Entropy Theory Research Articles

AK-SYS-IE: A novel adaptive Kriging-based method for system reliability assessment combining information entropy

Structural reliability assessment is a popular topic in engineering problems, particularly for the larger and more complex systems with implicit performance functions, also called black-box problems. The reliability assessment for a black-box problem must continuously be computed using simulation models, such as the finite element model, a highly time-consuming process with a high computational cost. The adaptive Kriging has gained considerable attention over the past decade. The Kriging-based reliability assessment method reduces the computational cost to a great extent, on the premise of ensuring the accuracy of reliability assessment. However, many of the currently published system reliability assessment methods, construct adaptive Kriging models by reducing the probability of incorrect prediction of the system state, and do not make full use of the uncertainty of the system state prediction information. To this end, a new Kriging-based method for structural system reliability assessment is proposed in this study. First, the probabilities of incorrect or correct system state predictions were understood from the perspective of information entropy. Second, an active learning strategy is proposed based on information entropy theory. Finally, the advantages of the proposed method are demonstrated and highlighted through several numerical examples. The results show that the proposed method achieves a good balance between the accuracy and computational cost, and the numerical magnitude effect does not affect the computational cost. Moreover, this is an effective method for assessing the reliability of complex systems.

A Good View for Graph Contrastive Learning.

Due to the success observed in deep neural networks with contrastive learning, there has been a notable surge in research interest in graph contrastive learning, primarily attributed to its superior performance in graphs with limited labeled data. Within contrastive learning, the selection of a "view" dictates the information captured by the representation, thereby influencing the model's performance. However, assessing the quality of information in these views poses challenges, and determining what constitutes a good view remains unclear. This paper addresses this issue by establishing the definition of a good view through the application of graph information bottleneck and structural entropy theories. Based on theoretical insights, we introduce CtrlGCL, a novel method for achieving a beneficial view in graph contrastive learning through coding tree representation learning. Extensive experiments were conducted to ascertain the effectiveness of the proposed view in unsupervised and semi-supervised learning. In particular, our approach, via CtrlGCL-H, yields an average accuracy enhancement of 1.06% under unsupervised learning when compared to GCL. This improvement underscores the efficacy of our proposed method.

Microbial entropy change and external dissipation process of urban sewer ecosystem.

As the initial stage of the sewage treatment system, the degradation of pollutants inevitably involves an entropy change process. Microorganisms play a vital role, where they interact with pollutants and constantly adjust own ecosystem. However, there is a lack of research on the entropy change and external dissipation processes within the sewer system. In this study, considering the characteristics of microbial population changes in the biofilm within the urban sewage pipe network, entropy theory is applied to characterize the attributes of different microorganisms. Through revealing the entropy change of the microbial population and chemical composition, a coupling relationship between the functional bacteria diversity, organic substances composition, and external dissipation in the pipeline network is proposed. The results show that the changes of nutrient availability, microbial community structure, and environmental conditions all affect the changes of information entropy in the sewer network. This study is critical for assessing the understanding of ecological dynamics and energy flows within these systems and can help researchers and operation managers develop strategies to optimize wastewater treatment processes, mitigate environmental impacts, and promote sustainable management practices.

An Emergency Plan Selection Method for Emergency Latency

Drawing upon a characteristic analysis of the latency period in emergencies, this paper proposes an emergency plan selection method based on interval language variables and information entropy to address the challenge of acquiring critical information during this crucial stage. Initially, decision-makers employ interval language variables to express the preference information regarding emergency plans, while also introducing an enhanced information entropy theory to derive the weight coefficients of key indicators. Subsequently, the weighted arithmetic average operator of interval language is applied twice to aggregate the preference information alongside the relative importance of decision-makers and the weight coefficients of key indicators. Finally, the ranking coefficients of each emergency plan are sorted to determine the optimal scheme. The feasibility and effectiveness of this method are demonstrated through a case study involving the selection of an emergency plan for a flood disaster in a specific location.

