Maximum Entropy Criterion Research Articles

A hybrid optimization method based on extreme learning machine aided factor graph for INS/GPS information fusion during GPS outages

To enhance the navigation capability of the microelectromechanical system (MEMS)-based inertial navigation system (INS)/global positioning system (GPS) integrated system under satellite denied, a hybrid optimization navigation method using minimal learning parameter (MLP) to improve extreme learning machine (ELM) aided adaptive factor graph (AFG) is proposed. The proposed method mainly contains two innovative optimizations: (1) Fully considering the key parameters of each sensor in the INS/GPS integrated navigation system, the factor graph technology is introduced to develop an information fusion model for the system. Based on the maximum correlation entropy criterion and adaptive technology, the existing factor graph method for information fusion is optimized to solve the problem that the abnormal output of each sensor in the INS/GPS integrated system caused by complex environments affects the accuracy of information fusion, thus enhancing the robustness and navigation performance of the INS/GPS integrated system; (2) Moreover, ELM is optimized by MLP to predict the velocity and position observation information of the INS/GPS integrated system and tackle the performance deterioration of the system during GPS outages. The structural parameters of ELM are optimized with the MLP method, aiming to abate the computational burden of the traditional neural network (NN) to avoid “dimension explosion”, as well as enhance the generalization ability and robustness of the network to make it learn from the uncertainty of the system smoothly and quickly. Relevant ground vehicle experiments are designed to evaluate the proposed method. The experimental results demonstrate that the proposed strategy has superior performance and is more feasible for real-time implementation than other comparison approaches.

A maximum entropy-driven support vector classification model for seismic collapse fragility curves estimation of reinforced concrete frame structures

A novel method called maximum entropy-driven support vector classification (MED-SVC) for estimating the seismic collapse fragility curves of reinforced concrete (RC) frames is proposed in this paper. In comparison to kernel-based learning (KBL) methods, a subset selection process based on the maximum Renyi entropy criterion is embedded into the proposed MED-SVC, which can actively select an informative small-scale subset from a large-scale training dataset. The selected subset can accurately reflect the data distribution of the large-scale training dataset, which can be further used to explicitly establish a high-dimensional feature variable. Due to this, the computational complexity of training the proposed MED-SVC model only depends on the dimension of the feature variable, which can effectively solve the problem related to the low efficacy of training the KBL model in the context of a large-scale training dataset. Meanwhile, the proposed MED-SVC model can also reduce the negative effect of randomness in the subset selection process on predictive performance. The robustness, accuracy, and efficiency of the proposed MED-SVC model are thoroughly validated by comparison with random sampling driven SVC (RSD-SVC), KBL methods, random forest, neural network, and naive bayes based on 33,000 damage data of RC frames under earthquakes. Then, the proposed MED-SVC model is applied to estimate the seismic collapse fragility curve of an RC frame structure outside the aforementioned dataset. The results show that the proposed MED-SVC model can generate seismic collapse fragility curves that agree well with those produced by the finite element method (FEM) and performs more robustly than RSD-SVC.

Cauchy kernel minimum error entropy centralized fusion filter

With the help of Information Theory Learning (ITL) theory, a kind of increasingly popular non-Gaussian filtering method has been designed in the sense of the maximum correntropy (MC) criterion or minimum error entropy (MEE) criterion. In MC or MEE criterion, Gaussian kernel function is usually chosen as the kernel function. Compared to the Gaussian kernel function, the Cauchy kernel function has a wider range of action and is insensitive to the kernel parameters. In this paper, a new Cauchy kernel MEE criterion is defined. In the sense of the new defined criterion, two kinds of non-Gaussian centralized fusion filtering algorithms are proposed with the help of fixed-point theory, which are Cauchy kernel minimum error entropy parallel centralized fusion filter and Cauchy kernel minimum error entropy sequential centralized fusion filter. The propagation equation is used to calculate the prior estimates of the state and covariance, and then the fixed-point iteration is used to calculate the posterior estimates of the state and covariance. The convergence of the iteration process included in the two proposed methods is analyzed by using Banach fixed-point theorem. The final two experimental simulations verify the superior performance of the two proposed fusion filtering algorithms.

