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762 812 862 912 962 1012 1062 1112 1162 1212 1262 1312 1362 1412 1462 1512 1562 1612 1662 1712 761.9108 0.000117 811.9119 0.000109 861.89 0.000128 911.8863 0.000125 961.8766 0.000128 1011.881 0.000117 1061.889 0.000105 1111.892 9.72E-05 1161.888 9.63E-05 1211.878 0.000101 1261.866 0.000106 1311.86 0.000107 1361.827 0.000127 1411.822 0.000126 1461.815 0.000126 1511.824 0.000117 1561.822 0.000114 1611.829 0.000106 1661.82 0.000108 1711.816 0.000107 2212 2262 2312 2315.83 2365.83 2367.06 2417.06 2467.06 2517.06 2567.06 2617.06 2666.98 2668.83 2718.83 2211.751 0.000112 2261.726 0.000121 2311.759 0.000104 2315.56 0.000116 2365.576 0.000107 2366.784 0.000117 2416.807 0.000105 2466.778 0.000114 2516.796 0.000105 2566.755 0.000119 2616.751 0.000118 2666.676 0.000114 2668.541 0.000108 2718.516 0.000115

附表二 变位进油 变位进油 变位进油 实际油量 修正后油量 相对误差 实际油量 修正后油量 相对误差 实际油量 修正后油量 相对误差 962.86 962.0046791 0.000889 1912.73 1913.481124 0.000393 2862.73 2861.243186 0.000519639 1012.86 1007.254797 0.005565 1962.73 1966.21197 0.001771 2912.73 2913.183687 0.000155736 1062.86 1063.419002 0.000526 2012.73 2016.14267 0.001693 2962.73 2966.445925 0.001252652 1112.86 1110.122783 0.002466 2062.73 2060.912356 0.000882 3012.73 3013.423176 0.000230029 1162.86 1161.82797 0.000888 2112.73 2114.315055 0.00075 3062.73 3066.500635 0.001229621 1212.86 1216.018289 0.002597 2162.73 2164.498879 0.000817 3112.73 3117.34487 0.001480385 1262.86 1262.021439 0.000664 2212.73 2215.319407 0.001169 3162.73 3163.572092 0.000266184 1312.79 1314.68058 0.001438 2262.73 2263.693388 0.000426 3212.73 3215.946654 0.00100022 1362.79 1363.536992 0.000548 2312.73 2314.304957 0.000681 3262.73 3268.942347 0.001900415 1412.73 1412.861172 9.28E-05 2362.73 2363.94171 0.000513 3312.73 3315.719688 0.000901671 1462.73 1462.09755 0.000433 2412.73 2409.83029 0.001203 3362.73 3362.768183 1.13545E-05 1512.73 1515.964794 0.002134 2462.73 2460.954568 0.000721 3412.73 3415.418492 0.000787163 1562.73 1567.535679 0.003066 2512.73 2512.333669 0.000158 3462.73 3462.772804 1.23611E-05 1612.73 1618.241478 0.003406 2562.73 2557.99151 0.001852 3512.73 3518.182814 0.001549895 1662.73 1669.300663 0.003936 2612.73 2610.292707 0.000934 3514.74 3522.227429 1712.73 1714.866964 0.001246 2662.73 2663.707785 0.000367 0.213% 精品文档

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1762.73 1765.866132 0.001776 2712.73 2714.678442 0.000718 1812.73 1816.045836 0.001826 2762.73 2764.050567 0.000478 1862.73 1867.763901 0.002695 2812.73 2813.836124 0.000393

MATLAB 程序

function [volumes]= totalEval(x) tic;

oilTank = getOil; global H alpha alpha = x(1); beta = x(2);

n = size(oilTank, 1); volumes = zeros(n, 1); for i = 1:31

H0 = (i - 1) / 10;

H = (H0 - 1.5) * cos(beta) + 1.5; [x1 x2] = calcL1(H, alpha); if H < 6 * tan(alpha)

volumes(i) = real(quad(@intV2, 0, x1) + quad(@intV1, 0, (H + 2 * tan(alpha))/ tan(alpha)));

elseif H < 1.5 - 3 * tan(alpha)

volumes(i) = real(quad(@intV1, 0,8) + quad(@intV2, 0, x1) + quad(@intV3, 0, x2));

elseif H < 1.5 + 7 * tan(alpha)

lmax = (H + 2 * tan(alpha) - 1.5) / tan(alpha);

volumes(i) = real(quad(@intV4, 0, 1) + quad(@intV5, 0, lmax) + quad(@intV1, lmax, 8) + quad(@intV3, 0, x2)); elseif H < 3 - 2 * tan(alpha)

volumes(i) = real(quad(@intV4, 0, 1) + quad(@intV1, 0,8) + quad(@intV6, 0,1)); else

volumes(i) = real(quad(@intV7, 0,1)) + 8 * pi * 2.25 - real(quad(@intV2, 0, x1) + quad(@intV1, 0, (H + 2 * tan(alpha))/ tan(alpha))); end end toc;

function [xmax1 xmax2] = calcL1(H, alpha) R = 1.625; R1 = 1.5;

talpha = tan(alpha);

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Rc = (R - 1) ./ cos(alpha);

xmax1 = ((R ^ 2 - (( R - 1) * talpha + R1 - (H + 2 * talpha)) .^ 2 * cos(alpha) ^2) .^ 0.5 - Rc + ...