Selection of representative indicators for flood risk assessment using marginal entropy and mutual information

AbstractFloods are the most frequent types of natural disasters. From the perspective of disaster management, indicators associated with floods are important for accurate flood risk assessment. However, the application of all indicators related to flood risk assessment decreases the evaluation efficiency, because the definitions of the indicators may overlap. Moreover, the volume of data required for collection and evaluation is significantly large, making the evaluation practically impossible. Thus, a scientific and objective method to select indicators for flood risk assessment based on the entropy theory was developed herein. First, the existing 28 assessment indicators were analyzed and probability‐based data were constructed for each indicator considering 28 districts in a midwestern region of Korea. The information quantity for each indicator was then obtained using marginal entropy and mutual information generated in the entropy theory. Next, the total information quantity based on the numbers of combination of indicators was derived by considering the information quantity for each indicator and the overlapping mutual information between the indicators. The maximum amount of information (161.55) was obtained by combining 18 out of the 28 flood risk indicators. The selected 18 indicators reflected regional characteristics better than those used in the existing method, demonstrating that the flood risk of the target area could be adequately assessed.

Social Optimization in Combination with the Theory of Entropy also

I have proposed to arrange the technology two-dimensionally, and to consider it three-dimensionally and in time series, as “the criteria for considering the technology”, since before.By the way, entropy express the concept which shows the randomness of molecular structure of material in thermodynamics. I thought whether the concept of entropy could be used in social phenomena in analogy to natural phenomena also, since social phenomena belong to natural phenomena.I think capitalism and democracy have more degree of freedom and diversity, compared to socialism and authoritarianism, therefore the formers is preferable to the latter. Entropy is larger in the former than in the latter.Current capitalism has the weakness of large disparity between rich and poor. The state participation should be required to diminish it. So it is rational that the public policy is based on the upper criteria.The value of the social system is for society to ensure the conditions of life and freedom. From this viewpoint, the coordination between the proper freedom and restriction to it is required. It should be decided by “democratic control by citizens”.Furthermore, whether populism is proper or not proper, is considered based on the upper model of social system, also.

Calculation of probabilistic harmonic power flow based on improved three-point estimation method and maximum entropy as distributed generators access to distribution network

Uncertainty and volatility are the features of distributed generation (DG), which can impact greatly on the operational status of distribution network. Thus, an improved three-point estimation method and maximum entropy theory (ITPEM&ME) for calculating the probabilistic harmonic power flow in distribution network is proposed in this study. Firstly, the probabilistic model is constructed according to the uncertainty of input variables and the improved three-point estimate method is utilized to convert a probabilistic problem into a deterministic problem. Secondly, in order to obtain the distribution of the random harmonics in distribution network, the maximum entropy theory is adopted to reconstruct the statistical characteristics after the deterministic calculation is realized for each harmonic voltages. The case of an IEEE-33 system under various conditions is conducted. The results by the different algorithms indicate that the proposed method ITPEM&ME has a smaller error than the traditional method, as well as the fitting effect of the probability density function (PDF) is much closer to the practical engineering. It is feasible and accurate in dealing with probabilistic harmonic power flow problems.

Probabilistic Small Signal Stability Analysis with Wind Power Based on Maximum Entropy Theory

The probability parameters for the small signal stability in a system are studied to quantify the impact of uncertain wind power on system stability. With the increase in the scale of wind power access systems, how to more efficiently and accurately obtain the probability of small signal stability is worthy of further investigation. Therefore, this work proposes an analysis method of probabilistic small signal stability (PSSS) based on maximum entropy (ME) theory for studying power systems with uncertain wind power from doubly fed induction generators (DFIGs). Firstly, the sensitivity of the eigenvalues to the variable power is obtained by linearization. Then, when the probability characteristic for wind is known, the probability characteristic for the system critical eigenvalues is approximated using the ME method and the derived sensitivity. The proposed ME method is used in the analysis of the PSSS for power systems with different wind power penetration scales in case studies. Compared to the probability function for the eigenvalue obtained by the conventional series expansion method, the proposed method has excellent accuracy and sufficient efficiency in analysing the PSSS for a system with uncertain wind power.

