Shannon Entropy Model Research Articles

A Novel Comprehensive Evaluation Method for Estimating the Bank Profile Shape and Dimensions of Stable Channels Using the Maximum Entropy Principle.

This paper presents an extensive and practical study of the estimation of stable channel bank shape and dimensions using the maximum entropy principle. The transverse slope () distribution of threshold channel bank cross-sections satisfies the properties of the probability space. The entropy of is subject to two constraint conditions, and the principle of maximum entropy must be applied to find the least biased probability distribution. Accordingly, the Lagrange multiplier (λ) as a critical parameter in the entropy equation is calculated numerically based on the maximum entropy principle. The main goal of the present paper is the investigation of the hydraulic parameters influence governing the mean transverse slope () value comprehensively using a Gene Expression Programming (GEP) by knowing the initial information (discharge (Q) and mean sediment size (d50)) related to the intended problem. An explicit and simple equation of the of banks and the geometric and hydraulic parameters of flow is introduced based on the GEP in combination with the previous shape profile equation related to previous researchers. Therefore, a reliable numerical hybrid model is designed, namely Entropy-based Design Model of Threshold Channels (EDMTC) based on entropy theory combined with the evolutionary algorithm of the GEP model, for estimating the bank profile shape and also dimensions of threshold channels. A wide range of laboratory and field data are utilized to verify the proposed EDMTC. The results demonstrate that the used Shannon entropy model is accurate with a lower average value of Mean Absolute Relative Error (MARE) equal to 0.317 than a previous model proposed by Cao and Knight (1997) (MARE = 0.98) in estimating the bank profile shape of threshold channels based on entropy for the first time. Furthermore, the EDMTC proposed in this paper has acceptable accuracy in predicting the shape profile and consequently, the dimensions of threshold channel banks with a wide range of laboratory and field data when only the channel hydraulic characteristics (e.g., Q and d50) are known. Thus, EDMTC can be used in threshold channel design and implementation applications in cases when the channel characteristics are unknown. Furthermore, the uncertainty analysis of the EDMTC supports the model’s high reliability with a Width of Uncertainty Bound (WUB) of ±0.03 and standard deviation () of 0.24.

Comparison and Research on Diversified Portfolios with Several Entropy Measures Based on Different Psychological States

In previous studies, there were few portfolio models involving investors’ psychological states, market ambiguity and entropy. Some entropy can make the model have the effect of diversifying investment, which is very important. This paper mainly studies four kinds of entropy. First, we obtained four definitions of entropy from the literature, and gave the function of fuzzy entropy in different psychological states through strict mathematical proof. Then, we construct a fuzzy portfolio entropy decision model based on the investor’s psychological states, and compared it with the possibilistic mean–variance model. Then we presented a numerical example and compared the five different models established. By comparing the results, we find that: (a) The possibilistic mean–Shannon entropy model solves the problem of the possibility of excessive concentration in the possibilistic mean–variance model, but the dispersion is not enough. Conversely, the possibilistic mean–Yager entropy is over–emphasized due to the definition of its own function, such that it gave an investment pattern of equal weight distribution or approximate average distribution. (b) The results of possibilistic mean–proportional entropy can be said to be the middle status of the portfolios of possibilistic mean–Shannon entropy and possibilistic mean–Yager entropy. This portfolio not only achieves a certain rate of return, but also disperses the risk to some extent. (c) The lines of satisfaction for portfolios derived from different models are approximately U–shaped with the increase in return preference. (d) The possibilistic mean–Shannon entropy model tends to have the highest portfolio satisfaction with the same psychological state of the investor.

The uncertainty of the Shannon entropy model for shear stress distribution in circular channels

The shear stress distribution at alluvial stream beds and banks is one of the essential parameters in channel stability analysis. In the current paper, a novel uncertainty analysis method based on the framework of a Bayesian Forecasting System (BFS) is presented to evaluate the Shannon entropy model for prediction of the shear stress distribution in both circular rigid-bed and alluvial-bed channels. The Johnson and Box-Cox transformation functions were applied to select the optimum sample size (SS) and corresponding transformation factor for determining a 95% confidence bound (CB) for the Shannon entropy model. The Shapiro-Wilk (SW) test is applied according to the SS used to evaluate the power of transformation functions in the data normalization. The results show that the error distribution between predicted and experimental shear stress values generated using the Box-Cox transformation is closer to a Gaussian distribution than the generated using the Johnson transformation. The indexes of the percentage of the experimental values within the CB (Nin) and Forecast Range Error Estimate (FREE) are applied for the uncertainty analyses. The lower values of FREE equal to 1.724 in the circular rigid-bed channel represent the low uncertainty of Shannon entropy in the prediction of shear stress values compared to the uncertainty for the circular alluvial-bed channel with a FREE value equal to 7.647.