Quantitative heterogeneous source apportionment of toxic metals through a hybrid method in spatial random fields

Toxic metals in soils pose hazards to food security and human health. Accurate source apportionment provides foundation for pollution prevention. In this study, a novel hybrid method that combines positive matrix factorization, Bayesian maximum entropy and integrative predictability criterion is proposed to provide a new perspective for exploring the heterogeneity of pollution sources in spatial random fields. The results suggest that Cd, As and Cu are the predominant pollutants, with exceedance rates of 27%, 12% and 11%, respectively. The new method demonstrates superiority in predicting toxic metals when combined major and all sources as auxiliary information., with the improvements of 44% and 46%, respectively, Although the major sources identified with the hybrid method are the primary contributors to the accumulation of toxic metals (e.g. coal combustion for Hg, traffic emission for Pb and Zn, industrial activities for As, agricultural activities for Cd and Cu and natural sources for Cr and Ni), the impact of nonmajor sources on toxic metal sin specific regions should not be ignored (e.g. industrial activities on Ni, Pb and Zn in the north and natural sources on Cd, Cu, As, Pb and Zn in the south). For better pollution control, specific local sources should be considered.

Maximum Correntropy Square-Root Cubature Kalman Filter with State Estimation for Distributed Drive Electric Vehicles

For nonlinear systems, both the cubature Kalman filter (CKF) and square-root cubature Kalman filter (SCKF) can get good estimation performance under Gaussian noise. However, the actual driving environment noise mostly has non-Gaussian properties, leading to a significant reduction in robustness and accuracy for distributed vehicle state estimation. To address such problems, this paper uses the square-root cubature Kalman filter with the maximum correlation entropy criterion (MCSRCKF), establishing a seven degrees of freedom (7-DOF) nonlinear distributed vehicle dynamics model for accurately estimating longitudinal vehicle speed, lateral vehicle speed, yaw rate, and wheel rotation angular velocity using low-cost sensor signals. The co-simulation verification is verified by the CarSim/Simulink platform under double-lane change and serpentine conditions. Experimental results show that the MCSRCKF has high accuracy and enhanced robustness for distributed drive vehicle state estimation problems in real non-Gaussian noise environments.

State-of-charge estimation of lithium-ion batteries based on MCC-AEKF in non-Gaussian noise environment

The extended Kalman filter (EKF) has low estimation accuracy for lithium-ion battery SOC under non-Gaussian noise interference. To solve this problem, an adaptive EKF based on maximum correlation-entropy criterion (MCC-AEKF) was proposed. In this algorithm, the maximum correlation entropy criterion is used to obtain accurate estimation results by replacing the overall solution with the local optimal solution. Meanwhile, the adaptive covariance matrix is established to update the process noise variance to reduce the SOC estimation error. MCC-AEKF were used to estimate the SOC based on two kinds of battery data. The experiments show that, under non-Gaussian noise interference and at operating temperature of 25 °C, compared with EKF and MCC-EKF, the estimation accuracy of MCC-AEKF improved by 80.3% and 24.2% separately for battery 1. For battery 2, its estimation accuracy improved by 72.6% and 22.0% separately, and are also the highest at 10 °C and 40 °C. Given wrong initial SOC values, MCC-AEKF can converges to real value within 30s. All results present the good accuracy and robustness of the proposed method under different cases.

Multi-index joint node selection protocol in UAV ad hoc network

In the application scenario of a UAV ad hoc network, aiming at the problems of low packet forwarding success rate and premature death of some nodes in greedy perimeter stateless routing (GPSR) protocol, a multi-index joint node selection-GPSR protocol (MT-GPSR) is proposed. Based on greedy forwarding, MT-GPSR protocol comprehensively considers the link holding time of adjacent nodes, the residual energy of adjacent nodes, and the node degree to jointly select the next hop node, and proposes an AHP maximum entropy criterion weighting algorithm, which reasonably weights the node index value, adds the weighted index values to obtain the selection priority value, and selects the neighbor node whose priority value is the best under the weighting condition as the next hop node for data forwarding, so as to improve the efficiency of data forwarding. At the same time, the network life is prolonged. The simulation results show that compared with the GPSR algorithm and GPSR-NMP algorithm, this algorithm ensures stable communication between UAVs, improves the network communication quality, and improves the network lifetime.