Quality of Mixedness Using Information Entropy in a Counter-Current Three-Phase Bubble Column

Knowledge of mixing phenomena is of great value in the mineral and other chemical and biochemical industries. This work aims to analyze the quality of mixedness (QM), the intrinsic mass transfer (MT) number, and the MT efficiency based on information entropy theory in the counter-current microstructured slurry bubble column. A thorough analysis is conducted to assess the effects of particle loading, gas and slurry velocity, and axial variation on the QM. The range of gas velocity, slurry velocity, particle size, and particle loading was 0.011–0.075 m/s, 0.018–0.058 m/s, 242.72–408.31 μm, and 15.54–88.94 kg/m3, respectively. QM is a time-dependent parameter, and the concept of contact time has been used for scale-up purposes. The maximum QM was achieved at dimensionless times of 0.40 × 10−3, 0.15 × 10−3, and 0.85 × 10−3 for the maximum superficial gas velocity, particle loading, and axial height, respectively. The gas velocity positively influenced both the intrinsic MT number and its efficiency. In contrast, the slurry velocity and particle loading had a negative effect. The present theoretical analysis will pave the path for industrial process intensification in counter-current flow systems.

Mine wind speed sensor location selection based on decision tree theory

Abstract In order to realize the scientific layout of underground roadway sensors, based on the information entropy theory, the decision tree algorithm is applied to the location selection of the underground wind speed sensor. Taking the air volume traversing the entire network branch as the goal, the node air volume balance and the characteristic relationship between air volume and wind pressure as the constraints, the conventional layout data of the mine wind speed sensor is selected as the training sample, and the reasonable decision node is selected by measuring the uncertainty of the characteristic attribute. The research shows that the smaller the information entropy of the layout elements, the greater the weight in determining the sensor location. The classification conditions obtained by the wind speed sensor are, in descending, order: airflow disturbance, roadway support, distance from the inlet (return) and outlet, and roadway type. Algorithms are applied to effectively combine downhole sensor siting with historical data containing unambiguous results.

A dynamics model for driving behavior based on coupling actuation of bounded rational cognition and diverse emotions

Precise comprehension about the impacts of drivers’ rational and perceptual characteristics on their behavioral decisions is crucial for the accurate prediction of driving behavior. In the previous research on driving behavior, drivers were regarded as homogeneous and absolutely rational individuals. To overcome this limitation, the coupling effects of bounded rational cognition and diverse emotions are considered, and a driving behavior model is proposed based on Dynamics Psychology. There are two parts in this research. In Study 1, the information entropy theory is applied to describe the vehicle cluster situation, and a method is established to quantify the cognitive uncertainty of the vehicle cluster situation for drivers in diverse emotions. In Study 2, with consideration of bounded rational and emotional cognition, the impacts of the vehicle cluster situation and drivers' features, which are their demands for the driving goals including safety, efficiency and comfort, emotional states, and cognitive characteristics, on driving behavior are uniformly expressed as the behavioral driving force, and a prediction model for driving behavior is proposed based on Dynamics Psychology. The results of validation based on the virtual driving data show the prediction accuracy of the proposed model for various driving behaviors of drivers in diverse emotions is over 80%. The results of verification based on NGSIM data suggest that the prediction accuracy of the proposed model for the natural driving behaviors is 82.07%. The research results can contribute to the study on the intrinsic mechanism of driving behavior and provide theoretical support for the development of traffic simulation, personalized active safety systems, human–machine interaction, and brain-inspired autonomous driving.

