Minimum Entropy Research Articles

An Assessment of Urban Residential Environment Quality Based on Multi-Source Geospatial Data: A Case Study of Beijing, China

Assessing the urban residential environment quality (REQ) is essential for advancing sustainable urban development and enhancing urban residents’ living standards. Traditional REQ assessments rely on statistical data, prone to delays and lacking holistic insight. This study takes residential blocks as the analysis units and is conducted within the area of the Sixth Ring Road in Beijing. It synthesizes multi-source geospatial data to devise a comprehensive framework for assessing urban REQ, incorporating facets of environmental health and comfort, housing comfort, transportation convenience, city security, and life convenience. Utilizing the principle of minimal relative informational entropy, this study integrates the Analytic Hierarchy Process (AHP) with the entropy method to determine the weight of each evaluative criterion. Subsequently, a linear weighting technique is employed to ascertain the scores for each evaluative criterion, thus facilitating a detailed examination of the REQ. Finally, the research probes into the complex interrelation between the assessed REQ and the city’s Gross Domestic Product (GDP) and carbon emissions across varying scales. Findings reveal that (1) the overall REQ within Beijing’s Sixth Ring Road is superior at the center and diminishes towards the periphery. (2) The dispersion of environmental health and comfort and city security metrics is relatively uniform, showing minor variations; however, a marked disparity is observed in the distribution of housing comfort metrics. (3) Regions characterized by higher GDP tend to demonstrate relatively higher levels of the REQ. Conversely, areas boasting higher-quality urban REQ are more inclined to exhibit increased levels of carbon emissions.

Thermodynamic optimization of heat exchanger circuitry via genetic programming

In this study, an evolutionary thermodynamic technique was developed for the optimization of heat exchanger circuitry. The proposed technique is capable of handling the unrestrained implementation of genetic operators while ensuring circuitry feasibility and basic manufacturability. The optimization tool was used to clarify the optimal heat transfer features in relation to the characteristics of the refrigerant and to provide a thermodynamic interpretation of the optimization results to extract general design guidelines. Evaporator circuitry optimization was conducted under given cooling capacity, superheating degree, and boundary conditions representative of air-conditioning applications. The consistency between the minimum entropy generation and the maximum coefficient of performance (COP) was demonstrated under these settings. Accordingly, heat exchanger configurations that take maximum advantage of the thermodynamic benefits of each refrigerant are proposed by optimizing the distribution of friction and heat transfer irreversibility. Consequently, the evaporator outlet pressure increases, thus lowering the compression ratio and maximizing the COP. The developed optimization method maximizes the benefits of low-GWP alternative refrigerants and shows that zeotropic mixtures may exhibit performance analogous to that of R32 and higher than that of R410A by approaching a Lorenz cycle operation.

Back to the future: the novel art of digital auscultation applied in a prospective observational study of critically ill Covid-19 patients

BackgroundThe Covid-19 pandemic has caused immense pressure on Intensive Care Units (ICU). In patients with severe ARDS due to Covid-19, respiratory mechanics are important for determining the severity of lung damage. Lung auscultation could not be used during the pandemic despite its merit. The main objective of this study was to investigate associations between lung auscultatory sound features and lung mechanical properties, length of stay (LOS) and survival, in adults with severe Covid-19 ARDS.MethodsConsecutive patients admitted to a large ICU between 2020 and 2021 (n = 173) were included. Digital stethoscopes obtained auscultatory sounds and stored them in an on-line database for replay and further processing using advanced AI techniques. Correlation and regression analysis explored relationships between digital auscultation findings and lung mechanics or the ICU outcome. The resulting annotated lung sounds database is also publicly available as supplementary material.ResultsThe presence of squawks was associated with the ICU LOS, outcome and 90-day mortality. Other features (age, SOFA score & oxygenation index upon admission, minimum crackle entropy) had significant impact on outcome. Additional features affecting the 90-d survival were age and mean crackle entropy. Multivariate logistic regression showed that survival was affected by age, baseline SOFA, baseline oxygenation index and minimum crackle entropy.ConclusionsRespiratory mechanics were associated with various adventitious sounds, whereas the lung sound analytics and the presence of certain adventitious sounds correlated with the ICU outcome and the 90-d survival. Spectral features of crackles sounds can serve as prognostic factors for survival, highlighting the importance of digital auscultation.

