To design the dam under the presupposition that the cost is minimum (cost of the dam may be evaluated by the formulation 3h2+B2)and the special design probability is no less than 95%. The stochastic design variables and parameters are presented in as follows: Stochastic design variable (m) B h Distribution form Normal Normal Variation 0.15 0.15 Stochastic parameters Vm.x(km/h) H(m) Distribution form Logarithm Normal Normal Mean 80.0 12.0 Variance 16.0 2.40 So far as the wave height H is concerned,the stochastic constraint is P{H-h≤0}≥95% Suppose the P.represents the pressure suffered by the dam,the Pa.m is the strength of the dam,other stochastic constraint is P{P。en-Pam≤0}≥95% The results obtained by the method are given in the following table, Table The results of dam design Method Cost Optimum R① b② Increment AR③ solution (x) of cost Stochastic 866.67 B=9.74Rp1=95%b1=0.4875△C=4%△R1=87.30% optimum design h=17.47Rp2=95%b2=0.5000 4R2=91.12% Determinate 833.33 B=8.33R41=51.0% optimum design h=16.00R42=49.5% 1 R-actual probability of stochastic constraint 2b-relating to the chebyshev point ③△R-increment of the constraint probability The curves in Fig.6 present the density functions of the above two stochastic constraints f(x,w)and f2(x,w)which show the probabilities of the design. In the Table,it can be seen that probability of the first stochastic constraint increases by 87.30%and probability of the second stochastic constraint increases by 91.12%,and based on deterministic results,the objective value only increas- by 4%.From this point of view,stochastic optimal method is a very mean- ingful method. 459五 皿 立 垃 了 么 。 一 ’ 。 石 犷 二 住 。 。 。 。 ， 尸 一 蕊。 写 。 。 。 ‘ 。 ， 五 ‘ 沮 ， 。 。 。 。 一 。 簇 。 异 住 。 ‘ ， 劣 ① ② 乙 ⑧ 爪 宜 。 。 。 。 。 。 。 △ 二 △ 二 。 。 。 二 。 二 。 ① 一 ② ‘ 一 ⑧ △ 一 二 。 五 ‘ ，， “ ‘ ，， 。 ， 。 写 。 ， ， 川 环 。 ， ‘ “