FedCMAPSS: A Benchmark for Federated Learning in Remaining Useful Life Estimation

# FedCMAPSS: A Benchmark for Federated Learning in Remaining Useful Life Estimation
Source: [https://arxiv.org/html/2608.26433](https://arxiv.org/html/2608.26433)
Matteo PennisiAffiliation:University of Catania, Italy matteo\.pennisi@unict\.itConcetto SpampinatoAffiliation:University of Catania, Italy concetto\.spampinato@unict\.itSimone PalazzoAffiliation:University of Catania, Italy simone\.palazzo@unict\.it

###### Abstract

Data\-driven prognostics and health management has emerged as a key enabler for Industry 4\.0, yet the development of robust remaining useful life \(RUL\) estimation models is often limited by the scarcity of run\-to\-failure data\. While federated learning offers a promising paradigm to collaboratively train predictive models without sharing sensor data, research efforts have operated so far in the absence of a common evaluation framework\. To address this gap, this paper introduces FedCMAPSS, a benchmark for federated RUL estimation based on the commonly\-used NASA C\-MAPSS dataset\. We define a set of five standardized tasks designed to simulate real\-world industrial challenges, ranging from ideal IID settings to extreme statistical heterogeneity, and conduct a systematic evaluation of state\-of\-the\-art federated optimization algorithms across multiple neural architectures\. By establishing reproducible baselines and making the source code and data splits publicly available, this work aims to provide a standard foundation for developing and comparing federated predictive maintenance solutions\.

###### Index Terms:

federated learning, predictive maintenance, remaining useful life

## IIntroduction

In modern industrial systems, predictive maintenance represents a critical shift from reactive and preventative strategies to data\-driven prognostics and health management \(PHM\)\[[1](https://arxiv.org/html/2608.26433#bib.bib1)\], with remaining useful life \(RUL\) estimation standing out as one of the primary prognostic objectives\[[2](https://arxiv.org/html/2608.26433#bib.bib14)\]\. In this context, deep neural networks have increasingly become the standard in PHM applications, leveraging their capacity to automatically extract high\-level representations from multidimensional sensor data\[[3](https://arxiv.org/html/2608.26433#bib.bib2),[4](https://arxiv.org/html/2608.26433#bib.bib3),[5](https://arxiv.org/html/2608.26433#bib.bib4)\]\.

Despite their success, these architectures require large amounts of centralized run\-to\-failure data for optimization, while organizations often lack sufficient samples to train robust generalized regression models, especially in real\-world edge deployments\[[6](https://arxiv.org/html/2608.26433#bib.bib5)\]; at the same time, they may not be willing to share their data with other stakeholders, due to intellectual property issues or data privacy laws \(such as the GDPR\)\[[7](https://arxiv.org/html/2608.26433#bib.bib6)\]\. A possible solution to these problems may lie in the adoption of federated learning \(FL\) techniques, which enable distributed nodes to collaboratively optimize a global model by transmitting only gradient updates or network weights rather than raw data\[[8](https://arxiv.org/html/2608.26433#bib.bib7),[9](https://arxiv.org/html/2608.26433#bib.bib8),[10](https://arxiv.org/html/2608.26433#bib.bib42),[11](https://arxiv.org/html/2608.26433#bib.bib44)\]\. The benefits of this solution have led to significant research efforts in the field, but the challenge is still open: implementing federated learning in resource\-constrained IoT environments introduces bandwidth and computational constraints\[[12](https://arxiv.org/html/2608.26433#bib.bib9)\], exacerbated by the communication overhead associated with transmitting deep neural networks\[[13](https://arxiv.org/html/2608.26433#bib.bib10)\]and by security aspects\[[14](https://arxiv.org/html/2608.26433#bib.bib11),[15](https://arxiv.org/html/2608.26433#bib.bib12)\]\.