Differential evolutionary optimization fuzzy entropy for gland segmentation based on breast mammography imaging

ObjectiveThe integration of fuzzy entropy into image segmentation techniques has proven effective in addressing issues related to ambiguous boundaries and uncertainties in complex image structures. This study aims to improve breast mammography image segmentation by optimizing minimum fuzzy entropy. The primary challenges identified are the presence of glandular burrs and irregular edges, as well as premature convergence and local optima in entropy optimization. MethodsWe propose an enhanced differential evolution algorithm combined with fuzzy entropy to address these challenges. This algorithm specifically targets glandular burrs, irregular edges, premature convergence, and local optimal entropy issues. The algorithm's performance was evaluated using breast mammography images representing four types of glands and benchmarked against five state-of-the-art algorithms. ResultsExperimental results demonstrate that the proposed algorithm significantly improves segmentation accuracy compared to the other advanced algorithms. It effectively resolves issues related to glandular burrs, irregular edges, premature convergence, and local optimal entropy, leading to superior segmentation outcomes. ConclusionThe proposed algorithm, which combines an improved differential evolution approach with fuzzy entropy, delivers the best segmentation results for breast gland segmentation. It successfully overcomes the challenges of glandular burrs, irregular edges, premature convergence, and local optimal entropy, thus enhancing breast mammography image segmentation.

Bearing Fault Diagnosis Based on SMA-VMD and CNN-LSTM

To address the challenges of manual parameter setting dependency and low accuracy in bearing fault diagnosis using Variational Mode Decomposition (VMD), a method integrating Slime Mould Algorithm (SMA), VMD, and Convolutional Neural Network-Long Short-Term Memory (CNN-LSTM) network is proposed. Firstly, the SMA is employed to optimize the critical parameters of VMD using minimum information entropy as the fitness function, which resolves the issues related to manual parameter settings in VMD. Subsequently, the optimal parameter combination is used to process the bearing signals and extract the relevant Intrinsic Mode Functions (IMF). Finally, these IMFs are input into the CNN-LSTM network for fault diagnosis. The results demonstrate that this method significantly enhances the accuracy of motor bearing fault diagnosis, further improving the fault diagnosis accuracy.

An end‐to‐end joint learning scheme of image compression and quality enhancement with improved entropy minimization

AbstractRecently, learned image compression methods based on entropy minimization have achieved superior results compared with conventional image codecs such as BPG and JPEG2000. However, they leverage single Gaussian models, which have a limited ability to approximate various irregular distributions of transformed latent representations, resulting in suboptimal coding efficiency. Furthermore, existing methods focus on constructing effective entropy models, rather than utilizing modern architectural techniques. In this paper, we propose a novel joint learning scheme called JointIQ‐Net that incorporates image compression and quality enhancement technologies with improved entropy minimization based on a newly adopted Gaussian mixture model. We also exploit global context to estimate the distributions of latent representations precisely. The results of extensive experiments demonstrate that JointIQ‐Net achieves remarkable performance improvements in terms of coding efficiency compared with existing learned image compression methods and conventional codecs. To the best of our knowledge, ours is the first learned image compression method that outperforms VVC intra‐coding in terms of both PSNR and MS‐SSIM.

