Standard Deviation Of Normal Distribution Research Articles

A Coverage Optimization Method for WSNs Based on the Improved Weed Algorithm.

Wireless sensor networks (WSNs) is a multi-hop wireless network composed of a group of static or mobile sensor nodes in the form of self-organization. Uneven distribution of nodes often leads to the problem of over coverage and incomplete coverage of monitoring areas. To solve this problem, this paper establishes a network coverage optimization model and proposes a coverage optimization method based on an improved hybrid strategy weed algorithm (LRDE_IWO). The improvement of the weed algorithm includes three steps. Firstly, the standard deviation of normal distribution based on the tangent function is used as the seed’s new step size in the seed diffusion stage to balance the ability of the global search and local search of weed algorithm. Secondly, to avoid the problem of premature convergence, a disturbance mechanism combining enhanced Levy flight and the adaptive random walk strategy is proposed in the process of seed breeding. Finally, in competition of invasive weed stage, the differential evolution strategy is introduced to optimize the competition operation process and speed up convergence. The improved weed algorithm is applied to coverage optimization of WSNs. The simulation results show that the coverage rate of LRDE_IWO is increased by about 1% to 6% compared with the original invade weed algorithm (IWO) and the differential evolution invasive weed optimization algorithm (DE_IWO), and the coverage rate of the LRDE_IWO algorithm is increased by 4.10%, 2.73% and 1.19%, respectively, compared with the antlion optimization algorithm (ALO), the fruit fly optimization algorithm (FOA) and the gauss mutation weed algorithm (IIWO). The results prove the superiority and validity of the improved weed algorithm for coverage optimization of wireless sensor networks.

A modified approach to cross entropy method: Elitist stepped distribution algorithm

This paper introduces a new algorithm named Elitist Stepped Distribution Algorithm (ESDA), which is inspired from the existing Cross Entropy Method (CEM) through the modification of elite sample based normal distribution used in CEM. Considering the natural behavior of normal distribution, ESDA is proposed to enhance the drawbacks of CEM through improving the efficiency in both exploration and exploitation processes when applying for complex function optimization problems. In ESDA, the elite sample percent defined in CEM is separated into two parts: (1) elite sample percent to calculate the mean value, and (2) elite sample percent to calculate standard deviation of normal distribution to construct an applicable balance between exploration and exploitation ability of the algorithm at a reasonable convergence speed. The elite sample percent parameter for the mean guides the algorithm to focus more on the better solutions and therefore improves the exploitation ability, whereas the elite sample percent parameter for the standard deviation controls the length of standard deviation to handle the exploration process more effectively. Performance of ESDA is investigated using unconstrained benchmark problems and compared with CEM, Simple Genetic Algorithm and Particle Swarm Optimization. The comparisons on unimodal and multi-modal functions confirm the efficiency of the algorithm in both exploration and exploitation process. In addition, the performance of ESDA is tested using constrained engineering problems commonly used in literature by comparing its performance with the other ones statistically. The results on engineering problems also prove that ESDA is perfectly applicable in real-world applications.

A Capacity-Restraint Transit Assignment Model When a Predetermination Method Indicates the Invalidity of Time Independence

The statistical independence of time of every two adjacent bus links plays a crucial role in deciding the feasibility of using many mathematical models to analyze urban transit networks. Traditional research generally ignores the time independence that acts as the ground of their models. Assumption is usually made that time independence of every two adjacent links is sound. This is, however, actually groundless and probably causes problematic conclusions reached by corresponding models. Many transit assignment models such as multinomial probit-based models lose their effects when the time independence is not valid. In this paper, a simple method to predetermine the time independence is proposed. Based on the predetermination method, a modified capacity-restraint transit assignment method aimed at engineering practice is put forward and tested through a small contrived network and a case study in Nanjing city, China, respectively. It is found that the slope of regression equation between the mean and standard deviation of normal distribution acts as the indicator of time independence at the same time. Besides, our modified assignment method performs better than the traditional one with more reasonable results while keeping the property of simplicity well.