The convergence of federated optimization protocols and continuous RUL estimation is a promising direction for scaling prognostic solutions across distributed edge devices\. Recent studies validate that decentralized neural networks optimized via federated topologies can achieve predictive accuracy comparable to centralized models\[[16](https://arxiv.org/html/2608.26433#bib.bib17),[17](https://arxiv.org/html/2608.26433#bib.bib43)\]\. However, complex and non\-stationary degradation signals present unique optimization challenges for distributed learning architectures: for instance, standard aggregation protocols like FedAvg\[[8](https://arxiv.org/html/2608.26433#bib.bib7)\]exhibit learning oscillations and high uncertainty during the optimization of multilayer perceptrons across heterogeneous sensor data distributions\[[18](https://arxiv.org/html/2608.26433#bib.bib18)\]\.

A significant obstacle to the advancement of federated RUL estimation is the lack of consistency in evaluation settings and data partitioning strategies across existing literature\. For instance, many works evaluate data\-driven RUL algorithms on the NASA Commercial Modular Aero\-Propulsion System Simulation \(C\-MAPSS\) dataset\[[19](https://arxiv.org/html/2608.26433#bib.bib15),[20](https://arxiv.org/html/2608.26433#bib.bib16)\], modeling damage propagation in aircraft turbofan engines\. However, even on the same dataset, the research community often utilizes inconsistent evaluation protocols, making it difficult to fairly compare competing prognostic algorithms\[[21](https://arxiv.org/html/2608.26433#bib.bib19),[22](https://arxiv.org/html/2608.26433#bib.bib20)\]\. For instance, the lack of consistency on how data samples are distributed among clients \(and on the number of clients itself\) can drastically affect evaluation variability, especially because of the nature of the dataset, which features samples deployed in significantly different operating conditions\. As a result, this statistical heterogeneity makes cross\-paper comparisons impossible\.

To address these systemic evaluation discrepancies, this paper introduces a standardized benchmark for FL applied to RUL estimation\. Based on the C\-MAPSS dataset, we define a set of standard tasks supporting the evaluation of FL methods in different data distribution settings, aligned to predictive maintenance contexts and objectives\. We also provide a thorough comparison between state\-of\-the\-art FL algorithms and neural network architectures employed for RUL estimation\. Overall, our goal is to provide the prognostic machine learning community with a common dataset and a reproducible framework, to accurately evaluate decentralized predictive maintenance algorithms\. All code for reproducing and extending the results of the paper is provided at[https://github\.com/perceivelab/FedCMAPSS](https://github.com/perceivelab/FedCMAPSS)\.

## IIRelated Work

Predictive maintenance has evolved from traditional analytical models to data\-driven diagnostic systems designed to detect and classify machinery faults, with deep learning architectures becoming central to these systems due to their ability to extract high\-level representations from complex multidimensional sensor streams\[[23](https://arxiv.org/html/2608.26433#bib.bib21),[24](https://arxiv.org/html/2608.26433#bib.bib28),[25](https://arxiv.org/html/2608.26433#bib.bib29)\]\. RUL estimation extends beyond classification to predict continuous degradation trajectories, requiring models capable of capturing long\-term temporal dependencies\. Foundational approaches adapted convolutional neural networks to replace manual feature engineering\[[26](https://arxiv.org/html/2608.26433#bib.bib30)\]\. Subsequently, LSTM\-based recurrent architectures became the standard for RUL estimation due to their ability to prevent gradient dispersion over long sequences\[[27](https://arxiv.org/html/2608.26433#bib.bib31),[28](https://arxiv.org/html/2608.26433#bib.bib32),[29](https://arxiv.org/html/2608.26433#bib.bib33)\]\. To address the limitation of LSTMs heavily weighing only the final time step, self\-attention mechanisms, including transformer architectures, have been introduced to dynamically assign importance weights across the entire time window\[[30](https://arxiv.org/html/2608.26433#bib.bib34)\]\.