Multi-attribute quantum group interference decision model considering minimum constraint and information entropy

About multi-attribute group decision making process, the opinions of different decisions will interfere with each other, or be affected by the decision-making environment, resulting in an unobserved interference effect, which is regarded as quantum entanglement in quantum theory. In this paper, an interference effect model based on minimum constraint and information entropy is proposed to measure the interference value in quantum decision models. Firstly, considering the interference effects of decision makers’ opinions, the evaluation opinions of decision makers are aggregated using Quantum-like Bayesian Network (QLBN), which are regarded as wave functions superimposed in the quantum model. Secondly, due to the uncertainty of decision process, information entropy and minimum constraint are combined to solve the interference effect. The minimum constraint is used to limit the range of interference values and the information entropy represents the uncertainty in the decision process. The grey relational degree represents the conditional probability of the decision maker about the alternatives. Thirdly, the weights of attributes and the probabilities of the alternatives are aggregated about decision makers by the proposed interference effect model, and then the alternatives are ranked by the aggregated probabilities. Subsequently, a numerical example is used to verify the validity and rationality of the model. Comparative analyses and sensitivity analyses are also implemented to demonstrate the stability and reliability of our method.

The Separability Problem in Molecular Quantum Systems: Information-Theoretic Framework for Atoms in Molecules.

Even though molecules are fundamentally quantum entities, the concept of a molecule retains certain classical attributes concerning its constituents. This includes the empirical separability of a molecule into its three-dimensional, rigid structure in Euclidean space, a framework often obtained through experimental methods like X-Ray crystallography. In this work, we delve into the mathematical implications of partitioning a molecule into its constituent parts using the widely recognized Atoms-In-Molecules (AIM) schemes, aiming to establish their validity within the framework of Information Theory concepts. We have uncovered information-theoretical justifications for employing some of the most prevalent AIM schemes in the field of Chemistry, including Hirshfeld (stockholder partitioning), Bader's (topological dissection), and the quantum approach (Hilbert's space definition). In the first approach we have applied the generalized principle of minimum relative entropy derived from the Sharma-Mittal two-parameter functional, avoiding the need for an arbitrary selection of reference promolecular atoms. Within the ambit of topological-information partitioning, we have demonstrated that the Fisher information of Bader's atoms conform to a comprehensive theory based on the Principle of Extreme Physical Information avoiding the need of employing the Schwinger's principle, which has been proven to be problematic. For the quantum approach we have presented information-theoretic justifications for conducting Löwdin symmetric transformations on the density matrix to form atomic Hilbert spaces generating orthonormal atomic orbitals with maximum occupancy for a given wavefunction.

An identification method of compound faults of rolling bearings blending variational mode decomposition and vector bispectrum

To solve the difficulty in correctly identifying a compound fault of rolling bearing, a method combining variational mode decomposition (VMD) and harmonic fusion vector bispectrum (HFVB) is proposed. Firstly, to achieve adaptive decomposition of signals, the characteristic ability of envelope entropy to represent signal sparsity is utilized. By employing the minimum envelope entropy as the fitness function for the sparrow search algorithm (SSA), the decomposition levels and penalty factors of VMD are adaptively determined. Secondly, root-mean-square value is treated as fault feature index to self-adaptively choose from intrinsic mode function (IMF) which can embody fault features of bearings. Thirdly, to further highlight fault features, HFVB is used to blend chosen IMFs. Finally, faults of bearings were recognized with spectrum of signals. To verify the effectiveness of proposed method, an analysis was given to vibration signals in different situations, and SSA-VMD-HFVB was compared with classical method. The results demonstrate that the proposed SSA-VMD-HFVB method facilitates the adaptive decomposition of VMD, enabling the selection and effective integration of sensitive fault component signals. This approach enhances the accuracy of complex fault diagnosing in rolling bearings.

Geometric phaselike effects of driven transport in presence of reservoir squeezing.

In a bare bosonic site coupled to two reservoirs, we explore the statistics of boson exchange in the presence of two simultaneous processes: squeezing the two reservoirs and driving the two reservoirs. The squeezing parameters compete with the geometric phaselike effect or geometricity to alter the nature of the steady-state flux and noise. The even (odd) geometric cumulants and the total minimum entropy are found to be symmetric (antisymmetric) with respect to exchanging the left and right squeezing parameters. Upon increasing the strength of the squeezing parameters, loss of geometricity is observed. Under maximum squeezing, one can recover a standard steady-state fluctuation theorem even in the presence of phase-different driving protocol. A recently proposed modified geometric thermodynamic uncertainty principle is found to be robust.

