, with an information compression rate of 98%, effectively retaining the 2-8kHz fault feature frequency band.

2.3. Permits and approvals

The study reported in this manuscript did not involve field sampling, access to protected or restricted sites, human participants, or animal subjects. All data were obtained through laboratory-based measurements, numerical simulations, and computational analyses conducted within institutional research facilities. Therefore, no permits or approvals from external authorities were required for this work.

3.1. Multi-scale discriminator structure optimization

Traditional GANs face the issue of a single receptive field in discriminators when modeling EMC data, making it difficult to simultaneously capture both the macroscopic envelope characteristics and microscopic transient details of interference waveforms. To address this, a multi-scale feature fusion architecture is proposed, deploying parallel convolutional paths at the input end:

(7)

The corresponding time resolution ranges from 0.5μs to 5μs [33]. The outputs from each path are compressed using depthwise separable convolution and then concatenated to form a mixed feature tensor:

(8)

This structure enables the discriminator to identify both the periodic characteristics of millisecond-level pulse trains and the nanosecond-level rising edge oscillation details when analyzing pantograph-catenary disturbance data [34].

Addressing the multi-task conflict in authenticity judgment and interference type classification within electromagnetic compatibility data, a task decoupling mechanism is designed. Feature splitting based on width calculation is implemented at the feature level:

(9)

The weight vector is adaptively generated through a gated unit, and the balance coefficient controls the task correlation strength. This structure enables the discriminator to achieve an accuracy of 92.3% in the classification branch during training, while reducing the Fréchet distance of generated data to 14.7 [35–37].

The gradient penalty strategy is introduced to stabilize the training process of the multi-scale discriminator. A Lipschitz constraint is imposed on the real data manifold:

(10)

Among them , interpolation samples and penalty factors . This constraint reduces the occurrence rate of mode collapse in the training of bearing current data to below 5% [38–40].

3.2. Design of pulse modulation generator

As shown in Fig 3, the traditional generators struggle to accurately reproduce the non-stationary transient characteristics of electromagnetic interference waveforms. Although the proposed generator is data-driven, its design is constrained by physically observed EMI behaviors. The resonant neuron model is parameterized to match measured damping factors and resonance frequency ranges, preventing the generation of non-physical oscillations. During validation, generated waveforms are screened using physics-derived indicators, including pulse width bounds, spectral roll-off characteristics, and coupling trends consistent with transmission-line and radiation models. This ensures that statistically realistic samples also remain physically plausible.

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Fig 3. Pulse modulation generator design.

https://doi.org/10.1371/journal.pone.0341052.g003

To address this, a pulse modulation architecture based on resonant neurons is proposed. The core of the generator employs a leaky integrate-and-fire-resonant neuron model:

(11)

The time constant controls the decay rate of membrane potential, the resonance factor enhances the response ability in specific frequency bands, and presynaptic pulses are input after being modulated by an exponential kernel . When generating bearing current data, this structure can accurately reproduce the damped oscillation characteristics in the frequency band of 100kHZ-2MHz, with a phase error less than 0.1 rad [41].

The discreteness of pulse firing leads to the interruption of generator gradient backpropagation, thus a piecewise linear surrogate gradient strategy is designed:

(12)

Set threshold voltage , softening parameter , and gradient scale . This approximation, while maintaining the sparsity of pulse events (firing rate <15%), accelerates the convergence speed of the generator in pantograph-catenary disturbance data training by 2.3 times, and reduces the Fréchet distance to 12.4 [42].

The generation quality is enhanced through multi-scale waveform similarity constraints. L2 norm matching is imposed in the discriminator feature space:

(13)

In this context, it represents the feature map of the K-th layer of the discriminator and the similarity weight . This constraint reduces the global difference in feature selection verification between the generated pulse sequence and the measured data to 0.22, with peak time jitter controlled within 5 ns [43–46]. The raw signal from the vibration sensor needs to be converted into a sparse pulse sequence to accommodate the neuromorphic computing architecture. Based on the integration-and-firing mechanism, the timing of the trigger pulse for the vibration envelope signal is determined by threshold conditions. The process is illustrated in the following pseudocode for pulse feature extraction:

Algorithm 1. # Pseudocode for Pulse Feature Extraction

# Define the biologically inspired neuron model

def leaky_integrate_and_fire_neuron(signal, threshold, decay_rate):

    membrane_potential = 0

    for t in range(len(signal)):

        membrane_potential = membrane_potential * decay_rate + signal[t]

        if membrane_potential > threshold:

            # Fire the neuron and reset the potential

            spike_time = t

            membrane_potential = 0

            return spike_time

    return None

# Extract pulses from vibration signals

def extract_pulses(vibration_signal, threshold=0.5, decay_rate=0.9):

    pulse_times = [ ]

    for signal_segment in vibration_signal:

        pulse_time = leaky_integrate_and_fire_neuron(signal_segment, threshold, decay_rate)

        if pulse_time is not None:

            pulse_times.append(pulse_time)

    return pulse_times

# Apply the extractor on vibration data

vibration_signal = [data_point1, data_point2,..., data_pointN]

pulse_times = extract_pulses(vibration_signal)

3.3. Engineering verification

The similarity between generated data and measured data is rigorously quantified through feature selection verification methods. The global difference index is as follows:

(14)

The amplitude difference degree and feature difference degree calculate the deviation of frequency domain energy distribution and time domain waveform envelope, respectively. On the high-speed rail traction converter noise dataset, the generated data has a mean of 0.18 and a standard deviation of 0.03, meeting the industrial verification threshold requirement of 0.25. The energy error at the key frequency point of 2.4 GHz is controlled within ±1.5 dB.

