Engee documentation

modalsd

Construction of a stabilization diagram for modal analysis.

Library

EngeeDSP

Syntax

Function call

  • modalsd(frf,f,fs) — builds a stabilization chart on the current chart. Function modalsd evaluates natural frequencies and damping coefficients from 1 before 50 The mod builds a diagram using the least-Squares Complex Exponential (LSCE) method. Argument fs sets the sampling rate. Argument f It is a vector, the number of elements of which is equal to the number of rows of the array of frequency characteristics. frf. The diagram allows you to distinguish between computational and physical modes.

  • modalsd(frf,f,fs,Name,Value) — sets additional parameters using arguments like «name-value».

  • fn=modalsd(_,out=:data) — returns the matrix fn natural frequencies identified as stable between successive orders of the model. First elements The th lines contain the natural frequencies of the stable poles. Poles that are not stable are returned as NaN. This syntax allows for any combination of input data from the previous syntax options.

Arguments

Input arguments

# frf — frequency characteristics

+ vector | the matrix | array

Details

Frequency characteristics specified as a vector, matrix, or array. Argument frf has a size of on on , where — number of frequency intervals, — the number of response signals, and — the number of excitation signals used to evaluate the transfer function.

Типы данных

Int64, Float32, Float64
Support for complex numbers

Yes

# f — frequencies

+ vector

Details

Frequencies specified as a vector. Number of vector elements f must match the number of rows in the array. frf.

Типы данных

Int64, Float32, Float64

# fs is the sampling rate of the measurement data

+ positive scalar

Details

The sampling frequency of the measurement data in Hz, set as a positive scalar.

Типы данных

Int64, Float32, Float64

Input arguments «name-value»

Specify optional argument pairs as Name,Value, where Name — the name of the argument, and Value — the appropriate value. Type arguments «name-value» they should be placed after the other arguments, but the order of the pairs does not matter. You can specify multiple pairs «name-value».

Use commas to separate the name and value, and Name enclose it in quotation marks, or use an equal sign to separate the name and value, and Name specify it without quotation marks.

Example: modalsd(frf,f,fs,"MaxModes",20,"FreqRange",[0 500]) or modalsd(frf,f,fs,MaxModes=20,FreqRange=[0 500]) calculates up to 20 physical modes and limits the frequency range to values from 0 before 500 Hz.

# FitMethod — approximation method

+ "lsce" (by default) | "lsrf"

Details

The approximation method, defined as "lsce" or "lsrf":

  • "lsce" — the least squares method for complex exponentials.

  • "lsrf" — evaluation of a rational function using the least squares method. The algorithm is described in [2]. This algorithm typically requires less data than nonparametric approaches.

# FreqRange — frequency range

+ two-element vector

Details

The frequency range specified as a two-element vector of increasing positive values lying in the range specified in f.

Типы данных

Int64, Float32, Float64

# MaxModes — maximum number of mods

+ 50 (default) | a positive integer

Details

The maximum number of modes, set as a positive integer.

Типы данных

Int64, Float32, Float64

# SCriteria — criteria for determining consistent stable natural frequencies and damping coefficients

+ [0.01 0.05] (default) | a two-element vector of positive numbers

Details

Criteria for determining stable natural frequencies and damping coefficients between successive degrees of freedom of the model, specified as a two-element vector of positive numbers. Argument SCriteria It contains the maximum relative differences between the poles, which are classified as stable. The first element of the vector refers to the natural frequencies, the second to the damping coefficients.

Типы данных

Int64, Float32, Float64

Output arguments

# fn — natural frequencies identified as stable

+ the matrix

Details

The natural frequencies identified as stable are returned as a matrix. First elements -th lines contain natural frequencies. Poles that are non-physical or unstable in frequency are returned as NaN.

Literature

  1. Brandt, Anders. Noise and Vibration Analysis: Signal Analysis and Experimental Procedures. Chichester, UK: John Wiley & Sons, 2011.

  2. Ozdemir, Ahmet Arda, and Suat Gumussoy. Transfer Function Estimation in System Identification Toolbox via Vector Fitting. Proceedings of the 20th World Congress of the International Federation of Automatic Control, Toulouse, France, July 2017.

  3. Vold, Havard, John Crowley, and G. Thomas Rocklin. New Ways of Estimating Frequency Response Functions. Sound and Vibration. Vol. 18, November 1984, pp. 34–38.