1、 Reference number ISO 18431-1:2005(E) ISO 2005INTERNATIONAL STANDARD ISO 18431-1 First edition 2005-11-15 Mechanical vibration and shock Signal processing Part 1: General introduction Vibrations et chocs mcaniques Traitement du signal Partie 1: Introduction gnrale ISO 18431-1:2005(E) PDF disclaimer
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6、uester. ISO copyright office Case postale 56 CH-1211 Geneva 20 Tel. + 41 22 749 01 11 Fax + 41 22 749 09 47 E-mail copyrightiso.org Web www.iso.org Published in Switzerland ii ISO 2005 All rights reservedISO 18431-1:2005(E) ISO 2005 All rights reserved iii Contents Page Foreword iv Introduction v 1
7、Scope . 1 2 Normative references . 1 3 Terms and definitions. 1 4 Symbols and abbreviated terms . 3 5 Signal conditioning. 4 5.1 Cautionary overview. 4 5.2 Filtering 4 5.3 Sampling 5 6 Determination of signal type . 5 6.1 Signal taxonomy . 5 6.2 Deterministic signals 6 6.3 Random signals 7 7 Analysi
8、s of signals . 8 7.1 Preprocessing of signals . 8 7.2 Time domain analysis. 9 7.3 Frequency domain analysis of signals. 13 7.4 Time-frequency distributions 17 7.5 Averages of random stationary, ergodic signals 18 Bibliography . 20 ISO 18431-1:2005(E) iv ISO 2005 All rights reservedForeword ISO (the
9、International Organization for Standardization) is a worldwide federation of national standards bodies (ISO member bodies). The work of preparing International Standards is normally carried out through ISO technical committees. Each member body interested in a subject for which a technical committee
10、 has been established has the right to be represented on that committee. International organizations, governmental and non-governmental, in liaison with ISO, also take part in the work. ISO collaborates closely with the International Electrotechnical Commission (IEC) on all matters of electrotechnic
11、al standardization. International Standards are drafted in accordance with the rules given in the ISO/IEC Directives, Part 2. The main task of technical committees is to prepare International Standards. Draft International Standards adopted by the technical committees are circulated to the member bo
12、dies for voting. Publication as an International Standard requires approval by at least 75 % of the member bodies casting a vote. Attention is drawn to the possibility that some of the elements of this document may be the subject of patent rights. ISO shall not be held responsible for identifying an
13、y or all such patent rights. ISO 18431-1 was prepared by Technical Committee ISO/TC 108, Mechanical vibration and shock. ISO 18431 consists of the following parts, under the general title Mechanical vibration and shock Signal processing: Part 1: General introduction Part 2: Time domain windows for F
14、ourier Transform analysis Part 4: Shock response spectrum analysis The following parts are under preparation: Part 3: Bilinear methods for joint time-frequency analysis Part 5: Methods for time-scale analysis ISO 18431-1:2005(E) ISO 2005 All rights reserved v Introduction In the recent past, nearly
15、all data analysis has been accomplished through mathematical operations on digitized data. This state of affairs has been accomplished through the widespread use of digital signal acquisition systems and computerized data-processing equipment. The analysis of data is therefore primarily a digital si
16、gnal-processing task. The analysis of experimental vibration and shock data should be thought of as a part of the process of experimental mechanics that includes all steps from experimental design through data evaluation and understanding. This part of ISO 18431 assumes that the data have been suffi
17、ciently reduced so that the effects of instrument sensitivity have been included. The data considered in this part of ISO 18431 are considered to be a sequence of time samples of a physical quantity, such as a component of velocity, acceleration, displacement or force. Experimental methods for obtai
18、ning these data are outside the scope of this part of ISO 18431. INTERNATIONAL STANDARD ISO 18431-1:2005(E) ISO 2005 All rights reserved 1 Mechanical vibration and shock Signal processing Part 1: General introduction 1 Scope This part of ISO 18431 defines the mathematical transformations, including
19、the physical units, that convert each category of vibration and shock data into a form that is suitable for quantitative comparison between experiments and for quantitative specifications. It is applicable to the analysis of vibration that is deterministic or random, and transient or continuous sign
