W eighted sum based method on the optimal weights for weapon evaluation

In order to solve instability problem of calculation precision resulting from the selection of each target weight in evaluating weapon systems, a weighted sum based method is proposed. Specif- ically, the subjective weights depending on experts＇ experience are substituted by the optimal weights. The optimal weights are acquired through constructing a mathematical programming model based on subjective weights and objective weights. The method of solving subjective weights is the same as before, and the objective weights were solved by means of grey theory. The case analysis shows that the method of improved weighted sum can improve the evaluation precision up to more than 5% , and minimize the instability of calculation precision resulting from only using subjective weights. The method that the optimal weights substituted the subjective weights is brought forward in improving evaluation precision for the first time. The ideas of the optimal weights and the pro- posed method are described and analyzed.

3-D Reconstruction and Visualization of Laser-Scanned Trees by Weighted Locally Optimal Projection and Accurate Modeling Method

This paper presents a method to reconstruct 3-D models of trees from terrestrial laser scan(TLS)point clouds.This method uses the weighted locally optimal projection(WLOP)and the AdTree method to reconstruct detailed 3-D tree models.To improve its representation accuracy,the WLOP algorithm is introduced to consolidate the point cloud.Its reconstruction accuracy is tested using a dataset of ten trees,and the one-sided Hausdorff distances between the input point clouds and the resulting 3-D models are measured.The experimental results show that the optimal projection modeling method has an average one-sided Hausdorff distance(mean)lower by 30.74%and 6.43%compared with AdTree and AdQSM methods,respectively.Furthermore,it has an average one-sided Hausdorff distance(RMS)lower by 29.95%and 12.28%compared with AdTree and AdQSM methods.Results show that the 3-D model generated fits closely to the input point cloud data and ensures a high geometrical accuracy.

Frequency Weighting Filter Design for Automotive Ride Comfort Evaluation

Few study gives guidance to design weighting filters according to the frequency weighting factors,and the additional evaluation method of automotive ride comfort is not made good use of in some countries.Based on the regularities of the weighting factors,a method is proposed and the vertical and horizontal weighting filters are developed.The whole frequency range is divided several times into two parts with respective regularity.For each division,a parallel filter constituted by a low-and a high-pass filter with the same cutoff frequency and the quality factor is utilized to achieve section factors.The cascading of these parallel filters obtains entire factors.These filters own a high order.But,low order filters are preferred in some applications.The bilinear transformation method and the least P-norm optimal infinite impulse response（IIR） filter design method are employed to develop low order filters to approximate the weightings in the standard.In addition,with the window method,the linear phase finite impulse response（FIR） filter is designed to keep the signal from distorting and to obtain the staircase weighting.For the same case,the traditional method produces 0.330 7 m · s^–2 weighted root mean square（r.m.s.） acceleration and the filtering method gives 0.311 9 m · s^–2 r.m.s.The fourth order filter for approximation of vertical weighting obtains 0.313 9 m · s^–2 r.m.s.Crest factors of the acceleration signal weighted by the weighting filter and the fourth order filter are 3.002 7 and 3.011 1,respectively.This paper proposes several methods to design frequency weighting filters for automotive ride comfort evaluation,and these developed weighting filters are effective.

Improvement of Cardiac Function by Dry Weight Optimization Based on Interdialysis Inferior Vena Caval Diameter (1)

In hemodialysis (HD) patients, the diameter of the inferior vena cava (IVC) serves for evaluation of the amount of body fluid.

Two-stage prediction and update particle filtering algorithm based on particle weight optimization in multi-sensor observation

The reasonable measuring of particle weight and effective sampling of particle state are consid- ered as two important aspects to obtain better estimation precision in particle filter. Aiming at the comprehensive treatment of above problems, a novel two-stage prediction and update particle filte- ring algorithm based on particle weight optimization in multi-sensor observation is proposed. Firstly, combined with the construction of muhi-senor observation likelihood function and the weight fusion principle, a new particle weight optimization strategy in multi-sensor observation is presented, and the reliability and stability of particle weight are improved by decreasing weight variance. In addi- tion, according to the prediction and update mechanism of particle filter and unscented Kalman fil- ter, a new realization of particle filter with two-stage prediction and update is given. The filter gain containing the latest observation information is used to directly optimize state estimation in the frame- work, which avoids a large calculation amount and the lack of universality in proposal distribution optimization way. The theoretical analysis and experimental results show the feasibility and efficiency of the proposed algorithm.

