The stakes of this problem are higher than they might appear. Conventional maintenance practice calls for regular offline cleaning of cooling systems according to fixed schedules, regardless of whether dust has actually accumulated to a harmful degree. This conservative approach drives up costs and wastes labor, yet it still cannot guarantee that a badly clogged heatsink between cleanings will be caught in time. What engineers really want is continuous, condition-based monitoring: a way to know, in real time, exactly how blocked a heatsink has become. The obstacle is that measuring the blockage directly is surprisingly difficult. The physical quantity that betrays a dusty heatsink is its thermal resistance, the efficiency with which heat flows from the power module into the moving air. As dust builds up, thermal resistance rises, and device temperatures climb. Extracting that resistance from temperature data, however, is a notoriously ill-posed task under real operating conditions.

Earlier physics-based monitoring techniques attacked the problem by building mathematical models of the heatsink and fitting them to measured temperatures, often using iterative schemes such as Gauss-Newton estimation or frequency-domain analysis of the thermal network. These methods share a painful common requirement: they need to know, very precisely, how much power is being dissipated in the converter at every instant. Computing that power loss demands high-speed sampling of voltages and currents, plus access to internal control signals such as the conduction duty cycles of the switches. Retrofitting existing converters with the sensors and data links necessary to provide this information is expensive and intrusive, which is precisely why such techniques have struggled to leave the laboratory. Meanwhile, the high thermal capacitance of a massive heatsink means its temperature changes sluggishly, so short windows of data contain little dynamic information to work with, while rapidly fluctuating train power profiles smear the temperature signal with confounding variation.

The new method, which the authors call VMD-NN, pairs variational mode decomposition with a neural network to sidestep both obstacles at once. Variational mode decomposition, or VMD, is an adaptive signal-processing technique that breaks a complicated signal into a small set of intrinsic mode functions, each confined to a narrow band of frequencies. Unlike older recursive decompositions such as empirical mode decomposition, VMD formulates the task as a constrained variational optimization problem, solved through the alternating direction method of multipliers with a quadratic penalty factor and Lagrange multipliers. Every mode is simultaneously optimized with an explicit bandwidth constraint, which suppresses mode mixing and prevents the cumulative errors that plague recursive sifting. Applied to the slowly wandering temperature trace of a heatsink, VMD can tease apart the component tied to the underlying thermal resistance from the ripples injected by ever-changing power dissipation, effectively letting the algorithm treat the erratic power profile as if it were replaced by a steady average.

Choosing the right number of modes is critical to making VMD work. Too few, and meaningful information is filtered away; too many, and closely spaced center frequencies cause mode mixing or noise amplification. The team devised a simple correlation-coefficient procedure: starting with two modes, they decompose the signal and check two statistical tests, the correlation of each mode with the original temperature record and the correlations among the modes themselves. If any mode correlates weakly with the source signal, below a threshold of 0.1, or if two modes correlate too strongly with each other, the count is reduced; otherwise it is incremented and the process repeats. In their experiments on a three-phase inverter with a forced-air cooling system, this procedure converged on three modes, and Hilbert spectral analysis confirmed the choice. The third mode alone carried 98.43 percent of the signal energy in the band below 0.0005 hertz, exhibited the lowest sample entropy of the three, and showed no frequency drift over time, exactly the signature expected of the fixed thermal inertia of a cooling system whose blockage degree is not changing.

With the temperature feature in hand, the remaining challenge was to estimate average power dissipation without peeking inside the converter’s control system. Here the authors exploited an elegant chain of inference rooted in the physics of space-vector pulse-width modulation, the standard switching scheme for traction inverters. The conduction duty cycle depends on the modulation ratio and the voltage vector angle, both of which can be reconstructed from the AC-side frequency of the inverter. That frequency, in turn, leaves a fingerprint on the DC-link current: during certain switching states the DC current reads zero, and in all other states it equals the maximum absolute value of the three phase currents. By analyzing this pattern in the DC current, the method infers the phase currents and hence the AC frequency, from which the duty cycle follows. Combined with the DC-link voltage, this is enough to compute turn-on and turn-off energy losses, conduction voltage drops, and ultimately the average power dissipation, using nothing more than the current and voltage sensors every converter already possesses.

These four quantities, the VMD-extracted temperature characteristic component, the ambient temperature, the DC voltage, and the DC current, feed a fully connected neural network with two hidden layers of 64 units each and tanh activations, trained with the Adam optimizer at a learning rate of 0.0001 and early stopping to prevent overfitting. The network’s single output is the blockage degree itself. Training data came from a purpose-built experimental platform comprising a three-phase inverter and its forced-air cooling system, tested at blockage degrees spanning the full range from 0 to 100 percent, with power dissipation varied every 100 milliseconds by modulating the modulation ratio. The extracted temperature component rose monotonically with blockage degree across all cases, a relationship the authors show is exactly what the heatsink’s transient thermal model predicts, since a higher thermal resistance drives a higher steady-state temperature for any given power level. This monotonicity confirms that the dominant mode genuinely encodes the thermal resistance-capacitance dynamics rather than artifacts of the decomposition.