Circular Fluid Heating—Transient Entropy Generation

A technical issue with fluid flow heating is the relatively small temperature increase as the fluid passes through the heating surface. The fluid does not spend enough time inside the heating source to significantly raise its temperature, despite the heating source itself experiencing a substantial increase. To address this challenge, the concept of the multiple circular heating of air was developed, forming the basis of this work. Two PTC heaters with longitudinal fins are located within a closed channel inside housing composed of a thermal insulation material. Air flows circularly from one finned surface to another. Analytical modeling and experimental testing were used in the analysis, with established restrictions and boundary conditions. An important outcome of the analysis was the methodology established for the optimization of the geometric and process parameters based on minimizing the transient thermal entropy. In conducting the analytical modeling, the temperature of the PTC heater was assumed to be constant at 150 °C and 200 °C. By removing the restrictions and adjusting the boundary conditions, the established methodology for the analysis and optimization of various thermally transient industrial processes can be applied more widely. The experimental determination of the transient thermal entropy was performed at a much higher air flow rate of 0.005 m3s−1 inside the closed channel. The minimum transient entropy also indicates the optimal time for the opening of the channel, allowing the heated air to exit. The novelty of this work lies in the controlled circular heating of the fluid and the establishment of the minimum transient thermal entropy as an optimization criterion.

Resource-efficient quantum principal component analysis

Principal component analysis (PCA) is an important dimensionality reduction method in machine learning and data analysis. Recently, the quantum version of PCA has been established to diagonalize quantum states. Although these quantum algorithms promise quantum advantages, they require substantial resources beyond the reach of state-of-the-art quantum technologies. This work aims to reduce resource requirements and improve the efficiency of quantum PCA. Assuming that the quantum state is accessed through a purified quantum query model and a sampling model, we propose quantum algorithms that use minimal resource requirements for ancillary qubits to reveal properties of eigenvectors and eigenvalues of a state. In particular, we show that estimating eigenvalue λ with error ε and success probability larger than λ(1−η) requests a query complexity O~(ϵ−1) and a sample complexity O~(ϵ−2η−1) , respectively. To our knowledge, our result is the first quantum speedup that achieves asymptotic linear scaling in 1/ϵ for quantum PCA. As applications, we discuss estimating the minimum relative entropy of entanglement of bipartite pure-states and performing quantum state discrimination tasks. We show that quantum speedups are maintained when the pure state has a low Schmidt number and states of discrimination have a low rank. This study opens up a new quantum PCA method for high-dimensional quantum data analysis and discusses its application in quantum information processing tasks.

Weakly supervised instance segmentation via class double-activation maps and boundary localization

Weakly supervised instance segmentation based on image-level class labels has recently gained much attention, in which the primary key step is to generate the pseudo labels based on class activation maps (CAMs). Most methods adopt binary cross-entropy (BCE) loss to train the classification model. However, since BCE loss is not class mutually exclusive, activations among classes occur independently. Thus, not only do foreground classes are wrongly activated as background, but also incorrect activations among confusing classes are occurred in the foreground. To solve this problem, we propose the Class Double-Activation Map, called Double-CAM. Firstly, the vanilla CAM is extracted from the multi-label classifier and then fused with the output feature map of backbone. The enhanced feature map of each class is fed into the single-label classification branch with softmax cross-entropy (SCE) loss and entropy minimization module, from which the more accurate Double-CAM is extracted. It refines the vanilla CAM to improve the quality of pseudo labels. Secondly, to mine object edge cues from Double-CAM, we propose the Boundary Localization (BL) module to synthesize boundary annotations, so as to provide constraints for label propagation more explicitly without adding additional supervision. The quality of pseudo masks is also improved substantially with the addition of BL module. Finally, the generated pseudo labels are used to train fully supervised instance segmentation networks. The evaluations on VOC and COCO datasets show that our method achieves excellent performance, outperforming mainstream weakly supervised segmentation methods at the same supervisory level, even those that depend on stronger supervision.