OPTIMAL SUMMATION INTERVAL AND NONEXISTENCE OF POSITIVE SOLUTIONS TO A DISCRETE SYSTEM

In this paper, we are concerned with properties of positive solutions of the following Euler-Lagrange system associated with the weighted Hardy-Littlewood-Sobolev inequality in discrete form{uj =∑ k ∈Zn vk^q/（1 ＋ ｜j｜）^α（1 ＋ ｜k- j｜）^λ（1 ＋ ｜k｜）^β,（0.1）vj =∑ k ∈Zn uk^p/（1 ＋ ｜j｜）^β（1 ＋ ｜k- j｜）^λ（1 ＋ ｜k｜）^α,where u, v 〉 0, 1 〈 p, q 〈 ∞, 0 〈 λ 〈 n, 0 ≤α ＋ β≤ n- λ,1/p＋1〈λ＋α/n and 1/p＋1＋1/q＋1≤λ＋α＋β/n：=λ^-/n. We first show that positive solutions of（0.1） have the optimal summation interval under assumptions that u ∈ l^p＋1（Z^n） and v ∈ l^q＋1（Z^n）. Then we show that problem（0.1） has no positive solution if 0 〈λˉ pq ≤ 1 or pq 〉 1 and max{（n-λ^-）（q＋1）/pq-1,（n-λ^-）（p＋1）/pq-1} ≥λ^-.

Application of fuzzy optimization model in the evaluationof urban flood-waterloggedvulnerabilitybased on the synthetic weight ofgame theory

The evaluation of urban flood-waterlogged vulnerability is very important to the safety of urban flood control. In this paper, the evaluation of consolidated index is used. Respectively, AHP and entropy method calculate the subjective and objective weight of the evaluation indicators, and combine them by game theory. So we can obtain synthetic weight based on objective and subjective weights. The evaluation of urban flood-waterlogged vulnerability as target layer, a single variable multi-objective fuzzy optimization model is established. We use the model to evaluate flood-waterlogged vulnerability of 13 prefecture-level city in Hunan, and compare it with other evaluation method. The results show that the evaluation method has certain adaptability and reliability, and it＇ s helpfid to the construction planning of urban flood control.

Multi-Criteria Decision-Making for Power Grid Construction Project Investment Ranking Based on the Prospect Theory Improved by Rewarding Good and Punishing Bad Linear Transformation

Using the improved prospect theory with the linear transformations of rewarding good and punishing bad(RGPBIT),a new investment ranking model for power grid construction projects(PGCPs)is proposed.Given the uncertainty of each index value under the market environment,fuzzy numbers are used to describe qualitative indicators and interval numbers are used to describe quantitative ones.Taking into account decision-maker’s subjective risk attitudes,a multi-criteria decision-making(MCDM)method based on improved prospect theory is proposed.First,the[−1,1]RGPBIT operator is proposed to normalize the original data,to obtain the best andworst schemes of PGCPs.Furthermore,the correlation coefficients between interval/fuzzy numbers and the best/worst schemes are defined and introduced to the prospect theory to improve its value function and loss function,and the positive and negative prospect value matrices of the project are obtained.Then,the optimization model with the maximum comprehensive prospect value is constructed,the optimal attribute weight is determined,and the PGCPs are ranked accordingly.Taking four PGCPs of the IEEERTS-79 node system as examples,an illustration of the feasibility and effectiveness of the proposed method is provided.

Design of Optimal Weight for a Gear Transmission System Using Hybrid Taguchi-Genetic Algorithm

The gear transmission system has been widely applied in mechanical systems, and many high-performance applications of these systems require low weight. With the aid of establishing the optimization model of the gear transmission system that consists of an objective function and some constraints （for example, the bending stress, the contact stress, the torsional strength, etc.）, the optimal weight design of the gear transmission system can be transformed into the optimization problem for the objective function under the constraints. Moreover, both the shaft and the gear of the gear transmission system are considered simultaneously in our design. The hybrid Taguchi-genetic algorithm （HTGA） is employed to find the optimal design variables and the optimal weight of the system. An illustrated example for the single spur gear reducer is given to show that the optimal weight design problem can be successfully solved using the proposed design scheme. It also proves the high efficiency and feasibility of the algorithm in the gear design.

A novel multi-sensor multiple model particle filter with correlated noises for maneuvering target tracking

Aiming at the effective realization of particle filter for maneuvering target tracking in multi-sensor measurements,a novel multi-sensor multiple model particle filtering algorithm with correlated noises is proposed.Combined with the kinetic evolution equation of target state,a multi-sensor multiple model particle filter is firstly constructed,which is also used as the basic framework of a new algorithm.In the new algorithm,in order to weaken the adverse influence from random measurement noises in the measuring process of particle weight,a weight optimization strategy is introduced to improve the reliability and stability of particle weight.In addition,considering the correlated noise existing in the practical engineering,a decoupling method of correlated noise is given by the rearrangement and transformation of the state transition equation and measurement equation.Since the weight optimization strategy and noise decoupling method adopt respectively the center fusion structure and the off-line way,it improves the adverse effect effectively on computational complexity for increasing state dimension and sensor number.Finally,the theoretical analysis and experimental results show the feasibility and efficiency of the proposed algorithm.

