Design Method of High-Order Kalman Filter for Strong Nonlinear System Based on Kronecker Product Transform

In this paper, a novel design idea of high-order Kalman filter based on Kronecker product transform is proposed for a class of strong nonlinear stochastic dynamic systems. Firstly, those augmenting systems are modeled with help of the Kronecker product without system noise. Secondly, the augmented system errors are illustratively charactered by Gaussian white noise. Thirdly, at the expanded space a creative high-order Kalman filter is delicately designed, which consists of high-order Taylor expansion, introducing magical intermediate variables, representing linear systems converted from strongly nonlinear systems, designing Kalman filter, etc. The performance of the proposed filter will be much better than one of EKF, because it uses more information than EKF. Finally, its promise is verified through commonly used digital simulation examples.

Study on the Optimal Operation of a Hydropower Plant Group Based on the Stochastic Dynamic Programming with Consideration for Runoff Uncertainty

Hydropower plant operation reorganizes the temporal and spatial distribution of water resources to promote the comprehensive utilization of water resources in the basin. However, a lot of uncertainties were brought to light concerning cascade hydropower plant operation with the introduction of the stochastic process of incoming runoff. Therefore, it is of guiding significance for the practice operation to investigate the stochastic operation of cascade hydropower plants while considering runoff uncertainty. The runoff simulation model was constructed by taking the cascade hydropower plants in the lower reaches of the Lancang River as the research object, and combining their data with the copula joint function and Gibbs method, and a Markov chain was adopted to construct the transfer matrix of runoff between adjacent months. With consideration for the uncertainty of inflow runoff, the stochastic optimal operation model of cascade hydropower plants was constructed and solved by the SDP algorithm. The results showed that 71.12% of the simulated monthly inflow of 5000 groups in the Nuozhadu hydropower plant drop into the reasonable range. Due to the insufficiency of measured runoff, there were too many 0 values in the derived transfer probability, but after the simulated runoff series were introduced, the results significantly improved. Taking the transfer probability matrix of simulated runoff as the input of the stochastic optimal operation model of the cascade hydropower plants, the operation diagram containing the future-period incoming water information was obtained, which could directly provide a reference for the optimal operation of the Nuozhadu hydropower plant. In addition, taking the incoming runoff process in a normal year as the standard, the annual mean power generation based on stochastic dynamic programming was similar to that based on dynamic programming (respectively 305.97 × 108kW⋅h and 306.91 × 108kW⋅h), which proved that the operation diagram constructed in this study was reasonable.

Supported Diagnosis of Attention Deficit and Hyperactivity Disorder from EEG Based on Interpretable Kernels for Hidden Markov Models

As a neurodevelopmental pathology, Attention Deficit Hyperactivity Disorder (ADHD) mainly arises during childhood. Persistent patterns of generalized inattention, impulsivity, or hyperactivity characterize ADHD that may persist into adulthood. The conventional diagnosis relies on clinical observational processes yielding high rates of overdiagnosis due to varying interpretations among specialists or missing information. Although several studies have designed objective behavioral features to overcome such an issue, they lack significance. Despite electroencephalography (EEG) analyses extracting alternative biomarkers using signal processing techniques, the nonlinearity and nonstationarity of EEG signals restrain performance and generalization of hand-crafted features. This work proposes a methodology to support ADHD diagnosis by characterizing EEG signals from hidden Markov models (HMM), classifying subjects based on similarity measures for probability functions, and spatially interpreting the results using graphic embeddings of stochastic dynamic models. The methodology learns a single HMM for EEG signal from each patient, so favoring the inter-subject variability. Then, the Probability Product Kernel, specifically developed for assessing the similarity between HMMs, fed a support vector machine that classifies subjects according to their stochastic dynamics. Lastly, the kernel variant of Principal Component Analysis provided a means to visualize the EEG transitions in a two-dimensional space, evidencing dynamic differences between ADHD and Healthy Control children. From the electrophysiological perspective, we recorded EEG under the Stop Signal Task modified with reward levels, which considers cognitive features of interest as insufficient motivational circuits recruitment. The methodology compares the supported diagnosis in two EEG channel setups (whole channel set and channels of interest in frontocentral area) and four frequency bands (Theta, Alpha, Beta rhythms, and a wideband). Results evidence an accuracy rate of 97.0% in the Beta band and in the channels where previous works found error-related negativity events. Such accuracy rate strongly supports the dual pathway hypothesis and motivational deficit concerning the pathophysiology of ADHD. It also demonstrates the utility of joining inhibitory and motivational paradigms with dynamic EEG analysis into a noninvasive and affordable diagnostic tool for ADHD patients.

Statistical Inference Using GLEaM Model with Spatial Heterogeneity and Correlation between Regions

A better understanding of the various patterns in the coronavirus disease 2019 (COVID-19) spread in different parts of the world is crucial to its prevention and control. Motivated by the celebrated GLEaM model (Balcan et al., 2010 [1]), this paper proposes a stochastic dynamic model to depict the evolution of COVID-19. The model allows spatial and temporal heterogeneity of transmission parameters and involves transportation between regions. Based on the proposed model, this paper also designs a two-step procedure for parameter inference, which utilizes the correlation between regions through a prior distribution that imposes graph Laplacian regularization on transmission parameters. Experiments on simulated data and real-world data in China and Europe indicate that the proposed model achieves higher accuracy in predicting the newly confirmed cases than baseline models.

Investigation of error in evaluation of spectral statistical characteristics of numerical solution of stochastic dynamic system

In this paper, an algorithm for numerical simulations is developed for calculating a discrete dynamic system with a stochastic perturbation and an analysis of the quality of numerical solutions is carried out. For this, an algorithm for the numerical solution of a second-order differential equation with a stochastic right-hand side was developed and this algorithm was implemented as a program. The next step was to carry out a set of computational studies by varying the parameters of numerical integration with the subsequent assessment of their impact on the error and accuracy of simulations. To estimate the spectral density, the Welch periodogram method was used. To check the quality of simulations and assess the accuracy of solutions, it is proposed to compare the results of numerical integration and subsequent digital processing with analytical solutions that are known for the linear problem, given by the equation. As a result of the work, a comparative analysis of the dispersion of displacements relative to the lengths of signals from a different number of blocks was carried out, into which the signal is divided for the Welch method; the confidence interval of the error at different signal lengths and the confidence interval of the error with a different number of blocks at a certain signal length. Comparison of the variance with a different number of blocks showed that with a signal length of 30 s and from 90 s, there is a slight scatter of the variance values within an error of ± 5%.

Identification and Stochastic Optimizing the UAV Motion Control in Turbulent Atmosphere

In a class of diffusion Markov processes, we formulate a problem of identification of nonlinear stochastic dynamic systems with random parameters, multiplicative and additive noises, control functions, and the state vector at a final time moment. For such systems, the identifiability conditions are being studied, and necessary conditions are formulated in terms of the general theory of extreme problems. The developed engineering methods for identification and optimizing nonlinear stochastic systems are presented as well as their application for unmanned aerial vehicles under wind disturbances caused by atmospheric turbulence, namely, for optimizing the autopilot parameters during a rotary maneuver of an unmanned aerial vehicle in translational motion, taking into account the identification of its angular velocities.