A practical method for vibration frequency response characterization of handheld probes using Bootstrap in building acoustics

Applied Acoustics 145 (2019) 125–136

Contents lists available at ScienceDirect

Applied Acoustics journal homepage: www.elsevier.com/locate/apacoust

A practical method for vibration frequency response characterization of handheld probes using Bootstrap in building acoustics Roberto San Millán-Castillo ⇑, Rebeca Goya-Esteban, Eduardo Morgado Department of Signal Theory and Communications, Rey Juan Carlos University (URJC), Camino del Molino, s/n 28943 Fuenlabrada, Madrid, Spain

a r t i c l e

i n f o

Article history: Received 8 June 2018 Received in revised form 24 September 2018 Accepted 27 September 2018

a b s t r a c t Vibration measurement in building acoustics can help understand and estimate different physical phenomena for both researchers and practitioners. Sound insulation and flanking sound transmission are just some of these phenomena and interesting information can be obtained from wall vibration. Different approaches are available in terms of instruments and techniques, ranging from laser interferometry to single axis accelerometers. The latter are simple and cost-effective solutions because they allow many practitioners to use them in an affordable way. In order to deal with the problem in a more efficient way, there is a need to employ a less intrusive mounting technique and we therefore performed a study of the handheld probe solution in detail. Calibration and theoretical data on probe tips attached to different sensors is extremely difficult to find in relation to frequency response, resonance or repeatability. A new and simple sensor characterization procedure is presented to study deviations in probes, depending on the mounting technique and its comparison to a more robust wax fixing method. Handheld probes modify accelerometer response, mainly due to the probe length and the material. Sensor size, weight and connector location were also observed as influencing variables, in addition to others, such as operator hand tremor and the way the sensor is held. Nevertheless, a study of all these variables would provide a very complex model and we therefore used a statistical approach to simplify the characterization tasks. In building acoustic vibration, a Gaussian probability distribution is usually assumed in the collected data, although not being true in all cases. An innovative Bootstrap approach was thus employed in this study without any assumptions on data probability distribution. Bootstrap is a non-parametric method that provides further information than typical average values on a particular experimental population, when the real population is unknown and difficult to estimate. Bootstrap statistical mean and its confidence interval are used as performance indexes. Ninety probe types and sensor set-ups were characterized according to their frequency response and repeatability in a real environment, as compared to regular Wax fixing. Probes show less repeatability than wax or simply handheld broadband techniques, but 95% Bootstrap statistical mean confidence intervals were less than 0.5 dB in a low frequency range, up to a maximum of 3.8 dB at higher frequency bands of interest. Higher deviations are found in system resonance. Nevertheless, uncertainty values on repeatability in building acoustics are not far from these values. A good similarity is found in a probe useful bandwidth ranging from 50 Hz to 800 Hz–1 kHz, depending on the probe’s features. Bootstrap statistical mean is useful to correct measurements of deviations in frequency response. This handheld vibration probe data approach can provide more efficient resource management in real test situations. Ó 2018 Elsevier Ltd. All rights reserved.

1. Introduction Sound insulation between rooms is measured according to the different detailed international standards indicated and wellknown in scientific and practitioner fields [1]. These standards attempt to estimate the two rooms’ common building element in field airborne insulation, test results in general being aimed at ⇑ Corresponding author. E-mail address: [email protected] (R. San Millán-Castillo). https://doi.org/10.1016/j.apacoust.2018.09.021 0003-682X/Ó 2018 Elsevier Ltd. All rights reserved.

compliance with local government limits or construction good practice [2]. This certification process is sufficient in many cases, however an improved insulation design may be necessary. The data gathered from traditional standard field measurement testing may not provide enough information to identify a cost-effective solution. Other than working in a transmission suite or similar situation, flanking transmission is likely. It therefore appears to be a wise decision to consider the airborne contribution of flanking transmission to calculate the real insulation value of the target building element. A lack of this information would mislead the

126

R. San Millán-Castillo et al. / Applied Acoustics 145 (2019) 125–136

scope and correct installation of control solutions [3–5]. To obtain more valuable and robust information, vibration levels on walls were used to collect data on airborne and structure-borne insulation features. Vibration velocity levels (Lv) were employed in many different tests on flanking transmission in the laboratory, field measurements [4–7] and building acoustic simulation frameworks [8]. Lv is also a classic variable used to define wall acoustic radiated power [9,10] and has proven useful in research on building acoustics. There are certain scientific references to the use of vibration in applied building acoustics problems. A widely used theory is the Discrete Calculation Method (DCM) developed to measure sound radiation efficiency [11]. Research led to the manufacture of a sound plus vibration handheld probe designed to measure surface intensity, but it did not have an extension or alternative pick-up on the accelerometer [12]. Other authors showed similar results in insulation estimation using pressure, acoustic intensity and vibration methods with accelerometers screwed on the walls [13]. Vibration signal was also observed to be useful to assess wall radiation in the laboratory using doppler laser vibration measurement in complete space and time sampling [14]. Certain studies providing data on building acoustic cases have also dealt with vibration signal in building acoustics, although under laboratory conditions where fixing was not an issue, with very good results [15]. The interesting new Transfer Path Analysis applied to building acoustics also shows the convenience of employing vibration signal to estimate acoustic insulation values, thus showing the need for quite a large number of accelerometer positions for measurement and the need to find a way of avoiding tedious and impractical testing [16]. Very recent laboratory and field measurements of the flanking transmission standard 10848 series [4] records vibration data measurements in well-known and controlled scenarios, where every single method and action is plausible for the sake of accuracy. ISO 10848 standard results are extremely valuable as entry parameters in prediction stages, as described in ISO 12354 [8]. However, these techniques are difficult to perform in real and common practitioner environments, due to equipment costs and the time invested in collecting data. Currently available equipment may have to comply with ISO 10848 requirements. However, in field measurement, some of the recommendations in the standard are difficult to employ at certain levels: wax or small metal washers glued/cemented to the walls are not possible in circumstances in which the surfaces should remain aesthetically the same, without any flaws after testing. Time consuming and expensive measurement method proposals end up as research and laboratory practices. For the sake of simplicity and cost-effectiveness, an approach based on a simple single axis piezoelectric accelerometer with a metallic probe/rod is a good substitute, as compared to other available procedures, such as intensity or laser vibrometers, even when using a probe as the mounting technique. This prioritizes comfortable, quick, cheaper and less intrusive testing in real life environments. As stated in previous work, the features can be summarized as follows, [17]: 1) A cost-effective solution, as only general purpose piezoelectric accelerometers plus a general purpose metallic rod are employed, suitable for most real-time analyzers. 2) Fast and straight forward access to wall surface vibration data collection without drilling or glue/wax flaws on the walls. Another author proposed wax fixing for accelerometers and, although the results with a simply handheld accelerometer seemed very similar, the study was only performed on one point and with very few measurements [3]. However, signals from such a simple sensor can mislead Lv assessment, due to accelerometer resonance frequency shift and under-estimation of the frequency levels [18].

