G12-NAOE9107-随机理论及其在海洋工程中的应用-作业代码

hw1

clearvars; clc; % hw1tx.m
random_N = 100;
seed = 0;
obj = gumbel(random_N, seed);
obj.plot();

test_N = 10000;
obj = confident(test_N);
obj.show_interval();

random_N = 108000;
obj = jacket(random_N, seed);
obj.plot();

% gumbel.m
classdef gumbel
    properties (Access = private)
        alpha;
        beta;
        random_N;
        seed;
    end
    methods
        function obj = gumbel(random_N, seed)
            obj.alpha = 2000;
            obj.beta = 300;
            obj.random_N = random_N;
            obj.seed = seed;
        end
        function plot(obj)
            x_rad = obj.get_random_x();
            y_rad = get_y_rad(obj);
            x_range = (1500:0.1:4500)';
            y_exp = obj.get_y_exp(x_range);
            y_rel = obj.get_y_rel(x_range);
            fig = figure(1);
            plts = [];
            strs = [];
            plt = scatter(x_rad, y_rad); hold on;
            plt.Marker = 'x';
            plt.SizeData = 60;
            plt.MarkerEdgeColor = 'Black';
            str = "Sample";
            plts = [plts; plt];
            strs = [strs; str];
            plt = plot(x_range, y_rel); hold on;
            plt.LineStyle = '-';
            plt.LineWidth = 1.5;
            plt.Color = 'Black';
            str = "True";
            plts = [plts; plt];
            strs = [strs; str];
            plt = plot(x_range, y_exp); hold on;
            plt.Color = 'Black';
            plt.LineWidth = 1.5;
            plt.LineStyle = '--';
            str = "Empirical";
            plts = [plts; plt];
            strs = [strs; str];
            fig.CurrentAxes.XLim = [1500, 4500];
            leg = legend(plts, strs);
            leg.FontSize = 17;
            leg.Box = "off";
            xl = xlabel("x");
            yl = ylabel("y");
            xl.FontSize = 17;
            yl.FontSize = 17;
            saveas(gcf, "fig1-1.png");
            close(gcf);
        end
        function [alpha_exp, beta_exp] = get_exp(obj)
            gumbel_x = obj.get_random_x();
            mean_num = mean(gumbel_x,1);
            std_num = std(gumbel_x,1);
            beta_exp = std_num/1.28255;
            alpha_exp = mean_num-0.57722*beta_exp;
        end
    end
    methods (Access = private)
        function gumbel_x = get_random_x(obj)
            random_y = obj.get_random_y();
            gumbel_x = obj.alpha-obj.beta*log(-log(random_y));
        end
        function y_rad = get_y_rad(obj)
            random_y = obj.get_random_y();
            y_rad = log(-log(random_y));
        end
        function y_rel = get_y_rel(obj, x_range)
            y_rel = -(x_range-obj.alpha)/obj.beta;
        end
        function y_exp = get_y_exp(obj, x_range)
            gumbel_x = obj.get_random_x();
            mean_num = mean(gumbel_x,1);
            std_num = std(gumbel_x,1);
            beta_exp = std_num/1.28255;
            alpha_exp = mean_num-0.57722*beta_exp;
            y_exp = -(x_range-alpha_exp)/beta_exp;
        end
        function random_y = get_random_y(obj)
            rng(obj.seed);
            random_y = rand(obj.random_N, 1);
        end
    end
end

