In this paper a new proposal of a straight line, the ＂modified Tukey＇s line＂, for fitting to a normal quantile-quantile Plot, or normal Q-Q plot, is presented. This probability plot allows us to determine whether a...In this paper a new proposal of a straight line, the ＂modified Tukey＇s line＂, for fitting to a normal quantile-quantile Plot, or normal Q-Q plot, is presented. This probability plot allows us to determine whether a set of sample observations is distributed according to a normal distribution. For this, the sample quantiles are represented against the quantiles of a theoretical probability model, which in this case is the normal distribution. If the data set follows the above mentioned distribution, the plotted points will have a rectilinear configuration. To verify this, there are different alternatives for fitting a straight line to the plotted points. Among the straight lines which can be fitted to a Q-Q plot, in this paper, besides the proposed straight line, the following straight lines are considered： straight line that passes through the first and third quartiles, straight line that passes through the 10th and 90th percentiles, straight line fitted by the method of least squares, straight line with slope s and constant the average of the data set, Theil＇s line and Tukey＇s line. In addition, an example, in which there are represented the different straight lines considered and the proposed straight line on a normal Q-Q plot obtained for the same set of observations, is developed. In this example the existing differences among the straight lines are observed.展开更多
The electrical power generation from low temperature heat source attracts more and more attentions but the temperature mismatching between the heat sources and working medium in the organic Rankine cycle(ORC)becomes a...The electrical power generation from low temperature heat source attracts more and more attentions but the temperature mismatching between the heat sources and working medium in the organic Rankine cycle(ORC)becomes an issue.The organic flash cycle(OFC)is an effective solution to this issue.In this paper,the OFC is analyzed by the concept of entransy loss and the T-Q(temperature-heat flow rate)diagram for the heat-work conversion.The equations for cycles of the basic OFC and the OFC whose heat source is the exhaust gas of the turbine in a Brayton cycle(the combined cycle)are derived theoretically and the results indicate that larger entransy loss rate leads to larger output power with prescribed inlet parameters of the hot stream in the discussed cases,which is displayed by the T-Qdiagram intuitively.Two numerical examples demonstrate that the optimal mass flow rate of the working medium for the maximum entransy loss rate is the same as that for the maximum output power.The T-Qdiagram analyses is in accordance with the numerical results.The concept of entransy loss can be used as the criteria for the OFC optimization.展开更多
文摘In this paper a new proposal of a straight line, the ＂modified Tukey＇s line＂, for fitting to a normal quantile-quantile Plot, or normal Q-Q plot, is presented. This probability plot allows us to determine whether a set of sample observations is distributed according to a normal distribution. For this, the sample quantiles are represented against the quantiles of a theoretical probability model, which in this case is the normal distribution. If the data set follows the above mentioned distribution, the plotted points will have a rectilinear configuration. To verify this, there are different alternatives for fitting a straight line to the plotted points. Among the straight lines which can be fitted to a Q-Q plot, in this paper, besides the proposed straight line, the following straight lines are considered： straight line that passes through the first and third quartiles, straight line that passes through the 10th and 90th percentiles, straight line fitted by the method of least squares, straight line with slope s and constant the average of the data set, Theil＇s line and Tukey＇s line. In addition, an example, in which there are represented the different straight lines considered and the proposed straight line on a normal Q-Q plot obtained for the same set of observations, is developed. In this example the existing differences among the straight lines are observed.
基金The National Natural Science Foundation of China(Grant No.51376101)Science Fund for Creative Research Groups(Grant No.51321002)Tsinghua University Initiative Scientific Research Program
文摘The electrical power generation from low temperature heat source attracts more and more attentions but the temperature mismatching between the heat sources and working medium in the organic Rankine cycle(ORC)becomes an issue.The organic flash cycle(OFC)is an effective solution to this issue.In this paper,the OFC is analyzed by the concept of entransy loss and the T-Q(temperature-heat flow rate)diagram for the heat-work conversion.The equations for cycles of the basic OFC and the OFC whose heat source is the exhaust gas of the turbine in a Brayton cycle(the combined cycle)are derived theoretically and the results indicate that larger entransy loss rate leads to larger output power with prescribed inlet parameters of the hot stream in the discussed cases,which is displayed by the T-Qdiagram intuitively.Two numerical examples demonstrate that the optimal mass flow rate of the working medium for the maximum entransy loss rate is the same as that for the maximum output power.The T-Qdiagram analyses is in accordance with the numerical results.The concept of entransy loss can be used as the criteria for the OFC optimization.