Details and further justification can be found in other studies [17,19]. Sensor manufacturers only provide frequency response characterization in a highly robust and stable mounting way: screw-on method. In general, practitioners find it difficult to apply the same procedure. The ISO 5348 standard recommends experimental research on sensor response depending on certain application. Available information on handheld probe performance is only an approximate indication of useful measurement of band frequency because of resonance frequency shift down to somewhere around 1–2 kHz [20]. All single-mounted techniques have their advantages and disadvantages, as described in the standard. However, it is difficult to find information on experimental sensor response in environments other than those included in the standards [21]. Handheld probe techniques are usually discarded as a low repeatability and non-robust method, although they allow fast testing [22]. Depending on the mounting technique, levels measured can be quite different and lead to incorrect results in useful calculations, such as wall sound power radiation. The Bootstrap method suggested in this paper is therefore useful to obtain an efficient handheld probe characterization. Bootstrap could be applied as a general approach for experimental research on all other mounting techniques that lack data on real performance. In general, the bootstrap method would be useful to all fixing methods, except the screw-on method, which is well characterized in calibration charts. However, screw-based techniques are far from being a fast and non-intrusive method of field measurement. Accordingly, handheld probes can be very useful in building acoustics environments and it is necessary to obtain more information on their performance: inherent noise, frequency response deviations and uncertainty-related values are important facts to take into account. As it is impossible to have a calibrated and accredited report on every single option, it is quite a useful practical approach for real jobs and environments. With respect to inherent noise and its influence, a preliminary study was performed and highlighted the relevance of taking into account the entire measurement system when working in a building acoustics framework [23]. There are recent research studies on the use of handheld probes and the possibility of frequency response modification beyond resonance frequency, which proves its performance when compared to other forms of fixing bearing vibration measurements [24]. However, they again provide for a certain probe version design that does not meet certain real and practical needs [25]. Many examples of handheld instruments can be found in scientific references used to facilitate data collection in other areas (haptics, ultrasound, optics) and even in closer acoustics and vibration fields of knowledge, such as hand-arm vibration. When it comes to handarm vibration, there are even more variables involved in measurement procedures and they are more difficult to assess, however handheld methods are not discarded systematically, but described in uncertainty terms as a substitute strategy [26]. In all of them, different situations are verified to analyze the factors influencing measurement. Highly complex hand movement and tremor models are found that require a great deal of data input, which is difficult to collect in a real-life context. It therefore appears that hand tremor influences up to 10 Hz and is not in our building acoustics interests, whereas hand movement is more difficult to assess, but can influence vibration measurements [27,28]. However, with simplicity in mind, it would be useless to include all plausible, controlled and not controlled factors, as it would mean increasing instrumentation and processing in a simple accelerometer-based set-up: constancy of measurement direction, constancy of pressure, sufficient pressure, contact area and probe orientation are some of the influencing variables [19]. Hence, our research was based on a statistical approach in which, using a medium-sized

127

R. San Millán-Castillo et al. / Applied Acoustics 145 (2019) 125–136

and simple to test database, knowledge can be gained on measurement and vibration probe performance. In this paper, the Bootstrap method is suggested to obtain crucial information at the vibration level acquisition stage. Based on several measurements in a simple test set-up, an experimental probability distribution was obtained. Experimental histograms, means and confidence intervals could therefore be inferred from the experiments. More information and precision are expected in testing, when the details become known of our vibration set-up and statistical inferred data on resonance frequency, experimental difference versus more robust mounting techniques, experimental means and experimental confidence intervals. As a statistical technique, Bootstrap has been proven extremely useful in measurement estimation problems, when a direct non-destructive amount of observation is not possible and large-scale repetition of an experiment is not feasible [29,30]. Fahy [31] discussed the complexity of deterministic and analytical models in vibroacoustics, resulting in a high dynamic response curve variability in vibration measurements and the convenience of probabilistic models. Similar works on determining uncertainty in handheld probes often take on a Gaussian value distribution [26]. Bootstrap has also been successfully used in acoustics to check environmental noise levels without a Gaussian distribution sampling strategy [32–34]. Bootstrap does not assume any particular probability distribution. Thus, a practical approach on repeatability of uncertainty values is provided that takes into account certain influencing test performance variables that are difficult to describe analytically. Handheld probe measurement set-ups are quite difficult, since they deal with numerous factors that can influence measurement performance and are difficult to correctly control. Bootstrap therefore seems to be a suitable way of dealing with this problem. From a Bootstrap point of view, this paper provides an original database on different handheld probes and sensors. All are simple and low-cost probes, based on general probe piezoelectric accelerometers and available metal rods. Wax mounting and simply handheld methods are also analyzed and compared. In this way, a general idea of frequency response and resonance change is obtained and can be used in other disciplines relating to vibration measurement. The contribution of this research consists in an original methodology to assess vibration handheld probe frequency response and measurement variability through statistical mean confidence interval widths based on Bootstrap and counting used by practitioners in a real-life measurement environment. The rest of the paper is organized as follows: In Section 2, the materials and methods used in testing are described: frequency response testing and the Bootstrap approach; Section 3 presents and analyses the results obtained from testing and Bootstrap data processing; Finally, Section 4 contains conclusions. 2. Materials and methods Data was collected in two different parts: 1) Frequency response testing; 2) Experimental probability distribution estimation. 2.1. Frequency response testing The first point deals with vibration measurements in a controlled test rig. Once again, an important issue was to maintain a simple and affordable testing environment. A block diagram of the testing system can be observed in Fig. 1. Since sensor performance was assessed, the acceleration level (La) was the chosen parameter in all measurements, referenced to 10 6 m/s2. La is an estimator normally used in sensor calibration charts that allows

Sensor

Real Time Analyzer

Signal Generator

Shaker

Power Amplifier

Fig. 1. Block diagram of a frequency response set-up in probe testing.

