The error-sum function of alternating Sylvester series is introduced. Some elementary properties of this function are studied. Also, the hausdorff dimension of the graph of such function is determined.
The error-sum function of alternating Lǖroth series is introduced, which, to some extent, discerns the superior or not of an expansion comparing to other expansions. Some elementary properties of this function are st...The error-sum function of alternating Lǖroth series is introduced, which, to some extent, discerns the superior or not of an expansion comparing to other expansions. Some elementary properties of this function are studied. Also, the Hausdorff dimension of graph of such function is determined.展开更多
The theoretical positioning accuracy of multilateration(MLAT) with the time difference of arrival(TDOA) algorithm is very high. However, there are some problems in practical applications. Here we analyze the location ...The theoretical positioning accuracy of multilateration(MLAT) with the time difference of arrival(TDOA) algorithm is very high. However, there are some problems in practical applications. Here we analyze the location performance of the time sum of arrival(TSOA) algorithm from the root mean square error(RMSE) and geometric dilution of precision(GDOP) in additive white Gaussian noise(AWGN) environment. The TSOA localization model is constructed. Using it, the distribution of location ambiguity region is presented with 4-base stations. And then, the location performance analysis is started from the 4-base stations with calculating the RMSE and GDOP variation. Subsequently, when the location parameters are changed in number of base stations, base station layout and so on, the performance changing patterns of the TSOA location algorithm are shown. So, the TSOA location characteristics and performance are revealed. From the RMSE and GDOP state changing trend, the anti-noise performance and robustness of the TSOA localization algorithm are proved. The TSOA anti-noise performance will be used for reducing the blind-zone and the false location rate of MLAT systems.展开更多
The L<sub>1</sub> regression is a robust alternative to the least squares regression whenever there are outliers in the values of the response variable, or the errors follow a long-tailed distribution. To ...The L<sub>1</sub> regression is a robust alternative to the least squares regression whenever there are outliers in the values of the response variable, or the errors follow a long-tailed distribution. To calculate the standard errors of the L<sub>1</sub> estimators, construct confidence intervals and test hypotheses about the parameters of the model, or to calculate a robust coefficient of determination, it is necessary to have an estimate of a scale parameterτ. This parameter is such that τ<sup>2</sup>/n is the variance of the median of a sample of size n from the errors distribution. [1] proposed the use of , a consistent, and so, an asymptotically unbiased estimator of τ. However, this estimator is not stable in small samples, in the sense that it can increase with the introduction of new independent variables in the model. When the errors follow the Laplace distribution, the maximum likelihood estimator of τ, say , is the mean absolute error, that is, the mean of the absolute residuals. This estimator always decreases when new independent variables are added to the model. Our objective is to develop asymptotic properties of under several errors distributions analytically. We also performed a simulation study to compare the distributions of both estimators in small samples with the objective to establish conditions in which is a good alternative to for such situations.展开更多
With increasing the number of wind power generators,the consumption time of electromagnetic simulation of the wind farm explodes.To reduce the simulation time while meeting the accuracy requirement,a genetic clusterin...With increasing the number of wind power generators,the consumption time of electromagnetic simulation of the wind farm explodes.To reduce the simulation time while meeting the accuracy requirement,a genetic clustering-based equivalent model is proposed for the wind farm with numerous doubly fed induction generators.In the proposed model,active power together with the reactive power and the wind speed are selected to form the set of clustering indicators.A normalization technique is utilized to cope with the multiple orders of magnitude in these factors.An exponential fitness value is formulated as a function of the sorting number of the primary fitness value,and the fitness-based selection probability is constructed to overcome the property of premature and slow convergence of the genetic clustering algorithm.The sum of squares due to error is used to determine the optimal clustering number.In addition,a decoupled parameter equivalence method is adopted to obtain the equivalent parameters of the collection network.Simulation results and comparisons with various methods under different voltage scenarios show the feasibility and effectiveness of the proposed model.展开更多
研究了航空发动机气路故障诊断的测量参数选择的问题.基于发动机故障诊断的主因子模型,结合预测平方残差和(prediction error sum of squares,简称PRESS)准则,建立了一种选择风扇流量、风扇出口压力、压气机出口压力、压气机出口温度、...研究了航空发动机气路故障诊断的测量参数选择的问题.基于发动机故障诊断的主因子模型,结合预测平方残差和(prediction error sum of squares,简称PRESS)准则,建立了一种选择风扇流量、风扇出口压力、压气机出口压力、压气机出口温度、涡轮后温度和燃油流量这6个测量参数进行单轴涡扇发动机故障诊断的方法.大量的实例表明,合理运用该方法选择测量参数的种类和数量,既能取得比较满意的诊断效果,又能利用发动机控制系统已有的测量参数,降低诊断成本,具有一定的工程应用价值.展开更多
文摘The error-sum function of alternating Sylvester series is introduced. Some elementary properties of this function are studied. Also, the hausdorff dimension of the graph of such function is determined.
