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The controlled autoregressive autoregressive moving average (CARARMA) models are of popularity to describe the evolution characteristics of dynamical systems. To overcome the identification obstacle resulting from colored noises, this paper studies the identification of the CARARMA models by forming an intermediate correlated noise model. In order to realize the real-time prediction function of the models, the on-line identification scheme is developed by constructing the dynamical objective functions based on the real-time sampled observations. Firstly, a rolling optimization cost function is built based on the observation at a single sampling instant to catch the modal information at a single time point and a generalized extended stochastic gradient (GESG) algorithm is proposed through the stochastic gradient optimization. Secondly, a rolling window cost function is built in accordance with the dynamical batch observations within data window by extending the proposed GESG algorithm and the multi-innovation generalized extended stochastic gradient algorithm is derived. Thirdly, from the perspective of theoretical analysis, the convergence proof of the proposed algorithm is provided based on the stochastic martingale convergence theory. Finally, the simulation analysis and comparison studies are provided to show the performance of the proposed algorithms.

High-dimensional data monitoring and diagnosis has recently attracted increasing attention among researchers as well as practitioners. However, existing process monitoring methods fail to fully use the information of high-dimensional data streams due to their complex characteristics including the large dimensionality, spatio-temporal correlation structure, and nonstationarity. In this article, we propose a novel process monitoring methodology for high-dimensional data streams including profiles and images that can effectively address foregoing challenges. We introduce spatio-temporal smooth sparse decomposition (ST-SSD), which serves as a dimension reduction and denoising technique by decomposing the original tensor into the functional mean, sparse anomalies, and random noises. ST-SSD is followed by a sequential likelihood ratio test on extracted anomalies for process monitoring. To enable real-time implementation of the proposed methodology, recursive estimation procedures for ST-SSD are developed. ST-SSD also provides useful diagnostics information about the location of change in the functional mean. The proposed methodology is validated through various simulations and real case studies. Supplementary materials for this article are available online.

The Recursive Pseudo Random Pursuit Strategy (RPRPS) is proposed to predict the frequency difference of atomic clocks relative to reference. It further improves the computational efficiency and reduces the time complexity. The core of RPRPS is to replace the refitting of the updated predictor and recalculating of the sum of square residuals of the unupdated predictors in a recursive process. In experiments, it is employed to predict the readings of the cesium clock and hydrogen maser relative to UTC (NIM). Compared with PRPS, the experimental results show that RPRPS reduces running time by about 70% without reducing predictive accuracy. This paper proposes a recursive prediction algorithm suitable for the relative frequency difference readings of atomic clocks. It has the characteristic of low time complexity. The initialisation process of the algorithm is shown in Figure 1, and the recursive update process is shown in Figure 2.

This article studies identification problems of multiple linear regression models, which may be described a class of multi-input multi-output systems (i.e. multivariable systems). Based on the coupling identification concept, a novel coupled-least-squares (C-LS) parameter identification algorithm is introduced for the purpose of avoiding the matrix inversion in the multivariable recursive least-squares (RLS) algorithm for estimating the parameters of the multiple linear regression models. The analysis indicates that the C-LS algorithm does not involve the matrix inversion and requires less computationally efforts than the multivariable RLS algorithm, and that the parameter estimates given by the C-LS algorithm converge to their true values. Simulation results confirm the presented convergence theorems.

Modal parameter estimation is crucial in vibration-based damage detection and deserves increased attention and investigation. Concrete arch dams are prone to damage during severe seismic events, leading to alterations in their structural dynamic characteristics and modal parameters, which exhibit specific time-varying properties. This highlights the significance of investigating the evolution of their modal parameters and ensuring their accurate identification. To effectively accomplish the recursive estimation of modal parameters for arch dams, an adaptive recursive subspace (ARS) method with variable forgetting factors was proposed in this study. In the ARS method, the variable forgetting factors were adaptively updated by assessing the change rate of the spatial Euclidean distance of adjacent modal frequency identification values. A numerical simulation of a concrete arch dam under seismic loading was conducted by using ABAQUS software, in which a concrete damaged plasticity (CDP) model was used to simulate the dam body’s constitutive relation, allowing for the assessment of damage development under seismic loading. Utilizing the dynamic responses obtained from the numerical simulation, the ARS method was implemented for the modal parameter recursive estimation of the arch dam. The identification results revealed a decreasing trend in the frequencies of the four initial modes of the arch dam: from an undamaged state characterized by frequencies of 0.910, 1.166, 1.871, and 2.161 Hz to values of 0.895, 1.134, 1.842, and 2.134 Hz, respectively. Concurrently, increases in the damping ratios of these modes were observed, transitioning from 4.44%, 4.28%, 5.42%, and 5.56% to 4.98%, 4.91%, 6.61%, and 6.85%%, respectively. The correlation of the identification results with damage progression validated the effectiveness of the ARS method. This study’s outcomes have substantial theoretical and practical importance, facilitating the immediate comprehension of the dynamic characteristics and operational states of concrete arch dam structures.

