Optimization 14DOF exact different than calculated periods

here is my code. When optimizing the T calculated are very different than my periods is there a problem with my interactions? clear all

% Number of Degrees of Freedom (DOFs) numDOF = 14;

% Mass data in kips (converted to slugs by dividing by 32.2) mass_values_kips = [ 481.3598137; 139.9818634; 139.9818634; 137.7838199; 135.5857453; 135.5857453; 135.5857453; 134.0534472; 133.7469876; 133.7469876; 133.7469876; 133.0730745; 132.9382919; 146.5049689 ]; % Masses in kips

% Convert to slugs mass_values = mass_values_kips / 32.2;

% Construct the mass matrix as a diagonal matrix M = diag(mass_values);

% Define target periods and frequencies as before periods = [5.016025, 4.130755, 1.048753, 0.9692, 0.843733, 0.498552, 0.425147, ... 0.314427, 0.258085, 0.254921, 0.219497, 0.175277, 0.165737, 0.161123]; frequencies = 2 * pi ./ periods; f_exact_Hz = frequencies;

% Initial stiffness values for a 14-DOF system min_val = 100; max_val = 5000; k_guess = min_val + (max_val - min_val) * rand(1, 14);

% Define bounds LB = ones(14, 1) * 1e-3; % Lower bounds UB = ones(14, 1) * 1e16; % Upper bounds

% Optimization options options = optimoptions('lsqnonlin', 'Display', 'iter', 'FunctionTolerance', 1e-20, ... 'StepTolerance', 1e-20, 'OptimalityTolerance', 1e-20, 'MaxFunEvals', inf, 'MaxIterations', 5000);

% Maximum number of iterations for updating k_initial max_iterations = 10; tolerance = 1e-3; % Tolerance for stopping criterion

for iter = 1:max_iterations % Perform optimization [K_opt_vec,~,res] = lsqnonlin(@(K) obj_function_reshaped_matrix(K, M, frequencies), k_guess, LB, UB, options);

    % Construct the optimized stiffness matrix
    K_opt = diag(K_opt_vec) + diag(-K_opt_vec(2:end), 1) + diag(-K_opt_vec(2:end), -1);

    % Solve eigenvalue problem
    [~, L] = eig(K_opt, M);
    f_calc_Hz = abs(diag(sqrt(L)) / (2 * pi));
    T_calc_s = 1 ./ f_calc_Hz; % Calculated periods

    % Display results for this iteration
    disp(['Iteration ', num2str(iter)]);
    disp('Calculated periods (T_calc_s):');
    disp(T_calc_s);

    % Check if the calculated periods are within tolerance
    if all(abs(T_calc_s - periods) < tolerance)
        disp('Calculated periods are within tolerance.');
        break;
    else
        % Adjust k_guess for the next iteration based on period error
        period_error = T_calc_s - periods;
        adjustment_factor = 1 + period_error ./ periods;

        % Update k_guess based on the adjustment factor
        k_guess = k_guess .* adjustment_factor';
    end
end

disp('Final optimized stiffness matrix (K):'); disp(K_opt); disp('Final calculated periods (T_calc_s):'); disp(T_calc_s);

%% Objective function definition for 14 DOF system with squared differences function diff = obj_function_reshaped_matrix(K_vec, M, f_exact_Hz) % Construct the 14x14 stiffness matrix K_mat = zeros(14, 14);

    % Fill in the diagonal and off-diagonal elements
    for i = 1:14
        if i == 1
            K_mat(i, i) = K_vec(i) + K_vec(i+1);
            K_mat(i, i+1) = -K_vec(i+1);
        elseif i == 14
            K_mat(i, i) = K_vec(i) + K_vec(i-1);
            K_mat(i, i-1) = -K_vec(i);
        else
            K_mat(i, i) = K_vec(i) + K_vec(i+1);
            K_mat(i, i+1) = -K_vec(i+1);
            K_mat(i, i-1) = -K_vec(i);
        end
    end

    % Solve the eigenvalue problem
    [~, L] = eig(K_mat, M);

    % Calculate natural frequencies from eigenvalues
    omega_calc = sqrt(diag(L));  % Rad/s
    f_calc_Hz = omega_calc / (2 * pi);  % Convert to Hz

    % Return the squared difference between calculated and exact frequencies
    diff = (f_calc_Hz - f_exact_Hz).^2;
end