Federated RUL estimation has typically established FedAvg as the baseline for aggregating local model parameters centrally without sharing raw data\[[8](https://arxiv.org/html/2608.26433#bib.bib7)\]\. This standard aggregation has been applied to various deep learning structures, from baseline multilayer perceptrons to recurrent networks\[[31](https://arxiv.org/html/2608.26433#bib.bib22),[16](https://arxiv.org/html/2608.26433#bib.bib17)\]\. However, since coordinate\-wise averaging may suffer from destructive interference between model parameters, more complex matching algorithms\[[32](https://arxiv.org/html/2608.26433#bib.bib13)\]have been adapted to RUL estimation\[[7](https://arxiv.org/html/2608.26433#bib.bib6)\]\. FedProx introduces a proximal term to restrict local optimization updates, reducing learning oscillations\[[33](https://arxiv.org/html/2608.26433#bib.bib26),[18](https://arxiv.org/html/2608.26433#bib.bib18)\]\. Other approaches combine this constraint with a shared\-data strategy to stabilize training across non\-IID \(independent and identically distributed\) data\[[34](https://arxiv.org/html/2608.26433#bib.bib35)\]\. Dynamic weighting mechanisms adjust the global aggregation based on client quality\[[6](https://arxiv.org/html/2608.26433#bib.bib5),[15](https://arxiv.org/html/2608.26433#bib.bib12)\]\. Adaptive client momentum approaches compute local momentum to outperform traditional server\-side momentum aggregation\[[35](https://arxiv.org/html/2608.26433#bib.bib36),[36](https://arxiv.org/html/2608.26433#bib.bib37)\]\. Federated personalization addresses non\-IID data by partitioning models into global base layers and local personalization layers, effectively applied to 1D CNNs for RUL prediction\[[37](https://arxiv.org/html/2608.26433#bib.bib38),[38](https://arxiv.org/html/2608.26433#bib.bib39)\]\. To reduce communication overhead in complex topologies, Fed\-TNP employs model pruning to sparsify network weights before transmission\[[13](https://arxiv.org/html/2608.26433#bib.bib10)\]\.

In terms of evaluation settings, a discrepancy among studies lies in the partitioning of client data\. Some approaches utilize homogeneous splits, leveraging random partitioning to simulate distributed environments\[[39](https://arxiv.org/html/2608.26433#bib.bib40)\]\. Conversely, other research applies non\-IID partitioning, which complicates the training process compared to homogeneous splits\[[7](https://arxiv.org/html/2608.26433#bib.bib6)\]\. Furthermore, preprocessing and target normalization strategies vary widely across the literature\. While some works rely on simple min\-max normalization across the entire dataset\[[39](https://arxiv.org/html/2608.26433#bib.bib40)\], others employ clustering to identify operating regimes prior to applying Z\-score standardizations\[[40](https://arxiv.org/html/2608.26433#bib.bib41),[18](https://arxiv.org/html/2608.26433#bib.bib18)\]\. Target label generation also exhibits variability, where piecewise linear rectification strategies are commonly employed with different capping values\[[38](https://arxiv.org/html/2608.26433#bib.bib39),[39](https://arxiv.org/html/2608.26433#bib.bib40)\]\.

## IIIMethod

### III\-ADataset

We build our federated RUL estimation benchmark upon the widely\-used C\-MAPSS dataset\[[19](https://arxiv.org/html/2608.26433#bib.bib15)\]\. The dataset simulates the degradation of aircraft turbofan engines over time, capturing multidimensional sensor readings under various operational states and fault conditions\. It is divided into four distinct sub\-datasets, namely FD001, FD002, FD003, and FD004, each presenting varying degrees of complexity\. Specifically, FD001 and FD003 simulate a single operating condition at sea level, whereas FD002 and FD004 encompass six different operational settings, increasing the statistical heterogeneity of the sensor data\. Furthermore, the datasets model different degradation mechanisms: FD001 and FD002 feature a single fault mode related to high\-pressure compressor degradation, while FD003 and FD004 introduce a second concurrent fault mode affecting the engine fan\. The volume of data also varies across the subsets, with FD001 and FD003 containing 100 training and 100 testing trajectories each, FD002 containing 260 training and 259 testing trajectories, and FD004 containing 248 training and 249 testing trajectories\.