straight forward comparison. Since this study is applied to building acoustics, the reference frequency range is from 50 Hz to 5 kHz, with a one-third octave band resolution as the expanded range provided in most relevant standards [1]. An acoustics and vibration general purpose frequency real time analyzer was the data hub in experiments, Type Soundbook from Sinus messtechnik. Only two signal channels are required: one input channel to collect vibration signals from sensors; one output channel to provide excitation signals. A stable vibration was generated by a miniature bench-top electro-dynamic shaker peak sine force rating of 17.8 N, Type LDS V201 from B&K, with a usable frequency from 5 Hz to 13 kHz in the amplitude and frequency range of interest, using a power amplifier, Type LDS PA25E from B&K [35]. The reference vibration signal was a filtered white noise in the interest frequency range provided by the real-time analyzer built-in signal generator. Amplitude levels in the shaker were adjusted to an equivalent favorable real situation in an insulation test to allow enough signal to noise ratio for the measurement system employed, in order to avoid inherent noise problems, as stated in previous work [23]. The excitation vibration signal was also suitable to the linear level and frequency ranges of the sensors tested. A small rigid metal plate screwed to the shaker was used as an expander in a more comfortable and larger place were all measurements were performed. Different probe frequency response testing was performed. To obtain valuable probe frequency response deviations, measurements on a mounting technique with a theoretical wider flat frequency response were also performed [19]. In the application environment, the most widely used robust mounting technique is wax attachment on walls [4,10], this method therefore being our reference measurement or gold standard. There are other methods which provide more precise and accurate calibration and frequency response results, however they are not suitable for daily engineering operations [17,36]. Interest was focused on the difference between handheld probe frequency response and wax frequency response, called Gain and defined in Section 3.4, therefore outcome deviations are independent of input signal, since we worked in the linear ranges of the accelerometers. Five piezoelectric CCLDTM or ICPTM suitable type sensors were used for testing with different features, see Table 1 in which the

128

R. San Millán-Castillo et al. / Applied Acoustics 145 (2019) 125–136

Table 1 Accelerometer types involved in experiments. ID

Sensitivity

Weight

Sensor Base diameter

Sensor height

Sensor connector location

Type

Manufacturer

10 50 100 500 1000

10.03 mv/g 46.69 mv/g 101.40 mv/g 526.70 mv/g 975.00 mv/g

5.9 g 8.6 g 5.8 g 8.6 g 25 g

10.9 mm 12 mm 10.9 mm 12 mm 18.8 mm

17 mm 13.8 mm 17 mm 13.8 mm 20.1 mm

Top-mounted Side-mounted Side-mounted Side-mounted Top-mounted

352C04 4533-B-004 352C33 4533-B-002 352B

PCB B&K PCB B&K PCB

global specifications are: general purpose design, low sensitivity to environmental factors, possibility of several mounting techniques, lightweight with regard to typical building materials and professional and precision use [37–40]. To build probes, general construction methods were used and easily available metal rods attached to the sensors, screwing them to their mounting holes. Two different materials with different Young modules were used in these experiments: stainless steel and brass. A range of probe lengths were then tested for each material and each sensor: 6.5 cm, 12 cm, 20 cm, 25 cm, 30 cm, 40 cm, 50 cm and 100 cm. Therefore, eighty different probe combinations were considered, along with five direct wax-fixed sensors and another five direct sensors simply handheld by the practitioner. In total, ninety frequency response measurements from different vibration probe set-ups were analyzed. Due to the large number of probes and sensor set-ups, an identification code was used to facilitate data analysis: ‘‘ID_Material_Length”, where ID is a number close to accelerometer sensitivity (See Table 1), Material denotes the probe material (S, Stainless Steel; B, Brass) and Length denotes the probe length in cm (i.e. ‘‘1000_B_30” represents a probe based on a 1000 mV/g sensitivity accelerometer with a 30 cm Brass rod). When dealing with handheld and wax-mounted accelerometers, the code evolved to ‘‘ID_Plain” and ‘‘ID_Wax”, respectively. As is common in building acoustics, frequency response is obtained from five-second block average time measurements [1,4]. Since statistical behavior needs to be described, this research performed a large number of tests for every mounting technique involved. Every single measurement was seventeen seconds’ long. Firstly, two seconds were discarded due to high value variability

resulting from initial probe location instabilities. Each test file was then split into three five-second files to obtain more data with a typical time measurement duration. To obtain data on repeatability, all measurement types were repeated eleven times by the same operator in a row. From test to test, the sensor/probe did not remain in the first position and was removed and located once again on the plate to start a new measurement, in order to simulate real measurement point location changes. For wax mounting, in every single test, wax was removed from the accelerometer’s metal stud base and a new quantity of wax placed on the back. Photographs of certain testing procedures with different set-ups are shown in Fig. 2. The tests were performed at the Rey Juan Carlos University facilities (Madrid, Spain). The experiments were carried out in a soundproof chamber (CEA) in the Acoustics Laboratory to avoid unwanted and difficult-to-identify airborne and structure borne signals, mainly in low frequency ranges; occasional events were discarded. Reproducibility would be another uncertainty fact to consider, since different types of equipment could be used and different operators could perform the tests. However, this is beyond the scope of this paper, which only focused on repeatability as a first stage of the study. 2.2. Bootstrap processing Data collection is always limited by a finite number of samplings, since a population is not available. Moreover, sample variability may be present due to many factors and their many combinations, as in the problem faced in this research. The Bootstrap method consists of a resampling procedure with replacement

Fig. 2. Different testing set-ups: a) Wax testing of a side-mounted connector accelerometer; b) Handheld (Plain) set-up of a side-mounted connector accelerometer; c) 50 mm long brass probe on a top-mounted connector accelerometer; d) 20 mm long steel probe on a top-mounted connector accelerometer; e) comprehensive test set-up.

