FedMamba-ChebKAN: Federated Mamba with Chebyshev-KAN for heterogeneous IIoT fault detection

Fault detection in edge-based Industrial Internet of Things (IIoT) systems requires models that generalise across heterogeneous devices while respecting data-governance and bandwidth constraints. Federated learning (FL) avoids raw-data exchange, but standard optimisers degrade under strong statistical heterogeneity, and Kolmogorov–Arnold Network (KAN) heads parameterised by client-adaptive B-splines add a grid-misalignment problem that weight averaging cannot resolve. We present FedMamba-ChebKAN, which couples a Mamba selective state-space encoder, with 𝒪 ( L ) cost over long sensor sequences, to a Chebyshev-KAN head whose polynomial activations share one client-invariant basis, so that coefficient averaging is well posed without re-interpolation. Its aggregation rule, SpectralFedAvg, truncates each KAN edge at a tail-energy threshold and averages coefficients at a consensus degree on the shared basis; a variant, SpectralFedAvg-BN, keeps BatchNorm on the clients. A proposition bounds the error of the aggregated edge function by a truncation term plus a client-heterogeneity term. We evaluate on CWRU, Paderborn and MIMII (12 clients each) and NASA C-MAPSS (20 clients), with splits made on recordings or engines before windowing, all federated baselines on the same architecture, eight seeds per configuration, and exact Wilcoxon tests with Benjamini–Hochberg correction. SpectralFedAvg-BN reaches 98.0 ± 0.5 % accuracy on CWRU, 12.3 points above FedAvg ( q = 0.023) and level with FedBN, and the lowest RMSE among the federated methods on C-MAPSS ( 20.29 ± 0.51 cycles, against 20.89 for FedAvg, q = 0.039). On Paderborn (98.0%) and MIMII (AUROC 0.805), the federated methods that share the architecture lie within about one standard deviation of each other. With DP-SGD on every client and an encoder pretrained on public data, the model keeps 89.5% CWRU accuracy at example-level ( ε ≈ 8 , δ = 10 − 5 ) -DP and 92.4% at ε ≈ 19 . Code, client partitions and per-seed results are public.