I can't integrate symbolic expression with abs(x), and using sign(real(x)) produces wrong results

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Sulaiman Ogungboyega 2021-12-1

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评论： Star Strider 2021-12-6

I am using symbolic expression and I need to integrate a function that contains abs(), this takes so long without producing any result, I tried using sign(x) instead I have same result as using abs(), I tried using sign(real(x)) and this produces results but with error in the results.

Please, can anyone help with this?

Result when I use sign(real(x))

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Answer 1

Star Strider 2021-12-1

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My version of MATLAB cannot run images of code.

Apparently the variables have numeric values or the plot would not exist, so one option is to use matlabFunction on ‘drag_cw_function_column’ and integrate the resulting anonymous function numerically.

.

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Star Strider 2021-12-2

在 MATLAB Online 中打开

I would appreciate a bit more information about this, since I can’t understand what the code does.

I looked at several sub-expressions in the function with the discontinuities, and have so far been unable to find the source.

rho = 1030;

C_d = 0.7;

C_m = 1.0;

omega = pi/6;

k_cw= 0.0242;

U_current = 1.5;

amplitude = 7.5;

diameter = [6, 8];

depth = 350;

phase_velocity_cw = 21.6184;

wave_length_cw = 259.4214;

du_dt_cw_max = @(z) amplitude*omega^2*(cosh(k_cw*(depth+z)))*(1-(U_current/phase_velocity_cw))/sinh(k_cw*depth);

inertia_cw_function_column = @(z) 0.25*C_m*rho*pi*diameter(1).^2*du_dt_cw_max(z);

syms z x t

% Forces on the column

phase_cw(x,t) = omega*(t) -k_cw*(x);

u_wave_current (z,x,t) = U_current+ (amplitude*omega*(cosh(k_cw*(depth+z)))*(1-(U_current/phase_velocity_cw))/sinh(k_cw*depth)).*(sin(phase_cw(x,t)));

drag_cw_function_column_trial(z,x,t)= 0.5*C_d*rho*diameter(1)*(u_wave_current(z,x,t)).^2*sign(real(u_wave_current(z,x,t)));

drag_cw_function_column = matlabFunction(drag_cw_function_column_trial);

figure ("Name","Plot of drag to chech sign(u)")

fsurf(drag_cw_function_column(z,x,0),[0 200 -34 0]); % plot of drag to show sign(u) is effective and drag is negative where needed

title ("Plot of drag to chech sign(u)");

%%

F_drag_column_cw = @(z,x,t) drag_cw_function_column(z,x,t); %general expression for F_drag on column at any point per unit length

F_inertia_column_cw = @(z,x,t) inertia_cw_function_column (z)*cos(phase_cw(x,t)); %general expression for F_inertial on column at any point

F_horizontal_cw_column = @(z,x,t) F_drag_column_cw(z,x,t) + F_inertia_column_cw(z,x,t); %general expression for Total horizontal force at any point on the column at any point per unit length

F_horizontal_moment(z,x,t) = F_horizontal_cw_column (z,x,t)*(z+34);

int_moment_horizontal_column(z,x,t) = int(F_horizontal_moment,z); %intergrated general expression over z

sum_horizontal_moment_column(x,t) = subs(int_moment_horizontal_column,z,0)-subs(int_moment_horizontal_column,z,-30); %integrated over interval -30 to 0

Moment_horizontal_column(x) = sum_horizontal_moment_column(x,0);

figure("Name","plot showing similar trend")

fplot(Moment_horizontal_column(x),[0 wave_length_cw]); % the plot shows similar trend like the surf plot posted earlier

title("Plot showing similar behaviour")

.

Star Strider 2021-12-3

在 MATLAB Online 中打开

I still don’t understand the code or the arguments.

Simply using ‘real(u_wave_current(z,x,t))’ produces a smooth sinusiodal curve with no discontinuities that the sign call introduces. Is there anything wrong with just using that instead of thresholding it? Also, that function appears to me to be pure real (although I have no idea what the values of ‘z’ and ‘t’ are supposed to be, so it could be complex in some instances).

rho = 1030;

C_d = 0.7;

C_m = 1.0;

omega = pi/6;

k_cw= 0.0242;

U_current = 1.5;

amplitude = 7.5;

diameter = [6, 8];

depth = 350;

phase_velocity_cw = 21.6184;

wave_length_cw = 259.4214;

du_dt_cw_max = @(z) amplitude*omega^2*(cosh(k_cw*(depth+z)))*(1-(U_current/phase_velocity_cw))/sinh(k_cw*depth);

inertia_cw_function_column = @(z) 0.25*C_m*rho*pi*diameter(1).^2*du_dt_cw_max(z);

syms z x t

% Forces on the column

phase_cw(x,t) = omega*(t) -k_cw*(x);

u_wave_current (z,x,t) = U_current+ (amplitude*omega*(cosh(k_cw*(depth+z)))*(1-(U_current/phase_velocity_cw))/sinh(k_cw*depth)).*(sin(phase_cw(x,t)));

drag_cw_function_column_trial(z,x,t)= 0.5*C_d*rho*diameter(1)*(u_wave_current(z,x,t)).^2*sign(real(u_wave_current(z,x,t)));

drag_cw_function_column = matlabFunction(drag_cw_function_column_trial);

figure ("Name","Plot of drag to chech sign(u)")

fsurf(drag_cw_function_column(z,x,0),[0 200 -34 0]); % plot of drag to show sign(u) is effective and drag is negative where needed

title ("Plot of drag to chech sign(u)");