R. San Millán-Castillo et al. / Applied Acoustics 145 (2019) 125–136

that can be used to draw population statistical properties from several samples [29]. An artificial population is generated from our measurement data, collected as described in Section 2.1. Bootstrap processing was performed by algorithms originally developed by the authors, with Python 2.7 programming language [41], using a Numpy [42] and Pandas library [43]; the plotting of results was performed by a Matplotlib library [44]. Bootstrap is a nonparametric statistical method that enables the determining of variable distribution without information on distribution class and in limited samples. The information on the population is the same, however it provides a way of analyzing sample variability. Therefore, an experimental probability distribution was established with no assumptions. Since there was no certainty of the underlying data distribution of these kinds of probes, a typical assumption on a normal distribution of measurements could lead to misleading results. The data probability distribution analysis can be found in Section 3.1, where the vibration measurements involved in this research are revealed as non-Gaussian in many of the studied cases. Vibration studies in building acoustics usually employ estimates based on time and space measurement averages as point estimates [4,31]. In this work, the objective was to provide more information on the complex vibration measurement procedure based on probes other than averages. The Bootstrap method provided certain other statistical estimates of La, since an experimental probability distribution for an estimator was available. This

129

research focused on the Bootstrap statistical mean and its 95% confidence intervals (BCI) of experimental probability distribution as an estimate of uncertainty and a source of knowledge on the experimental set-up used in the study. The experimental statistical mean distribution or Bootstrap statistical mean for each probe and for each one-third octave band was calculated using Bootstrap techniques. Thus, eleven acceleration vibration level measurements, La, of ninety different probe/sensor set-ups and their twenty-one one-third octave band values of interest were employed in the process, La, probe n, t-f; where n is the probe set-up from 1 to ninety, t the 5 s vibration measurement block from one to thirty-three and f the one-third octave band central frequency from 50 Hz to 5 kHz. These data vectors belonged to an unknown probability distribution observed from real measurements, whose statistical mean estimates would be b h a; probe n f . From the thirty-three 5 s measurement blocks, for every probe and one-third octave, one observed random sample was drawn to be included in the experimental distribution. The observed sample was replaced and another sample drawn and the process repeated until thirty-three samples yielded the first Bootstrap resample. This procedure was performed up to 1000 times (B), since it is a general recommendation in resampling to infer 95% confidence intervals from an experimental probability distribution [45]. Further discussion on precision of different values of B can be found in Section 3.2. Therefore, one thousand Bootstrap

Fig. 3. Schematic diagram of a Bootstrap processing framework.

130

R. San Millán-Castillo et al. / Applied Acoustics 145 (2019) 125–136

resamples were obtained after the resampling process, La; probe n; b f ; where b is the Bootstrap resample order from 1 to 1000 (B). To outline a representative artificial population, at least twenty samples are recommended to avoid significant outliers and aiming BCI inference, as recommended in literature [45]. A schematic diagram of the Bootstrap technique applied is provided in Fig. 3. Once 1000 Bootstrap resamples were available for each probe and one-third octave band, the Bootstrap statistical mean and BCI of all probe set-ups were calculated and analyzed. Hence, the Bootstrap statistical mean probability distribution was available, b h , as a Bootstrap replicate statistical estimator. a; probe n f

BCI is readily obtained by arranging b h a; probe n f . The Bootstrap statistical mean was analyzed using histograms and computed with B Bootstrap resamples, while the BCI was considered according to its width in dB as a performance estimator, as in other acoustics studies [33]. 3. Results and discussion This section is divided firstly into a sub-section, in which an initial analysis of the data employed in this study is discussed and a second section, in which Bootstrap precision is provided, a third

in which the results of all probes/sensors are analyzed generally and a fourth that analyzes certain specific probes/sensors. 3.1. Data probability distribution analysis The procedures involved in vibration building acoustics usually assume Gaussian probability distribution in data and work on average point values as estimators. The objective of this Section was to provide evidence on the lack of Normality in all vibration signals and to support the hypothesis that Bootstrap data processing would benefit probe frequency response characterization. The data collection process is explained in detail in Section 2. From these measurements, we obtained ninety data vectors with information on their twenty-one one-third octave bands. 1890 experimental La data distributions were then processed and reviewed in 990 measurements, which provided 62,370 useful five-second measurement blocks. To characterize statistical data distribution, La histograms of the ninety probe/sensor set-ups in twenty-one one-third octave bands were studied and a Normality Shapiro-Wilk test [46] carried out. The null hypothesis was rejected when p-values were lower than a level of 0.05 a significance. Almost 43% of the nine hundred and ninety measurements was found not to be normally distributed in the tests. When analyzing according to frequency bands, as shown in Fig. 4, there was more Normality and stable values at medium frequencies. Resonance influence could generate a more normal behavior, since it adds more variability in measurements. Following a similar analysis of probes in Fig. 5, it was very interesting to verify that Wax cases were the least normal of all cases, in spite of being the gold standard. Plain set-ups also reached high percentages in nonnormal values. Apart from these observed results, no more tendencies were inferred. Normal distribution assumption from measurements would not be correct for these data sets. Hence, a typical procedure of simplifying variable probability distributions would be incorrect. Bootstrap methods were more appropriate from a proper characterization perspective. 3.2. Bootstrap precision analysis

Fig. 4. Null normality test hypothesis rejection percentages vs. frequency of onethird octave bands.

Bootstrap resampling is related with the precision of BCI. The general recommendation of 1000 trials (B) was checked for the data available in this work [45]. Thus, BCI values were also performed with other different number of trials ranging 10, 50, 100, 10,000 and 50,000. A comparison among BCI of 1000 trials and

Fig. 5. Null normality test hypothesis rejection percentages vs. probe/sensor set-ups.

