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Content introduction
In the field of structural engineering, understanding and analyzing the modal parameters of a structure is critical to assessing the health and performance of the structure. Traditionally, the identification of modal parameters usually requires extensive experimental measurements and complex data processing. However, with the continuous development of technology, a new algorithm, the SSI-COV algorithm, provides a more efficient and accurate method for automatically identifying the modal parameters of linear structures.
The SSI-COV algorithm is a method based on the structural system identification (SSI) theory, which uses environmental vibration data to identify the modal parameters of the structure. This algorithm extracts the modal parameters of the structure, such as natural frequency, damping ratio, and modal shape, by correlating the dynamic response of the structure with the environmental excitation signals.
Compared with traditional modal recognition methods, the SSI-COV algorithm has the following advantages. First, it does not require additional excitation experiments and only requires the use of vibration response data of the structure in the natural environment. This can greatly reduce the time and cost of experiments. Second, the algorithm is able to automatically identify multiple modal parameters without manual intervention. This is particularly important for complex structural systems, as they may have multiple modes.
When using the SSI-COV algorithm for modal parameter identification, you need to pay attention to some key steps. First, the environmental vibration data needs to be preprocessed, including filtering and denoising. Then, a suitable correlation function needs to be selected to calculate the correlation between the dynamic response of the structure and the excitation signal. Finally, through feature extraction and model fitting of the correlation function, the modal parameters of the structure can be obtained.
Although the SSI-COV algorithm has many advantages in modal parameter identification, it also has some limitations. First of all, this algorithm has high requirements on the quality of environmental vibration data, and the accuracy and completeness of the data need to be ensured. Secondly, this algorithm makes certain assumptions about the linear properties of the structure, so some errors may occur when applied to nonlinear structures.
In summary, the SSI-COV algorithm is an effective method that can be used to automatically identify the modal parameters of linear structures. It can reduce the time and cost of experiments and provide accurate and comprehensive modal parameter information. However, in practical applications, we still need to choose appropriate algorithms and methods according to specific situations to ensure the accuracy and reliability of modal parameters.
Part of the code
function [h] = plotStabDiag(fn,Az,fs,stablity_status,Nmin,Nmax)</code><code>% -------------------------- -------------------------------------------------- ---</code><code>% [h] = plotStabDiag(fn,Az,fs,stablity_status,Nmin,Nmax) plots the</code><code>% stabilization diagram of the identified eigen frequencies as a function</code><code>% of the model order, calculated with the SSI-COV method.</code><code>% ----------------------- -------------------------------------------------- -</code><code>% Input:</code><code>% fn: cell : eigen frequencies identified for multiple system orders.</code><code>% Az : vector: Time serie of acceleration response (illustrative purpose)</code><code>% fs: sampling frequency</code><code>% stability_status: cell of stability status for each model order</code><code>% Nmin: scalar: minimal number of model order</code><code>% Nmax: scalar: maximal number of model order</code><code>% Output: h: handle of the figure</code><code>% ---------- -------------------------------------------------- -------------</code><code>% See also: SSICOV.m</code><code>% --------------- -------------------------------------------------- --------</code><code>% Author: Etienne Cheynet, UIS</code><code>% Updated on: 08/03/2016</code><code>% ---- -------------------------------------------------- ------------------</code><code>Npoles =Nmin:1:Nmax;</code><code>[Saz,f]=pwelch(Az ,[],[],[],fs);</code><code>?</code><code>?</code><code>h = figure;</code><code>ax1 = axes ;</code><code>hold on;box on</code><code>for jj=0:4,</code><code> y = [];</code><code> x = [] ;</code><code> for ii=1:numel(fn)</code><code> ind = find(stablity_status{ii}==jj);</code><code> x = [x;fn {ii}(ind)'];</code><code> y = [y;ones(numel(ind),1).*Npoles(ii)];</code><code> end</code><code> x1{jj + 1}=x;</code><code> y1{jj + 1}=y;</code><code>end</code><code>?</code><code>h1=plot(x1{1},y1{1},'k + ','markersize',5);% new pole</code><code>h2=plot(x1{2} ,y1{2},'ko','markerfacecolor','r','markersize',5); % stable pole</code><code>h3=plot(x1{3 },y1{3},'bo','markersize',5); % pole with stable frequency and vector</code><code>h4=plot(x1{4},y1{4}, 'gsq','markersize',5); % pole with stable frequency and damping</code><code>h5=plot(x1{5},y1{5},'gx',\ 'markersize',5); % pole with stable frequency</code><code>if isempty(h1), h1=0;</code><code>elseif isempty(h2), h2=0;</code><code>elseif isempty(h3), h3=0;</code><code>elseif isempty(h4), h4=0;</code><code>elseif isempty(h5), h5=0;</code> code><code>end</code><code>?</code><code>?</code><code>?</code><code>H = [h1(1),h2(1), h3(1),h4(1),h5(1)];</code><code>legend(H,...</code><code> 'new pole',...</code><code> 'stable pole',...</code><code> 'stable freq. & amp; MAC',...</code><code> 'stable freq. & amp ; damp.',...</code><code> 'stable freq.',...</code><code> 'location','Northoutside','orientation\ ','horizontal');</code><code>?</code><code>ylabel('number of poles');</code><code>xlabel('f (Hz) ')</code><code>xlim([0,max([fn{:}])*1.1])</code><code>hold off</code><code>?</code><code>ax2 = axes('YAxisLocation', 'Right');</code><code>linkaxes([ax1,ax2])</code><code>plot(ax2,f,Saz./ max(Saz).*0.001,'k');</code><code>ax2.YLim = [0,Nmax];</code><code>ax2.XLim = [0,max([fn {:}])*1.1];</code><code>set(ax2,'yscale','log')</code><code>ax2.Visible = 'off';</code><code>ax2.XTick = [];</code><code>ax2.YTick = [];</code><code>set(gcf,'color','w') </code><code>?</code><code>?</code><code>?</code><code>end
Operation results
References
[1] Magalhaes, F., Cunha, A., & Caetano, E. (2009). Online automatic identification of the modal parameters of a long span arch bridge. Mechanical Systems and Signal Processing, 23(2), 316 -329.
[2] Cheynet, E., Jakobsen, J. B., & Sn?bj?rnsson, J. (2016). Buffeting response of a suspension bridge in complex terrain. Engineering Structures, 128, 474-487.
[3] Cheynet, E., Jakobsen, J. B., & Sn?bj?rnsson, J. (2017). Damping estimation of large wind-sensitive structures. Procedia Engineering, 199, 2047-2053.
[4] Cheynet, E., Sn?bj?rnsson, J., & Jakobsen, J. B. (2017). Temperature Effects on the Modal Properties of a Suspension Bridge. In Dynamics of Civil Structures, Volume 2 (pp. 87 -93). Springer.
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Traveling salesman problem (TSP), vehicle routing problem (VRP, MVRP, CVRP, VRPTW, etc.), UAV three-dimensional path planning, UAV collaboration, UAV formation, robot path planning, raster map path planning , multimodal transportation problems, vehicle collaborative UAV path planning, antenna linear array distribution optimization, workshop layout optimization
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