Nonuniform State Space Reconstruction for Multivariate Chaotic Time Series

Weak Monotonicity With Trend Analysis for Unsupervised Feature Evaluation

Performance in an engineering system tends to degrade over time due to a variety of wearing or ageing processes. In supervisory controlled processes there are typically many signals being monitored that may help to characterize performance degradation. It is preferred to select the least amount of information to obtain high quality of predictive analysis from a large amount of collected data, in which labeling the data is not always feasible. To this end a novel unsupervised feature selection method, robust with respect to significant measurement disturbances, is proposed using the notion of "weak monotonicity" (WM). The robustness of this notion makes it very attractive to identify the common trend in the presence of measurement noises and population variation from the collected data. Based on WM, a novel suitability indicator is proposed to evaluate the performance of each feature. This new indicator is then used to select the key features that contribute to the WM of a family of processes when noises and variations among processes exist. In order to evaluate the performance of the proposed framework of the WM and suitability, a comparative study with other nine state-of-the-arts unsupervised feature evaluation and selection methods is carried out on well-known benchmark datasets. The results show a promising performance of the proposed framework on unsupervised feature evaluation in the presence of measurement noises and population variations.

A remaining useful life prediction method based on PSR-former

The non-linear and non-stationary vibration data generated by rotating machines can be used to analyze various fault conditions for predicting the remaining useful life(RUL). It offers great help to make prognostic and health management(PHM) develop. However, the complexity of the mechanical working environment makes the vibration data collected easily affected, so it is hard to form an appropriate health index(HI) to predict the RUL. In this paper, a PSR-former model is proposed including a Phase space reconstruction(PSR) layer and a Transformer layer. The PSR layer is utilized as an embedding to deepen the understanding of vibration data after feature fusion. In the Transformer layer, an attention mechanism is adopted to give different assignments, and a layer-hopping connection is used to accelerate the convergence and make the structure more stable. The effectiveness of the proposed method is validated through the Intelligent Maintenance Systems (IMS) bearing dataset. Through analysis, the prediction accuracy is judged by the parameter RMSE which is 1.0311. Some state-of-art methods such as LSTM, GRU, and CNN were also analyzed on the same dataset to compare. The result indicates that the proposed method can effectively establish a precise model for RUL predictions.

Learning Both Dynamic-Shared and Dynamic-Specific Patterns for Chaotic Time-Series Prediction

In the real world, multivariate time series from the dynamical system are correlated with deterministic relationships. Analyzing them dividedly instead of utilizing the shared-pattern of the dynamical system is time consuming and cumbersome. Multitask learning (MTL) is an effective inductive bias method to utilize latent shared features and discover the structural relationships from related tasks. Base on this concept, we propose a novel MTL model for multivariate chaotic time-series prediction, which could learn both dynamic-shared and dynamic-specific patterns. We implement the dynamic analysis of multiple time series through a special network structure design. The model could disentangle the complex relationships among multivariate chaotic time series and derive the common evolutionary trend of the multivariate chaotic dynamical system by inductive bias. We also develop an efficient Crank-Nicolson-like curvilinear update algorithm based on the alternating direction method of multipliers (ADMM) for the nonconvex nonsmooth Stiefel optimization problem. Simulation results and analysis demonstrate the effectiveness on dynamic-shared pattern discovery and prediction performance.

Neuromuscular Control Modelling of Human Perturbed Posture Through Piecewise Affine Autoregressive With Exogenous Input Models

In this study, the neuromuscular control modeling of the perturbed human upright stance is assessed through piecewise affine autoregressive with exogenous input (PWARX) models. Ten healthy subjects underwent an experimental protocol where visual deprivation and cognitive load are applied to evaluate whether PWARX can be used for modeling the role of the central nervous system (CNS) in balance maintenance in different conditions. Balance maintenance is modeled as a single-link inverted pendulum; and kinematic, dynamic, and electromyography (EMG) data are used to fit the PWARX models of the CNS activity. Models are trained on 70% and tested on the 30% of unseen data belonging to the remaining dataset. The models are able to capture which factors the CNS is subjected to, showing a fitting accuracy higher than 90% for each experimental condition. The models present a switch between two different control dynamics, coherent with the physiological response to a sudden balance perturbation and mirrored by the data-driven lag selection for data time series. The outcomes of this study indicate that hybrid postural control policies, yet investigated for unperturbed stance, could be an appropriate motor control paradigm when balance maintenance undergoes external disruption.

Refined nonuniform embedding for coupling detection in multivariate time series

State-space reconstruction is essential to analyze the dynamics and internal interactions of complex systems. However, it is difficult to estimate high-dimensional conditional mutual information and select the optimal time delays in most existing nonuniform state-space reconstruction methods. Therefore, we propose a nonuniform embedding method framed in information theory for state-space reconstruction. We use a low-dimensional approximation of conditional mutual information criterion for time delay selection, which is effectively solved by the particle swarm optimization algorithm. The obtained embedded vector has relatively strong independence and low redundancy, which better characterizes multivariable complex systems and detects coupling within complex systems. In addition, the proposed nonuniform embedding method exhibits good performance in coupling detection of linear stochastic, nonlinear stochastic, chaotic systems. In the actual application, the importance of small airports that cause delay propagation has been demonstrated by constructing the delay propagation network.

Modeling a recurrent, hidden dynamical system using energy minimization and kernel density estimates

In this paper we develop a kernel density estimation (KDE) approach to modeling and forecasting recurrent trajectories on a suitable manifold. For the purposes of this paper, a trajectory is a sequence of coordinates in a phase space defined by an underlying hidden dynamical system. Our work is inspired by earlier work on the use of KDE to detect shipping anomalies using high-density, high-quality automated information system data as well as our own earlier work in trajectory modeling. We focus specifically on the sparse, noisy trajectory reconstruction problem in which the data are (i) sparsely sampled and (ii) subject to an imperfect observer that introduces noise. Under certain regularity assumptions, we show that the constructed estimator minimizes a specific energy function defined over the trajectory as the number of samples obtained grows.

Prediction of Air Pollution Concentration Based on mRMR and Echo State Network

Air pollution has become a global environmental problem, because it has a great adverse impact on human health and the climate. One way to explore this problem is to monitor and predict air quality index in an economical way. Accurate monitoring and prediction of air quality index (AQI), e.g., PM2.5 concentration, is a challenging task. In order to accurately predict the PM2.5 time series, we propose a supplementary leaky integrator echo state network (SLI-ESN) in this paper. It adds the historical state term of the historical moment to the calculation of leaky integrator reservoir, which improves the influence of historical evolution state on the current state. Considering the redundancy and correlation between multivariable time series, minimum redundancy maximum relevance (mRMR) feature selection method is introduced to reduce redundant and irrelevant information, and increase computation speed. A variety of evaluation indicators are used to assess the overall performance of the proposed method. The effectiveness of the proposed model is verified by the experiment of Beijing PM2.5 time series prediction. The comparison of learning time also shows the efficiency of the algorithm.