R. San Millán-Castillo et al. / Applied Acoustics 145 (2019) 125–136

the rest was set to assess the convenient trade-off value of B. The deviation of BCI of 10, 50, 100, 10,000 and 50,000 trials from the chosen value of 1000 trials were evaluated for all probe types and all their one-third octave bands. Deviations were declared as BCI values for the rest of B choices subtracted from the BCI value for B = 1000, so called BCId. The use of 10,000 and 50,000 trials presented very similar and stable differences with 1000 trials. BCId maximum was 0.3 dB for 50,000 trials and 0.2 dB for 10,000 trials, but they only occurred once and the average BCId is less than 0.1 in both cases. Regarding 10, 50 and 100 resamples, BCId were randomly distributed and reached up to 1.5 dB, 1 dB and 0.6 dB often respectively. For instance, up to 33 cases presented higher differences than 0.5 dB when employing 50 trials and up to 33 cases presented higher differences than 0.2 dB with 100 trials. A value over 0.5 dB was considered as relevant in general applied acoustics calculation procedures (e.g. background noise correction), so it became the deviation threshold of this research. Statistical variance and mean analysis of BCId provided also valuable information to choose B. B = 50,000 was assumed as the more accurate resamples value. Thus, deviation between 50,000 trials version and the rest trials version was analyzed. BCId_50k was declared as BCI values for the rest of B choices subtracted from BCI value for B = 50,000. The comparison of BCId_50k of different resampling rates referenced to statistical estimators of 50,000 trials version shown that lower rates than 1000 trials provided much higher variance and mean values, see Fig. 6. Thus, uncertainty would be increased in average and in point values and it would be reasonable to avoid the range of lower resampling rates. Depending on the number of trials the time required to perform calculations is linearly increased or decreased. The chosen tradeoff value considers a reasonable precision in dB and a reasonable performance time of calculations, which matches scientific literature recommendations [45]. B = 1000 was revealed as the more balanced value. 3.3. Data population results The first analysis performed dealt with BCI widths from a global point of view. Fig. 7 shows BCI widths in dB for all probes and the different mounted sensors analyzed regarding frequency, thus revealing a certain general behavior. In the lower frequency range, from 50 Hz to 800 Hz 1 kHz, BCI widths were lower than 1 dB. Even most of results, namely between 80 Hz and 500 Hz, were below widths of 0.5 dB. As from 800 to 1 kHz, BCI widths increased their values, reaching a maximum of 3.8 dB. At a higher frequency,

Fig. 6. Comparison of BCId_50k statistical estimator referenced to 50,000 resampling rate estimators in percentage terms (%): Variance and mean.

131

Fig. 7. BCI width vs. frequency of all probes and sensors tested: maximum BCI, minimum BCI, Bootstrap statistical mean and Bootstrap statistical median.

widths were much larger and there was more variability in values than in lower bands. Further information was extracted when reviewing Figs. 8 and 9, which present BCI width for Plain and Wax tests, respectively. In the first, Wax provided extremely low and stable BCI widths in most bands of interest, always much less than 0.5 dB. As from 2.5 kHz to 3.15 kHz, the values peak at the last three higher frequency bands. A maximum peak at 4 kHz is common to all sensors, however only reaching 1.2 dB. Performance in Plain tests was very similar to Wax tests. There was a slight difference up to a 200 Hz band in certain accelerometers, where BCI widths were even worse than in some probes, reaching differences of 0.5 dB, but always below 1 dB. A clearer increase was found at higher frequencies, where some values increased up to 2.3 dB. Wax results agreed with warnings in certain recent standards [4]. The first warning verified that the initial hypothesis regarding the wax mounting technique as a gold standard was correct and could be taken as a reference, since it obtained the most similar frequency response to accelerometer response in ideal fixing conditions of calibration charts. Secondly, some effects on high frequencies could be considered as differences in the wax layer quantity, location and mounting difference from test to test, since the conditions were not the same as in real-life environments [19]. Therefore, Bootstrap processing seems to be useful, even for ISO

Fig. 8. BCI width vs. frequency of all Wax sensors tested.

132

R. San Millán-Castillo et al. / Applied Acoustics 145 (2019) 125–136

Fig. 9. BCI width vs. frequency of all Plain sensors tested.

recommended and initially more robust fixing techniques and provides experimentally valuable information. Plain sensors proved to be quite a good mounting method in relation to the gold standard, due to lower values in broadband BCI widths in longer probe setups. As expected, probe results were much worse in comparison to the gold standards, see Figs. 7 and 10. A high variability in frequency showed a complex process also in frequency response. Nevertheless and focusing on the Bootstrap statistical mean data population results, BCI values were in a promising and controlled range, since they did not differ that much from other estimators used in building acoustics. Pressure levels or reverberation time uncertainties values are in a similar range or even worse in terms of variability, depending on the room [47–49]. These results were useful in providing information on deviation that could be taken into account when using this kind of sensor and its different wall-fixing methods. Not only point estimates are provided, but also repeatability uncertainty to improve and control a vibration measurement procedure. Although it was confirmed that the probe measurements were not sufficiently accurate, this new procedure seemed to be precise enough and provided the right information for adjustment, if required, to a more accurate procedure by further simple signal processing.

Fig. 10. BCI width for an example probe vs. frequency in different accelerometer set-up comparisons: 10 mV/g.

All the variability found in probe frequency response at higher frequencies was linked to accelerometer frequency resonance shift. One of the main effects of attaching a rod to an accelerometer is the shift in the sensor resonance frequency, because of a decrease in rigidity with respect to calibration charts when the sensor is mounted in an optimal way for the best response; on the other hand, this is not suitable in real engineering environments. The sensor range employed in this research featured resonance frequencies above 25 kHz [36–39]. However, when the sensor became a probe, there were changes in frequency response. Figs. 10 and 11 provide a comparison with the gold standard, 10_Wax, frequency response with some 10 mV/g sensor set-ups (10_Plain, 10_S_6.5, 10_S_25, 10_S_50, 10_S_100). In general terms, differences in probe frequency response first appeared in the range of 800–1 kHz, the same value as the increase detected in BCI. Depending on the probe length, different signal peaks distorted the wax flatter response. A more detailed analysis is provided in Section 3.4 for certain probes. By locating such peaks, shifted resonance frequencies are relocated. There was agreement when matching new resonance frequencies and increased BCI widths. The system responded in a natural and difficult to control way and depended on damping, which was highly influenced by all the factors highlighted regarding probe measurement variability and led to more variability of the measurements. Data population results showed that Wax was a good gold standard, although not perfect. Plain was the best way to obtain probe operation advantages, with a close agreement to gold standard levels and lower variability observed in BCI widths all through the frequency range. An example probe analysis confirmed frequency response degradation from reference levels and wider BCI widths remarkably close to resonance frequency levels. 3.4. Detailed results Once all the probe set-up population was scrutinized, certain probe set-ups were further analyzed in relation to frequency response and its relationship with BCI widths, for their dependence on sensor features or probe length and materials. The first analysis dealt with the frequency resonance effect of probes. Results of probe frequency response were compared to those of the gold standard for each sensor. Instead of frequency response, Gain frequency response was recorded. Gain response means subtracting each sensor’s Wax frequency response band levels from those of the probe or Plain set-up Difference

Fig. 11. Bootstrap statistical mean frequency response in different accelerometer set-up comparisons: 10 mV/g.

