7.6.1 Signal Analysis and Data Processing
Sound and vibration signals produced by transducers are not normally in a suitable form for the study of noise and vibration problems. Frequency analysis is the most common approach used in the solution of such problems. This is because the human ear acts in many ways like a frequency analyzer [29] and also because frequency analysis can often be used to reveal information that can be related to the operation of machines, in particular rotating machinery and to the properties and the behavior of structures [30].
Until the late 1970s, frequency analysis mostly was carried out with dedicated instruments that incorporated analog filters. Since that time, with the advent of the fast Fourier transform (FFT) algorithm, frequency analysis has been increasingly carried out using digital computers, either as part of a dedicated instrument or after appropriate conversion of the analog signal to digital form (known as A/D conversion). The analog signal is converted into a series of discrete values (also known as a time series). Dual and multichannel analyzers are also in common use for the parallel analysis of the signals from several transducers. Besides carrying out frequency analysis of signals, analyzers have been made to calculate various other functions including cross‐spectra, coherence between signals, and the like (see Chapter 1). Reference [31] explains how measured noise and vibration data can be acquired, processed, shared, and stored using the power of modern digital computer systems. The A/D conversion process, digital data storage and retrieval, basic computations used in noise and vibration data analysis, and errors associated with the various calculations are summarized in Ref. [32]. Important considerations in signal processing include sampling rate, sampling interval, resolution, and data format. The analog data must be sampled so that at least two sample values per cycle of the highest frequency of interest in the analog signal are obtained. The format of the data is also important, and it must be ensured that the data produced are in a form that they can be read directly by any computer program written in a common programming language.
7.6.2 Sound Level Meters (SLMs) and Dosimeters
The SLM is an instrument designed to measure sound pressure over a frequency range and a sound pressure level range similar to the human ear. The basic SLM consists of a microphone, amplifier, frequency weighting circuit(s), detector averaging circuit, and an analog or digital read‐out device [33–37]. Miniaturization of electrical circuits and components has allowed small lightweight SLMs to be built, which possess considerable sophistication and capabilities. Also, standards for SLMs written by successive national and international standards committees have resulted in different requirements and additional changes in SLM design and manufacture so that there is a wide variety of SLMs in use.
There are four main types of SLM: 0–3. Types 0–2 are the most accurate and type 3 the least. The tolerances for the different types are specified in these standards. The different SLM types are generally used for precision, laboratory, field, and survey measurements. Dosimeters are similar in design to SLMs, except that the time constant, threshold, and exponent circuits are omitted [23, 38]. Dosimeters are worn on the person and are normally designed to measure the so‐called noise dose, which is a percentage of a criterion exposure, where exposure is measured in pascal‐squared hours (see Chapter 5). The noise dose calculated depends on the exchange rate used. In the United States, the Occupational Safety and Health Administration (OSHA) requires a 5‐dB exchange rate while the National Institute for Occupational Safety and Health (NIOSH) and most other countries use the 3‐dB (equal energy) exchange rate. Reference [39] reviews the main aspects of SLM design and also briefly describes dosimeter design. Reference [40] reviews dosimeters in more detail.
7.6.3 Sound Power and Sound Intensity
Measurements of the sound power of machines are frequently needed. The European Union requires some machines to be provided with labels giving their sound power output. From knowledge of the sound power level, the sound pressure level can be calculated at a certain distance from a machine, either outside in free space or in a building, provided certain environmental conditions are known. Reference [41] describes several methods that can be used and that have been standardized both nationally and internationally. Also, measurement surfaces including the spherical and box surfaces are described. Reverberation time and comparison methods of measuring sound power are also reviewed in Ref. [41]. Sound intensity measurements described in Ref. [3] provide another method of determining the sound power output of sources, and this approach is particularly useful when the machine cannot be moved into a special facility such as an anechoic room or a reverberation room. In addition, the sound intensity approach can still be used to determine the sound power of a sound source when there is a hostile background noise present. Provided that the background noise is steady, good estimates of the sound power of a source can be made, even if the background noise level is very high. In such situations, the approaches described to obtain the sound power of sources in Ref. [41] normally fail. Sound intensity and sound power measurements are discussed in more detail in Chapter 8 of this book.
7.6.4 Modal Analysis
Modal analysis can be used to provide information concerning the natural frequencies, modal damping factors, and mode shapes of structures and machinery [42]. This information can be obtained either from mathematical analysis of a structure’s dynamic response derived from a set of equations and knowledge of its mass and stiffness distributions or from experimental measurements of the structure’s response to excitation. Experimental modal analysis (often simply known as modal testing) is discussed in detail in Ref. [43]. As explained in this chapter, however, modal testing cannot be divorced from mathematical models of the structure’s dynamical behavior and the objective of modal testing in reality is an attempt to construct or validate a mathematical model of this behavior. Unfortunately, such mathematical models obtained through modal testing can never be quite complete because, in practice, the amount of experimental data obtained is inevitably limited. Usually, the mathematical model to be validated is a finite element model of the structure. Modal analysis is used for several main purposes. These include (i) monitoring the dynamic properties of a structure or machine to obtain early indications of structural deterioration or impending failure (often known as structural or machinery health monitoring), (ii) modification of a structure’s mass or stiffness distributions so as to change natural frequencies to avoid high‐amplitude resonant vibration, the resulting structural fatigue and the possibility of failure, and (iii) troubleshooting – the display of animated modes of vibration of the structure so that the dynamic behavior of certain critical areas of the structure can be understood, thus making possible practical solutions to vibration problems.