The improvement in bearing fault diagnosis performance is evaluated through the change in accuracy of the confusion matrix. Define the gain in diagnostic accuracy:

(15)

Where is the training result of the original data, and is the training result of the enhanced data. Experiments show that the generated data improves the accuracy of inner crack diagnosis by 9.2% and outer spalling by 11.7%. The confusion matrix shows that the false alarm rate has decreased from 7.3% to 3.1%, and the missed alarm rate has decreased from 6.9% to 2.8%.

3.4. Network architecture and training configuration

The generator receives a one-dimensional latent vector of shape [B, 128], where B denotes the batch size, and progressively maps it to a single-channel EMI waveform of length T with output shape [B, 1, T]. The mapping is implemented using four pulse sparse convolution blocks with kernel sizes {7, 5, 5, 3} and channel widths {64, 128, 128, 64}. Each block employs a leaky integrate-and-fire (LIF) activation, which introduces temporal sparsity and an inductive bias toward transient pulse events.

The discriminator adopts a multi-scale architecture composed of three parallel branches operating at different temporal resolutions. Each branch consists of three convolutional layers with ReLU activation and spectral normalization, followed by a linear layer producing a scalar authenticity score. This configuration enables joint modeling of local transient features and global waveform statistics. Training is performed using the Adam optimizer with parameters β₁ = 0.5 and β₂ = 0.999. The initial learning rates for the generator and discriminator are set to 2 × 10 ⁻ ⁴ and 1 × 10 ⁻ ⁴, respectively, and are linearly decayed after 60% of the total training epochs. All models are trained for 200 epochs with a batch size of 64. Gradient penalty is applied to the discriminator to improve training stability.

4.1. Heterogeneous spiking neural network architecture

As shown in Fig 4, the extraction of electromagnetic compatibility features requires a balance between broadband spectrum coverage and transient response capability. Traditional convolutional neural networks face power consumption and real-time performance bottlenecks due to their continuous activation mechanism. To address this, a leaky integrate-and-fire (LIF) and leaky resonant-frequency (LRF) dual-path heterogenous pulse architecture is constructed, with membrane potential dynamics described by a system of differential equations:

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Fig 4. Heterogeneous pulse neural network.

https://doi.org/10.1371/journal.pone.0341052.g004

(16)

The time constant controls the rate of integral decay, the resonance factor enhances selectivity in specific frequency bands, and the synaptic weights are optimized adaptively. The LIF pathway is sensitive to the strength of cable crosstalk signals (gain coefficient ), while the LRF pathway precisely captures the resonance frequency of pantograph-catenary disturbances (integral kernel ).

The heterogeneous spiking neural network is implemented as a shallow temporal convolutional architecture composed of an input encoding layer, two parallel spiking feature extraction paths, and a shared readout layer. The LIF pathway is designed to capture broadband energy variations, while the LRF pathway emphasizes resonance-sensitive transient components. Both pathways operate on the same input spike stream and are fused at the feature level through spike-time aggregation. The membrane dynamics of all spiking neurons are simulated in discrete time with a fixed time step of Δt = 10 ns, which is sufficient to resolve the fastest transient events observed in the measured EMI waveforms. Continuous input signals are converted into spike trains using an event-based threshold encoding scheme, where spikes are generated only when the accumulated signal energy exceeds an adaptive threshold, ensuring sparse activation and low switching activity. Network training is performed using backpropagation through time with surrogate gradients to address the non-differentiability of spike events. A piecewise linear surrogate function is adopted around the firing threshold to approximate the gradient of the spike activation. The loss function combines a task-driven classification or regression loss with a sparsity regularization term that penalizes excessive firing rates, thereby explicitly enforcing the energy–accuracy tradeoff. Temporal credit assignment is handled by unfolding the network over a finite temporal window and accumulating gradients across time steps, which enables stable convergence without requiring long unrolled sequences. This concrete formulation links neuron-level dynamics, network topology, and training strategy into a unified and reproducible framework, allowing the reported energy consumption and accuracy metrics to be directly traced back to identifiable architectural and algorithmic design choices.

Although sparse pulse encoding based on LIF neurons inevitably reduces signal density, its impact on diagnostically relevant information was explicitly evaluated. Information preservation was assessed from three complementary perspectives: spectral feature retention in diagnostic frequency bands, temporal alignment accuracy of transient pulses, and downstream diagnostic performance. Experimental results show that, after pulse encoding, more than 95% of spectral energy is preserved within the 2–8 kHz bearing fault band and the dominant EMI transient bands above 30 MHz. The temporal deviation between encoded pulse events and original transient peaks remains below 5 ns on average, which is negligible relative to the microsecond-scale EMI pulse width. Furthermore, fault diagnosis experiments conducted using encoded pulse sequences achieve comparable accuracy to those using raw waveforms, with no statistically significant performance degradation observed. These results indicate that the proposed sparse encoding strategy achieves substantial data compression while retaining the temporal and spectral information critical for EMC diagnosis.

The dynamic sparsity constraint is implemented through Hoyer regularization:

(17)

The spiking matrix in the pulse represents the time step, and the number of neurons represents the constraint factor. When the sparsity is below 0.8, the penalty is increased to force the network to activate less than 15% of the neurons. In the analysis of vibration data from industrial robots, this mechanism increases the information compression rate to 96.5%, while maintaining an energy retention rate of over 95% in the fault feature frequency band of 2-8kHz.

Near-field radiation feature extraction incorporating the impedance superposition principle:

(18)

The term represents the intensity of the th dipole moment, which is linearly mapped by the pulse firing rate. This model replaces traditional fast Fourier transform (FFT) analysis, reducing power consumption from 3.2W to 0.7W and processing delay from 8ms to 1.2ms in the 30–300MHz frequency band.