R. San Millán-Castillo et al. / Applied Acoustics 145 (2019) 125–136

133

Fig. 12. Gain response from different probe/sensor set-ups: Bootstrap statistical mean, maximum BCI and minimum BCI, for different materials (B, Brass; S, Steel). Arranged in 5 rows, according to probe length; and 3 columns according to the sensors.

quantification was therefore easier to verify. We decided to analyze four probe lengths in order to provide abbreviated and more representative information: 6.5 cm, 25 cm, 50 cm and 100 cm; Plain

fixing was added at this stage. The same strategy was used for sensors, choosing the side and top-mounted ones and one with a very different weight: 10 mV/g, 500 mV/g and 1000 mV/g, see Table 1.

134

R. San Millán-Castillo et al. / Applied Acoustics 145 (2019) 125–136

Table 2 Resonance frequency relocation in a one-third octave resolution for different probe materials.

Brass Steel

6.5 cm

25 cm

50 cm

100 cm

2 kHz 3.15 kHz

2 kHz 2 kHz

1.25 kHz + 3.15 kHz 1.6 kHz 2kHz

1 kHz + 2 kHz + 3.15 kHz 1.25 kHz + 2.5 kHz + 4 kHz

Both the materials involved in the testing were checked: 1) B, Brass; 2) S, Stainless Steel. Although not presented here, results found in 500 mv/g configurations were very similar to those in 100 mv/g and 50 mv/g, see Fig. 12 (columns 1 and 2). Fig. 12 shows all presented probe set-ups, in order to provide a global view of the detailed results; it is divided into 3 columns according to sensor sensitivity and 5 rows according to probe rod length. As in Section 3.3, changes resulting from probe lengths and materials were clearly observed, see Fig. 12 (all rows and columns). With regard to Plain probe set-ups in Fig. 12 (row 1), there was a tendency for them to be similar to a very short probe with very high frequency shift; although frequency shape was not as clear as with probes, the difference with respect to the gold standard was obvious, because of the fixing rigidity decrease. The best agreement with Wax was found in 10_Plain, Fig. 12 (row 1, column 1). Only a slight difference remained at 50_Plain, 100_Plain, and 500_Plain accelerometers linked to the hand position on handheld sensors, Fig. 12 (row 1). All of them were side-mounted and some of a similar size and weight (Table 1), while the rest were topmounted and very different in size and weight. The heaviest sensor, 1000_Plain in Fig. 12 (row 3, column 1), showed distorted response at a high frequency, the causes of which were discussed in the previous section. Certain conclusions can clearly be drawn on resonance frequency shift down: 1) The longer the probe length, the lower the resonance frequency; 2) the lowest resonance frequency was found in Brass probes, see Fig. 12 (rows 2–5). The most relevant effect of attaching a probe to a sensor was the resonance frequency shift down to the measurement frequency range of interest. In Table 2, resonance frequency relocations can be observed in a one-third octave resolution. This abbreviated data was only classified according to the probe material, since the results from a different sensitivity accelerometer were almost negligible, as validated in Fig. 12 (all columns and rows). Only a slight shift down was found in certain graphs of a 1000 mv/g sensor, due to the large difference in weight, as compared to the rest of probes and the differences in the way the probe was held, Fig. 12 (rows 3–5, column 3). We not only observed resonance shift, but also the appearance of higher system resonance frequency shift to the frequency range of interest in the longest probes, Fig. 12 (rows 3–5). From this point of view, Brass probes differed with the gold standard at lower frequencies and provided more resonance frequencies than Steel probes, Fig. 12 (rows 2–5, all columns). Gain response shape was also very similar in all the different configurations of sensor probes, except in 1000 mv/g probes above a length of 50 cm in both materials, see Fig. 12 (rows 4–5, all columns). The weight increase of these set-ups triggered other system resonance in the frequency range of interest that is not present in lighter probes, whose weight increase was lower, as the sensors were much lighter. With respect to the level differences as compared to the gold standard, the resonance effect boosted the signal collected with probe set-ups at resonance frequency peaks, but was attenuated at high frequencies directly after such resonance peaks. These attenuated levels in certain bands were linked to the resonance phenomenon [18], see Fig. 12 (rows 2–3). In this case, the longest probes also showed a remarkable attenuation at low frequencies, due to the large increase in probe damping, due to higher values of length and weight of the rods, Fig. 12 (rows 4–5). However, there was not a substantial difference in new reso-

nance peaks of different accelerometers. All of them were quality sensors and signal to noise ratio prevented major measurement changes. This was validated by the results in Wax testing and at low frequencies, where the results were not influenced by resonance shift, Fig. 12 (all rows and columns). The differences between sensors with regard to response profile had more to do with the way an operator held the probes and sensors. As already discussed, the effect on Plain fixing due to connector location was also verified for 50 mv/g and 100 mv/g set-ups. Accelerometer size was also relevant in data collection, since it influenced the hand holding position and measurement stabilization. Fig. 12 (rows 2–5) shows how shapes from 10 mv/g and 500 mv/g set-ups were in most cases more similar to 1000 mv/g set-ups, whose size and weight always obtained higher values due to the sensors, see Table 1. These effects were also verified for 100 mv/g and 50 mv/g set-ups, which are also lighter and smaller than 1000 mv/g. It therefore appeared that connector location was only relevant when a probe was not involved. However, nearly flat accelerometer frequency response from Bootstrap mean (typical ±3 dB deviations in levels) is observed from 50 Hz to 800 Hz 1.6 kHz for the shortest probes, depending on the set-up, which were the best in this respect, with up to 20–25 cm, see Fig. 12 (rows 2–3). Plain set-ups were even better that the shortest probes and 80–100 Hz to 3.15 kHz 4 kHz frequency response was almost flat, Fig. 12 (row 1); other than in typical resonance values, Gain values were very low. Thus, a large so-called probe useful bandwidth was within typical tolerance levels of Wax mountings. As probe lengths were increased, the probe useful bandwidth was trimmed, depending on the probe length, but response levels were also outside typical flat response tolerance. Hence, levels changed from 3.5 dB to 11 dB and response became more curved as damping increased when using longer probes, Fig. 12 (all columns and rows). Another interesting effect was the BCI behavior of probe setups. The most stable results were found in the 1000 mv/g series, Fig. 12 (column 3). Wider BCI is again confirmed in all probe cases at resonance frequencies, as discussed above. Surprisingly, there was wider BCI in shorter probe lengths. In all sensor types, wider BCI is found in lighter configurations, see Fig. 12 (row 2). This is linked to weight, which allows more hand movement to be stabilized. BCI width decrease at low frequencies was once again confirmed for these specific cases and already inferred from aggregate data, Fig. 12 (all rows and columns). Detailed results showed that probe frequency response was substantially different to the gold standard in most of the cases studied and highly dependent on probe length and the material used. Probe weights and sizes and the way they were held also influenced response to a lesser extent. However, sensor sensitivity did not show any relevance to response deviations. BCI width variability was again relevant in resonance and mainly in short probes.