7.6.5 Condition Monitoring
Condition monitoring is discussed in Ref. [44]. Such monitoring of machinery may give sufficient advance warning of wear and possible imminent breakdown and failure so that replacement parts can be obtained in time to avoid costly machine downtime and/or loss of production. Costs savings can be considerable, for instance, in the case of downtime of a city electrical power plant, where unexpected downtime losses can exceed several million U.S. dollars each day. The savings in avoiding unnecessary downtime costs often vastly exceed the costs of replacement machine parts. In cases such as aircraft power plants, predictive maintenance can even prevent the possibility of catastrophic failure of the compressor blades and other components of the engines.
Reference [44] describes two main approaches to condition monitoring: (i) monitoring the relative displacement of a rotating machine shaft or bearing with a proximity probe and (ii) monitoring the vibration of the cover of a machine. Proximity probes are normally built into machines during manufacture; while, on the other hand, accelerometers can be placed on the cover of a machine at any time during service to monitor its vibration. Proximity probes are usually used to monitor changes in absolute shaft displacement and to measure so‐called shaft orbits. Chapter 57 in the Handbook of Acoustics [8] also contains useful information concerning monitoring changes in shaft motion with the use of proximity probes. Reference [44] is mainly concerned with vibration measurements of machine casings made with accelerometers. If a machine is monitored in its original new condition, measurements made later may reveal changes indicating wear and the possibility of failure. Faults related to the frequency of the shaft speed include: misalignment, imbalance, and cracks in the drive shaft. It is usually difficult to distinguish between these faults. Useful information is given in Ref. [44] about the changes in the vibration signature, which manifest themselves with electrical machines, gears, bearings, and reciprocating machinery such as internal combustion engines, pumps, compressors, and the like.
7.6.6 Advanced Noise and Vibration Analysis and Measurement Techniques
Wavelets are starting to become of practical use in the solution of noise and vibration problems, machinery diagnostics, and health monitoring. Wavelet analysis is concerned with the decomposition of time signals into short waves or wavelets. Any waveform may be used for such decomposition, provided that it is localized at a particular time (or position). Reference [45] provides an in‐depth discussion of the basics of wavelet analysis of signals, and in this chapter time is taken as the independent variable, although, in practice, any physical variable can be used. The Fourier coefficients of a signal are obtained by averaging over the full length of the signal, and the result is that no information is provided about how the frequency content of the signal may be changing with time.
In principle, the short‐time Fourier transform (STFT) does provide this needed frequency time variation information, by dividing the time record of the signal into sections, each of which is analyzed separately. The frequency coefficients of the signal computed by the STFT depend on the length and time (or position) of the short record that the calculation process assumes is one period of an infinitely long periodic signal [32, 42, 46]. The difficulty remains, however, that infinitely long harmonic functions are being used to decompose a transient signal. Wavelets are short functions that avoid this difficulty. A set of wavelet functions is used as the basis for the decomposition of transient time‐history signal records.
Near‐field acoustical holography is a technique that can be used to reconstruct the frequency spectrum of any sound field descriptor (i.e. sound pressure, particle velocity, and sound intensity) at any location in space, normal surface velocity/displacement, directivity patterns, and the total sound power of a source. This is achieved by making a sound pressure measurement on a planar surface located near to the source’s surface with either a scanning microphone (or hydrophone) or an array of microphones. If a scanning microphone is used, it should be robot‐controlled. The procedure essentially creates a near‐field hologram and relies on the measurement of the phase relationship between all of the sensor elements in the array that is used. If a scanning microphone is used instead, then the phase relationship is obtained by comparisons with a reference signal, which is kept stationary throughout the measurement. The approach can be used both with sources that are random in nature (such as fluid flow or boundary layer noise sources) and with deterministic sources (such as those containing pure tones like noise from a propeller). Although the approach is not simple, it eliminates the need for costly facilities and relies on the use of software instead, some of which is becoming commercially available. Reference [47] describes the theory behind this approach and also describes its use in practice to determine the in‐flight sound pressure, normal surface velocity, and sound intensity on the interior fuselage surface and the floor of a passenger commuter aircraft.
More recently, a measuring technique called beamforming has been used to characterize complex noise sources. The theoretical fundamentals of the technique were developed in the area of antennas but have also been applied to sonar, telecommunications, seismology, and radioastronomy [48]. In acoustical applications, the noise from the source is detected in the far field by an array of standard microphones. The signals from the array are digitized, time‐delayed, summed, and digital‐signal processed with some beamforming algorithm (under the assumption of a certain source model) in order to produce a very directional sensor [49].
Beamformers have poor spatial resolution at low frequencies but are more accurate than near‐field acoustical holography at higher frequencies. The frequency limits of the system are mainly dependent on the number of microphones, the size of the array, and the distance to the source. Several configurations of arrays can be used for this purpose, and examples include linear, random, star, spiral, circular, planar, and spherical arrays [49, 50]. The technique produces acoustical images that can be superimposed to pictures or video where sound pressure levels are represented by colors similar to a thermal camera. Depending on the capabilities of the processing system, the noise source analysis can be done as post‐processing or in real‐time, which is very useful in the study of moving sources. In this case, however, corrections due to the effect of Doppler shift must be incorporated [51].
Although the signal processing resources to implement beamforming in practice are not simple [52], this technique allows one to get very detailed information about the sound field, performing noise source identification and classification. Applications of beamforming to identification of noise sources include industrial, machinery, automotive, railway, wind turbine blade, and aircraft flying noise [49–51]. At present some of these systems are commercially available.
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