The following pseudo code shows the feature extraction process based on biological neuron dynamics and sparse convolution, focusing on how to use the LIF-LRF dual-path architecture to achieve real-time EMC feature extraction:

Algorithm 2. # Define the Leaky Integrate and Fire (LIF) neuron model

def LIF_neuron(input_signal, decay_rate=0.9, threshold=1.0):

    membrane_potential = 0

    spikes = [ ]

    for t in range(len(input_signal)):

        # Update membrane potential based on input signal

        membrane_potential = membrane_potential * decay_rate + input_signal[t]

        # Check if the neuron fires

        if membrane_potential >= threshold:

            spikes.append(t) # Fire at time t

            membrane_potential = 0 # Reset membrane potential after firing

    return spikes # Return the times when the neuron fires

# Define the Leaky Resonance Frequency (LRF) pathway

def LRF_neuron(input_signal, resonance_factor=1.5, decay_rate=0.8, threshold=1.0):

    membrane_potential = 0

    spikes = [ ]

    for t in range(len(input_signal)):

        # Update membrane potential considering resonance factor

        membrane_potential = membrane_potential * decay_rate + resonance_factor * input_signal[t]

        # Fire when threshold is reached

        if membrane_potential >= threshold:

            spikes.append(t)

            membrane_potential = 0 # Reset after firing

    return spikes

# Heterogeneous Spiking Neural Network Architecture (LIF + LRF)

def heterogeneous_SNN(input_signal):

    # Path 1: LIF pathway for general signal processing

    lif_spikes = LIF_neuron(input_signal)

    # Path 2: LRF pathway for frequency-specific resonance processing

    lrf_spikes = LRF_neuron(input_signal)

    # Combine the spikes from both paths

    combined_spikes = lif_spikes + lrf_spikes # Merge spike times from both paths

    return combined_spikes

# Example usage

input_signal = [0.1, 0.3, 0.5, 1.2, 0.7, 0.2, 1.5, 0.9, 1.0, 0.4] # Example input signal

spikes = heterogeneous_SNN(input_signal)

# Output the spike times (the times when the neuron fires)

print(“Spike times:”, spikes)

Based on the performance analysis of electromagnetic feature extraction using pulse sparse convolution, this study obtains core operational indicators under different interference types. As shown in Table 2, the offline disturbance of pantograph-catenary system achieves a pulse firing rate of 14.7kHz and a feature retention rate of 97.3% at a center frequency of 132.5MHz. When the information compression rate reaches 95.8%, the power consumption is only 0.72W, indicating that this method has efficient characterization capabilities for transient pulse groups. The traction return current harmonic maintains a gain tolerance of 15.3dB at the 87.4MHz frequency point, verifying the robustness of the algorithm to low-frequency conducted interference. It is worth noting that the high-frequency wireless crosstalk scenario at 2.45GHz still maintains a feature retention rate of 91.8%, demonstrating wideband adaptability, and its ± 2.3dB error tolerance meets industrial-grade accuracy requirements.

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Table 2. Comparison of pulse feature extraction performance under different interference types.

https://doi.org/10.1371/journal.pone.0341052.t002

By comparing the resource consumption with traditional FFT methods, this study quantifies the innovative advantages of the computing architecture. As shown in Table 3 and Fig 5a, in the high-speed rail traction converter scenario, the pulse convolution power consumption at a sampling rate of 5GS/s is reduced to 0.71W, a decrease of 78.2% compared to the traditional scheme, while the processing delay is compressed from 8.2ms to 1.3ms. As shown in Fig 5b, the industrial robot controller platform achieves a speedup ratio of 6.09 times, with memory occupation reduced to 31.5MB, while the accuracy loss is controlled within 1.1dB. Especially in the photovoltaic inverter application scenario, the ultra-low power consumption of 0.29W and real-time response of 0.5ms provide hardware feasibility for online monitoring of electromagnetic compatibility in new energy equipment.The breakthrough optimization of energy efficiency algorithms in UAV systems has reduced power consumption from 0.78W in traditional FFT to 0.21W, achieving a 73.1% decrease-the second-highest reduction in the table (second only to high-speed rail traction converters). The ultra-low power design directly reduces heat dissipation requirements, enabling weight reduction for drones. As shown in Fig 5c, the alculated based on a 0.2-second endurance gain per gram of payload, this innovation extends the flight duration of 500g-class drones by approximately 6–8 minutes.

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Table 3. Comparison of resource consumption with traditional FFT methods.

https://doi.org/10.1371/journal.pone.0341052.t003

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Fig 5. Resource-efficiency comparison of pulse-sparse convolution versus traditional FFT-based EMC analysis across industrial platforms.

(a) Tractioner performance. (b) Industrial robot performance. (c) Drone related performance.

https://doi.org/10.1371/journal.pone.0341052.g005

4.2. Real-time extraction of near-field radiation characteristics

Traditional near-field radiation analysis relies on full-wave simulation, and the computational complexity increases exponentially as the frequency rises. A real-time calculation model is established based on the principle of reactance superposition:

(19)

Among them , the wavenumber and dipole moment are linearly correlated with the cable pulse firing rate:

(20)

The coefficient is calibrated by a vector network analyzer and represents the length of the cable segments. This model reduces the computational complexity from 30 to 300 MHZ and decreases the memory usage by 98%.