4. Conclusion This study presents an original and innovative approach to vibration probe measurement frequency response estimation and calibration. The Bootstrap method provides very useful information when probability distribution is unknown, as in this case, where a global assumption of normality is proven to be wrong for almost half of the configurations. Even gold standard Wax

R. San Millán-Castillo et al. / Applied Acoustics 145 (2019) 125–136

testing does not satisfy a normal distribution in most of the measurements. A trade-off value of 1000 bootstrap resamples is proved as convenient regarding precision and computation time. This procedure is useful for the characterization of different vibration handheld probes that is not normally provided by manufacturers or scientific literature, which is now affordable and available with a simple rig. Therefore, practitioners have valuable information at their disposal regarding the frequency response of a range of handheld probes calibrated in an experimental framework that is more reasonable than accelerometer stand-alone calibration charts. Probe frequency response was confirmed to be worse than that of the gold standard method, however this new procedure provides quantification of the deviations in a large database of set-ups, which now is available to researchers and practitioners. Resonance frequency response shifting was confirmed and quantified in several probe set-ups and certain qualitative features of probes were linked to their experimental performance. Response information can be useful for weighting and to correct handheld probe response in relation to the gold standard by signal processing methods, thus providing more accurate measurement when required for absolute measurements. BCI width revealed that the uncertainty associated to this measurement set-up is within a range of 3.8 dB, which is not a low value, but close to other uncertainty values in building acoustic measurement variables and is therefore currently reasonable. Probes are validated as a cost-effective method to collect vibration data in a building acoustics environment with quality data, in which many measurements are required from many walls and is a good substitute for practitioner work on a daily basis. The results can be applied to other fields related to vibration measurement, in which an efficiency versus accuracy trade-off technique would be useful and to cases in which there is a lack of information on a certain sensor mounting method. Measurement set-up performance is chosen for different applications. Plain response coincides well with the gold standard and is very repeatable; but more efficient from an operating point of view. Probes provide good and stable performance in a probe useful bandwidth ranging from low frequencies up to 800 Hz–1 kHz. Probe useful bandwidth becomes wider as the probe material becomes more rigid and the probe length shorter; however, worse repeatability of resonance is also observed. Better repeatability results are obtained with heavier probes, as hand movement is lower. Long probes may be useful in certain operation circumstances to reach difficult walls, but their frequency response becomes increasingly complex in broadband and remarkably in resonance terms. Accelerometer sensitivities in the experiment did not change the results in general, however sensor size and weight influence probe response. Heavier and bigger sensors are preferred to provide hand movement stability, as long as they comply with specimen mass restrictions and signal to noise ratios. More research on reproducibility will add information to more accurately assess uncertainty in signals. Reproducibility testing is difficult to perform, since a close collaboration between different laboratories is required and substantial resources needed. Nevertheless, the Bootstrap approach would be useful, as it could provide valuable information with a limited number of samples. Horizontal probe position can also be tested to check the changes in these initial experiments. Further research will test models to predict probe frequency behavior and the use of measurements performed with handheld probes to resolve building acoustics problems linked to flanking transmission in a more efficient way.

References [1] ISO 16283-1:2014 – Acoustics – Field measurement of sound insulation in buildings and of building elements – Part 1: Airborne sound insulation; n.d.