20、als. The categories of signals are defined in Clause 6. Extreme care is to be exercised to identify correctly the type of signal being analysed in order to use the correct transformation and units, especially with the frequency domain analysis. The data may be obtained experimentally from measuremen
21、ts of a mechanical structure or obtained from numerical simulation of a mechanical structure. This category of data is very broad because there is a wide variety of mechanical structures, for example, microscopic instruments, musical instruments, automobiles, manufacturing machines, buildings and ci
22、vil structures. The data can determine the response of machines or of humans to mechanical vibration and shock. 2 Normative references The following referenced documents are indispensable for the application of this document. For dated references, only the edition cited applies. For undated referenc
23、es, the latest edition of the referenced document (including any amendments) applies. ISO 2041:1990, Vibration and shock Vocabulary 3 Terms and definitions For the purposes of this document, the terms and definitions given in ISO 2041 and the following apply. 3.1 aliasing false representation of spe
24、ctral energy caused by mixing of spectral components above the Nyquist frequency with those spectral components below the Nyquist frequency 3.2 confidence interval range within which the true value of a statistical quantity will lie, given a value of the probability 3.3 data sampled measurements of
25、a physical quantity ISO 18431-1:2005(E) 2 ISO 2005 All rights reserved3.4 statistical degrees of freedom number of independent variables in a statistical estimate of a probability 3.5 frequency resolution difference between two adjacent spectral lines 3.6 number of lines number of spectral lines tha
26、t are displayed 3.7 Nyquist frequency maximum usable frequency available in data taken at a given sampling rate Ns 2 ff = where f Nis the Nyquist frequency; f sis the sampling frequency 3.8 record length number of data points comprising a contiguous set of sampled data points 3.9 sampling measuremen
27、t of a varying physical quantity at a sequence of values of time, angle, revolutions or other mechanical, independent variable 3.10 sampling frequency number of samples per unit of time for uniformly sampled data 3.11 sampling interval number of units (e.g. time, angle, revolutions) between two succ
28、essive samples 3.12 sampling period duration of time between two successive samples 3.13 sampling rate number of samples per unit of time, angle, revolutions or other mechanical, independent variable for uniformly sampled data 3.14 side-lobes sequence of peaks in the frequency domain caused by the u
29、se of a finite time window with the Fourier Transform 3.15 signal bandwidth interval over frequency between the upper and lower frequencies of interest ISO 18431-1:2005(E) ISO 2005 All rights reserved 3 3.16 spectral leakage width of the peak in the power spectrum due to a single spectral component
30、caused by using a finite window with the Fourier Transform 4 Symbols and abbreviated terms ADC analog-to-digital converter B signal bandwidth B eequivalent noise bandwidth C aamplitude scaling factor DFT Discrete Fourier Transform E expectation operator that computes the statistical mean value or av
31、erage value F(n) time-dependent force H 1 (m) frequency response function of the first type H 2 (m) frequency response function of the second type K summation limit of time delay k or length of window w(k) I number of data blocks L record length L ilevel in units U xfor amplitude histogram of signal
32、 x(n) N data block length: the number of sampled points that are transformed O x (k,m) wavelet transform of x(n) P xx (m) power spectral density of signal x(n) P xx,low (m) low frequency part of the power spectral density of signal x(n) P x2,low (m) low frequency part of the power spectral density o
33、f signal x 2 (n) P xy (m) cross power spectral density of signal x(n) with y(n) Q quality factor of a single degree-of-freedom system R xx (m) r.m.s. spectrum of signal x(n) S x (m,n) short-time Fourier Transform of x(n) T total time of a block of digital data = Nt V(k,m) Cohen class filter for smoo
34、thing the Wigner distribution X(m) Discrete Fourier transform of x(n) Y(m) Discrete Fourier transform of y(n) b number of increments, also known as bits, in an ADC c xx (k,n) auto-covariance of x(n) c xy (k,n) cross-covariance of x(n) with y(n) e xx (m) energy spectral density of signal x(n) e xy (m