Outlier detection using conditional information entropy and rough set theory

Outlier detection is critically important in the field of data mining. Real-world data have the impreciseness and ambiguity which can be handled by means of rough set theory. Information entropy is an effective way to measure the uncertainty in an information system. Most outlier detection methods may be called unsupervised outlier detection because they are only dealt with unlabeled data. When sufficient labeled data are available, these methods are used in a decision information system, which means that the decision attribute is discarded. Thus, these methods maybe not right for outlier detection in a a decision information system. This paper proposes supervised outlier detection using conditional information entropy and rough set theory. Firstly, conditional information entropy in a decision information system based on rough set theory is calculated, which provides a more comprehensive measure of uncertainty. Then, the relative entropy and relative cardinality are put forward. Next, the degree of outlierness and weight function are presented to find outlier factors. Finally, a conditional information entropy-based outlier detection algorithm is given. The performance of the given algorithm is evaluated and compared with the existing outlier detection algorithms such as LOF, KNN, Forest, SVM, IE, and ECOD. Twelve data sets have been taken from UCI to prove its efficiency and performance. For example, the AUC value of CIE algorithm in the Hayes data set is 0.949, and the AUC values of LOF, KNN, SVM, Forest, IE and ECOD algorithms in the Hayes data set are 0.647, 0.572, 0.680, 0.676, 0.928 and 0.667, respectively. The advantage of the proposed outlier detection method is that it fully utilizes the decision information.

Arc entropy of uncertain random variables and its applications

Due to the complexity of the real world, randomness and uncertainty are ubiquitous and interconnected in the real world. In order to measure the research objects that contain both randomness and uncertainty in practical problems, and extend the entropy theory of uncertain random variables, this paper introduces the arc entropy of uncertain random variables and the arc entropy of their functions. On this basis, the mathematical properties of arc entropy and two key formulas for calculating arc entropy are also studied and derived. Finally, two types of the mean variance entropy model with the risk and diversification are established, and the corresponding applications to rare book selection for the rare book market are also introduced.

Wind speed monitoring using entropy theory and a copula-based approach

In this study, wind speeds in the Lut desert (Iran) was monitored at the Bam, Tabas and Birjand stations during the period 1973–2020 using entropy theory. The conventional entropy method was improved by considering the interaction between stations by a copula-based approach. Two different methods were examined for this purpose: 1) A trivariate vine copula was used to evaluate the interaction among the stations. For this purpose, a d-vine copula was considered to simulate the wind speed at each station as a function of the wind speed at the other stations. 2) A bivariate copula was used to model the simulated and observed wind speed at each station. In particular, a Frank copula was used to perform the joint probability analysis. The results indicate that implementing the proposed method for wind speed monitoring increases the Information Transfer Index (ITI) by approximately 24 %, 10 %, and 33 % at the Bam, Birjand, and Tabas stations, respectively, compared to using the conventional entropy method.

Interprovincial Transfer Entropy Analysis on Electricity Consumption by Secondary and Tertiary Industries

As electricity consumption is direct feedback of the production and operation state of an industry, there should be links between lead-lag relation in electricity consumption volumes and driving/transferring effects cross regions and industries. In this paper, lead-lag relation between provincial secondary industry (SI) and tertiary industry (TI) electricity consumption volumes is studied based on transfer entropy (TE) theory. Significant TE flow from SI to TI is observed both intra-provincially and interprovincially in a large part of China and periodic fluctuations in electricity consumption curves of SI emerge stably one month ahead of that of TI. It is also found that the curves of SI electricity consumption show more significant correlation with economic cycle in GDP than that of TI. Meanwhile, in both SI and TI cases, Shanghai (SH) manifests noticeable driving effect on other provinces, especially those in Yangtze River Economic Belt. Maximum spanning arborescence topology is built to exhibit direct affecting routes with maximized TE flows of SI and TI from SH to other provinces in the Belt. It is deduced that in SI case it takes stages for the influence from SH to spread while in TI case the influence tends to directly radiate elsewhere. The study attempts to propose an approach to looking through the economy from a perspective of electricity consumption and provide a reference for making industrial strategy.

Feature Selection for Unbalanced Distribution Hybrid Data Based on ${k}$-Nearest Neighborhood Rough Set

Neighborhood rough sets are now widely used to process numerical data. Nevertheless, most of the existing neighborhood rough sets are not able to distinguish class mixture samples well when dealing with classification problems. That is, it cannot effectively classify categories when dealing with data with an unbalanced distribution. Because of this, in this aiticle, we propose a new feature selection method that takes into consideration both heterogeneous data and feature interaction. The proposed model well integrates the ascendancy of δ-neighborhood and <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">k</i> -nearest neighbor. Such heterogeneous data can be handled better than existing neighborhood models. We utilize information entropy theories such as mutual information and conditional mutual information, and employ an iterative strategy to define the importance of each feature in decision-making. Furthermore, we design a feature extraction algorithm based on above idea. Experimental results displays that the raised algorithm has superior effect than some existing algorithms, particularly the δ-neighborhood rough set model and <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">k</i> -nearest neighborhood rough set model.

