Xiaolei Fang

Chengyu Zhou, Xiaolei Fang

This paper proposes a supervised dimension reduction methodology for tensor data which has two advantages over most image-based prognostic models. First, the model does not require tensor data to be complete which expands its application to incomplete data. Second, it utilizes time-to-failure (TTF) to supervise the extraction of low-dimensional features which makes the extracted features more effective for the subsequent prognostic. Besides, an optimization algorithm is proposed for parameter estimation and closed-form solutions are derived under certain distributions.

Xiaolei Fang, Peilan Xu, Wenjian Luo

Multi-party multi-objective optimization problems (MPMOPs) require consensus among autonomous decision makers and therefore differ from flattened many-objective formulations. Existing runtime theory for multi-objective evolutionary algorithms is largely tailored to single-party Pareto-front approximation and does not directly explain common-solution search in MPMOPs. We investigate cross-party recombination in two representative settings. On MP-JCG, a pseudo-Boolean benchmark with an explicit gap region, we prove that a payoff-guided mutation baseline faces a gap-crossing bottleneck requiring \(Θ(n^2)\) expected fitness evaluations. In contrast, an analytical CPR-NSGA-II variant discovers both common Pareto-optimal solutions in \(O(n\log n)\) expected evaluations by directly assembling complementary prefix and suffix templates distributed across party populations. Comparing this with the flattened four-objective formulation F-JCG, our full-front coverage analysis illustrates the additional coverage burden introduced by flattening. For BPBOMST, the bi-party, two-objective-per-party specialization of the multi-party multi-objective minimum spanning tree problem, we develop a layered support-cover analysis. For each common Pareto objective vector, the symmetric average projection induces an auxiliary bi-objective MST instance, and suitable support representatives yield a \(2λ\)-common approximation cover with \(λ\in[1,2]\). We further derive an instance-parameterized expected runtime bound for a representative-pool CPR-NSGA-II variant using edge-union recombination and uniform repair. This bound separates the effects of local auxiliary-front filling, cross-party recombination shortcuts, and edge-union repair ambiguity.

Madi Arabi, Xiaolei Fang

Most prognostic methods require a decent amount of data for model training. In reality, however, the amount of historical data owned by a single organization might be small or not large enough to train a reliable prognostic model. To address this challenge, this article proposes a federated prognostic model that allows multiple users to jointly construct a failure time prediction model using their multi-stream, high-dimensional, and incomplete data while keeping each user's data local and confidential. The prognostic model first employs multivariate functional principal component analysis to fuse the multi-stream degradation signals. Then, the fused features coupled with the times-to-failure are utilized to build a (log)-location-scale regression model for failure prediction. To estimate parameters using distributed datasets and keep the data privacy of all participants, we propose a new federated algorithm for feature extraction. Numerical studies indicate that the performance of the proposed model is the same as that of classic non-federated prognostic models and is better than that of the models constructed by each user itself.

Yuqi Su, Xiaolei Fang

Complex systems such as aircraft engines, turbines, and industrial machinery often operate under dynamically changing conditions. These varying operating conditions can substantially influence degradation behavior and make prognostic modeling more challenging, as accurate prediction requires explicit consideration of operational effects. To address this issue, this paper proposes a novel multi-head attention-based fusion neural network. The proposed framework explicitly models and integrates three signal components: (1) the monotonic degradation trend, which reflects the underlying deterioration of the system; (2) discrete operating states, identified through clustering and encoded into dense embeddings; and (3) residual random noise, which captures unexplained variation in sensor measurements. The core strength of the framework lies in its architecture, which combines BiLSTM networks with attention mechanisms to better capture complex temporal dependencies. The attention mechanism allows the model to adaptively weight different time steps and sensor signals, improving its ability to extract prognostically relevant information. In addition, a fusion module is designed to integrate the outputs from the degradation-trend branch and the operating-state embeddings, enabling the model to capture their interactions more effectively. The proposed method is validated using a dataset from the NASA repository, and the results demonstrate its effectiveness.

Yuhan Hu, Xiaolei Fang

Federated prognostics enable clients (e.g., companies, factories, and production lines) to collaboratively develop a failure time prediction model while keeping each client's data local and confidential. However, traditional federated models often assume homogeneity in the degradation processes across clients, an assumption that may not hold in many industrial settings. To overcome this, this paper proposes a personalized federated prognostic model designed to accommodate clients with heterogeneous degradation processes, allowing them to build tailored prognostic models. The prognostic model iteratively facilitates the underlying pairwise collaborations between clients with similar degradation patterns, which enhances the performance of personalized federated learning. To estimate parameters jointly using decentralized datasets, we develop a federated parameter estimation algorithm based on proximal gradient descent. The proposed approach addresses the limitations of existing federated prognostic models by simultaneously achieving model personalization, preserving data privacy, and providing comprehensive failure time distributions. The superiority of the proposed model is validated through extensive simulation studies and a case study using the turbofan engine degradation dataset from the NASA repository.