A Novel Improved Variational Mode Decomposition-Temporal Convolutional Network-Gated Recurrent Unit with Multi-Head Attention Mechanism for Enhanced Photovoltaic Power Forecasting

Photovoltaic (PV) power forecasting plays a crucial role in optimizing renewable energy integration into the grid, necessitating accurate predictions to mitigate the inherent variability of solar energy generation. We propose a novel forecasting model that combines improved variational mode decomposition (IVMD) with the temporal convolutional network-gated recurrent unit (TCN-GRU) architecture, enriched with a multi-head attention mechanism. By focusing on four key environmental factors influencing PV output, the proposed IVMD-TCN-GRU framework targets a significant research gap in renewable energy forecasting methodologies. Initially, leveraging the sparrow search algorithm (SSA), we optimize the parameters of VMD, including the mode component K-value and penalty factor, based on the minimum envelope entropy principle. The optimized VMD then decomposes PV power, while the TCN-GRU model harnesses TCN’s proficiency in learning local temporal features and GRU’s capability in rapidly modeling sequence data, while leveraging multi-head attention to better utilize the global correlation information within sequence data. Through this design, the model adeptly captures the correlations within time series data, demonstrating superior performance in prediction tasks. Subsequently, the SSA is employed to optimize GRU parameters, and the decomposed PV power mode components and environmental feature attributes are inputted into the TCN-GRU neural network. This facilitates dynamic temporal modeling of multivariate feature sequences. Finally, the predicted values of each component are summed to realize PV power forecasting. Validation using real data from a PV station corroborates that the novel model demonstrates a substantial reduction in RMSE and MAE of up to 55.1% and 54.5%, respectively, particularly evident in instances of pronounced photovoltaic power fluctuations during inclement weather conditions. The proposed method exhibits marked improvements in accuracy compared to traditional PV power prediction methods, underscoring its significance in enhancing forecasting precision and ensuring the secure scheduling and stable operation of power systems.

Graph-based minimum error entropy Kalman filtering

When the Gaussian kernel function is chosen with a small kernel bandwidths, the minimum error entropy Kalman filter (MEEKF) exhibits excellent performance. However, further narrowing the kernel bandwidths leads to a degradation in performance. To address this issue, this paper proposed a Graph-based MEEKF (G-MEEKF) algorithm based on Graph Signal Processing (GSP) theory. The G-MEEKF algorithm addresses the problem by smoothing the errors using graph filtering and incorporating graph topology into the cost function. The convergence of the algorithm is theoretically analyzed and simulations demonstrate that G-MEEKF improves the performance of MEEKF under small kernel bandwidths. Furthermore, it is emphasized that the topology of the graph abstracted from the minimum error entropy (MEE) definition also influences the performance of the algorithm.

An adaptive Morlet wavelet-based iterative filtering method for locating informative frequency band

Locating the informative frequency band of rolling bearing fault signals is of great significance for feature extraction and fault diagnosis. Benefiting from the adjustable center frequency and bandwidth as well as the similarity to impulse-like characteristics induced by bearing failures, Morlet wavelets are commonly used in resonance demodulation. However, fault impulses are highly susceptible to contamination by strong noise, which impedes the efficacy of existing wavelet parameter selection strategies and frequency band optimization methods. In this paper, an adaptive Morlet wavelet-based iterative filtering (AMIF) method is proposed for frequency band optimization under strong noise. The resonance frequency band is pinpointed based on adaptive Morlet wavelet filter banks, with off-band noise being canceled and fault features being refined during the level-by-level filtering process. Additional iterative operations are leveraged to enhance fault features of in-band signals to facilitate the optimization of the filtering parameters. Effectiveness of the proposed AMIF method and its superiority over the wavelet packet transform-based kurtogram and minimum entropy deconvolution are verified through simulation and experimental analysis. The results demonstrate that AMIF can accurately localize the informative frequency band, thereby extracting high-quality fault features, making it suitable for bearing fault diagnosis under strong noise condition with different fault types.