The mapping from pulse firing rate to radiation field strength is achieved through a convolution kernel:

(21)

The kernel function is expressed in the frequency domain as:

(22)

The symbol represents the inverse Fourier transform. In the verification of the industrial robot harness platform, the processing delay of this model is only 1.8 μS, meeting the real-time control requirements. Based on the near-field radiation feature extraction based on the principle of reactance superposition, this study verifies the engineering applicability of different cable configurations. The coaxial cable RG174 requires only 1.8μs of computation time at a frequency of 87.4MHz, with a field strength error of 0.8dB and a memory footprint of 12.3KB, meeting the real-time requirements of in-vehicle systems. As shown in Table 4, when the twisted-pair CAT6 maintains a pulse rate of 18.7kHz in the 132.5MHz frequency band, it exhibits a processing delay of 2.3μs and a field strength error of 1.1dB, demonstrating adaptability in complex harness environments. Crucially, the data cable SFP+ maintains a pulse rate of 22.8kHz at a high frequency of 6GHz, with a computation time and temperature drift rate of 0.04%/°C, providing empirical evidence for the electromagnetic compatibility design of 5G equipment.

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Table 4. Extraction performance of near-field radiation characteristics for different cable configurations.

https://doi.org/10.1371/journal.pone.0341052.t004

Using the same near-field radiation calculation method based on the principle of reactance superposition, this study obtained resource consumption comparison data with traditional full-wave simulation methods. As shown in Table 5, within the wideband range of 0–3GHz, this method requires only 0.028GB of memory and 0.0021 seconds of calculation time, achieving a 99.7% reduction in memory usage compared to the finite-difference time-domain (FDTD) scheme and an 880,000-fold increase in calculation speed. The hardware cost is compressed from $15,000 to $350, and the calibration complexity is reduced from level 5 to level 2. Especially in the 5G frequency band (6GHz), it maintains an ultra-low power consumption of 0.078W, providing an economically feasible technical path for real-time monitoring in industrial sites.

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Table 5. Comparison of resource consumption with traditional methods.

https://doi.org/10.1371/journal.pone.0341052.t005

4.3. Hardware deployment plan

4.3.1. Architecture mapping and FPGA implementation.

To improve implementation reproducibility, the resource mapping strategy of the proposed pulse sparse convolution architecture is described as follows. Convolution kernels and synaptic weights are mapped onto digital signal processing (DSP) slices using a systolic array organization, while intermediate spike buffers and membrane potential states are stored in on-chip block random access memory (BRAM). Sparse pulse events are streamed through Advanced eXtensible Interface Stream (AXI-Stream) interfaces, enabling event-driven computation and reducing unnecessary memory access. This mapping strategy balances parallelism and resource reuse, allowing efficient utilization of DSP and BRAM resources on the target FPGA. The hardware design was implemented using a standard FPGA toolflow. High-level modules were described in hardware description language (HDL) and synthesized using Xilinx Vivado. Post-synthesis optimization, place-and-route, and timing closure were performed with default optimization settings, followed by bitstream generation and deployment on the Zynq UltraScale+ ZU9EG platform. Functional correctness was verified through cycle-accurate simulation, and hardware measurements were obtained using on-chip logic analyzers and external power monitoring instruments. All computations in the FPGA implementation adopt fixed-point arithmetic to reduce hardware complexity and power consumption. Synaptic weights and convolution outputs are represented in signed Q1.15 format, membrane potentials use Q4.12 format to accommodate accumulation dynamics, and spike events are encoded as binary signals with timestamp indices. Quantization parameters were selected based on empirical range analysis to avoid overflow while maintaining numerical stability, and no observable degradation in EMC feature extraction accuracy was observed compared to floating-point simulations.

The implementation of pulse sparse convolution architecture on FPGA platform requires resolving the contradiction between parallel computing and resource reuse. Designing a systolic array processing unit:

(23)

The weight matrix is preloaded into the BRAM, and pulse events are input in real-time through the AX1-Stream interface. At the clock frequency , the processing delay for a convolution kernel size of $3\times3$ is $\Delta t_{\text{latency}}=12 ns$, achieving a throughput of 1.2 TOPS/W. Resource consumption meets the following criteria:

(24)

The measured DSP utilization rate of the Xilinx Zynq UltraScale+ ZU9EG device is 68.3%, and the BRAM utilization rate is 76.5%.

4.3.4. Compute–memory balance analysis.

The reported throughput and energy efficiency metrics are obtained under a clearly defined benchmark workload and measurement setup. The systolic array is evaluated using a representative pulse sparse convolution workload corresponding to a 3 × 33\times33 × 3 kernel applied to spiking feature maps, which reflects the dominant operation in the proposed EMC feature extraction pipeline. Weights and activations are represented in 8-bit fixed-point precision during inference, while accumulation/state variables (e.g., membrane potentials) use a wider internal format to avoid overflow and preserve numerical stability. The array operates at a clock frequency of 200 MHz on the FPGA platform, which is below the timing-closure limit to avoid frequency-induced power inflation. Power is measured under steady-state operation using on-board power monitors integrated in the Xilinx Zynq UltraScale+ platform, and the reported values correspond to sustained execution over a continuous input stream rather than short burst activity.

To explicitly determine whether the evaluated operating point is compute-bound or memory-bound, we analyze the compute–memory balance in terms of (i) memory traffic assumptions and (ii) the implied operational intensity. Under the stated benchmark, the 3 × 33\times33 × 3 weight tensor is preloaded into on-chip BRAM and reused across the streamed feature-map tiles; activations are delivered through AXI-Stream and buffered on-chip to form local sliding windows. Therefore, the dominant data movement occurs within on-chip BRAM/interconnect, while off-chip transfers are amortized over multiple MAC operations. In this setting, each output computation involves 999 MACs per output element, whereas the corresponding off-chip traffic is limited to the initial streaming of the activation tiles (and no repeated off-chip fetch of weights during steady-state inference). This yields a high effective operational intensity, which is the necessary condition for compute-bound behavior.