Each trajectory represents a multivariate time series extracted from a single engine\. Raw data describe 26 features, which include the engine unit identifier, the elapsed time expressed in cycles, three operational settings, and 21 distinct sensor measurements contaminated with realistic sensor noise\. At the beginning of each time series, the engine operates normally, possessing an unknown degree of initial wear that does not constitute a fault condition\. In the training subsets, this degradation grows until system failure; conversely, the test trajectories are truncated at a random point prior to failure\.

### III\-BTasks

We organize the C\-MAPSS dataset into five*tasks*, designed to model real\-world industrial challenges\. Each task defines a fixed number of clients, among which dataset samples are distributed, based on the task’s specific objective\. To ensure the statistical validity and reproducibility of the benchmark, we generate 10 independent random splits for each task\. Within each split, the data allocated to every client is partitioned into a*training*subset, utilized for local model optimization; a*testing*subset, consisting of the standard truncated C\-MAPSS test trajectories and used to compute the global evaluation metrics; and a*full testing*subset, which holds unused training samples containing complete run\-to\-failure trajectories, reserved for generating plots of actual RUL versus predicted RUL\. Except where constrained by specific task settings, we generally apply an 85% subsampling ratio to allocate trajectories to the training subset, reserving the remaining 15% for the full testing subset\. In detail, tasks are defined as follows:

- •Task A: IID baseline\.This task assesses convergence in an ideal scenario\. We utilize the FD001 dataset, distributing engine trajectories among 10 clients following an IID partitioning strategy\. No domain shift or label skew is introduced between clients\.
- •Task B: domain shift\.This task emulates cross\-silo collaboration, where client data distributions reflect different mechanical paradigms or fault modes\. We leverage all four C\-MAPSS sub\-datasets and assign each to one client\.
- •Task C: label skew\.This task introduces label skew, with each client observing different lifecycle lengths\. We utilize the FD004 dataset \(with six operational conditions and two fault models\) and sort units by their total lifespan\. The sorted trajectories are then sequentially assigned to 10 clients, forcing them to train exclusively on engines with a specific lifespan range\.
- •Task D: feature skew\.This task assigns skewed sensor measurement distributions among 6 clients\. Using the FD004 dataset, we apply k\-means clustering to the operational settings features to isolate the data by condition\. Each of the 6 clients is then exclusively assigned data corresponding to one specific operational cluster\. Note that this implies that the same engine can be assigned to multiple clients; however, each of them will “see” only the cycles in which the engine operated at the client’s assigned condition, potentially introducing temporal gaps in the time series\.
- •Task E: few\-shot learning\.This task scales the network to 85 clients using the FD001 dataset, assigning one unique training trajectory to each client, thus forcing the aggregation of model parameters from highly biased local datasets\.

### III\-CArchitectures

We evaluate representative neural architectures for federated RUL prediction, inspired by recent literature, including recurrent, convolutional, and attention\-based models\. Implementation details can be found in the source code repository\. The architectures under comparison are:

- •LSTM\[[7](https://arxiv.org/html/2608.26433#bib.bib6)\]: a simple LSTM network with a single layer\.
- •RNN\[[31](https://arxiv.org/html/2608.26433#bib.bib22)\]: a five\-layer RNN progressively reducing hidden dimensionality, followed by a multi\-layer perceptron \(MLP\) for prediction\.
- •CNN\[[41](https://arxiv.org/html/2608.26433#bib.bib23)\]: a convolutional architecture treating a multivariate time series as a 2D matrix with asymmetric kernels, followed by an MLP for RUL estimation\.
- •AFT\[[15](https://arxiv.org/html/2608.26433#bib.bib12)\]: an Attention\-Free Transformer \(AFT\) processes the input sequence, before feeding it to two 2D convolutional layers, followed by an MLP for prediction\.
- •AttBiGRU\[[6](https://arxiv.org/html/2608.26433#bib.bib5)\]: a bidirectional GRU is followed by 4\-head self\-attention to dynamically weigh the contribution of different signal parts; the resulting attention map is flattened and processed by an MLP with dropout\.