%%

F_drag_column_cw = @(z,x,t) drag_cw_function_column(z,x,t); %general expression for F_drag on column at any point per unit length

F_inertia_column_cw = @(z,x,t) inertia_cw_function_column (z)*cos(phase_cw(x,t)); %general expression for F_inertial on column at any point

F_horizontal_cw_column = @(z,x,t) F_drag_column_cw(z,x,t) + F_inertia_column_cw(z,x,t); %general expression for Total horizontal force at any point on the column at any point per unit length

F_horizontal_moment(z,x,t) = F_horizontal_cw_column (z,x,t)*(z+34);

int_moment_horizontal_column(z,x,t) = int(F_horizontal_moment,z); %intergrated general expression over z

sum_horizontal_moment_column(x,t) = subs(int_moment_horizontal_column,z,0)-subs(int_moment_horizontal_column,z,-30); %integrated over interval -30 to 0

Moment_horizontal_column(x) = sum_horizontal_moment_column(x,0);

figure("Name","plot showing similar trend")

fplot(Moment_horizontal_column(x),[0 wave_length_cw]); % the plot shows similar trend like the surf plot posted earlier

title("Plot showing similar behaviour")

z = 1;

t = 1;

figure

fplot(sign(real(u_wave_current(z,x,t))), [0 wave_length_cw])

grid

ylim([-1 1]*1.1)

figure

fplot((real(u_wave_current(z,x,t))), [0 wave_length_cw], '-b')

hold on

% fplot((imag(u_wave_current(z,x,t))), [0 wave_length_cw], '-g')

fplot((abs(u_wave_current(z,x,t))), [0 wave_length_cw], '-r')

hold off

grid

.

Walter Roberson 2021-12-4

在 MATLAB Online 中打开

td = tempdir();

trialfile = fullfile(td, 'drag_cw_function_column_trial.m');

addpath(td);

rho = 1030;

C_d = 0.7;

C_m = 1.0;

omega = pi/6;

k_cw= 0.0242;

U_current = 1.5;

amplitude = 7.5;

diameter = [6, 8];

depth = 350;

phase_velocity_cw = 21.6184;

wave_length_cw = 259.4214;

du_dt_cw_max = @(z) amplitude*omega^2*(cosh(k_cw*(depth+z)))*(1-(U_current/phase_velocity_cw))/sinh(k_cw*depth);

inertia_cw_function_column = @(z) 0.25*C_m*rho*pi*diameter(1).^2*du_dt_cw_max(z);

syms z x t

% Forces on the column

phase_cw(x,t) = omega*(t) -k_cw*(x);

u_wave_current (z,x,t) = U_current+ (amplitude*omega*(cosh(k_cw*(depth+z)))*(1-(U_current/phase_velocity_cw))/sinh(k_cw*depth)).*(sin(phase_cw(x,t)));

drag_cw_function_column_trial(z,x,t)= 0.5*C_d*rho*diameter(1)*(u_wave_current(z,x,t)).^2*piecewise(real(u_wave_current(z,x,t))<0,-1,1);

drag_cw_function_column = matlabFunction(drag_cw_function_column_trial, 'File', trialfile, 'Optimize', false);

figure ("Name","Plot of drag to chech sign(u)")

fsurf(drag_cw_function_column_trial(z,x,0),[0 200 -34 0]); % plot of drag to show sign(u) is effective and drag is negative where needed

title ("Plot of drag to chech sign(u)");

%%

F_drag_column_cw = drag_cw_function_column; %general expression for F_drag on column at any point per unit length

F_inertia_column_cw = @(z,x,t) inertia_cw_function_column (z)*cos(phase_cw(x,t)); %general expression for F_inertial on column at any point

F_horizontal_cw_column = @(z,x,t) drag_cw_function_column_trial(z,x,t) + F_inertia_column_cw(z,x,t); %general expression for Total horizontal force at any point on the column at any point per unit length

F_horizontal_moment(z,x,t) = F_horizontal_cw_column (z,x,t)*(z+34);

int_moment_horizontal_column(z,x,t) = int(F_horizontal_moment,z) %intergrated general expression over z

int_moment_horizontal_column(z, x, t) =

sum_horizontal_moment_column(x,t) = subs(int_moment_horizontal_column,z,0)-subs(int_moment_horizontal_column,z,-30) %integrated over interval -30 to 0

sum_horizontal_moment_column(x, t) =

Moment_horizontal_column(x) = sum_horizontal_moment_column(x,0)

Moment_horizontal_column(x) =

figure("Name","plot showing similar trend")

fplot(Moment_horizontal_column(x),[0 wave_length_cw]); % the plot shows similar trend like the surf plot posted earlier

title("Plot showing similar behaviour")

z = 1;

t = 1;

figure

fplot(sign(real(u_wave_current(z,x,t))), [0 wave_length_cw])

grid

ylim([-1 1]*1.1)

figure

fplot((real(u_wave_current(z,x,t))), [0 wave_length_cw], '-b')

hold on

% fplot((imag(u_wave_current(z,x,t))), [0 wave_length_cw], '-g')

fplot((abs(u_wave_current(z,x,t))), [0 wave_length_cw], '-r')

hold off

grid

Sulaiman Ogungboyega 2021-12-6

Thank you @Star Strider and @Walter Roberson, I had to go with numerical expression for this.

Star Strider 2021-12-6

I figured that was the best option.

(I still don’t understand the code!)

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I can't integrate symbolic expression with abs(x), and using sign(real(x)) produces wrong results

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I can't integrate symbolic expression with abs(x), and using sign(real(x)) produces wrong results

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