This inference is consistent with the observed utilization: the systolic array sustains an average utilization exceeding 80% over a long continuous input stream, with no periodic stalls attributable to external memory service. Consequently, the performance and energy efficiency at the reported operating point are primarily limited by compute throughput (DSP utilization and array scheduling), rather than by off-chip memory bandwidth. We note that the operating regime is not universal: for smaller feature maps, reduced tile reuse, or constrained on-chip buffering (leading to more frequent off-chip accesses), the operational intensity would decrease and the system could transition toward a memory-bound regime. Such scenarios are outside the scope of the benchmark configuration reported here, and the reported TOPS/W should be interpreted as the post-layout efficiency under the specified compute-dominated workload and measurement boundary.

Dynamic routing optimization achieves real-time decision-making through hardware description language. Wiring cost function:

(25)

Among them, path length weight , crosstalk constraint weight , and crosstalk tolerance are obtained from a table based on cable type, while the overlap length is calculated in real-time through coordinate transformation. The actual routing decision-making time for the industrial robot’s wiring harness platform is less than 10ms.

The specific algorithmic steps of this study are presented in Table 6.

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Table 6. Implementation steps of pulse sparse convolution on FPGA.

https://doi.org/10.1371/journal.pone.0341052.t006

4.4. Unified benchmark configuration and fair comparison criteria

To ensure a fair and reproducible comparison with conventional full-wave solvers, a unified benchmark configuration is adopted for FDTD, MoM, FEM, and the proposed method. The benchmark geometry consists of a multi-conductor cable harness installed inside an industrial robot control cabinet with overall dimensions of 1.2 m × 0.8 m × 0.6 m. The harness includes twelve parallel conductors with typical spacing and length distributions representative of practical industrial wiring layouts.

For numerical discretization, FDTD simulations employ a uniform Yee grid with spatial resolution set to λ/20 at the highest analyzed frequency of 6 GHz, resulting in approximately 2.5 million cells. FEM simulations use second-order tetrahedral elements with adaptive refinement, yielding around 5.4 million elements, while MoM adopts surface discretization with an average element size of λ/15, corresponding to roughly 180,000 unknowns. Perfectly matched layers are applied in FDTD and FEM to truncate the computational domain, whereas radiation boundary conditions are used in MoM. Identical broadband current excitation is applied at the cable terminals in all cases.

To eliminate bias caused by different accuracy requirements, all methods are evaluated under the same convergence criteria, with field amplitude errors constrained within ±2 dB and phase errors within 3° at all observation points. Under these unified conditions, the reported differences in computational speed and memory consumption directly reflect intrinsic algorithmic efficiency rather than variations in problem size or numerical tolerance.

6.1. Test platform

Industrial-grade electromagnetic compatibility verification requires performance evaluation under real-world operating conditions. The industrial robot wire harness testing platform integrates a six-axis robotic arm, a control cabinet, and a cable management system. The key parameters are shown in Table 9.

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Table 9. Parameters of industrial robot wire harness platform.

https://doi.org/10.1371/journal.pone.0341052.t009

Key parameters of the industrial robot wire harness testing platform have been verified in this study for their adaptability to technical indicators under complex working conditions. The maximum length of 15 meters, coupled with a bending radius of 80 mm, meets the full-pose movement requirements of a six-axis robotic arm. The sampling rate of 1000kS/s and voltage accuracy of ±1.0% ensure the complete capture of broadband interference signals. The environmental simulation module achieves 3g acceleration vibration and a temperature rise of 50°C, supporting the data validity of the platform under extreme working conditions and establishing a standardized benchmark for electromagnetic compatibility industrial verification.

By referencing the time-frequency domain characteristic parameters of pantograph-catenary interference, this study quantifies the propagation patterns of transient interference. The 200MHz frequency point interference pulse has a pulse width of 1.2μs and a rise time of 22 ns, with a radiated field strength reaching 128dBμV/m. As shown in Table 10, when the pulse width is compressed to 0.8μs in the 300MHz frequency band, the field strength increases to 135dBμV/m, revealing a positive correlation between frequency and field strength. The impedance parameter remains stable at 150 Ω, indicating the impedance matching characteristics of the conduction path, providing key input parameters for the protection design of on-board systems.

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Table 10. Pantograph-catenary interference parameters.

https://doi.org/10.1371/journal.pone.0341052.t010

In addition to point-estimate metrics such as FID and GDM, the stability and uncertainty of the proposed framework can be inferred from existing experimental results. In Section 3.3 (Engineering verification), the global difference index (GDI) evaluated on the traction converter noise dataset achieves a mean value of 0.18 with a standard deviation of 0.03, indicating low dispersion across samples and stable generation behavior. Furthermore, Table 14 reports the uncertainty values for crosstalk prediction, where the proposed method yields uncertainty levels of 0.3 at 30 MHz and 0.5 at 100 MHz, which are consistently lower than those of classical numerical solvers. These results provide practical evidence that the generated and inferred waveforms exhibit limited variability and therefore a high level of confidence from an engineering perspective.

6.2. Performance comparison

This study quantitatively evaluates the data quality of generative adversarial networks and verifies the waveform reproduction capability of key frequency points, As shown in Table 11. In the 100MHz frequency point, the pantograph-catenary interference achieves a Fréchet distance of 14.3 and a pulse width error of 0.08, with a phase deviation of only 1.8°. In the 2.4GHz communication crosstalk scenario, it maintains a Fréchet Inception Distance (FID) value of 13.1 and a feature retention rate of 91.8%. Especially in bearing fault diagnosis, the generated data increases the recognition accuracy to 93.6%, which verifies the effectiveness of the data augmentation scheme for industrial equipment condition monitoring.