Chengyu Zhou, Yuqi Su, Tangbin Xia et al.

Multilinear Principal Component Analysis (MPCA) is a widely utilized method for the dimension reduction of tensor data. However, the integration of MPCA into federated learning remains unexplored in existing research. To tackle this gap, this article proposes a Federated Multilinear Principal Component Analysis (FMPCA) method, which enables multiple users to collaboratively reduce the dimension of their tensor data while keeping each user's data local and confidential. The proposed FMPCA method is guaranteed to have the same performance as traditional MPCA. An application of the proposed FMPCA in industrial prognostics is also demonstrated. Simulated data and a real-world data set are used to validate the performance of the proposed method.

Benjamin Peters, Ayush Mohanty, Xiaolei Fang et al.

Deep-space habitats are complex systems that must operate autonomously over extended durations without ground-based maintenance. These systems are vulnerable to multiple, often unknown, failure modes that affect different subsystems and sensors in mode-specific ways. Developing accurate remaining useful life (RUL) prognostics is challenging, especially when failure labels are unavailable and sensor relevance varies by failure mode. In this paper, we propose an unsupervised prognostics framework that jointly identifies latent failure modes and selects informative sensors using only unlabeled training data. The methodology consists of two phases. In the offline phase, we model system failure times using a mixture of Gaussian regressions and apply a novel Expectation-Maximization algorithm to cluster degradation trajectories and select mode-specific sensors. In the online phase, we extract low-dimensional features from the selected sensors to diagnose the active failure mode and predict RUL using a weighted regression model. We demonstrate the effectiveness of our approach on a simulated dataset that reflects deep-space telemetry characteristics and on a real-world engine degradation dataset, showing improved accuracy and interpretability over existing methods.

Yuqi Su, Xiaolei Fang

Industrial prognostics aims to develop data-driven methods that leverage high-dimensional degradation signals from assets to predict their failure times. The success of these models largely depends on the availability of substantial historical data for training. However, in practice, individual organizations often lack sufficient data to independently train reliable prognostic models, and privacy concerns prevent data sharing between organizations for collaborative model training. To overcome these challenges, this article proposes a statistical learning-based federated model that enables multiple organizations to jointly train a prognostic model while keeping their data local and secure. The proposed approach involves two key stages: federated dimension reduction and federated (log)-location-scale regression. In the first stage, we develop a federated randomized singular value decomposition algorithm for multivariate functional principal component analysis, which efficiently reduces the dimensionality of degradation signals while maintaining data privacy. The second stage proposes a federated parameter estimation algorithm for (log)-location-scale regression, allowing organizations to collaboratively estimate failure time distributions without sharing raw data. The proposed approach addresses the limitations of existing federated prognostic methods by using statistical learning techniques that perform well with smaller datasets and provide comprehensive failure time distributions. The effectiveness and practicality of the proposed model are validated using simulated data and a dataset from the NASA repository.

Yuqi Su, Xiaolei Fang

Industrial prognostics focuses on utilizing degradation signals to forecast and continually update the residual useful life of complex engineering systems. However, existing prognostic models for systems with multiple failure modes face several challenges in real-world applications, including overlapping degradation signals from multiple components, the presence of unlabeled historical data, and the similarity of signals across different failure modes. To tackle these issues, this research introduces two prognostic models that integrate the mixture (log)-location-scale distribution with deep learning. This integration facilitates the modeling of overlapping degradation signals, eliminates the need for explicit failure mode identification, and utilizes deep learning to capture complex nonlinear relationships between degradation signals and residual useful lifetimes. Numerical studies validate the superior performance of these proposed models compared to existing methods.

Jiewen Sheng, Xiaolei Fang

This article introduces differentially private log-location-scale (DP-LLS) regression models, which incorporate differential privacy into LLS regression through the functional mechanism. The proposed models are established by injecting noise into the log-likelihood function of LLS regression for perturbed parameter estimation. We will derive the sensitivities utilized to determine the magnitude of the injected noise and prove that the proposed DP-LLS models satisfy $ε$-differential privacy. In addition, we will conduct simulations and case studies to evaluate the performance of the proposed models. The findings suggest that predictor dimension, training sample size, and privacy budget are three key factors impacting the performance of the proposed DP-LLS regression models. Moreover, the results indicate that a sufficiently large training dataset is needed to simultaneously ensure decent performance of the proposed models and achieve a satisfactory level of privacy protection.