Groundwater potential assessment of the Sero plain using bivariate models of the frequency ratio, Shannon entropy and evidential belief function

The goal of the present research is to evaluate three bivariate models of the frequency ratio, Shannon entropy (SE) and evidential belief function in the spatial prediction of groundwater at the Sero plain located in west Azerbaijan, Iran. In the first phase, well locations with groundwater yields $${>}11\hbox { m}^{3}$$ /hr were identified (75 well locations). Ten groundwater conditioning factors affecting the occurrence of groundwater, namely, altitude, slope degree, curvature, slope aspect, rainfall, soil, land-use, geology and distance from the fault and the river, were selected for modelling. Finally, the groundwater potential map results were drawn from three implemented models and they were validated using testing data by area under the receiver operating characteristic curve (AUC). The AUCs of these models were 0.84, 81 and 85%, respectively. The results of the current study demonstrated that these models could be successfully employed for spatial prediction modelling. Moreover, the results of the SE model demonstrated that the most and the least important factors in groundwater occurrences in the area under study were altitude, curvature and rainfall, respectively. The results of this study are helpful for the Regional Water Authority of Urmia and the decision makers to comprehensively assess the groundwater exploration development and environmental management in future planning.

Content Analysis of First Elementary School Grades’ Textbooks Based on Assumptions of Health Education System: Shannon Entropy Model

Content Analysis of First Elementary School Grades’ Textbooks Based on Assumptions of Health Education System: Shannon Entropy Model

A Novel Interference Suppression Method for Interrupted Sampling Repeater Jamming Based on Singular Spectrum Entropy Function.

As a new type of jamming, the interrupted sampling repeater jamming (ISRJ) derived from the digital radio frequency memory (DRFM) technology, can generate coherent multiple false targets after pulse compression. At present, the traditional interference suppression method and its improved methods have insufficient characteristics and poor detection performance under the condition of low signal-to-noise ratio (SNR). Aiming at addressing this defect, this paper proposes an interference suppression method for ISRJ based on singular spectrum entropy function (SSEF) from the aspects of singular value decomposition (SVD) and information entropy theories. In this method, firstly, considering the local fine characteristics and extraction efficiency, an adaptive multi-scale segmentation (AMS) method is proposed. The purpose of this processing is to extend the salient characteristics while to smooth the similar ones. In AMS, the segmentation criterion based on average energy of segments and the constraint of minimum segmentation is also proposed, then the improved delay embedded matrix is established from the improved trajectory matrix by AMS and delay embedded mapping. Secondly, the singular spectrum of the improved delay embedded matrix is extracted by SVD. Thirdly, because the recognition algorithms based on singular spectrum analysis (SSA), classical SSE and other characteristics fail at low SNR, this paper proposes a characteristic named as SSEF retrieved from the Shannon entropy model. The following proposed entropy-based threshold detection is carried out on the echo signal to realize the band-pass filtering and interference suppression. Finally, experiment results show that in comparison with other interference suppression approaches, SSEF can increase the probability of target detection and the peak-to-side-lobe ratio (PSR) after pulse compression, which validates its stability to noise and jamming especially in the condition of low SNRs.

Formulating the shear stress distribution in circular open channels based on the Renyi entropy

The principle of maximum entropy is employed to derive the shear stress distribution by maximizing the Renyi entropy subject to some constraints and by assuming that dimensionless shear stress is a random variable. A Renyi entropy-based equation can be used to model the shear stress distribution along the entire wetted perimeter of circular channels and circular channels with flat beds and deposited sediments. A wide range of experimental results for 12 hydraulic conditions with different Froude numbers (0.375 to 1.71) and flow depths (20.3 to 201.5 mm) were used to validate the derived shear stress distribution. For circular channels, model performance enhanced with increasing flow depth (mean relative error (RE) of 0.0414) and only deteriorated slightly at the greatest flow depth (RE of 0.0573). For circular channels with flat beds, the Renyi entropy model predicted the shear stress distribution well at lower sediment depth. The Renyi entropy model results were also compared with Shannon entropy model results. Both models performed well for circular channels, but for circular channels with flat beds the Renyi entropy model displayed superior performance in estimating the shear stress distribution. The Renyi entropy model was highly precise and predicted the shear stress distribution in a circular channel with RE of 0.0480 and in a circular channel with a flat bed with RE of 0.0488.