Joint Optimization of Jamming Link and Power Control in Communication Countermeasures: A Multiagent Deep Reinforcement Learning Approach

Due to the nonconvexity feature of optimal controlling such as jamming link selection and jamming power allocation issues, obtaining the optimal resource allocation strategy in communication countermeasures scenarios is challenging. Thus, we propose a novel decentralized jamming resource allocation algorithm based on multiagent deep reinforcement learning (MADRL) to improve the efficiency of jamming resource allocation in battlefield communication countermeasures. We first model the communication jamming resource allocation problem as a fully cooperative multiagent task, considering the cooperative interrelationship of jamming equipment (JE). Then, to alleviate the nonstationarity feature and high decision dimensions in the multiagent system, we introduce a centralized training with decentralized execution framework (CTDE), which means all JEs are trained with global information and rely on their local observations only while making decisions. Each JE obtains a decentralized policy after the training process. Subsequently, we develop the multiagent soft actor-critic (MASAC) algorithm to enhance the exploration capability of agents and accelerate the learning of cooperative policies among agents by leveraging the maximum policy entropy criterion. Finally, the simulation results are presented to demonstrate that the proposed MASAC algorithm outperforms the existing centralized allocation benchmark algorithms.

A Novel UWB Positioning Method Based on a Maximum-Correntropy Unscented Kalman Filter

Aiming at the problem of measurement-information abnormal-error and nonlinear filtering in UWB navigation and positioning, an ultra wideband position algorithm based on a maximum cross-correlation entropy unscented Kalman filter is proposed. The algorithm first obtains the predictive state estimate and the covariance matrix through traceless transformation. Then, it reconstructs observation information using the nonlinear regression method based on the maximum cross-correlation entropy criterion, which enhances the robustness of the unscented Kalman filter algorithm for heavy-tailed noise. The simulation and actual test results show that this algorithm has better positioning accuracy and stability than the traditional filter algorithm in a non Gaussian noise environment. This algorithm effectively solves the problem that UWB indoor location is easily affected by indoor environments, resulting in fixed deviation for that location.

Optimal Inspection Scheduling Model for Monitoring Railway Track Grids

The optimization of railway track inspection schedules is of great significance for the monitoring of railway track conditions and reasonable organization of track maintenance tasks. Here, an optimal inspection scheduling model for monitoring railway tracks is proposed. Railway track inspection activities are divided into equal‐length units in the time and spatial location dimensions. The various constraints and objectives on the time and location of different track inspection activities are defined in detail regarding subdivisions of individual management units. The objectives of the model development are to achieve a more optimized equilibrium and robustness of the track inspection schedule. Based on the maximum entropy criterion, entropy is used to measure the distribution equilibrium of the inspection schedule in the time dimension. The proposed model is verified using actual data from the Lanxin railway.

Spatial-Temporal Minimum Error Random Interaction Networks for Distributed Estimation

In this letter, we study the problem of adaptive parameter estimation for distributed wireless sensor networks (WSNs), where the non-Gaussian impulsive noises in the communication links are considered. In such cases, if the traditional distributed collaborative strategy is still adopted, the estimation performance of the network will decline significantly. Aiming at this problem, we propose a new spatial-temporal minimum error random interaction strategy for the distributed estimation in the presence of impulsive link noises. Furthermore, the maximum correlation entropy criterion and the stochastic gradient descent method are used to update the combination factor so that the network has dynamic and real-time adaptability to the link noises. The proposed algorithm is also compared with the classic DLMS algorithm and a state-of-the-art algorithm designed for the impulsive link noises. Simulation results show that the proposed algorithm can not only reduce the network traffic effectively, but also be robust to the non-Gaussian link impulsive noises while maintaining its advantage over the non-cooperative algorithm and achieving the optimal estimation performance.

An Improved SLIC Algorithm for Segmentation of Microscopic Cell Images

Accurate nuclear and cell segmentations plays an important role in improving the accuracy of target recognition in microscopic cell images. As the traditional SLIC (Simple Linear Iterative Clustering) algorithm cannot segment microscopic cell images well, an improved SLIC superpixel segmentation algorithm based on gray scale enhancement and regional equalization is proposed. According to the characteristics of microscopic cell images, selecting different transformation parameters with the conditional iterative algorithm, the best classification multi-threshold method based on maximum entropy criterion is used to nonlinearly enhance the gray scale of the original images, while enhancing the contrast of the image, it also greatly improves the balance of each classification region. Then the gray distance and spatial distance are calculated respectively in the circle neighborhood of the cluster center to realize the superpixel segmentation of the image. Finally, the improved SLIC algorithm and the comparison algorithm are tested and evaluated. The experimental results show that our improved SLIC algorithm model has higher segmentation accuracy and is more suitable for cell segmentation in microscopic cell images than original SLIC algorithm.