A computer simulation of continuous ion exchange membrane electrodialysis for desalination of saline water

A computer simulation program including the principle of ① mass transport, ② current density distribution, ③ energy consumption and ④ limiting current density is developed for predicting desalinating performance of a continuous (one-pass flow) electrodialysis process. In this simulation the following parameters are inputted; ① membrane characteristics such as overall transport number, overall solute permeability, overall electro-osmotic permeability, overall hydraulic permeability, direct current electric resistance etc. ② electrodialyzer specifications such as flow-pass thickness, flow-pass width and flow-pass length of a desalting cell etc. and ③ electrodialytic conditions such as current density, electrolyte concentration in a feeding solution, linear velocity in desalting cells, standard deviation of normal distribution of solution velocity ratio etc. In a practical-scale electrodialyzer, electrolyte concentration in a desalting cell is decreased along a flow-pass and it gives rise to electrolyte concentration distribution. It causes electric resistance distribution and current density distribution. Solution velocities in desalting cells vary between the cells, and give rise to solution velocity distribution. In this simulation, these distributions are taken into account assuming that the frequency distribution of solution velocity ratio is equated by the normal distribution. Further, the influences of electrodialyzer specifications and elctrodialysis conditions described above on the performances of an electrodialyzer (desalting ratio, current efficiency, electrolyte concentration at the outlets of desalting cells, cell voltage, energy consumption, electrolyte concentration distribution, current density distribution, and limiting current density) are predicted. The simulation model is developed on the basis of the experiments and its reasonability is supported by the performance of electrodialyzers operating in salt-manufacturing plants.

A computer simulation of batch ion exchange membrane electrodialysis for desalination of saline water

A computer simulation program is developed for predicting desalinating performance of a batch electrodialysis process. The program includes the principle of ① mass transport, ② current density distribution, ③ cell voltage, ④ mass balance/energy consumption and ⑤ limiting current density. In this simulation the following parameters are inputted; ① membrane characteristics such as overall transport number, overall solute permeability, overall electro-osmotic permeability, overall hydraulic permeability, direct current electric resistance etc., ② electrodialyzer specifications such as flow-pass thickness, flow-pass width and flow-pass length in a desalting cell etc. and ③ electrodialytic conditions such as voltage, electrolyte concentration in a feeding solution, linear velocity in desalting cells, standard deviation of normal distribution of solution velocity ratio etc. The following phenomena were computed and discussed; ① Changes of electrolyte concentration and current density with operation time. ② Influence of cell voltage on operation time (batch duration), water recovery and energy consumption. ③ Influence of volume of an electrolyte solution prepared at first on operation time. ④ Influence of cell voltage, electrolyte concentration and standard deviation of solution velocity ratio in desalting cells on limiting current density. ⑤ Energy consumption in a reverse osmosis process. ⑥ Excepting limiting current density, the performance of an electrodialyzer is never influenced by the standard deviation of normal distribution of solution velocity ratio in desalting cells. ⑦ Energy consumption in electrodialysis is less than that in reverse osmosis at feeding saline water concentration less than about 2000 mg/l .

Limiting current density of an ion-exchange membrane and of an electrodialyzer

The limiting current density of an ion-exchange membrane was measured using a small-scale electrodialysis apparatus and was expressed by the function of NaCl concentration and linear velocity of a solution in a desalting cell. The limiting current density under a flowing solution in a desalting cell was understandable based on the Nernst-diffusion model assuming that the thickness of a boundary layer is equivalent to that of a diffusion layer, and expressed by the function of NaCl concentration and linear velocity of a solution in a desalting cell. A spacer is usually considered to function as turbulence promoter. However, it seems block the main stream of laminar flow in a desalting cell, generate dead spaces between the spacer and a membrane and decrease the limiting current density. In order to increase the limiting current density, the solution velocity and the Reynolds number must be increased and create turbulent flow. In an ion-exchange membrane electrodialyzer, solution velocities in desalting cells are not uniform between the cells incorporated in a stack. This event produces electrolyte concentration distribution between the cells and current density distribution in an electrodialyzer. When an electric current reaches the limiting current density of an ion-exchange membrane at the outlet of a desalting cell in which velocity and electrolyte concentration are the least, the average current density applied to an electrodialyzer is defined as the limiting current density of the electrodialyzer. In this study, the solution velocity distribution was measured using a practical and a semi-practical electrodialyzer. Further, we computed the relationship between the standard deviation of normal distribution of linear velocities in desalting cells and electrolyte concentration at the outlet of the desalting cell in which velocity and electrolyte concentration are the least. Based on the above computation and the evaluation of the limiting current of an ion-exchange membrane, the limiting current density of an electrodialyzer was determined.

An Explanation for Depressed Semi-circular Arcs in Interfacial Impedance Plots of the Interface between Metal and Electrolyte

A new electrical equivalent circuit accounting for metal/solution interface about the surface heterogeneity of electrodes was proposed instead of the known semi-circular law. The present equivalent model consists of a ladder network of elements, where each element is made of a solution resistance in series with a parallel combination of double layer of capacitance and charge transfer resistance. The parameter σ, the standard deviation of normal distribution of double layer capacitance affected the depressed semi-circular arcs of different extent, which may be caused by various heterogeneities of the surface reactivity. The circuit which gives a depressed semi-circular arc is in agreement with the results of electrodeposition of copper from acidic copper sulphate solution.