TECO: A Unified Feature Map Compression Framework Based on Transform and Entropy.

The massive memory accesses of feature maps (FMs) in deep neural network (DNN) processors lead to huge power consumption, which becomes a major energy bottleneck of DNN accelerators. In this article, we propose a unified framework named Transform and Entropy-based COmpression (TECO) scheme to efficiently compress FMs with various attributes in DNN inference. We explore, for the first time, the intrinsic unimodal distribution characteristic that widely exists in the frequency domain of various FMs. In addition, a well-optimized hardware-friendly coding scheme is designed, which fully utilizes this remarkable data distribution characteristic to encode and compress the frequency spectrum of different FMs. Furthermore, the information entropy theory is leveraged to develop a novel loss function for improving the compression ratio and to make a fast comparison among different compressors. Extensive experiments are performed on multiple tasks and demonstrate that the proposed TECO achieves compression ratios of 2.31 × in ResNet-50 on image classification, 3.47 × in UNet on dark image enhancement, and 3.18 × in Yolo-v4 on object detection while keeping the accuracy of these models. Compared with the upper limit of the compression ratio for original FMs, the proposed framework achieves the compression ratio improvement of 21%, 157%, and 152% on the above models.

High-Success-Rate and Fast ISAR Imaging of Nonstationary Moving Platform-Attitude Rapidly Changing Ship Target With DS Evidence and Minimum Entropy Theory

High-Success-Rate and Fast ISAR Imaging of Nonstationary Moving Platform-Attitude Rapidly Changing Ship Target With DS Evidence and Minimum Entropy Theory

Blockchain-Based Renewable Energy Trading Using Information Entropy Theory

Renewable energy sources (RES) and electric vehicles (EVs) are widely recognized as primary ways to reduce carbon emissions and essential components of low-carbon power systems. However, both of them have strong uncertainties which bring great challenges to power transactions and the operation of power grids. This paper defines the uncertainty cost of wind power producer(WPP) in day-ahead(DA) market pricing based on information entropy theory for the first time and proposes a EV charging management strategy with DA contract. The constructed low-carbon emission electricity market(LCEM) quantifies the uncertainty cost and contracts the disordered charging of EVs. It reduces the uncertainty and ensures the balance of power supply and demand. In addition, the transaction between WPP and EVs is described as the Stackelberg game, and its communication network is constructed through a blockchain network to ensure transaction efficiency and privacy security. Experiments show that LCEM can accurately measure the uncertainty of wind power generation, increase the net profit for WPP by more than 2% when the prediction error is greater than 10%, and adopt EV contract charging management in the DA market to minimize charging costs.

A quantitative safety assessment for offshore equipment evaluation using fuzzy FMECA: A case study of the hydraulic submersible pump system

The Hydraulic submersible pump system (HSPS) is integral to the offloading of oil on offshore platforms and oil tankers. Due to the inflammable and explosive properties of the oil, the working process of HSPS is of high risk. Therefore, this study focused on the safety assessment of HSPS, key potential failure modes of HSPS were identified. A Fuzzy Failure Mode Effects and Criticality Analysis (FFMECA) model was proposed based on fuzzy logic theory and failure mode effects and criticality analysis (FMECA) method. Fuzzy linguistic terms were used to assess the Occurrence (O), Severity (S), and Detection (D) of the identified failure modes. The weights for O, S, and D were calculated based on experts’ ratings and entropy theory. A case study was carried out and the Fuzzy Risk Priority Numbers (FRPNs) for the failure modes were obtained. The results highlighted that 5 failure modes, namely wear of bearings, failure of mechanical seal, failure of rotary seal, zero pressure on the outlet and influence of excessive temperatures, were of critical level and required immediate preventive action. Risk control measures were proposed to ensure the safety of HSPS in practical application and to improve the reliability of system operation.