135

[2] Ministerio de Fomento G de E. Código Técnico de la edificación (CTE). Documento básico HR, Protección frente al ruido (DB-HR); 2009. [3] Rosão V, Carreira AS da S. Use of vibration measurements to determine the most suitable locations to improve sound insulation in buildings. In: 21st Int. Congr. Sound Vib., International Congress on Sound and Vibration; 2014, p. 1–8. [4] ISO 10848-1:2017 – Acoustics – laboratory and field measurement of flanking transmission for airborne, impact and building service equipment sound between adjoining rooms – Part 1: frame document; n.d. [5] ISO 10848-2:2017 – Acoustics – laboratory and field measurement of flanking transmission for airborne, impact and building service equipment sound between adjoining rooms – Part 2: application to Type B elements when the junction has a small influence; n.d. [6] ISO 10848-3:2017 – Acoustics – laboratory and field measurement of flanking transmission for airborne, impact and building service equipment sound between adjoining rooms – Part 3: application to Type B elements when the junction has a substantial influ.; n.d. [7] ISO 10848-4:2017 – Acoustics – laboratory and field measurement of flanking transmission for airborne, impact and building service equipment sound between adjoining rooms – Part 4: application to junctions with at least one Type A element; n.d. [8] ISO 12354-1:2017 – Building acoustics – estimation of acoustic performance of buildings from the performance of elements – Part 1: airborne sound insulation between rooms; n.d. [9] Cremer L, Heckl M, Petersson BAT. Structure-borne sound: structural vibrations and sound radiation at audio frequencies. Springer; 2005. [10] Hopkins C. Sound insulation. Elsevier/Butterworth-Heinemann; 2007. [11] Hashimoto N. Measurement of sound radiation efficiency by the discrete calculation method. Appl Acoust 2001;62:429–46. https://doi.org/10.1016/ S0003-682X(00)00025-6. [12] Hirao Y, Yamamoto K, Nakamura K, Ueha S. Development of a hand-held sensor probe for detection of sound components radiated from a specific device using surface intensity measurements. Appl Acoust 2004;65:719–35. https://doi.org/10.1016/J.APACOUST.2003.11.011. [13] Andrade CAR. Evaluation of flanking airborne sound transmission involving intensity and vibration measurement techniques for in situ condition. Twelfth Int. Congr. Sound Vib., 2005. n.d.. [14] Roozen NB, Labelle L, Rychtáriková M, Glorieux C. Determining radiated sound power of building structures by means of laser Doppler vibrometry. J Sound Vib 2015;346:81–99. https://doi.org/10.1016/J.JSV.2015.02.029. [15] Hoeller C, Mahn J, Quirt D. Apparent sound insulation in cross-laminated timber buildings. J Acoust Soc Am 2017;141:3479. https://doi.org/10.1121/ 1.4987243. [16] Patil N, Moorhouse A, Elliott AS. Blocked pressure based transfer path analysis (TPA) method to diagnose airborne sound transfer through building partitions. J Acoust Soc Am 2017;141:3596. https://doi.org/10.1121/1.4987682. [17] Millán-Castillo S, García P. Evolución de una sonda de vibraciones para simplificar la evaluación de transmisión sonora por flancos entre recintos. 46° Congr. Español Acústica-Encuentro Ibérico Acústica, 2015. n.d.. [18] Zusman G, Klyuev V. New effects of one-point mechanical metal-to-metal contact allowing the measurement of high-frequency vibration using handheld probes and heavy vibration sensors. Int J Cond Monit 2016;6:9–12. https://doi.org/10.1784/204764216819257141. [19] ISO 5348:1998 – Mechanical vibration and shock – mechanical mounting of accelerometers; n.d. [20] Senldge M, Llcht TR. Piezoelectric accelerometers and vibration preamplifiers handbook; 1987. [21] Laizans K, Vendt R. A method for characterization of vibration testing setups; 2014. [22] Moschioni G, Saggin B, Tarabini M. Prediction of data variability in hand-arm vibration measurements. Meas J Int Meas Confed 2011;44:1679–90. https:// doi.org/10.1016/j.measurement.2011.06.022. [23] San Millán-Castillo R, Morgado E, Goya-Esteban RF-PC. Instrumentation inherent noise considerations in building acoustics vibration velocity. In: European symposium on sustainable building acoustics. Eur. Symp. Sustain. Build. Acoust; 2017; n.d. [24] Zusman GV. Vibration Sensing technique for monitoring condition of ball/ rolling bearings and gearboxes. In: 11th Eur. Conf. Non-destructive test. (ECNDT); 2014; n.d. [25] US Patent for Hand-held vibration sensor Patent (Patent # 9,523,626 issued December 20, 2016) – Justia Patents Search n.d. https://patents. justia.com/patent/9523626 [accessed May 18, 2018]. [26] Ainsa I, Gonzalez D, Lizaranzu M, Bernad C. Experimental evaluation of uncertainty in hand-arm vibration measurements. Int J Ind Ergon 2011. https://doi.org/10.1016/j.ergon.2011.01.002. [27] Gilbertson MW, Anthony BW. Force and position control system for freehand ultrasound. IEEE Trans Robot 2015;31:835–49. https://doi.org/10.1109/ TRO.2015.2429051. [28] Speich JE, Shao L, Goldfarb M. Modeling the human hand as it interacts with a telemanipulation system. Mechatronics 2005;15:1127–42. https://doi.org/ 10.1016/j.mechatronics.2005.06.001. [29] Efron B, Tibshirani RJ. An Introduction to the Bootstrap; 1993; n.d. [30] DelaRosa JI, Fleury GA. Bootstrap methods for a measurement estimation problem. IEEE Trans Instrum Meas 2006;55:820–7. https://doi.org/10.1109/ TIM.2006.873779. [31] Foundations of Engineering Acoustics by Frank J. Fahy 2000-09-12: Amazon. es: Frank J. Fahy: Libros n.d. https://www.amazon.es/Foundations-

136

[32]

[33] [34]

[35]

[36]

[37] [38] [39] [40]

R. San Millán-Castillo et al. / Applied Acoustics 145 (2019) 125–136 Engineering-Acoustics-Frank-2000-09-12/dp/B01K0RTWM4/ref=asap_bc?ie= UTF8 [accessed May 18, 2018]. Liguori C, Ruggiero A, Sommella P, Russo D. Choosing bootstrap method for the estimation of the uncertainty of traffic noise measurements. IEEE Trans Instrum Meas 2017;66:869–78. https://doi.org/10.1109/TIM.2016.2627260. Ste˛pien´ B. Bootstrap confidence intervals for noise indicators. Acta Acust United Acust 2016;102:389–97. https://doi.org/10.3813/AAA.918955. Mateus M, Dias Carrilho JA, Gameiro da Silva MC. Assessing the influence of the sampling strategy on the uncertainty of environmental noise measurements through the bootstrap method. Appl Acoust 2015;89:159–65. https://doi.org/10.1016/J.APACOUST.2014.09.021. Permanent magnet shaker LDS V201 – Brüel & Kjær Sound & Vibration n.d. https://www.bksv.com/en/products/shakers-and-exciters/LDS-shakersystems/permanent-magnet-shakers/V201 [accessed May 18, 2018]. Usuda T, Kurosawa T. Calibration methods for vibration transducers and their uncertainties. Metrologia 1999;36:375–83. https://doi.org/10.1088/00261394/36/4/17. PCB Model 352B n.d. http://www.pcb.com/Products/model/352B. PCB Model 352C04 n.d. https://www.pcb.com/products.aspx?m=352C04. PCB Model 352C33 n.d. http://www.pcb.com/Products.aspx?m=352C33. TYPE 4533-B – Brüel&Kjær; n.d.

[41] van Rossum G. Python tutorial, Technical report CS-R9526. Centrum voor Wiskunde en Informatica (CWI); 1995. [42] Oliphant TE. Guide to NumPy; 2006. [43] McKinney W. Data structures for statistical computing in python; 2010. p. 51–6. [44] Hunter JD. Matplotlib: a 2D graphics environment. Comput Sci Eng 2007;9:90–5. https://doi.org/10.1109/MCSE.2007.55. [45] Kaplan Macalester College DT, To Maya I, Daniel Kaplan by T. Resampling Stats in MATLAB; 1999. [46] Razali NM, Wah YB. Power comparisons of Shapiro-Wilk, KolmogorovSmirnov, Lilliefors and Anderson-Darling tests. J Stat Model Anal 2011;2:21–33. [47] Machimbarrena M, Monteiro CRA, Pedersoli S, Johansson R, Smith S. Uncertainty determination of in situ airborne sound insulation measurements. Appl Acoust 2015;89:199–210. https://doi.org/10.1016/J. APACOUST.2014.09.018. [48] Hopkins C, Turner P. Field measurement of airborne sound insulation between rooms with non-diffuse sound fields at low frequencies. Appl Acoust 2005;66:1339–82. https://doi.org/10.1016/J.APACOUST.2005.04.005. [49] ISO 12999-1 Acoustics – Determination and application of measurement uncertainties in building acoustics – Part 1: sound insulation; 2014. p. :20.