Urban Sprawl Monitoring using Remote Sensing and GIS Techniques of the City Jaipur, India

The rapid increase in population of India forced people to migrate from rural areas and small towns to metropolitan cities for better employment, education, and, good lifestyle. Major cities of India were industrialized and required more work force in metropolitan cities, leading to uncoordinated and unplanned growth, often termed as urban sprawl. Urban sprawl destroyed the natural resources such as open green space, agricultural land, open water bodies and ground water. In this paper, an attempt has been made to monitor urban sprawl using Shannon's Entropy model, Remote Sensing, and GIS for city Jaipur, India. The changed entropy value during the years 1972–2013 proves more dispersed growth in the city. The built-up area of Jaipur has increased from 40 km2 in 1972 to 400 km2 in 2013. Land use percentage of urban settlement is doubled as compared to the urban population of Jaipur during 1972–2013. This study shows remarkable urban sprawl in fringe areas of Jaipur city in the last 41 years.

Designing Appraisal Pattern for Performance of Superior League Football Teams by Emphasizing on Stakeholders' Benefits

Performance assessment by stakeholders is a strategic process that this research formed based on Freeman Stakeholders’ theory (1986) and Lee Stakeholders’ model and its goal is replying to following questions in order to present proper model for performance assessment: Who are most important stakeholders of superior football teams? What are their most important purposes? What are most important actions for fulfilling their needs? The research information collected from ministry of sport and youth, federation, club universalities, library and filed experts and in first stage based on Freeman theory and past studies and experts’ opinions, a questionnaire was developed with Cronbach alpha coefficient of 0.891 and by using Shannon entropy model and TOPSIS method extracted 9 priorities out of 21. In second stage, a second questionnaire was developed with Cronbach alpha coefficient of 0.928 and 20 most important requests out of 71extracted by TOPSIS method. In 3rd stage, a third questionnaire was developed through interview with managers of 3 superior leagues and took measures to examine most implorations actions for providing stakeholders requests that 49 executive actions was recognized and performed by QFD model and quality house model indicated relation among requests of stakeholders, actions, weighting and ranked ultimately 24 important actions was recognized and by using results and normalization, performance assessment model extracted from above three processes that indicated victory result and monetary benefits included their most important requests and teams shall take action to establish clear financial and planning unit and shall be assessed periodically.

Analyzing the Skeleton-spatial Development in Yazd and Measuring Its Conformity with the Smart Growth Pattern

This article aims at and analyzing the skeleton –spatial pattern in Yazd and measuring its conformity with the smart urban growth pattern. This research is the applied type and its method is descriptive and analytic. Data gathering method has been of two methods, library and field study. To measure the skeleton farm and recognize the skeleton development pattern of the city, Garry coefficient, Mara, coefficient, Shannon Entropy model and intender model have been used. To measure the conformity of Yazd Skeleton growth pattern by using Constant development indicators ,experts were asked to do same surveys and questionnaires results of questionnaire are analyzed by using spss software .results of the research and calculating Moran and Gary coefficient , indicates that according to the degree of gathering and dispersion of population and activity ,Yazd follows a random to sprawl pattern .Copulating Shannon Entropy also confirms the urban sprawl growth in Yazd . According to the results of Heldern model 60 percent of Yazd growth during 1981 to 2011 , is related to population growth and 40 percent is based on city’s spiral and horizontal growth that has led to the reduction in population compression and increase in shared urban land at last expansion in Yazd horizontal spiral form .Measure the growth pattern conformity and development of Yazd with the indicators of smart urban growth pattern indicates its lock of conformity ,The final result would be that during the past few decades ,growth and development pattern in Yazd been desirable and is not conforming to Smart Urban development. DOI: 10.5901/mjss.2015.v6n4s2p555

Analysis of physical expansion and sprawl growth factors of Sari city using Shannon and Heldern entropy models

population growth and rapid urbanization growth in recent decades has not only led to unbalanced physical expansion of cities, but also the growth and development of cities is heavily influenced. As cities developed with no plans and urban areas in a short time reached their primary area several times. Sari, like many other cities in the country is not immune from these changes. So that the city population has increased by 16 times over the last fifty years. The increasing population growth, uncontrolled physical expansion has resulted in the city. In order to prevent these inefficiencies of urban problems, the present study was done to determine the factors influencing the process of expanding Sari and to find out proposed solutions to fix and prevent this process. the method used in this study, descriptive–analytical method, to data analysis and heldern and Shannon entropy model is used and the results show that: 82% of the physical growth of the city between 2006-1956 was related to the population growth and the remaining 18 percent, is related to the horizontal growth and city sprawl, the metropolitan area of the city has denser structure and the surrounding areas have a more dispersed structure. Also the effects of synthetic and natural factors restricting Sari physical development has made the city exorbitance horizontal and linear developed. from the findings that could help prevent the horizontal development of the city, it could be said that we can make the city vertically developed rather than horizontal expansion, improvement and renovation of old texture of implementation and more use of the land, filling the empty spaces and etc.