% jacket.m
classdef jacket
    properties (Access = private)
        random_N;
        seed;
    end
    methods
        function obj = jacket(random_N, seed)
            obj.random_N = random_N;
            obj.seed = seed;
        end
        function plot(obj)
            strs = [];
            plts = [];
            fig = figure(1);
            hold on;
            [p_f, QcQ, xx] = get_Qcap(obj);
            QcQ1 = QcQ(QcQ < 0);
            xx1 = xx(QcQ < 0);
            QcQ2 = QcQ(QcQ >= 0);
            xx2 = xx(QcQ >= 0);
            % bad
            plt = scatter(xx1, QcQ1);
            hold on;
            plt.Marker = 'x';
            plt.SizeData = 38;
            plt.MarkerEdgeColor = 'Red';
            plt.MarkerEdgeAlpha = 1.0;
            plt.SizeData = 18;
            str = "结构失效";
            plts = [plts; plt];
            strs = [strs; str];
            % good
            plt = scatter(xx2, QcQ2);
            hold on;
            plt.Marker = 'x';
            plt.SizeData = 38;
            plt.MarkerEdgeColor = 'Blue';
            fig.CurrentAxes.XLim = [1,108000];
            fig.CurrentAxes.YLim = [-350,350];
            plt.MarkerEdgeAlpha = 1.0;
            str = "结构不失效";
            plts = [plts; plt];
            strs = [strs; str];
            hold on;
            disp("p_f = " + p_f);
            % zero
            ze = zeros(size(xx, 1), 1);
            plt = plot(xx, ze);
            plt.LineStyle = '--';
            plt.Color = 'Black';
            plt.LineWidth = 1.5;
            ld = legend(plts, strs);
            ld.FontSize = 17;
            ld.Box = 'off';
            ld.Location = 'Best';
            xl = xlabel("实验序号");
            xl.FontSize = 17;
            yl = ylabel("Qcap-Q");
            yl.FontSize = 17;
            saveas(fig, "fig1-3.png");
            close(fig);
        end
    end
    methods (Access = private)
        function n = get_rad_n(obj)
            rng(obj.seed);
            n = rand(obj.random_N,4);
        end
        function [H, U, FB, RSR] = get_HU(obj)
            m = obj.random_N;
            n = obj.get_rad_n();
            H = zeros(m,1);
            U = zeros(m,1);
            FB = zeros(m,1);
            RSR = zeros(m,1);
            for i = 1:m
                H(i,1) = 30.1493-2.34*log(-log(n(i,1)));
                U(i,1) = 0.4+0.6*n(i,2);
                FB(i,1) = 24+2*n(i,3);
                RSR(i,1) = norminv(n(i,4),2.2,0.1);
            end
        end
        function [p_f, QcQ, xx] = get_Qcap(obj)
            m = obj.random_N;
            Q = zeros(m,1);
            Qcap = zeros(m,1);
            a1 = 0.03;
            a2 = 3;
            a3 = 2.2;
            a4 = 0.65;
            a5 = 0.25;
            b = 80;
            h001 = 28;
            u01 = 1;
            k = 0;
            [H, U, FB, RSR] = obj.get_HU();
            for j = 1:m
                if 0.65*H(j,1) < FB(j,1)
                    Q(j,1) = a1*(H(j,1)+a2*U(j,1))^a3;
                else
                    Q(j,1) = a1*(H(j,1)+a2*U(j,1))^a3+a5*b*(a4*H(j,1)-FB(j,1));
                end
                Qcap(j,1) = RSR(j,1)*a1*(h001+a2*u01)^a3;
                if Q(j,1) > Qcap(j,1)
                    k = k+1;
                end
            end
            p_f = k/m;
            QcQ = Qcap-Q;
            xx = (1:1:m)';
        end
    end
end

% confident.m
classdef confident
    properties (Access = private)
        test_N;
    end
    methods
        function obj = confident(test_N)
            obj.test_N = test_N;
        end
        function show_interval(obj)
            [alpha, beta] = obj.get_exp();
            alpha_mean = mean(alpha);
            alpha_std = std(alpha);
            beta_mean = mean(beta);
            beta_std = std(beta);
            alpha_left = alpha_mean-1.645*alpha_std/sqrt(obj.test_N);
            alpha_right = alpha_mean+1.645*alpha_std/sqrt(obj.test_N);
            beta_left = beta_mean-1.645*beta_std/sqrt(obj.test_N);
            beta_right = beta_mean+1.645*beta_std/sqrt(obj.test_N);
            disp("alpha_left = " + alpha_left);
            disp("alpha_right = " + alpha_right);
            disp("beta_left = " + beta_left);
            disp("beta_right = " + beta_right);
        end
    end
    methods (Access = private)
        function [alpha, beta] = get_exp(obj)
            alpha = zeros(obj.test_N,1);
            beta = zeros(obj.test_N,1);
            for ii = 1:obj.test_N
                random_N = 100;
                seed = ii;
                obj_gumbel = gumbel(random_N, seed);
                [alpha_exp, beta_exp] = obj_gumbel.get_exp();
                alpha(ii, 1) = alpha_exp;
                beta(ii, 1) = beta_exp;
            end
        end
    end
end

hw4_prj1

clearvars; clc; % main.m
sampleN = 20;
obj = solution(sampleN);
obj.solve();

% solution.m
classdef solution
    properties (Access = private)
        sampleN;
    end
    methods
        function obj = solution(sampleN)
            obj.sampleN = sampleN;
        end
        function solve(obj)
            samples = obj.get_samples();
            objGumbel = gumbel(samples);
            CDF_gumbel = objGumbel.solve();
            objWeibull = weibull(samples);
            CDF_weibull = objWeibull.solve();
            fig = figure(1);
            plts = [];
            strs = [];
            plt = plot(samples, CDF_gumbel);
            hold on;
            plt.LineStyle = '--';
            plt.Color = 'Black';
            plt.LineWidth = 1.5;
            str = "Gumbel";
            plts = [plts, plt];
            strs = [strs, str];
            plt = plot(samples, CDF_weibull);
            plt.LineStyle = '-.';
            plt.Color = 'Black';
            plt.LineWidth = 1.5;
            str = "Weibull";
            plts = [plts, plt];
            strs = [strs, str];
            xl = xlabel('Heave/H');
            yl = ylabel('CDF');
            xl.FontSize = 17;
            yl.FontSize = 17;
            ld = legend(plts, strs);
            ld.FontSize = 17;
            ld.Box = 'off';
            ld.Location = 'best';
            saveas(fig, './fig1-5.png');
            close(fig);
        end
    end
    methods (Access = private)
        function samples = get_samples(obj)
            rng(1);
            N = obj.sampleN;
            samples = 0.6 + 0.01*rand(N, 1);
            samples = sort(samples);
        end
    end
end