35、) cross energy spectral density of signals x(n) and y(n) f frequency = mf f NNyquist frequency, the highest frequency present in a sampled signal f nnatural frequency of a single degree-of-freedom system f ssampling frequency = 1/t i index of data block k index of time shift l index of summation m i
36、ndex of frequency or scale () xn mean of non-stationary signal x(n) ISO 18431-1:2005(E) 4 ISO 2005 All rights reservedx mean of stationary signal x(n) n index of time p lower limit of summation q upper limit of summation r upper limit of summation r xx (k,n) auto-correlation of non-stationary data x
37、(n) r xx (k) auto-correlation of stationary data x(n) r xy (k,n) cross-correlation of non-stationary data x(n) with y(n) r xy (k) cross-correlation of stationary data x(n) with y(n) t time = nt v x (n) variance of the non-stationary data x(n) v xvariance of the data x(n) w(n) window function x(n) ph
38、ysical data in the time domain y(n) physical data in the time domain t sample period f frequency resolution rrelative random error xy 2 (m) coherence function (n) noise component of measured signal (n) mother wavelet x 2statistical variance of x x (m,n) Cohen class Wigner distribution using Cohen cl
39、ass filter V(n,m) x (m,n) Wigner distribution of signal x(n) 5 Signal conditioning 5.1 Cautionary overview The electrical signal from a transducer shall be properly conditioned for digitization by an analog-to-digital converter (ADC). This signal conditioning requires the determination of several pa
40、rameters associated with amplification, filtering and digitization. The selection of these parameters is very important for the acquisition of data that is appropriate for signal processing. 5.2 Filtering Before the signal can be successfully digitized by the ADC, the signal shall be low-pass filter
41、ed to prevent aliasing. Aliasing occurs when there are components of the signal at a frequency that is too high. The highest frequency in the signal is limited by the sampling frequency, f s , of the ADC. The range of settings of f sare found in the specifications of the ADC. The highest frequency c
42、omponent of the signal may be no greater than f N= f s /2, which is known as the Nyquist frequency. The upper frequency of the low-pass filter depends on the roll-off characteristics of the filter and the spectral properties of the signal. If the phase of the data is important, attention shall also
43、be paid to the phase characteristics of the filter. The following test should be performed to check the adequacy of the low-pass filter. A signal should be digitized and recorded. Then a Fourier transform should be performed on the data. The amplitude of the Fourier-transformed signal at the Nyquist
44、 frequency should be less than or equal to the expected noise level of the Fourier-transformed signal at the frequency of interest. If this is not the case, then the sampling rate should be increased or the upper frequency of the low-pass filter should be lowered. ISO 18431-1:2005(E) ISO 2005 All ri
45、ghts reserved 5 In addition to the low-pass filter, a high-pass filter may also be required because a non-negligible d.c. component of the signal may reduce the useful range of the ADC. Reducing or eliminating this offset prior to digitizing is preferable unless the d.c. component or low-frequency c
46、omponents are important. The external analog anti-aliasing filtering considerations for a sigma delta ADC are different. The analog signal shall meet the Nyquist criterion for the high frequency 1-bit digitizer, not the frequency for the end result. With sigma delta digitizers, the manufacturer usua
47、lly includes the low-pass filter needed for the analog input and an internal digital low-pass filter to match the output sample rate. 5.3 Sampling The ADC converts an analog signal into a sequence of integers. The output integers are proportional to the input over a range of voltage. This range of v
48、oltage is given in the specifications of the ADC and determines the proper gain setting discussed in 5.1. NOTE The number of increments b in the largest output number determines the dynamic range of the ADC, which is specified in terms of decibels, 6b + 1,8 dB. The sequence of numbers is sampled at
49、a rate called the sampling frequency, f s , discussed in 5.1. A signal may be resampled to order track the signal into samples that are equal increments of units other than time, for example angular displacement or degrees. Another parameter to be selected is the number of samples, the record length. The record length shall be large enough to capture the whole signal if the signal is transient or limited in time. The sampling frequency, f s , fixes the following parameters: the maximum (Nyquist) frequenc