Six decades of urban growth using remote sensing and GIS in the city of Bandar Abbas, Iran

Bandar Abbas is the capital city of Hormozgan province, is the south of Iran. The city has witnessed rapid growth in the last three decades, mostly because of its economic, commercial and social attractions. However, forms and operations of urban sprawl may vary in important manners according to determine geographical and historical characteristics, and these difference need to be reviewed with creation geodatabase of spatial and attribute data during past periods until now of urban formation and expansion. We implemented this research to understand Bandar Abbas city growth dynamic during last six decades using aerial photo, Remote Sensing (RS) data and Geographical Information System (GIS), to investigate its sprawl for the during six decades and to prepare a basis for urban planning and management. We calibrated it with geospatial data derived from a time series of aerial photos and satellite images. Treated remote sensing data covering the six decades were used to calculate land use/cover and urban growth. The application of classification techniques to the remote sensing data enabled the extraction of eight main types of land use: agricultural, barren, coastal, hole, river, rocky hill, urban, and built-up. Growth was calculated through Shannon's entropy model. The urbanized area increased from 403.77 ha to 4959.59 ha from 1956 to 2012, a rate almost five times that of the population growth observed in the same period. Such findings make the case of Bandar Abbas important for several reasons. First, Bandar Abbas has undergone a rapid increase in urban sprawl according to urban growth indicators. Second, the urban sprawl quickly grew from medium-sized to large a process considered inappropriate according to physical and structural limitations on urban growth. Lastly, the excessive extension of the built-up boundary in the city resulted in the loss of coastal land and open space, two main sources of tourist attraction and economic sustainable development.

Groundwater qanat potential mapping using frequency ratio and Shannon’s entropy models in the Moghan watershed, Iran

The purpose of current study is to produce groundwater qanat potential map using frequency ratio (FR) and Shannon's entropy (SE) models in the Moghan watershed, Khorasan Razavi Province, Iran. The qanat is basically a horizontal, interconnected series of underground tunnels that accumulate and deliver groundwater from a mountainous source district, along a water- bearing formation (aquifer), and to a settlement. A qanat locations map was prepared for study area in 2013 based on a topographical map at a 1:50,000-scale and extensive field surveys. 53 qanat locations were detected in the field surveys. 70 % (38 locations) of the qanat locations were used for groundwater potential mapping and 30 % (15 locations) were used for validation. Fourteen effective factors were considered in this investigation such as slope degree, slope aspect, altitude, topographic wetness index (TWI), stream power index (SPI), slope length (LS), plan curvature, profile curvature, distance to rivers, distance to faults, lithology, land use, drainage density, and fault density. Using the above conditioning factors, groundwater qanat potential map was generated implementing FR and SE models, and the results were plotted in ArcGIS. The predictive capability of frequency ratio and Shannon's entropy models were determined by the area under the relative operating characteristic curve. The area under the curve (AUC) for frequency ratio model was calculated as 0.8848. Also AUC for Shannon's entropy model was 0.9121, which depicts the excellence of this model in qanat occurrence potential estimation in the study area. So the Shannon's entropy model has higher AUC than the frequency ratio model. The produced groundwater qanat potential maps can assist planners and engineers in groundwater development plans and land use planning.

Monitoring Urban Sprawl Using Remote Sensing and GIS Techniques of a Fast Growing Urban Centre, India

India's urban population has grown tremendously in the last four decades from 79 million in 1961 to 285 million in 2001. This fast rate of increase in urban population is mainly due to large scale migration of people from rural and smaller towns to bigger cities in search of better employment opportunities and good life style. This rapid population pressure has resulted in unplanned growth in the urban areas to accommodate these migrant people which in turn leads to urban sprawl. It is a growing problematic aspect of metropolitan and bigger city's growth and development in recent years in India. Urban sprawl has resulted in loss of productive agricultural lands, open green spaces, loss of surface water bodies and depletion of ground water. Therefore, there is a need to study, understand and quantify the urban sprawl. In this paper an attempt has been made to use Shannon's entropy model to assess urban sprawl using IRS P-6 data and topographic sheet in GIS environment for one of the fastest growing city of South India and its surrounding area. The built-up area of the city has increased from 135 km <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2</sup> in 1971 to 370 km <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2</sup> in 2005. The study shows that there is a remarkable urban sprawl in and around the twin city between 1971 and 2005 because 215 km <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2</sup> of agricultural land has lost to built-up land during this period. As a result the urban ecosystem has changed in the last four decades.