Model hyperparameters are set to default values from the corresponding papers, when available, or following established heuristics\.

### III\-DFederated methods

We benchmark different federated optimization methods, including classical baselines and more recent approaches designed for non\-IID federated training:

- •FedAvg\[[8](https://arxiv.org/html/2608.26433#bib.bib7)\]is the classical FL baseline\. At each communication round, clients train the shared model locally and the server aggregates client updates through weighted averaging, typically proportional to local sample sizes\.
- •SCAFFOLD\[[42](https://arxiv.org/html/2608.26433#bib.bib27)\]addresses*client drift*caused by data heterogeneity using control variates maintained by the server and each client, improving convergence speed and final accuracy in non\-IID settings\.
- •FedDyn\[[43](https://arxiv.org/html/2608.26433#bib.bib25)\]introduces a*dynamic regularization*objective to align local optima with the global objective, especially under non\-IID data\.
- •FedCross\[[44](https://arxiv.org/html/2608.26433#bib.bib24)\]proposes a multi\-model cross\-aggregation strategy rather than relying on a single global model during each round, using multiple middleware models\.

Method\-specific hyperparameters for FL methods are set to default values in the PFLLib111[https://www\.pfllib\.com](https://www.pfllib.com/)library\.

### III\-EEvaluation metrics

We evaluate RUL prediction performance using theRoot Mean Square Error\(RMSE\) and theNASA Score, which are both standard in prognostics benchmarks\.

Given ground\-truth RUL valuesyiy\_\{i\}and predictionsy^i\\hat\{y\}\_\{i\}forNNtest samples, the RMSE is defined as

RMSE=1N​∑i=1N\(yi−y^i\)2\.\\mathrm\{RMSE\}=\\sqrt\{\\frac\{1\}\{N\}\\sum\_\{i=1\}^\{N\}\(y\_\{i\}\-\\hat\{y\}\_\{i\}\)^\{2\}\}\.\(1\)RMSE measures the average magnitude of prediction errors and is easy to interpret in the same unit as the target RUL\.

In addition, we report the NASA Score, an asymmetric metric that penalizes late predictions \(i\.e\., overestimation of RUL\) more severely than early predictions\. LetΔi=y^i−yi\\Delta\_\{i\}=\\hat\{y\}\_\{i\}\-y\_\{i\}\. The score is computed as

Score=∑i=1Nsi,si=\{exp⁡\(−Δi13\)−1,Δi<0,exp⁡\(Δi10\)−1,Δi≥0\.\\mathrm\{Score\}=\\sum\_\{i=1\}^\{N\}s\_\{i\},\\quad s\_\{i\}=\\begin\{cases\}\\exp\\\!\\left\(\-\\frac\{\\Delta\_\{i\}\}\{13\}\\right\)\-1,&\\Delta\_\{i\}<0,\\\\\[4\.0pt\] \\exp\\\!\\left\(\\frac\{\\Delta\_\{i\}\}\{10\}\\right\)\-1,&\\Delta\_\{i\}\\geq 0\.\\end\{cases\}\(2\)Lower values indicate better performance for both metrics\. The asymmetric NASA Score is particularly relevant in maintenance applications, where overly optimistic RUL estimates may lead to delayed interventions\. The NASA Score is commonly reported cumulatively over all test samples\.