文摘The error-sum function of alternating Lǖroth series is introduced, which, to some extent, discerns the superior or not of an expansion comparing to other expansions. Some elementary properties of this function are studied. Also, the Hausdorff dimension of graph of such function is determined.
基金supported by the Joint Civil Aviation Fund of National Natural Science Foundation of China(Nos.U1533108 and U1233112)
文摘The theoretical positioning accuracy of multilateration(MLAT) with the time difference of arrival(TDOA) algorithm is very high. However, there are some problems in practical applications. Here we analyze the location performance of the time sum of arrival(TSOA) algorithm from the root mean square error(RMSE) and geometric dilution of precision(GDOP) in additive white Gaussian noise(AWGN) environment. The TSOA localization model is constructed. Using it, the distribution of location ambiguity region is presented with 4-base stations. And then, the location performance analysis is started from the 4-base stations with calculating the RMSE and GDOP variation. Subsequently, when the location parameters are changed in number of base stations, base station layout and so on, the performance changing patterns of the TSOA location algorithm are shown. So, the TSOA location characteristics and performance are revealed. From the RMSE and GDOP state changing trend, the anti-noise performance and robustness of the TSOA localization algorithm are proved. The TSOA anti-noise performance will be used for reducing the blind-zone and the false location rate of MLAT systems.
文摘The L<sub>1</sub> regression is a robust alternative to the least squares regression whenever there are outliers in the values of the response variable, or the errors follow a long-tailed distribution. To calculate the standard errors of the L<sub>1</sub> estimators, construct confidence intervals and test hypotheses about the parameters of the model, or to calculate a robust coefficient of determination, it is necessary to have an estimate of a scale parameterτ. This parameter is such that τ<sup>2</sup>/n is the variance of the median of a sample of size n from the errors distribution. [1] proposed the use of , a consistent, and so, an asymptotically unbiased estimator of τ. However, this estimator is not stable in small samples, in the sense that it can increase with the introduction of new independent variables in the model. When the errors follow the Laplace distribution, the maximum likelihood estimator of τ, say , is the mean absolute error, that is, the mean of the absolute residuals. This estimator always decreases when new independent variables are added to the model. Our objective is to develop asymptotic properties of under several errors distributions analytically. We also performed a simulation study to compare the distributions of both estimators in small samples with the objective to establish conditions in which is a good alternative to for such situations.
基金the National Key R&D Program of China(No.2019YFE0114700)the Key R&D Program in Hunan Province of China(No.2021GK2020)+1 种基金the Natural Science Foundation of Hunan Province of China(No.2021JJ30079)the Project of Philosophy and Social Science Research in Yiyang City(No.2022YS191)。
文摘With increasing the number of wind power generators,the consumption time of electromagnetic simulation of the wind farm explodes.To reduce the simulation time while meeting the accuracy requirement,a genetic clustering-based equivalent model is proposed for the wind farm with numerous doubly fed induction generators.In the proposed model,active power together with the reactive power and the wind speed are selected to form the set of clustering indicators.A normalization technique is utilized to cope with the multiple orders of magnitude in these factors.An exponential fitness value is formulated as a function of the sorting number of the primary fitness value,and the fitness-based selection probability is constructed to overcome the property of premature and slow convergence of the genetic clustering algorithm.The sum of squares due to error is used to determine the optimal clustering number.In addition,a decoupled parameter equivalence method is adopted to obtain the equivalent parameters of the collection network.Simulation results and comparisons with various methods under different voltage scenarios show the feasibility and effectiveness of the proposed model.
文摘研究了航空发动机气路故障诊断的测量参数选择的问题.基于发动机故障诊断的主因子模型,结合预测平方残差和(prediction error sum of squares,简称PRESS)准则,建立了一种选择风扇流量、风扇出口压力、压气机出口压力、压气机出口温度、涡轮后温度和燃油流量这6个测量参数进行单轴涡扇发动机故障诊断的方法.大量的实例表明,合理运用该方法选择测量参数的种类和数量,既能取得比较满意的诊断效果,又能利用发动机控制系统已有的测量参数,降低诊断成本,具有一定的工程应用价值.