A microscopic ancient river channel identification method based on maximum entropy principle and Wigner-Ville Distribution and its application

In view of the problem of fine characterization of narrow and thin channels, the maximum entropy criterion is used to enhance the focusing characteristics of Wigner-Ville Distribution. On the basis of effectively improving the time-frequency resolution of seismic signal, a new method of microscopic ancient river channel identification is established. Based on the principle of the equivalence between the maximum entropy power spectrum and the AR model power spectrum, the prediction error and the autoregression coefficient of AR model are obtained using the Burg algorithm and Levinson-Durbin recurrence rule. Under the condition of the first derivative of autocorrelation function being 0, the Wigner-Ville Distribution of seismic signal is calculated, and the Wigner-Ville Distribution time-frequency power spectrum (MEWVD) is obtained under the maximum entropy criterion of the microscopic ancient river channel. Through analysis of emulational seismic signal and forward numerical simulation signal of narrow thin model, it is found that MEWVD can effectively avoid the interference of cross term of Wigner-Ville Distribution, and obtain more accurate spectral characteristics than STFT and CWT signal analysis methods. It is also proved that the narrow and thin river channels of different scales can be identified effectively by MEWVD of different frequencies. The method is applied to the third member of Jurassic Shaximiao Formation (J2s33-2) gas reservoir of the Zhongjiang gas field in Sichuan Basin. The spatial information of width and direction of narrow and thin river channels with width less than 500 m and sandstone thickness less than 35 m is accurately identified, providing bases for well deployment and horizontal well fracturing section selection.

Modeling players with random “data access”

I present an approach to static equilibrium modeling with non-rational expectations, which is based on enriching players' typology. A player is characterized by his “data access”, consisting of: (i) “news access”, which corresponds to a conventional signal in the Harsanyi model, and (ii) “archival access”, a novel component representing the player's piecemeal knowledge of steady-state correlations. Drawing on prior literature on correlation neglect and coarse reasoning, I assume the player extrapolates a well-specified probabilistic belief from his “archival data” according to the maximum-entropy criterion. I show with a series of examples how this formalism extends our ability to represent and analyze strategic interactions without rational expectations.

Allocation method of communication interference resource based on deep reinforcement learning of maximum policy entropy

In order to solve the optimization of the interference resource allocation in communication network countermeasures, an interference resource allocation method based on the maximum policy entropy deep reinforcement learning (MPEDRL) was proposed. The method introduced the idea of deep reinforcement learning into the communication countermeasures resource allocation, it could enhance the exploration of the policy and accelerate the convergence to the global optimum with adding the maximum policy entropy criterion and adaptively adjusting the entropy coefficient. The method modeled interference resource allocation as Markov decision process, then established the interference strategy network to output allocation scheme, constructing the interference effect evaluation network of the clipped twin structure for efficiency evaluation, and trained the policy network and the evaluation network with the goal of maximizing the strategy entropy and the cumulative interference efficacy, then decided the optimal interference resource allocation scheme. The simulation results show that the algorithm can effectively solve the resource allocation problem in communication network confrontation, comparing with the existing deep reinforcement learning methods, it has faster learning speed and less fluctuation in the training process, and achieved 15% higher jamming efficacy than DDPG-based method.

Univariate kernel sums correntropy for adaptive filtering

In this paper, we focus on a special form of univariate kernel and, by specifying the relationship between its parameters, make its first derivative close to a neat form. By using this kind of univariate kernel sums instead of Gaussian kernel function, we put forward the sum of univariate kernels maximum correntropy criterion (SKMCC) on the basis of maximum entropy criterion (MCC) and apply it to adaptive filtering. We study the characteristics of the performance surface of the new algorithm and confirm the theoretical results in the simulation. Its superior performance is proved by comparing with other latest adaptive algorithms.

Stochastic model updating of rotor support parameters using Bayesian approach

Uncertainties due to assembling, installation, and operational conditions are extensively involved in rotating systems' parameters. Stochastic characteristics of these parameters may seriously affect rotating systems' vibrational characteristics, such as their critical speeds and vibration amplitudes. These effects make the variability of parameters in the modeling of rotary machines inevitable. In rotating machinery, material properties and geometric parameters of the rotor, bearing characteristics and supports stiffness determine the system's dynamic response. Stochastic model updating methods consider model response variability and allocate them to the model parameters; however, they are not commonly employed in rotor dynamics, and deterministic approaches are still prevalent in this field. Due to the cost and efforts needed to set up experiments and obtain outcomes that reflect the machine's actual characteristics, stochastic updating practices of industrial rotating systems are rarely reported in the literature. This paper adopts an appropriate parameter selection procedure and suitable sampling strategy for stochastic model updating to investigate variability in the dynamic behavior of a complex turbo compressor rotor-bearing-support system, leading to successful parameter identification results. The compressor rotor is mounted on hydrodynamic journal bearings with speed-dependent stiffness and damping. Due to the rotating system complex model, a variance-based global sensitivity method is employed for parameter selection to eliminate non-influential parameters in the model updating and to alleviate updating complexity and computational burden. The Bayesian approach in the stochastic model updating is applied to estimate parameter uncertainty in the rotor with speed-dependent characteristics. Advanced Markov chain Monte Carlo sampling method using delayed rejection adaptive Metropolis algorithm is employed in the stochastic model updating. The updating procedure obtains marginal posterior probabilities of parameters, and uncertain parameter distributions are evaluated using the maximum entropy criterion.