TABLE I:Local client performance in the isolated setting \(RMSE\)\.TABLE II:Results on Task A by architecture and federated method\.
### III\-FEvaluation protocol

Following common RUL estimation practice, sensor signals are split into fixed\-length temporal windows and paired with the corresponding RUL labels\. We apply client\-side preprocessing only \(e\.g\., normalization and windowing\) before local training\. During training, local optimization aims to minimize the mean squared error \(MSE\) loss between the predicted and ground\-truth RUL\. This objective may be augmented by any loss terms introduced by the respective FL algorithms\. Following the piecewise linear degradation assumption, widely adopted in C\-MAPSS literature, the continuous target RUL values are clipped to a maximum number of cycles, set to 125, and linearly normalized to the\[0,1\]\[0,1\]interval\.

Model training is carried out using standard stochastic gradient descent; relevant hyperparameters \(learning rate, batch size\) are tuned for each model architecture by conducting a grid search using a centralized training paradigm on the FD001 dataset\. We currently do not tune optimization hyperparameters in the federated setting, nor model\-specific or algorithm\-specific hyperparameters\. In the federated setting, we train all algorithms for 100 rounds, varying the number of epochs of local training per round \(1, 5 and 10\)\.

Our experimental framework omits a dedicated validation set during the federated evaluation phase, and unconditionally evaluates the global model aggregated at the final communication round\. This is chosen to maximize procedural simplicity and reflect realistic edge deployment constraints, where auxiliary validation data is often unavailable\. Moreover, empirical observations from the initial centralized hyperparameter selection showed that the optimization trajectory is generally smooth, exhibiting minimal oscillatory behavior across epochs\. Nevertheless, researchers utilizing our benchmark who wish to employ alternative model selection criteria, such as early stopping, should independently partition the local training sets to construct validation splits, to ensure methodological rigor\.

Finally, to ensure statistical significance, we evaluate all combinations of model and FL algorithm on all 10 independent random splits generated for each task, reporting mean and standard deviation of both the RMSE and the NASA Score on the test set\.

## IVExperimental Results

We evaluate the proposed benchmark across the five defined tasks\. We first evaluate isolated local training and full\-data centralized optimization\. We then present a comparative analysis of model architectures and FL algorithms\. Finally, we analyze the optimization dynamics concerning communication overhead and provide a qualitative assessment of the predicted degradation trajectories\.

### IV\-ALocal baseline

To contextualize the performance of the FL methods, we establish an empirical lower\-bound baseline under a local\-only training regime, where each client updates its model using only its isolated partition without any parameter synchronization\.

Results for all tasks and model architectures are reported in Tab\.[I](https://arxiv.org/html/2608.26433#S3.T1)in terms of RMSE\. Averaging results across architectures within each task highlights a pronounced difficulty gap in the isolated setting\. Overall, however, all models struggle when tackling each task locally\.

TABLE III:Results on Task B by architecture and federated method\.TABLE IV:Results on Task C by architecture and federated method\.TABLE V:Results on Task D by architecture and federated method\.TABLE VI:Results on Task E by architecture and federated method\.
### IV\-BTask evaluation

We then evaluate the model architectures and FL methods introduced in Sect\.[III\-C](https://arxiv.org/html/2608.26433#S3.SS3)and[III\-D](https://arxiv.org/html/2608.26433#S3.SS4)\. Results are reported, for each task, in Tab\.[II](https://arxiv.org/html/2608.26433#S3.T2)\-[VI](https://arxiv.org/html/2608.26433#S4.T6)\.

As shown in Tab\.[II](https://arxiv.org/html/2608.26433#S3.T2), under the IID conditions of Task A, all methods achieve strong RMSE, with FedAvg and SCAFFOLD performing generally better\. Across architectures, LSTM is the only one which does not exhibit method sensitivity, remaining competitive with all FL strategies\.

