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Unbalanced data with very few samples for special abnormal conditions frequently occur in actual production processes, which can make accurate monitoring of the process state challenging. This article proposes a multimodal few-shot learning method (MMFSL) within a fault diagnosis framework for unbalanced data modeling of industrial bearings. MMFSL can handle two modes of data and therefore contains two data generation channels. The first channel deals with time-series data and the second deals with images. The two modes of generated data are then evaluated using the MMFSL evaluation modules, image evaluation index (IEI), and time-series evaluation index (TEI), to guarantee the quality of the generated data. In addition, the time-series data are analyzed in the time-frequency domain to ensure the consistency of the frequency distribution. Original unbalanced and insufficient data samples are expanded so that the fault diagnosis model can be trained adequately. Through experiments using data from Case Western Reserve University (CWRU) and Pardborn University (PU), generated data by using the MMFSL model can increase fault detection accuracy from 80.9% to 97.5%. At the same time, false alarm rate can be reduced significantly from 4.6% to 0.1%. Moreover, fault classification model accuracy can reach 98.1% compared to 95.4% for the original time-series dataset, and 99.3% compared with 96.5% for the image data extension. Various visualizations of comparison results are also provided to show the reliability of the MMFSL framework.

• Control performance assessment (CPA) benchmark is built upon rational entropy (RE). • Dynamic data reconciliation is used to enhance the minimum RE control performance. • Probability function of non-Gaussian noise is estimated by Gaussian mixture model. • RE-CPA is more suitable for industrial processes with non-Gaussian noise. Control performance of the industrial process is inevitably influenced by the measurement noises and non-Gaussian external disturbances. This influence has not been fully considered in the traditional variance-based controller design. To reduce the influence, a novel scheme that can enhance the control performance is developed by integrating dynamic data reconciliation (DDR) into minimum rational entropy control (MREC) in this paper. Firstly, the influence of measurement noise is fully considered, and a novel DDR method is proposed to deal with the minimum entropy control (MEC) process such that the influence of measurement noise can be reduced, and the control performance will be improved. Then, based on the DDR-MREC performance index, a benchmark for evaluating the control performance of non-Gaussian systems is established. Finally, the proposed control performance assessment (CPA) method is applied to the wind energy conversion system and compared with the CPA method based on DDR-minimum variance control. The experimental results have demonstrated that the proposed new method is more effective than existing works. [ABSTRACT FROM AUTHOR]

In this paper, a two-layer model predictive control (MPC) hierarchical architecture of dynamic economic optimization (DEO) and reference tracking (RT) is proposed for non-Gaussian stochastic process in the framework of statistical information. In the upper layer, with state feedback and dynamic economic information, the economically optimal trajectories are estimated by entropy and mean based dynamic economic MPC, which uses the nonlinear dynamic model instead of the steady-state model. These estimated optimal trajectories from the upper layer are then employed as the reference trajectories of the lower layer control system. A survival information potential based MPC algorithm is used to maintain the controlled variables at their reference trajectories in the nonlinear system with non-Gaussian disturbances. The stability condition of closed-loop system dynamics is proved using the statistical linearization method. Finally, a numerical example and a continuous stirred-tank reactor are used to illustrate the merits of the proposed economic optimization and control method. [ABSTRACT FROM AUTHOR]

Effective feature extraction provides multifarious benefits such as improved accuracy and reliability for soft sensor. Based on deep belief network (DBN) and support vector machine (SVM), a novel soft sensor approach is proposed in this paper to solve the problem of measurement of fill level inside the ball mill. This measurement methodology of ball mill fill level using the DBN based soft sensor can be structured in two consecutive stages: first, DBN is employed to construct a deep architecture to obtain the high level representation of the vibration frequency spectrum of the ball mill bearing; second, SVM is then trained to model the relationship between the learned deep features and fill level. The effectiveness of the proposed approach can be clearly seen by comparing with other methods based on traditional feature extraction algorithms and machine learning algorithms. Experimental results prove that the model based on DBN and SVM performs effectively, especially in the condition with a few labelled samples.

Minimum entropy control has been proven to be an effective method in control of non-Gaussian stochastic systems. In this case, the entropy is proposed as a generalization of the variance measure to characterize the randomness of the process. Minimum entropy corresponds to small uncertainty (or derivation), but it cannot guarantee the tracking error approaching to zero. Therefore, mean square error also should be added in the criterion. In this paper, by using a simple example, the method of generating a representative approximation of the Pareto optimal control set is investigated in both analytical and numerical ways. And simulation results show the feasibility of the proposed double-objective optimal control method.

In this technical note, a new stochastic control algorithm is presented for nonlinear and non-Gaussian continuous-time systems. Based on the recently developed generalized density evolution equation, which is more tractable than the classical Liouville equation, the relationship is established among the probability density function (PDF) of tracking error, control input and disturbances. An improved performance index is then constructed for this stochastic control strategy, which includes quadratic information potential of the tracking error, mean value of squared tracking error and constraints on the control input energy. By minimizing the performance index, a recursive optimal control algorithm is obtained using the gradient descent method. Moreover, the statistical linearization technique is adopted to formulate the boundedness condition of the closed-loop system. An illustrative example is given to demonstrate the validity and efficiency of the proposed stochastic optimal control methodology. [ABSTRACT FROM PUBLISHER]

This paper considers the problem of designing a non-fragile guaranteed cost controller for a class of non-linear uncertain systems with time-varying delays and controller gain perturbations. Based on the Lyapunov stability theory and the linear matrix inequality (LMI) approach, a sufficient condition to get a guaranteed cost controller is given, which results in the closed-loop system being asymptotically stable and the system's cost function value being less than a determinate upper bound. Finally, a numerical example and simulation diagram are provided to illustrate the design developed in this paper.

In this paper, the problem of delay-dependent robust stability for uncertain stochastic neural networks with time-varying delay is considered. Based on Lyapunov stability theory combined with linear matrix inequalities (LMI) techniques, some new delay-dependent stability criteria in terms of LMI are derived by introducing some free weighing matrices and using Leibniz-Newton formula which can be selected properly to lead to less conservative results. Finally, two examples are given. One is given to illustrate, the other is an extended model for prevenient systems.

In this paper, a new model-free control strategy for general nonlinear and non-Gaussian multivariable stochastic systems has been proposed. The strategy applies minimum survival information potential control (MSIPC) scheme to decrease the closed-loop randomness of the output in the information theory framework. Compared with traditional entropy measures, survival information potential (SIP) has many advantages, such as validity in a wide range of distributions, robustness, the simplicity in computation, and so on. In order to calculate the SIP, the empirical SIP formulation under scalar data case is derived directly based on ordered error sample data. By minimizing the performance index mainly consists of SIP, a new model-free control algorithm is obtained for the considered multivariable nonlinear and non-Gaussian stochastic systems. The analysis on the proposed MSIPC convergence is made and a numerical example is provided to show the effectiveness of the obtained control algorithm, where encouraging results have been obtained. [ABSTRACT FROM AUTHOR]