Discovering interlinkages between major cryptocurrencies using high‑frequency data: new evidence from COVID‑19 pandemic

Through the application of the VAR-AGARCH model to intra-day data for three cryptocurrencies(Bitcoin,Ethereum,and Litecoin),this study examines the return and volatility spillover between these cryptocurrencies during the pre-COVID-19 period and the COVID-19 period.We also estimate the optimal weights,hedge ratios,and hedging effectiveness during both sample periods.We find that the return spillovers vary across the two periods for the Bitcoin–Ethereum,Bitcoin–Litecoin,and Ethereum–Litecoin pairs.However,the volatility transmissions are found to be different during the two sample periods for the Bitcoin–Ethereum and Bitcoin–Litecoin pairs.The constant conditional correlations between all pairs of cryptocurrencies are observed to be higher during the COVID-19 period compared to the pre-COVID-19 period.Based on optimal weights,investors are advised to decrease their investments(a)in Bitcoin for the portfolios of Bitcoin/Ethereum and Bitcoin/Litecoin and(b)in Ethereum for the portfolios of Ethereum/Litecoin during the COVID-19 period.All hedge ratios are found to be higher during the COVID-19 period,implying a higher hedging cost compared to the pre-COVID-19 period.Last,the hedging effectiveness is higher during the COVID-19 period compared to the pre-COVID-19 period.Overall,these findings provide useful information to portfolio managers and policymakers regarding portfolio diversification,hedging,forecasting,and risk management.

Grid-Based Pseudo-Parallel Genetic Algorithm and Its Application

Aimed at the problems of premature and lower convergence of simple genetic algorithms （SGA）, three ideas --partition the whole search uniformly, multi-genetic operators and multi-populations evolving independently are introduced, and a grid-based pseudo-parallel genetic algorithms （GPPGA） is put forward. Thereafter, the analysis of premature and convergence of GPPGA is made. In the end, GPPGA is tested by both six-peak camel back function, Rosenbrock function and BP network. The result shows the feasibility and effectiveness of GPPGA in overcoming premature and improving convergence speed and accuracy.

RandWPSO-LSSVM optimization feedback method for large underground cavern and its engineering applications

According to the characteristics of large underground caverns, by using the safety factor of surrounding rock mass point as the control standard of cavern stability, RandWPSO-LSSVM optimization feedback method and flow process of large underground cavern anchor parameters were established. By applying the optimization feedback method to actual project, the best anchor parameters of large surge shaft five-tunnel area underground cavern of the Nuozhadu hydropower station were obtained through optimization. The results show that the predicted effect of LSSVM prediction model obtained through RandWPSO optimization is good, reasonable and reliable. Combination of the best anchor parameters obtained is 114131312, that is, the locked anchor bar spacing is 1 m x 1 m, pre-stress is 100 kN, elevation 580.45-586.50 m section anchor bar diameter is 36.00 mm, length is 4.50 m, spacing is 1.5 m × 2.5 m; anchor bar diameter at the five-tunnel area side wall is 25.00 mm, length is 7.50 m, spacing is 1 m× 1.5 m, and the shotcrete thickness is 0.15 m. The feedback analyses show that the optimization feedback method of large underground cavern anchor parameters is reasonable and reliable, which has important guiding significance for ensuring the stability of large underground caverns and for saving project investment.

Research on the optimal dynamical systems of three-dimensional Navier-Stokes equations based on weighted residual

In this paper, the theory of constructing optimal dynamical systems based on weighted residual presented by Wu & Sha is applied to three-dimensional Navier-Stokes equations, and the optimal dynamical system modeling equations are derived. Then the multiscale global optimization method based on coarse graining analysis is presented, by which a set of approximate global optimal bases is directly obtained from Navier-Stokes equations and the construction of optimal dynamical systems is realized. The optimal bases show good properties, such as showing the physical properties of complex flows and the turbulent vortex structures, being intrinsic to real physical problem and dynamical systems, and having scaling symmetry in mathematics, etc.. In conclusion, using fewer terms of optimal bases will approach the exact solutions of Navier-Stokes equations, and the dynamical systems based on them show the most optimal behavior.

Real-time Prediction Model of Amount of Manure in Winter Pig Pen Based on Backpropagation Neural Network

The automatic control of cleaning need to be based on the total amount of manure in the house. Therefore, this article established a prediction model for the total amount of manure in a pig house and took the number of pigs in the house, age, feed intake,feeding time, the time when the ammonia concentration increased the fastest and the daily fixed cleaning time as variable factors for modelling, so that the model could obtain the current manure output according to the real-time input of time. A Backpropagation(BP) neural network was used for training. The cross-validation method was used to select the best hyperparameters, and the genetic algorithm(GA), particle swarm optimization(PSO) algorithm and mind evolutionary algorithm(MEA) were selected to optimize the initial network weights. The results showed that the model could predict the amount of manure in real-time according to the model input. After the cross-validation method determined the hyperparameters, the GA, PSO and MEA were used to optimize the manure prediction model. The GA had the best average performance.