Tab\.[III](https://arxiv.org/html/2608.26433#S4.T3)introduces the difficulties associated with non\-IID scenarios, as clients optimize on different operating regimes and fault patterns in Task B\. In this setting, drift\-mitigation methods tend to be more effective, with FedCross and SCAFFOLD providing the strongest overall performance across architectures\. An observation should be made here regarding the NASA Score\. Since it applies exponential penalties, it is strongly sensitive to even a small number of samples with large prediction errors, leading to cases where the mean and standard deviation are both very large and comparable\. Therefore, rather than reporting a meaningless average, in these cases we only show the standard deviation, to give an idea of the degree of score variability\. We emphasize that this is a significant limitation of the metric, and more outlier\-robust alternatives should be explored in future work\. For readability, we report NASA Score values scaled by10−310^\{\-3\}in all tables\.

Continuing with Task C, a comparable level of difficulty is observed, where clients are exposed to different lifespan ranges \(Tab\.[IV](https://arxiv.org/html/2608.26433#S4.T4)\)\. Here, FedCross emerges as the most effective approach, and the improvements are most pronounced with the LSTM, AFT and RNN models\. In contrast, Task D appears comparatively less critical than the other non\-IID regimes \(Tab\.[V](https://arxiv.org/html/2608.26433#S4.T5)\): despite the distribution shift in the input space, most methods achieve solid performance and the gap among federated strategies narrows, with the notable exception of FedDyn, which exhibits significantly lower prediction accuracy\.

Task E is the most challenging setting, as evidenced by the results in Tab\.[VI](https://arxiv.org/html/2608.26433#S4.T6)\. Under extremely limited and highly biased local datasets, LSTM and CNN provide the most stable performance among the considered architectures, consistent with reduced sensitivity to local overfitting in this few\-shot regime\.

![Refer to caption](https://arxiv.org/html/2608.26433v1/figures/local_epochs/bar_plot_task_B.png)\(a\)Task B
![Refer to caption](https://arxiv.org/html/2608.26433v1/figures/local_epochs/bar_plot_task_C.png)\(b\)Task C
![Refer to caption](https://arxiv.org/html/2608.26433v1/figures/local_epochs/bar_plot_task_D.png)\(c\)Task D

Fig\. 1:Average RMSE across all architectures for different numbers of local training epochs per round\.![Refer to caption](https://arxiv.org/html/2608.26433v1/figures/rounds/line_plot_task_A.png)\(a\)Task A
![Refer to caption](https://arxiv.org/html/2608.26433v1/figures/rounds/line_plot_task_B.png)\(b\)Task B
![Refer to caption](https://arxiv.org/html/2608.26433v1/figures/rounds/line_plot_task_C.png)\(c\)Task C

Fig\. 2:Average RMSE across all architectures over communication rounds, using 10 local epochs per round\.![Refer to caption](https://arxiv.org/html/2608.26433v1/figures/ruls/A/FedCMAPSSWindow_FedAvg_RUL_Chen_CNN_RUL_A_7_20260330-054247_aggregated.png)\(a\)Task A: FedAvg using CNN
![Refer to caption](https://arxiv.org/html/2608.26433v1/figures/ruls/C/FedCMAPSSWindow_FedCross_RUL_RNN_RUL_C_1_20260405-191514_aggregated.png)\(b\)Task C: FedCross using RNN
![Refer to caption](https://arxiv.org/html/2608.26433v1/figures/ruls/E/FedCMAPSSWindow_FedAvg_RUL_LSTM_RUL_E_1_20260329-185955_aggregated.png)\(c\)Task E: FedAvg using LSTM

Fig\. 3:Aggregated RUL trajectories over the life percentage\.
### IV\-CSensitivity to optimization hyperparameters

A challenge in deploying federated solutions to edge environments lies in how to handle bandwidth limitations\. Formally, the communication cost can be modeled asC=2​R​N​PC=2RNP, whereRRdenotes the total number of synchronization rounds,NNrepresents the number of clients participating in each round, andPPdefines the total number of shared trainable parameters for a specific network architecture\. Because the payload sizePPand number of clientsNNare fixed for a given experimental configuration, the communication overhead scales linearly withRR\. Therefore, deployment feasibility may be evaluated by analyzing the interaction between local training epochs and global synchronization frequency\.