((R -1) * talpha + R1 - (H + 2 * talpha)) * sin(alpha)) * cos(alpha);

xmax2 = ((R ^ 2 - ( -( R - 1) * talpha + R1 - (H - 6 * talpha)) .^ 2 * cos(alpha) ^2) .^ 0.5 - Rc - ...

( -(R -1) * talpha + R1 - (H - 6 * talpha)) * sin(alpha)) * cos(alpha);

%function V1 = intV1(H, x, alpha) function V1 = intV1(x) R1 = 1.5; global H alpha %H = 1.29; %alpha = 0.07;

HH = H + 2 * tan(alpha);

V1 = R1 ^ 2 .* acos( (R1 - ( HH - x .* tan(alpha))) / R1) - ... (R1 - HH + x .* tan(alpha)) .* ((HH - x .* tan(alpha)) .* (2 * R1 - HH + x .* tan(alpha))) .^ 0.5;

function V = intV2(x) global H alpha R = 1.625; R1 = 1.5;

R2 = (R^2 - (R - 1 + x) .^ 2) .^ 0.5; %R3 = R2;

talpha = tan(alpha);

H1 = R2 - ( R1 - H - 2 * talpha - x * talpha); %H2 = R3 - ( R1 - H + 6 * talpha + x .* talpha);

V = R2 .^ 2 .* acos((R2 - H1) ./ R2) - (R2 - H1) .* ( H1 .* ( 2 .* R2 - H1)) .^ 0.5;

function V = intV3(x) global H alpha R = 1.625; R1 = 1.5;

R3 = (R^2 - (R - 1 + x) .^ 2) .^ 0.5; talpha = tan(alpha);

H2 = R3 - ( R1 - H + 6 * talpha + x .* talpha);

V = R3 .^ 2 .* acos((R3 - H2) ./ R3) - (R3 - H2) .* ( H2 .* ( 2 .* R3 - H2)) .^ 0.5;

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function V = intV4(x) global H alpha R = 1.625; R1 = 1.5;

R2 = (R^2 - (R - 1 + x) .^ 2) .^ 0.5; %R3 = R2;

H1 = R2 + H + 2 * tan(alpha) + x * tan(alpha) - R1; %H2 = R3 - ( R1 - H + 6 * talpha + x .* talpha);

V = R2 .^ 2 .* ( pi - acos(-(R2 - H1) ./ R2)) - (R2 - H1) .* ( H1 .* ( 2 .* R2 - H1)) .^ 0.5;

function V = intV5(x) global H alpha R = 1.625; R1 = 1.5;

R2 = (R^2 - (R - 1 + x) .^ 2) .^ 0.5; %R3 = R2;

%H1 = R2 + H + 2 * tan(alpha) + x * tan(alpha) - R1; %H2 = R3 - ( R1 - H + 6 * talpha + x .* talpha);

V = R1 .^ 2 .* ( pi - acos( (H + 2 .* tan(alpha) - x .* tan(alpha) - R1) / R1)) + ...

(H + 2 * tan(alpha) - x .* tan(alpha) - R1) .* ...

((H + 2 * tan(alpha) - x .* tan(alpha)) .* (2 * R1 - H - 2 * tan(alpha) + x .* tan(alpha))) .^ 0.5;

function V = intV6(x) global H alpha R = 1.625; R1 = 1.5;

R3 = (R^2 - (R - 1 + x) .^ 2) .^ 0.5; %R3 = R2;

%H1 = R2 + H + 2 * tan(alpha) + x * tan(alpha) - R1; talpha = tan(alpha);

H2 = R3 - ( R1 - H + 6 * talpha + x .* talpha);

V = R3 .^ 2 .* (pi - acos((H2 - R3) ./ R3)) + (H2 - R3) .* (H2 .* ( 2 * R3 - H2)) .^ 0.5; function V = intV7(x) global H alpha R = 1.625; R1 = 1.5;

R2 = (R^2 - (R - 1 + x) .^ 2) .^ 0.5; %R3 = R2;

%H1 = R2 + H + 2 * tan(alpha) + x * tan(alpha) - R1;

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