1、BRITISH STANDARDBS ISO 18431-1:2005Mechanical vibration and shock Signal processing Part 1: General introduction ICS 17.160g49g50g3g38g50g51g60g44g49g42g3g58g44g55g43g50g56g55g3g37g54g44g3g51g40g53g48g44g54g54g44g50g49g3g40g59g38g40g51g55g3g36g54g3g51g40g53g48g44g55g55g40g39g3g37g60g3g38g50g51g60g53
2、g44g42g43g55g3g47g36g58Incorporating corrigendum May 2009National forewordThis British Standard is the UK implementation of ISO 18431-1:2005, incorporating corrigendum May 2009.The UK participation in its preparation was entrusted by Technical Committee GME/21, Mechanical vibration and shock, to Sub
3、committee GME/21/2, Vibration and shock measuring instruments and testing equipment.A list of organizations represented on this subcommittee can be obtained on request to its secretary.This publication does not purport to include all the necessary provisions of a contract. Users are responsible for
4、its correct application.Compliance with a British Standard cannot confer immunity from legal obligations.BS ISO 18431-1:2005Amendments/corrigenda issued since publicationDate Comments 31 August 2009 Implementation of ISO corrigendum May 2009. Equation 9 in Subclause 7.2.3.3 replacedThis British Stan
5、dard was published under the authority of the Standards Policy and Strategy Committee on 30 January 2006 BSI 2009ISBN 978 0 580 68180 6Reference numberISO 18431-1:2005(E)INTERNATIONAL STANDARD ISO18431-1First edition2005-11-15Mechanical vibration and shock Signal processing Part 1: General introduct
6、ion Vibrations et chocs mcaniques Traitement du signal Partie 1: Introduction gnrale BS ISO 18431-1:2005ii iiiContents Page Foreword iv Introduction v 1 Scope . 1 2 Normative references . 1 3 Terms and definitions. 1 4 Symbols and abbreviated terms . 3 5 Signal conditioning. 4 5.1 Cautionary overvie
7、w. 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 Analysis 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 distr
8、ibutions 17 7.5 Averages of random stationary, ergodic signals 18 Bibliography . 20 BS ISO 18431-1:2005iv Foreword ISO (the International Organization for Standardization) is a worldwide federation of national standards bodies (ISO member bodies). The work of preparing International Standards is nor
9、mally carried out through ISO technical committees. Each member body interested in a subject for which a technical committee 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
10、the work. ISO collaborates closely with the International Electrotechnical Commission (IEC) on all matters of electrotechnical 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 prepar
11、e International Standards. Draft International Standards adopted by the technical committees are circulated to the member bodies 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 som
12、e of the elements of this document may be the subject of patent rights. ISO shall not be held responsible for identifying any 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 ge
13、neral title Mechanical vibration and shock Signal processing: Part 1: General introduction Part 2: Time domain windows for Fourier 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:
14、 Methods for time-scale analysis BS ISO 18431-1:2005vIntroduction In the recent past, nearly 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 com
15、puterized data-processing equipment. The analysis of data is therefore primarily a digital signal-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 da
16、ta evaluation and understanding. This part of ISO 18431 assumes that the data have been sufficiently 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
17、 a component of velocity, acceleration, displacement or force. Experimental methods for obtaining these data are outside the scope of this part of ISO 18431. BS ISO 18431-1:2005blank1Mechanical vibration and shock Signal processing Part 1: General introduction 1 Scope This part of ISO 18431 defines
18、the mathematical transformations, including 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
19、 or random, and transient or continuous signals. 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 ma
20、y be obtained experimentally from measurements 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, automobil
21、es, manufacturing machines, buildings and civil 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
22、 edition cited applies. For undated references, 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 app
23、ly. 3.1 aliasing false representation of spectral 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 p
24、robability 3.3 data sampled measurements of a physical quantity BS ISO 18431-1:20052 3.4 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 spe
25、ctral lines that are displayed 3.7 Nyquist frequency maximum usable frequency available in data taken at a given sampling rate Ns2ff= where fNis the Nyquist frequency; fsis the sampling frequency 3.8 record length number of data points comprising a contiguous set of sampled data points 3.9 sampling
26、measurement 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) betwee
27、n two successive 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 cause