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Table 11. GAN-generated data quality indicators.

https://doi.org/10.1371/journal.pone.0341052.t011

To clarify the training and generalization strategy, the proposed framework is not independently trained from scratch for each application scenario. Instead, the core GAN and pulse encoding modules are trained once on a combined industrial EMC dataset that aggregates data from traction systems, industrial robots, CNC drives, photovoltaic inverters, and UAV electronic controllers. This unified training enables the model to learn cross-domain electromagnetic interference characteristics shared among different types of automated equipment. During deployment, only lightweight fine-tuning is applied to the pulse-based feature extraction and decision layers to accommodate system-specific operating conditions and hardware configurations, while the parameters of the core generative model remain fixed. This strategy allows consistent generation and feature representation across platforms while maintaining adaptability at low computational cost.

By introducing the performance advantages of spiking neural networks in real-time monitoring, this study has achieved empirical evidence of multi-scenario deployment. As shown in Table 12, the traction converter scenario achieves a processing delay of 1.8μs and an ultra-low power consumption of 0.71W at a frequency of 100MHz, with a feature retention rate of 97.3% and a false alarm rate of only 3.1%. The photovoltaic inverter platform achieves an information compression rate of 96.8% and a diagnostic accuracy rate of 94.3%. It is worth noting that the feature retention rate remains at 91.8% under high-frequency interference at 2.45GHz, verifying the applicable boundary of the algorithm in 5G industrial Internet scenarios.

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Table 12. Pulse feature extraction performance.

https://doi.org/10.1371/journal.pone.0341052.t012

Based on the quantitative evaluation of optimization effects in industrial-grade electromagnetic compatibility, this study has empirically demonstrated multi-dimensional performance improvements. The traction system achieves 23.6dB crosstalk suppression and a 7.5% failure rate, with wiring length reduced by 40%; As shown in Table 13, the decision-making delay of industrial robots is compressed to 18ms, and the energy efficiency ratio is increased to 1.28 TOPS/W. Crucially, the maintenance cycle has been extended from 3 months to 18 months, demonstrating the long-term reliability of the protection scheme and providing technical support for the continuous operation of the production line.

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Table 13. EMC optimization effect.

https://doi.org/10.1371/journal.pone.0341052.t013

6.3. Comparative experiment

Based on experimental data comparing crosstalk prediction accuracy, this study verifies the technological superiority of the reactance superposition principle under complex operating conditions. At the high-frequency band of 100MHz, the single-ended prediction error of this method is only 0.8dB, which is 55.6%, 46.7%, and 61.9% lower than that of FDTD (1.8dB), MoM (1.5dB), and FEM (2.1dB) methods, respectively. As shown in Table 14, The differential signal prediction error is 0.5dB with a phase deviation of 1.8°, significantly outperforming the traditional method’s mean deviation of 3.2°. Crucially, the pulse width control accuracy reaches 8 ns (compared to 15–22 ns for traditional methods), and the mutual capacitance parameter inversion error is ≤ 1.8% (compared to 3.8-5.8% for traditional schemes). In terms of hardware resource consumption, the calibration time is shortened to 0.5 hours (compared to 4.2-8.7 hours for traditional methods), the memory occupation is only 0.028GB (0.22% of the FEM scheme), and the power consumption is 0.049W (99.98% lower than FDTD). This performance has been successfully replicated in real-world measurements of high-speed rail traction converters, demonstrating the algorithm’s precise modeling capability for multi-conductor coupling effects.

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Table 14. Comparison of crosstalk prediction accuracy.

https://doi.org/10.1371/journal.pone.0341052.t014

The methods compared in Table 14 are instantiated using representative and practically adopted configurations to ensure a fair and technically meaningful evaluation. The FDTD, MoM, and FEM results correspond to conventional full-wave electromagnetic solvers configured under identical geometric models, boundary conditions, and accuracy criteria, as described in Section 4. The reported errors reflect numerical discretization limits under industrially accepted convergence thresholds rather than solver-specific tuning. The CNN-based EMC model adopts a standard one-dimensional convolutional architecture consisting of three convolutional layers with kernel sizes of 5, 7, and 9, followed by max-pooling and two fully connected layers. The channel widths are set to 32, 64, and 128, respectively. The model is trained on time-domain and time–frequency representations using cross-entropy loss with a learning rate of 1 × 10 − 31\times10^{−3}1 × 10 − 3 and batch size of 64, reflecting common practice in data-driven EMI classification. The autoencoder-based EMC model employs a symmetric encoder–decoder structure with four encoding layers and four decoding layers. Each layer consists of one-dimensional convolutions with progressively reduced channel dimensions from 128 to 32 in the encoder and mirrored expansion in the decoder. Mean squared error is used as the reconstruction loss, and anomaly or interference parameters are inferred from reconstruction residuals. This configuration represents a typical unsupervised baseline used for EMI feature extraction and parameter estimation.

To address the reviewer’s concern that CNN/autoencoder baselines alone may not sufficiently cover state-of-the-art sequence modeling, Table 14 further includes two practically adopted temporal-learning baselines: a dilated residual TCN and a Transformer-Encoder. The TCN baseline is implemented with stacked residual blocks using 1D dilated convolutions (kernel size 3) and an exponential dilation schedule to enlarge the receptive field while retaining local transient details; it is trained under the same data split, input representation, and training budget as CNN/autoencoder. The Transformer baseline uses linear token embeddings of the waveform (or time–frequency tokens) and a multi-head self-attention encoder, likewise trained under identical optimization settings to ensure fair comparison.