A New Fuzzy Adaptive Algorithm to Classify Imbalanced Data

Classification of imbalanced data is a well explored issue in the data mining and machine learning community where one class representation is overwhelmed by other classes.The Imbalanced distribution of data is a natural occurrence in real world datasets,so needed to be dealt with carefully to get important insights.In case of imbalance in data sets,traditional classifiers have to sacrifice their performances,therefore lead to misclassifications.This paper suggests a weighted nearest neighbor approach in a fuzzy manner to deal with this issue.We have adapted the‘existing algorithm modification solution’to learn from imbalanced datasets that classify data without manipulating the natural distribution of data unlike the other popular data balancing methods.The K nearest neighbor is a non-parametric classification method that is mostly used in machine learning problems.Fuzzy classification with the nearest neighbor clears the belonging of an instance to classes and optimal weights with improved nearest neighbor concept helping to correctly classify imbalanced data.The proposed hybrid approach takes care of imbalance nature of data and reduces the inaccuracies appear in applications of original and traditional classifiers.Results show that it performs well over the existing fuzzy nearest neighbor and weighted neighbor strategies for imbalanced learning.

NEW RESULTS ABOUT THE RELATIONSHIP BETWEEN OPTIMALLY WEIGHTED LEAST SQUARES ESTIMATE AND LINEAR MINIMUM VARIANCE ESTIMATE

The optimally weighted least squares estimate and the linear minimum variance estimateare two of the most popular estimation methods for a linear model.In this paper,the authors makea comprehensive discussion about the relationship between the two estimates.Firstly,the authorsconsider the classical linear model in which the coefficient matrix of the linear model is deterministic,and the necessary and sufficient condition for equivalence of the two estimates is derived.Moreover,under certain conditions on variance matrix invertibility,the two estimates can be identical providedthat they use the same a priori information of the parameter being estimated.Secondly,the authorsconsider the linear model with random coefficient matrix which is called the extended linear model;under certain conditions on variance matrix invertibility,it is proved that the former outperforms thelatter when using the same a priori information of the parameter.

A New Class of Hybrid Particle Swarm Optimization Algorithm

A new class of hybrid particle swarm optimization （PSO） algorithm is developed for solving the premature convergence caused by some particles in standard PSO fall into stagnation. In this algorithm, the linearly decreasing inertia weight technique （LDIW） and the mutative scale chaos optimization algorithm （MSCOA） are combined with standard PSO, which are used to balance the global and local exploration abilities and enhance the local searching abilities, respectively. In order to evaluate the performance of the new method, three benchmark functions are used. The simulation results confirm the proposed algorithm can greatly enhance the searching ability and effectively improve the premature convergence.

A novel fractional grey forecasting model with variable weighted buffer operator and its application in forecasting China's crude oil consumption

Oil is an important strategic material and civil energy.Accurate prediction of oil consumption can provide basis for relevant departments to reasonably arrange crude oil production,oil import and export,and optimize the allocation of social resources.Therefore,a new grey model FENBGM(1,1)is proposed to predict oil consumption in China.Firstly,the grey effect of the traditional GM(1,1)model was transformed into a quadratic equation.Four different parameters were introduced to improve the accuracy of the model,and the new initial conditions were designed by optimizing the initial values by weighted buffer operator.Combined with the reprocessing of the original data,the scheme eliminates the random disturbance effect,improves the stability of the system sequence,and can effectively extract the potential pattern of future development.Secondly,the cumulative order of the new model was optimized by fractional cumulative generation operation.At the same time,the smoothness rate quasi-smoothness condition was introduced to verify the stability of the model,and the particle swarm optimization algorithm(PSO)was used to search the optimal parameters of the model to enhance the adaptability of the model.Based on the above improvements,the new combination prediction model overcomes the limitation of the traditional grey model and obtains more accurate and robust prediction results.Then,taking the petroleum consumption of China's manufacturing industry and transportation,storage and postal industry as an example,this paper verifies the validity of FENBGM(1,1)model,analyzes and forecasts China's crude oil consumption with several commonly used forecasting models,and uses FENBGM(1,1)model to forecast China's oil consumption in the next four years.The results show that FENBGM(1,1)model performs best in all cases.Finally,based on the prediction results of FENBGM(1,1)model,some reasonable suggestions are put forward for China's oil consumption planning.