28、d by the use of a finite time window with the Fourier Transform 3.15 signal bandwidth interval over frequency between the upper and lower frequencies of interest BS ISO 18431-1:200533.16 spectral leakage width of the peak in the power spectrum due to a single spectral component caused by using a fin
29、ite window with the Fourier Transform 4 Symbols and abbreviated terms ADC analog-to-digital converter B signal bandwidth Beequivalent noise bandwidth Caamplitude scaling factor DFT Discrete Fourier Transform E expectation operator that computes the statistical mean value or average value F(n) time-d
30、ependent force H1(m) frequency response function of the first type H2(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 Lilevel in units Uxfor amplitude histogram of signal x(n) N data block length: th
31、e number of sampled points that are transformed Ox(k,m) wavelet transform of x(n) Pxx(m) power spectral density of signal x(n) Pxx,low(m) low frequency part of the power spectral density of signal x(n) Px2,low(m) low frequency part of the power spectral density of signal x2(n) Pxy(m) cross power spe
32、ctral density of signal x(n) with y(n) Q quality factor of a single degree-of-freedom system Rxx(m) r.m.s. spectrum of signal x(n) Sx(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 smoothing the Wigner distribution X(m) Discrete F
33、ourier transform of x(n) Y(m) Discrete Fourier transform of y(n) b number of increments, also known as bits, in an ADC cxx(k,n) auto-covariance of x(n) cxy(k,n) cross-covariance of x(n) with y(n) exx(m) energy spectral density of signal x(n) exy(m) cross energy spectral density of signals x(n) and y
34、(n) f frequency = mf fNNyquist frequency, the highest frequency present in a sampled signal fnnatural frequency of a single degree-of-freedom system fssampling frequency = 1/t i index of data block k index of time shift l index of summation m index of frequency or scale ()xn mean of non-stationary s
35、ignal x(n) BS ISO 18431-1:20054 x 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 rxx(k,n) auto-correlation of non-stationary data x(n) rxx(k) auto-correlation of stationary data x(n) rxy(k,n) cross-correlation of non-st
36、ationary data x(n) with y(n) rxy(k) cross-correlation of stationary data x(n) with y(n) t time = nt vx(n) variance of the non-stationary data x(n) vxvariance of the data x(n) w(n) window function x(n) physical data in the time domain y(n) physical data in the time domain t sample period f frequency
37、resolution rrelative random error xy2(m) coherence function (n) noise component of measured signal (n) mother wavelet x2statistical variance of x x(m,n) Cohen class Wigner distribution using Cohen class filter V(n,m) x(m,n) Wigner distribution of signal x(n) 5 Signal conditioning 5.1 Cautionary over
38、view 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 parameters associated with amplification, filtering and digitization. The selection of these parameters
39、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 filtered to prevent aliasing. Aliasing occurs when there are components of the signal at a frequency that is
40、 too high. The highest frequency in the signal is limited by the sampling frequency, fs, of the ADC. The range of settings of fsare found in the specifications of the ADC. The highest frequency component of the signal may be no greater than fN= fs/2, which is known as the Nyquist frequency. The uppe
41、r 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 be paid to the phase characteristics of the filter. The following test should be performed to check the adeq
42、uacy 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 frequency should be less than or equal to the expected noise level of the Fourier-transformed signal at the
43、 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. BS ISO 18431-1:20055In addition to the low-pass filter, a high-pass filter may also be required because a non-negligible d.c. component of the
44、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 components are important. The external analog anti-aliasing filtering considerations for a sigma delta ADC are different. The analog signal
45、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 usually 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 S
46、ampling 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 voltage is given in the specifications of the ADC and determines the proper gain setting discussed in 5.1. NOTE The number of increments b i
47、n 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 a rate called the sampling frequency, fs, discussed in 5.1. A signal may be resampled to order track the signal into samples that are equal
48、 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,
49、fs, fixes the following parameters: the maximum (Nyquist) frequency fN= fs/2 the sampling interval t = 1/fs6 Determination of signal type 6.1 Signal taxonomy The signals that make up the data are considered to be approximate members of idealized categories. In this part of ISO 18431, the signals are categorized by the taxonomy shown in Table 1.The category of signal often determines the methods of analysis. If an inappropriate analysis is used, then the results may be misleading or inconclusive. Usually data contain a mixture of two types of sig