Fragmentary label distribution learning via graph regularized maximum entropy criteria

• The GRME was proposed to solve the incomplete label distribution learning problem. • We explore the label correlations based on graph regularization, together with a classifier for categorization. • Compared with most of traditional transductive methods, our method is inductive. • The experimental results on real datasets show excellent performance of GRME in comparison with the latest methods. Label distribution learning (LDL) is a new learning paradigm, which assumes that the labels are related to each instance to some degree. It has been successfully applied in many scenarios due to its ability to tackle label ambiguity. Nevertheless, LDL has also enlarged the labeling costs and difficulties. In many real application areas, such as pattern recognition and image classification, the labeling information is often incomplete, i.e., we cannot determine each label degree to each instance. The performance of traditional LDL algorithm will degrade since they often require complete supervised information. In this paper, we have proposed fragmentary LDL algorithm via Graph Regularized Maximum Entropy criteria (GRME) to solve this problem. It explores the relationship among the labels to recover missing label factors, together with a classifier for categorization. The integration of these two components facilitate the performance enhancement of GRME. Besides, compared with most of traditional methods which are transductive, another advantage of our method is the inductive nature to predict for new coming data directly. We have also extended ADMM algorithm to fit this particular nonconvex problem. The effectiveness of our method is verified by the experimental results on real-world data sets with different settings.

GLAGC: Adaptive Dual-Gamma Function for Image Illumination Perception and Correction in the Wavelet Domain.

Low-contrast or uneven illumination in real-world images will cause a loss of details and increase the difficulty of pattern recognition. An automatic image illumination perception and adaptive correction algorithm, termed as GLAGC, is proposed in this paper. Based on Retinex theory, the illumination of an image is extracted through the discrete wavelet transform. Two features that characterize the image illuminance are creatively designed. The first feature is the spatial luminance distribution feature, which is applied to the adaptive gamma correction of local uneven lighting. The other feature is the global statistical luminance feature. Through a training set containing images with various illuminance conditions, the relationship between the image exposure level and the feature is estimated under the maximum entropy criterion. It is used to perform adaptive gamma correction on global low illumination. Moreover, smoothness preservation is performed in the high-frequency subband to preserve edge smoothness. To eliminate low-illumination noise after wavelet reconstruction, the adaptive stabilization factor is derived. Experimental results demonstrate the effectiveness of the proposed algorithm. By comparison, the proposed method yields comparable or better results than the state-of-art methods in terms of efficiency and quality.

Robust Ellipse Fitting With Laplacian Kernel Based Maximum Correntropy Criterion.

The performance of ellipse fitting may significantly degrade in the presence of outliers, which can be caused by occlusion of the object, mirror reflection or other objects in the process of edge detection. In this paper, we propose an ellipse fitting method that is robust against the outliers, and thus maintaining stable performance when outliers can be present. We formulate an optimization problem for ellipse fitting based on the maximum entropy criterion (MCC), having the Laplacian as the kernel function from the well-known fact that the l1 -norm error measure is robust to outliers. The optimization problem is highly nonlinear and non-convex, and thus is very difficult to solve. To handle this difficulty, we divide it into two subproblems and solve the two subproblems in an alternate manner through iterations. The first subproblem has a closed-form solution and the second one is cast as a convex second-order cone program (SOCP) that can reach the global solution. By so doing, the alternate iterations always converge to an optimal solution, although it can be local instead of global. Furthermore, we propose a procedure to identify failed fitting of the algorithm caused by local convergence to a wrong solution, and thus, it reduces the probability of fitting failure by restarting the algorithm at a different initialization. The proposed robust ellipse fitting method is next extended to the coupled ellipses fitting problem. Both simulated and real data verify the superior performance of the proposed ellipse fitting method over the existing methods.