The design of neural network models exhibiting rich dynamical behaviors remains a central topic in nonlinear science. In this study, we propose a novel memristive neural network (MNN) comprising only two neurons, yet capable of producing highly intricate hidden multi-butterfly attractors. First, three distinct memristor models are developed using a generalized design approach, with their memristive properties validated through both numerical simulations and analog circuit experiments. These memristors are then integrated into a two-neuron Hopfield neural network: one emulates the coupling synapse between neurons, another represents a self-synapse, and the third models external electromagnetic interference. Remarkably, the proposed system lacks equilibrium points and can generate an arbitrary number of multi-butterfly attractors, including the coexistence of infinitely many hidden attractors. Moreover, both the number and spatial distribution of these attractors can be flexibly controlled by tuning the memristor parameters and initial conditions. To confirm the practicality of these dynamics, we design a corresponding analog circuit, demonstrating through Multisim simulations that the model can be realized using simple hardware components. Finally, to explore its practical value, an image encryption algorithm tailored for the Internet of Medical Things (IoMT) is constructed based on the MNN. Security analysis confirms the algorithm’s robustness, highlighting the proposed model’s significant potential in secure information processing.

Structural decoupling has played an essential role in model-based fault isolation (FI) and estimation in past decades, which facilitates accurate fault localization and reconstruction thanks to the diagonal transfer matrix design. However, traditional methods exhibit limited effectiveness in modeling high-dimensional nonlinearity and big data, and the decoupling idea has not been well-valued in data-driven frameworks. Known for big data and complex feature extraction capabilities, deep learning has recently been used to develop residual generation models. Nevertheless, it lacks decoupling-related diagnostic designs. To this end, this article proposes a transfer learning (TL)-based input–output decoupled network (TDN) for diagnostic purposes, which consists of an input–output decoupled network (IDN) and a pretrained variational autocoder (VAE). In IDN, uncorrelated residual variables are generated by diagonalization and parallel computing operations. During the TL phase, knowledge of normal status is provided according to VAE’s loss and maximum mean discrepancy loss to guide the training of IDN. After training, IDN learns the mapping from faulty to normal, thereby serving as the fault detection (FD) index and the estimated fault signal simultaneously. At last, the effectiveness of the developed TDN is verified by a numerical example, a chemical simulation, and a real-world chemical production dataset.

This paper presents a segmental autoencoder-based fault detection (FD) framework for nonlinear dynamic systems. The basic idea behind the proposed FD scheme is to identify a generalized kernel representation based on the representation knowledge learned from an autoencoder. By using the system data, several cascades, linking nonlinear operators, are employed to obtain a data-based model which describes the nonlinear dynamic behaviors. With the help of the segmental structure of an autoencoder, a residual generator is then constructed. Rigorous mathematical analysis and an application on a continuous stirred tank reactor demonstrate the effectiveness of the proposed FD method.

Unsupervised neural networks (NNs) specialize in mining potential patterns from unlabeled data in a self-organizing manner. Recently, they have also been employed as observers for process monitoring using the generated residual signals. However, few studies have explained the model behavior and analyzed the monitoring performance of unsupervised NNs awing to their multilayer nonlinear structure. The interpretability of NN covers the analysis of its working principle to seek better network design and achieve improved performance. Thus, this paper develops explainable residual generators based on unsupervised NNs, which are applicable to deep autoencoder (DAE) and variational autoencoder (VAE). Through Taylor expansion, the residual deviation caused by the fault signal, a.k.a. the fault-affected term, is proven not to disappear in the presence of a non-zero Hessian matrix. Then, the consistency of achieving the optimal monitoring performance and the training loss of NNs is presented. A new indicator function is established based on the sum martingale, a representative of a weakly dependent stochastic process. Freedman’s inequality is first applied to describe the reliability of the learned thresholds during fault evaluation, which requires a smaller sample size for training. Finally, simulations on the continuous stirred tank reactor verify the effectiveness of the proposed methods.