Estimation procedures based on recursive algorithms are interesting and powerful techniques that are able to deal rapidly with very large samples of high dimensional data. The collected data may be contaminated by noise so that robust location indicators, such as the geometric median, may be preferred to the mean. In this context, an estimator of the geometric median based on a fast and efficient averaged nonlinear stochastic gradient algorithm has been developed by [Bernoulli 19 (2013) 18-43]. This work aims at studying more precisely the nonasymptotic behavior of this nonlinear algorithm by giving nonasymptotic confidence balls in general separable Hubert spaces. This new result is based on the derivation of improved L² rates of convergence as well as an exponential inequality for the nearly martingale terms of the recursive nonlinear Robbins-Monro algorithm.

A Bayesian framework is attractive in the context of prediction, but a fast recursive update of the predictive distribution has apparently been out of reach, in part because Monte Carlo methods are generally used to compute the predictive. This article shows that online Bayesian prediction is possible by characterizing the Bayesian predictive update in terms of a bivariate copula, making it unnecessary to pass through the posterior to update the predictive. In standard models, the Bayesian predictive update corresponds to familiar choices of copula but, in nonparametric problems, the appropriate copula may not have a closed-form expression. In such cases, our new perspective suggests a fast recursive approximation to the predictive density, in the spirit of Newton's predictive recursion algorithm, but without requiring evaluation of normalizing constants. Consistency of the new algorithm is shown, and numerical examples demonstrate its quality performance in finite-samples compared to fully Bayesian and kernel methods. Supplementary materials for this article are available online.

High‐precision positioning is critical in modern industrial applications, yet the inherent hysteresis of piezoelectric actuators limits their accuracy and control performance. To address this problem, this paper proposes an adaptive control method combining feedforward and feedback control. Hammerstein structure is applied to characterize a piezoelectric actuator, which consists of a Prandtl‐Ishlinskii model and a second‐order linear model. The pseudo‐inverse of the Prandtl‐Ishlinskii model is applied as a feedforward controller to compensate for the hysteresis characteristics. As to the feedback control, a recursive least square with adaptive forgetting factor is proposed to estimate system parameters. Based on the estimated parameters, an adaptive self‐tuning controller is designed to track the dynamic characteristics and reduce the feedforward compensation error. Finally, the proposed method is validated on a piezoelectric positioning platform. The results show that the feedforward pseudoinverse can compensate the hysteresis nonlinearity and the compensation error is close to 0. Compared to the PID composite control, the mean absolute error and the root mean square error are reduced by more than 12% and 13%, respectively. This paper proposes an adaptive control method combining feedforward and feedback. The pseudo‐inverse of the Prandtl‐Ishlinskii model is applied as a feedforward controller to compensate for the hysteresis characteristics. As to the feedback close loop, a recursive least square with adaptive forgetting factor (RLS‐AFF) method is proposed to estimate system parameters and then a minimum variance adaptive controller is designed to track the dynamic characteristics.

Phasor measurement units (PMUs) are essential tools for monitoring, protection and control of power systems. The optimal PMU placement (OPP) problem refers to the determination of the minimal number of PMUs and their corresponding locations in order to achieve full network observability. This paper introduces a recursive Tabu search (RTS) method to solve the OPP problem. More specifically, the traditional Tabu search (TS) metaheuristic algorithm is executed multiple times, while in the initialisation of each TS the best solution found from all previous executions is used. The proposed RTS is found to be the best among three alternative TS initialisation schemes, in regard to the impact on the success rate of the algorithm. A numerical method is proposed for checking network observability, unlike most existing metaheuristic OPP methods, which are based on topological observability methods. The proposed RTS method is tested on the IEEE 14, 30, 57 and 118-bus test systems, on the New England 39-bus test system and on the 2383-bus power system. The obtained results are compared with other reported PMU placement methods. The simulation results show that the proposed RTS method finds the minimum number of PMUs, unlike earlier methods which may find either the same or even higher number of PMUs.

This article proposes an online solution to address the problem of closed‐loop system identification using multiple recursive least squares estimation protocols. Some control systems cannot be analysed in an open‐loop form for stability reasons or the requirement for online control system operation. So, it is necessary to identify plant dynamics and controller parameters based on input–output data from the feedback structure. The presented method identifies real‐time parameters of plant dynamics and controller parameters by utilising a series of recursive least square estimation algorithms that estimate open‐loop data from noisy input–output data measured from the closed‐loop feedback structure. The proposed method can effectively identify abrupt variations in both the controller parameters and plant dynamics. This capability makes it valuable for deployment as a supervisory component, enabling the detection of any faults that may arise in operating systems. Mathematical formulations and theorems are developed, and two numerical case studies are presented to examine the feasibility and performance of the presented closed‐loop system identification protocol.