To this end, we conduct an analysis of the local optimization hyperparameters, reporting results averaged across model architectures for each task, shown in Fig\.[1](https://arxiv.org/html/2608.26433#S4.F1)for tasks B, C and D\. We first evaluate the effect of varying the number of local training epochs \(1, 5, and 10\) while keeping the total number of global communication rounds fixed at 100\. In highly non\-IID federated settings, performing multiple consecutive local gradient steps typically exacerbates client drift, pushing the local weights toward divergent, isolated minima\. However, our findings indicate that the final generalization performance remains largely robust to the specific number of local epochs\.

Building on this stability, we evaluate the impact of varying the total number of global rounds \(from 10 to 100\) while holding the local computation fixed to 10 epochs, to ensure that we capture long\-training effects\. As summarized in Fig\.[2](https://arxiv.org/html/2608.26433#S4.F2), 100 communication rounds are sufficient to reach stable performance; in some cases, notably for Task A, the trend seems to indicate further possible improvements; a trade\-off is however necessary when training in an edge\-oriented regime\. On a negative note, FedDyn exhibits an almost\-constant trend which questions its suitability to the tasks at hand\.

### IV\-DQualitative analysis of degradation trajectories

Finally, we visualize common plots of actual RUL versus predicted RUL, to assess the models’ capability to reliably estimate a component’s lifespan during its operation\. Fig\.[3](https://arxiv.org/html/2608.26433#S4.F3)shows examples for a representative subset of the evaluated FL methods, models and tasks, visualizing the average predicted RUL, with confidence intervals computed across task splits\. In the plots, it can be noticed that the length of the constant segment of the target RUL is not fixed across tasks\. This is due to the target RUL clipping at 125, which has a different impact depending on the average length of samples in the task\.

The degradation trajectories provide useful insight into the predictive uncertainty exhibited at different stages of a component lifecycle, which reflects the intrinsic difficulty of each task\. As the degradation progresses toward the failure threshold, the fault signature becomes increasingly pronounced, leading to a narrowing of the error bars\. Notably, there appears to be a tendency to slightly overestimate RUL as the device reaches the failure point\. This should be further investigated and possibly addressed through ad\-hoc loss terms that target end\-of\-life behavior\.

## VConclusions

Given the lack of consistent evaluation protocols and client partitioning schemes in current federated prognostics research, this paper introducesFedCMAPSS, a standardized benchmark for RUL estimation in federated learning\. Built on the widely used NASA C\-MAPSS dataset, the benchmark defines five tasks spanning an IID baseline, several forms of statistical heterogeneity, and an extreme data\-scarcity regime\. Beyond task specification, FedCMAPSS provides a reproducible experimental protocol, including client\-side preprocessing, windowing and target construction, a standardized training schedule, and multiple randomized splits\. Together with publicly released code and data partitions, these elements enable fair and transparent comparisons across future methods\.

Our experiments across architectures and FL methods yield practical insights\. In the IID regime \(Task A\), FedAvg performs strongly overall; under domain shift and label skew \(Tasks B\-C\), drift\-mitigation strategies are generally more reliable\. Feature skew \(Task D\) is comparatively mild in our setup, whereas few\-shot federation \(Task E\) is the most challenging, and performance becomes more sensitive to the selected model architecture\.

Further analysis indicates that final performance is relatively robust to the number of local epochs in the tested configurations\. Moreover, convergence curves over communication rounds show that most methods reach a stable regime within 100 rounds, although in some cases additional rounds may be of benefit\.

In future work, we plan to perform systematic hyperparameter optimization tailored to federated settings, extend the benchmark to additional FL paradigms, include outlier\-robust evaluation criteria, and expand the suite with additional datasets\.

## Acknowledgment

S\. Palazzo and M\. Pennisi acknowledge the project ECS4DRES, supported by the Chips Joint Undertaking under grant agreement number 101139790 and its members, including the top\-up funding by Germany, Italy, Slovakia, Spain and The Netherlands\.

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