The performance figures are striking. On the training set the network achieved a mean square error below 0.0001, an average blockage error of 1 percent, and a maximum error of 8 percent. On an independent test set in which the blockage degree stepped from 20 to 40, 60, and finally 80 percent every 30 minutes, the steady-state error never exceeded 8 percent, and the method responded to each change in under 180 seconds. Ten repeated experiments yielded tight 95 percent confidence intervals at every blockage level, for instance a mean estimate of 0.1903 for a true value of 0.2, underscoring the reproducibility of the approach. Online inference takes roughly 25 milliseconds per sample on the test hardware, comfortably faster than the one-second sampling interval, and the trained model occupies less than 5 megabytes of memory, small enough for low-cost edge devices and embedded controllers. Head-to-head comparisons against a physics-based Gauss-Newton scheme, a plain artificial neural network, a long short-term memory network, and a hybrid convolutional-LSTM architecture showed the VMD-NN method achieving the lowest mean square error at 3.53 percent and the smallest maximum absolute error at 7.61 percent, with a response latency of 180 seconds that was competitive with the fastest rival while demanding only low sampling rates.

The broader implications reach well beyond one laboratory rig. Because the method requires no new sensors, no high-speed data acquisition, and no access to proprietary control signals, it can be deployed as a software upgrade on converters already in service, turning fixed-interval cleaning into condition-based maintenance that responds to the actual state of the dust filter. The authors note that their validation focused on dust blocking the inlet filter, the most common failure mode, and that other faults such as fan degradation or fin obstruction were not directly tested, although the underlying thermal-resistance logic suggests the framework could generalize with further study. If the approach migrates from the test bench to real trains, the humble heatsink may finally gain the digital nervous system it has lacked, catching a slow-motion dust disaster long before it becomes a delayed departure or, worse, an overheated power module stranded in service.

Subject of Research: An online variational mode decomposition and neural network method for identifying the blockage degree of dust-clogged heatsinks in rail transit traction converter air-cooling systems.

Article Title: A VMD-NN based blockage degree identification method for air-cooling systems

Article References: Chen, J., Jia, H., Xie, J., & Kang, Y. (2026). A VMD-NN based blockage degree identification method for air-cooling systems. Results in Engineering, 32, Article 112995. https://doi.org/10.1016/j.rineng.2026.112995

Image Credits: AI Generated

DOI: 10.1016/j.rineng.2026.112995

Keywords: VMD, neural network, heatsink blockage, traction converter, air-cooling systems, thermal resistance, rail transit, condition monitoring, variational mode decomposition, power electronics, predictive maintenance, dust accumulation

The study, authored by Hongye Cao of Xianyang Normal University and the China Jikan Research Institute of Engineering Investigation and Design, presents a model named VMD-DSTCN-GA, which stands for a variational mode decomposition-based dual-stream temporal convolutional network with gated attention. Evaluated on thirty years of daily hydro-meteorological observations from the Jingcun hydrological station on China’s Jing River, the framework achieved a coefficient of determination of 0.9872 and a Nash–Sutcliffe efficiency of 0.9631 during the independent evaluation period from 2010 to 2019, outperforming a suite of established benchmark models including deep learning hybrids and the widely used physically based SWAT model.

The central innovation of the work lies in how it disentangles two fundamentally different kinds of signal. Rivers possess a kind of internal dynamic memory: water stored in the subsurface, in snowpack and in channel banks is released slowly, producing smooth, slowly varying components of flow. Superimposed on this are abrupt responses to external forcing, when a rainstorm delivers a pulse of energy and water to the catchment and the hydrograph spikes within hours. Conventional single-stream neural networks must learn both behaviours simultaneously from raw inputs, which often blurs the distinction between the two regimes. The new architecture instead decomposes the historical runoff record using variational mode decomposition, a signal-processing technique that adaptively splits a time series into a set of frequency-specific sub-series, or modes, each capturing oscillations at a characteristic scale.

Variational mode decomposition, first formalised by Dragomiretskiy and Zosso in 2014, differs from classical empirical decomposition methods by framing the decomposition as a variational optimisation problem, seeking the set of modes whose sum reproduces the input signal while each mode remains narrow-banded around its own centre frequency. This makes it considerably more robust to noise and mode mixing than older approaches, a property that matters greatly in hydrology, where observed flows carry measurement error and the underlying signal is anything but stationary. In the new framework, the decomposed runoff components are fed into what the author calls a runoff-state stream, a temporal convolutional network built from causal dilated convolutions and residual blocks.