Weighted information entropy‐based Kalman filter for outliers and structural noise

AbstractStructural noise and outliers are widely present in real‐world state estimate scenarios, and they significantly degrade the performance of most filtering algorithms based on minimum mean square error (MMSE) criterion. To address this problem, this paper first models structural noise and outliers as independent and piecewise identical distribution (IPID). Then, a minimum error weighted entropy‐based Kalman filter (MEWE‐KF) is proposed, where a new cost function is constructed by introducing a weight function related to error location distances in an original information space into the minimum error entropy (MEE) criterion. Further, the iterative formulations of the proposed filter are derived, and the computational complexity and the convergence are also analyzed. Simulation results show that the proposed filter with adaptive weights has the superior performance for suppressing structural noise and outliers.

An information entropy-based fuzzy stochastic configuration network for robust data modeling

In data-driven modeling, the generalization performance of a neural network based on the minimum mean square error criterion may be affected when the samples contain noise. To handle uncertain data modeling problems, this study contributes a novel robust data modeling method called information entropy-based fuzzy stochastic configuration networks (IEFSCNs), which incorporates the maximum correntropy criterion (MCC) to reflect the squared error of the training sample set and uses the quantized minimum error entropy (QMEE) criterion to mine the distribution structure of the modeling data and suppress outlier data. Fuzzy systems are designed to generate nodes in the fuzzy transformation layer. A nonlinear enhancement layer is established as a hidden layer to enhance the representational capacity of the target system. The fuzzy transformation and nonlinear enhancement layers are fully connected to determine the outputs of the IEFSCNs. In addition, an incremental parameter learning algorithm is developed based on a supervision mechanism for optimizing the cost function, and its convergence property is demonstrated. Owing to the superiorities of the cost function by synthesizing MCC and QMEE, IEFSCNs can improve the modeling accuracy and reduce noise suppression. The performances are evaluated using various regression and classification tasks. Compared with existing methods, including SCNs, RVFL, F-SCNs, RSC-KDE, RSC-MCC, and SM-RSC, the proposed method demonstrates an effective robust modeling performance by reducing network structure redundancy while enhancing its ability to suppress noisy data.

Minimum nonprobabilistic entropy deconvolution for fault diagnosis of rolling element bearings

The blind deconvolution methods (BDMs) is one of the most common methods for fault diagnosis of rolling bearings, and it is essential to maintain the safe and reliable operation of mechanical equipment. However, noise interference and the need for prior periods limit the scope of application of the BDMs. In this paper, a new minimum nonprobabilistic entropy deconvolution (MNPED) method is proposed. According to the correlation between fault impact and non-Gaussianity, the Gaussian membership function in fuzzy set theory is used to map the sample points to the membership degree of Gaussian distribution, and then the nonprobabilistic entropy (NPE) is formed to measure the impact characteristics of the signal. Then NPE is incorporated into the iterative process of solving the filter coefficient. Finally, the target signal and the optimal filter coefficient are selected based on the criterion of minimum NPE. MNPED is capable of adaptively extracting the periodic pulse of a signal without requiring prior knowledge of the period, even in the presence of strong noise interference. The effectiveness and robustness of the proposed approach are validated through simulation and experimental data.

Fixed-matrix regenerators optimization with wire mesh screens using entropy generation minimization method

The thermodynamic efficiency of a wire mesh fixed matrix regenerative heat exchanger mainly depends on the regenerator’s heating performance and losses. This paper aims to increase the effectiveness and decrease the pressure loss of static regenerators with wire mesh screens as packing geometry. The entropy generated for several combinations of mesh screens is calculated by using the entropy generation minimization method (EGM), and this method helps in finding the right combination with the minimum entropy generation. The study aims to minimize entropy generation by dividing the conventional uniform mesh regenerator pack length into multiple zones by accommodating different combinations of wire mesh screens. For the sample flow condition, it is observed that 3.94 × 103 W/K entropy is generated by uniform mesh, and from 68 hybrid mesh combinations, 80–120–200 generated 2.11 × 103 W/K. By balancing pressure loss and thermal efficiency, the potential of EGM-based optimization is underscored during this study, which improves the regenerator’s performance.