% gumbel.m
classdef gumbel
    properties (Access = private)
        samples;
    end
    methods
        function obj = gumbel(samples)
            obj.samples = samples;
        end
        function CDF = solve(obj)
            x0 = obj.samples;
            N = size(x0, 1);
            hh = 1.0/(N+1);
            y0 = 0.0:hh:1.0;
            y0 = y0(2:end-1);
            % Least square fitting
            x = x0;
            y = -log(-log(y0));
            coefficient = polyfit(x, y, 1);
            y1 = polyval(coefficient, x);
            % 0.90 confidence
            beta = 1/coefficient(1);
            alpha = coefficient(2)*(-beta);
            CDF = exp(-exp(-((x0-alpha)/beta)));
            target = 0.90;
            ultimate = interp1(CDF, x0, target, 'spline');
            ultimate_left = ultimate - 1.645*beta/sqrt(N);
            ultimate_right = ultimate + 1.645*beta/sqrt(N);
            disp('gumbel method : ');
            disp(['value = ', num2str(ultimate)]);
            disp(['left = ', num2str(ultimate_left)]);
            disp(['right = ', num2str(ultimate_right)]);
            % plot figure
            fig = figure(1);
            plts = [];
            strs = [];
            plt = scatter(x, y);
            hold on;
            plt.Marker = 'x';
            plt.MarkerEdgeColor = 'Black';
            plt.LineWidth = 1.5;
            str = "samples";
            plts = [plts, plt];
            strs = [strs, str];
            plt = plot(x, y1);
            hold on;
            plt.Color = 'Black';
            plt.LineStyle = '--';
            plt.LineWidth = 1.5;
            str = "fitting";
            plts = [plts, plt];
            strs = [strs, str];
            xl = xlabel('Heave/H');
            yl = ylabel('-ln(-ln(Fx))');
            xl.FontSize = 17;
            yl.FontSize = 17;
            ld = legend(plts, strs);
            ld.FontSize = 17;
            ld.Box = 'off';
            ld.Location = 'best';
            saveas(fig, './fig1-3.png');
            close(fig);
        end
    end
end

% weibull.m
classdef weibull
    properties (Access = private)
        samples;
    end
    methods
        function obj = weibull(samples)
            obj.samples = samples;
        end
        function CDF = solve(obj)
            x0 = obj.samples;
            N = size(x0, 1);
            hh = 1.0/(N+1);
            y0 = 0.0:hh:1.0;
            y0 = y0(2:end-1);
            y0 = y0';
            % Least square fitting
            x = log(x0);
            y = log(-log(1-y0));
            coefficient = polyfit(x, y, 1);
            y1 = polyval(coefficient, x);
            % plot figure
            fig = figure(1);
            plts = [];
            strs = [];
            plt = scatter(x, y);
            hold on;
            plt.Marker = 'x';
            plt.MarkerEdgeColor = 'Black';
            plt.LineWidth = 1.5;
            str = "samples";
            plts = [plts, plt];
            strs = [strs, str];
            plt = plot(x, y1);
            hold on;
            plt.Color = 'Black';
            plt.LineStyle = '--';
            plt.LineWidth = 1.5;
            str = "fitting";
            plts = [plts, plt];
            strs = [strs, str];
            xl = xlabel('ln(Heave/H)');
            yl = ylabel('-ln(-ln(Fx))');
            xl.FontSize = 17;
            yl.FontSize = 17;
            ld = legend(plts, strs);
            ld.FontSize = 17;
            ld.Box = 'off';
            ld.Location = 'best';
            saveas(fig, './fig1-4.png');
            close(fig);
            % 0.90 confidence
            k = coefficient(1);
            lamda = exp(coefficient(2)/(-k));
            CDF = 1-exp(-(x0./lamda).^k);
            target = 0.90;
            ultimate = interp1(CDF, x0, target, 'spline');
            % Bootstrapping m=100
            hh = x0(1)/100.0;
            x0 = [x0(1)-hh; x0; x0(end)+hh];
            CDF_ex = [0; CDF; 1];
            ultimates = zeros(100, 1);
            rng(1);
            CDF_MonteC = random('unif',0,1,N+2,100);
            for i = 1 : 100
                yi = CDF_MonteC(:,i);
                xi = interp1(CDF_ex, x0, yi);
                x = log(xi);
                y = log(-log(1-yi));
                coefficient = polyfit(x, y, 1);
                k = coefficient(1);
                lamda = exp(coefficient(2)/(-k));
                CDFs = 1-exp(-(x0./lamda).^k);
                ultimates(i) = interp1(CDFs, xi, target, 'spline');
            end
            ultimates = sort(ultimates,'descend');
            ultimates = ultimates(6:95);
            ultimate_right = ultimates(1);
            ultimate_left = ultimates(end);
            disp('weibull method : ');
            disp(['value = ', num2str(ultimate)]);
            disp(['left = ', num2str(ultimate_left)]);
            disp(['right = ', num2str(ultimate_right)]);
        end
    end
end