In addition to classical numerical solvers, Table 14 thus provides a comprehensive benchmark spanning full-wave solvers and learning-based predictors. The results show that data-driven baselines reduce errors compared with FEM/FDTD/MoM in several metrics, and that stronger temporal models further improve over CNN/autoencoder, yet still lag behind the proposed pulse-aware framework, especially on transient-sensitive indicators. For example, at 30 MHz, the pulse-width error decreases from 12 (FDTD)/ 15 (FEM)/ 8 (MoM) to 10 (CNN) and 9 (autoencoder), and is further reduced to 7.5 (TCN) and 6.8 (Transformer), while the proposed method reaches 5. Similarly, the phase error drops from 2.5 (FDTD) and 3.2 (FEM) to 2.4 (CNN) and 2.1 (autoencoder), and further to 1.8 (TCN) and 1.6 (Transformer), but remains higher than 1.2 achieved by the proposed method. At 100 MHz, the same trend persists: the pulse-width error is 18 (FDTD)/ 22 (FEM)/ 15 (MoM), improves to 16 (CNN) and 14 (autoencoder), further decreases to 12 (TCN) and 11 (Transformer), and is reduced to 8 by the proposed method. Rise-related error also decreases from 12.7 (FDTD) and 16.2 (FEM) to 11.2 (CNN) and 10.5 (autoencoder), and further to 9.0 (TCN) and 8.2 (Transformer), reaching 6.3 with the proposed method. These quantitative comparisons indicate that advanced sequence models can better capture longer-range dependencies than simple convolutional or reconstruction-based baselines, but they still exhibit noticeable deviations in preserving fine-grained transient structures and impedance-consistent behaviors. In contrast, the proposed method integrates physically constrained generative modeling with pulse sparse convolution and a heterogeneous spiking neural network, and its superior accuracy across amplitude, phase, pulse width, and mutual capacitance metrics arises from explicit incorporation of transient coupling physics and event-driven computation rather than from increased model capacity or relaxed numerical tolerances.

As shown in Fig 6a, the based on the comparison of engineering benefits in wiring optimization, this study quantifies the economic value of the maximum overlap length constraint equation. In the industrial robot wiring harness platform, this method optimizes the wiring length from 8.7m to 3.1m, achieving a more than 2.1-fold improvement compared to genetic algorithms and reinforcement learning. The crosstalk exceedance rate is reduced from 26.5% to 7.1%, and the downtime due to faults is reduced by 71.3%. The decision delay is reduced to 18ms, coupled with an energy efficiency ratio of 1.28 TOPS/W, meeting the real-time dynamic adjustment requirements of the production line. As shown in Fig 6b, the especially in terms of cost, although the hardware investment increases to 15.2k USD, the maintenance cycle is extended from 3 months to 18 months, resulting in a 68.9% reduction in annual maintenance costs and an investment recovery period of only 1.2 years. These data confirm the engineering guidance value of the constraint equation for quantitative decision-making in cable layout.

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Fig 6. Engineering-benefit summary of the crosstalk-constrained routing scheme versus empirical, GA and RL baselines. 

(a) Comparison of computing resources. (b) Maintenance costs.

https://doi.org/10.1371/journal.pone.0341052.g006

Based on a comparison of resource consumption across the entire process, this study reveals the disruptive advantages of this method in industrial deployment, As shown in Table 15. The calculation time is reduced by 880,000 times to 0.0021 seconds, and the memory footprint is reduced to 0.028GB. The hardware cost is compressed to $350, and the calibration complexity is simplified from levels 4–6 to level 2. At the production line operation and maintenance level, cable usage is reduced by 57.7% to 5.2m, and annual downtime due to failures (FEM 45 hours) is reduced by 82.2% to 8 hours. It is worth noting that the ultra-low power consumption of 0.049W (traditional average 317W) keeps the equipment temperature rise under control at 9.2°C (traditional 18.7°C), providing thermal management support for high-density electrical cabinet deployment. These indicators collectively establish a feasible paradigm for industrial real-time monitoring systems.

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Table 15. Comprehensive engineering indicators.

https://doi.org/10.1371/journal.pone.0341052.t015

6.4. Ablation experiment

Based on the ablation experiment data of the generative adversarial network module, this study first verifies the decisive role of the multi-scale discriminator in industrial electromagnetic interference modeling. As shown in Fig 7a, the removing this structure results in a sharp drop of 6.9 percentage points in the retention rate of 2.4GHz high-frequency interference features, and an increase in phase deviation to 2.1°, which directly restricts the physical authenticity of interference waveforms under complex working conditions. This analysis confirms the core value of the cross-scale feature fusion mechanism (Equations 7–9) in breaking through the limitations of the traditional Fourier transform frequency domain, providing a high-quality data foundation for subsequent pulse feature extraction.

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Fig 7. Ablation-study evidence of component contributions to crosstalk-prediction accuracy.

(a) Single end error. (b) Differential prediction error.

https://doi.org/10.1371/journal.pone.0341052.g007

Following the data generation stage, the ablation test of the spiking neural network component reveals the crucial significance of biological neuron dynamics for real-time analysis. As shown in Fig 7b, when the local receptive field pathway is removed, the processing delay of the traction converter scenario deteriorates by 77.8%, and the crosstalk prediction error increases by 140%. This is due to the inability of traditional continuous activation mechanisms to adapt to microsecond-level transient pulse characteristics. This result supports the necessity of the resonance factor (Equation 16) for enhancing selectivity against broadband interference. Its phase accuracy of 0.1 rad ensures the engineering applicability of electromagnetic coupling modeling, directly supporting the core goal of “millisecond-level real-time extraction” in the research topic. Furthermore, the ablation results of the electromagnetic compatibility optimization module highlight the engineering transformation efficiency of the theoretical constraint equation. When the overlap length constraint is not adopted, the wiring length increases by 119%, resulting in a 16.5% decrease in crosstalk suppression of industrial robots. This verifies the guiding role of the closed-form solution for multi-conductor transmission lines in quantitative decision-making. This analysis establishes a technical closed loop from algorithmic innovation to protection effectiveness, enabling the optimization achievement of a 145% reduction in failure rate to be directly traced back to the maximum overlap length constraint equation, strengthening the academic proposition of “quantifiable theoretical tools” in the research topic.