Temporal convolutional networks have been gaining ground on the long short-term memory (LSTM) architectures that dominated hydrological machine learning for much of the past decade. Where LSTMs process sequences step by step through gated recurrent units, temporal convolutional networks apply one-dimensional convolutions across the time axis, using dilated kernels to expand their receptive field exponentially with network depth. The causal design ensures that predictions at any time step depend only on past information, avoiding future leakage, while residual connections stabilise training in deep stacks. The practical advantages are considerable: convolutions can be computed in parallel across the entire input window, making training dramatically faster, and the hierarchical receptive field allows the network to capture dependencies operating at multiple timescales, from the daily rhythm of rainfall events to the seasonal pulse of snowmelt.

The second stream of the network is dedicated entirely to meteorological forcing. Precipitation, maximum and minimum temperature, solar radiation, relative humidity and wind speed are processed through an independent encoder, so that the atmospheric drivers of runoff are represented in their own feature space rather than being forced to share a representation with the river’s internal state. Only after both streams have produced their encoded features are they combined, and the combination is far from a simple concatenation. A gated fusion mechanism learns, for each time step and each feature channel, how much weight to assign to the runoff-state representation versus the meteorological representation, effectively letting the model decide dynamically whether the river’s own memory or the prevailing weather matters more at any given moment.

On top of this gated fusion sits a temporal attention module, which reweights the contributions of different time steps in the input history, allowing the network to focus on the days that matter most for the forecast, such as the immediate aftermath of a storm. The authors also introduce a peak-sensitive loss function, deliberately penalising errors on high-flow events more heavily than errors during low-flow periods. This addresses a chronic weakness of machine learning hydrology models, which, trained on ordinary mean-squared error, tend to fit the abundant mid-range flows well and systematically underestimate the extreme peaks that matter most for flood risk.

The evaluation protocol was deliberately stringent. The model was trained on daily data from 1990 to 2009 at the Jingcun station and tested on the entirely withheld decade from 2010 to 2019. Against observed flows, VMD-DSTCN-GA recorded an R² of 0.9872, a root mean square error of 7.3734 cubic metres per second, a percent bias of 13.0314 percent, and a Nash–Sutcliffe efficiency of 0.9631, the latter being a standard measure in hydrology where values above roughly 0.75 are generally considered very good and values above 0.9 exceptional. Among all models evaluated, the new framework achieved the highest R², indicating the strongest ability to reproduce the full range of observed runoff variability.

The comparison with benchmarks was informative rather than one-sided. A CNN–LSTM–Attention hybrid achieved a slightly lower root mean square error of 6.6113 cubic metres per second and the highest NSE of 0.9703, while the physically based SWAT model produced the smallest absolute percent bias, reflecting its grounding in water-balance physics. These results suggest a nuanced picture: the proposed dual-stream architecture excels at capturing the shape and variability of the hydrograph, while purely physics-driven approaches retain an advantage in reproducing total volumes. When the same framework was applied at monthly resolution, its performance improved further, yielding an R² of 0.9929, an NSE of 0.9660 and an RMSE of 6.1879 cubic metres per second, a finding consistent with the general observation that aggregation smooths daily noise and makes underlying dynamics easier to learn.

The Jing River basin, a major tributary of the Yellow River, provides a demanding test case. The basin is subject to pronounced hydrological droughts whose propagation from meteorological drought has intensified under environmental change, and its semi-arid to semi-humid climate produces highly variable flows with episodic floods. Data for the study were drawn from the Chinese Hydrological Yearbook of the Yellow River Basin and the China National Meteorological Information Center, spanning the full suite of variables a modern forecasting system would need in operation.

The significance of the approach extends beyond one basin. Signal decomposition combined with machine learning has become one of the most active fronts in hydrological forecasting research, with recent studies pairing wavelet methods, CEEMDAN and empirical mode decomposition variants with gradient boosting, LSTMs and other learners. What distinguishes the new work is the architectural separation of internal state and external forcing, which mirrors how hydrologists conceptually understand catchment behaviour, and the explicit attention to peak flows through the loss function. In effect, the model encodes domain knowledge about the physics of runoff generation into its structure rather than hoping a sufficiently large generic network will discover it from data alone.

The author is candid about the framework’s limitations. A systematic volume bias of just over thirteen percent persists, meaning the model tends to misestimate the total water passing the gauge even as it tracks the timing and shape of flow variations closely. More importantly, the study evaluated the model at a single station; whether the architecture transfers across basins with different geology, land cover and climate remains an open question that will be essential for real-world deployment. Generalisation, or the lack of it, has long been the dividing line between models that impress in benchmarks and models that serve water managers.

Nevertheless, the results arrive at a moment when the demand for accurate streamflow prediction is intensifying. Climate change is amplifying hydrological extremes in many of the world’s major basins, stressing water allocation systems designed around the statistics of a more stable past. Hybrid frameworks that combine signal processing, deep learning and physically informed architectures offer a pragmatic path forward, and the demonstration that a dual-stream, attention-equipped temporal convolutional network can reach NSE values above 0.96 on out-of-sample daily data marks a genuine step in that direction. The work was supported by several Chinese research programmes, including projects from Sinomach Group, Xianyang City and Chang’an University’s Fundamental Research Funds, and the full technical details, along with supplementary material, are available in the journal article.