Ultimately, the ablation test of the hardware deployment plan completed the final proof of technical implementation. Removing the systolic array reduced the clock frequency by 25%, resulting in a 66.7% loss of accuracy in the 2.45GHz scenario, which exposed the inefficiency of traditional parallel computing architectures in handling sparse events. The synergistic effect of the AXI-Stream interface and dynamic routing optimization extended the calibration cycle by 100%, demonstrating the feasibility of the “perception-analysis-decision” integrated design in industrial real-time monitoring and providing hardware-level verification for the development of highly reliable automation equipment.

To provide a quantitative attribution of each GAN component, we further conducted an ablation study under identical training settings and evaluated generation quality using Fréchet Distance (FID) and the Global Difference Metric (GDM). Specifically, we compared (i) a baseline GAN with a single-scale discriminator and no gradient penalty, (ii) a GAN with the proposed multi-scale discriminator enabled while keeping other settings unchanged, and (iii) the full model with both the multi-scale discriminator and gradient penalty. The results show that introducing the multi-scale discriminator leads to a clear reduction in both Fréchet Distance (FID) and Global Difference Metric (GDM), indicating improved preservation of transient pulse structures and cross-scale waveform features. This improvement is particularly evident in high-frequency interference scenarios, where single-scale discriminators fail to simultaneously capture envelope-level and fine-grained transient characteristics. When the gradient penalty is further applied, the training process becomes more stable, and both FID and GDM values are consistently reduced, reflecting a closer match between generated and measured waveform distributions. These results confirm that the multi-scale discriminator and gradient penalty make complementary and measurable contributions to generation quality rather than acting as redundant stabilizing components. Table 16 summarizes the quantitative comparison of FID and GDM under different ablation settings.

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Table 16. Ablation study of multi-scale discriminator and gradient penalty.

https://doi.org/10.1371/journal.pone.0341052.t016

6.5. Technical discussion

The multi-scale discriminator architecture of the generative adversarial network has successfully addressed the bottleneck of sample scarcity in industrial electromagnetic compatibility analysis.As shown in Fig 8, in the bow net harassment scenarioIn the pantograph-catenary disturbance scenario, a Fréchet distance of 14.3 and a pulse width error of 0.08 microseconds verify the waveform reproduction accuracy, achieving a speedup of 880,000 times compared to traditional full-wave simulation. This breakthrough stems from the physical constraints imposed by the resonant neuron model on non-stationary transient features, and its phase accuracy of 0.1 radians has improved the accuracy of bearing fault diagnosis to 93.6%. It is worth noting that removing the gradient penalty mechanism resulted in a 6.9 percentage point deterioration in the retention rate of 2.4 gigahertz frequency features, supporting the role of physical mechanism embedding in ensuring data authenticity. This modeling capability provides an interference database covering the 0−6 gigahertz frequency band for automation equipment, filling the gap in high-frequency operating conditions not covered by the international standard IEC 61000−4.

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Fig 8. Waveform comparison: (a) Measured waveform; (b) Measured waveform; Traditional method waveform; (c) The optimized waveform.

https://doi.org/10.1371/journal.pone.0341052.g008

Spiking neural networks achieve millisecond-level response in electromagnetic compatibility analysis through biological mechanism simulation. As shown in Table 17, the heterogeneous spiking architecture achieves a processing delay of 1.8 microseconds and a feature retention rate of 97.3% in the traction converter scenario, with a power consumption of only 0.71 watts, a reduction of 78.2% compared to traditional Fast Fourier Transform. This performance stems from the frequency band selection characteristics of the local receptive field pathway, and its dynamic sparse constraint compresses the neuron activation rate to less than 15%. Ablation experiments show that removing this pathway leads to a 140% increase in crosstalk prediction error, confirming the key support of the spiking modulation mechanism for gradient backpropagation. This event-driven characteristic reduces the decision-making delay of the industrial robot platform to 18 milliseconds, reconstructing the real-time protection technology path for automation equipment under 5 gigahertz high-frequency interference.

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Table 17. Comparison of key technical indicators.

https://doi.org/10.1371/journal.pone.0341052.t017

The maximum overlap length constraint equation achieves closed-loop optimization of cable layout. Differential signals maintain a wiring margin of 0.8 meters in the 200 MHz frequency band, enabling industrial robot crosstalk suppression to reach 21.8 decibels, an improvement of 17% over empirical rules. This achievement relies on the synergy between GANs and Spiking Neural Networks (SNNs): without joint optimization, wiring length increases by 119%, and the failure rate climbs by 145 percentage points. Hardware deployment compresses routing decision time to 10 milliseconds through a systolic array, and the advanced scalable interface ensures a 1.5 decibel accuracy loss in a 2.45 GHz scenario through streaming transmission. Ultimately, a technical closed loop of data generation, feature extraction, and dynamic wiring is formed, extending the maintenance cycle from one month to 12 months, verifying the engineering value of quantifiable theoretical tools for electromagnetic compatibility design in production lines.