Considerations on variability in acoustic measurements in timber property assessment

ABSTRACT Reliability of measurement with acoustic NDT applied to timber structures improves in-situ assessments. The aim of this research is to carry out simulated in-situ measurements with acoustic NDT devices in order to analyse the influence of different sensor positions, repeatability and measurement lengths. Time-of-Flight and dynamic modulus of elasticity (MOEdyn) variability were quantified on the faces and edges of Scots pine timber from a sawmill. A comparison was also made of the models obtained at different distances between the sensors and a mean model independent of the distance between the sensors. Linear regressions between the static modulus of elasticity (MOEsta) and MOEdyn or wave velocity depending on the distance between sensors yielded coefficients of determination (R 2) from 0.59 to 0.86 and residual standard errors (StE) from 737 to 1232 N mm−2. It was found that measurements taken at 1 m distance did not represent the piece as a whole, and that mean statistical models provided a better relationship, increasing by up to 14% in R 2 and decreasing StE by up to 11%. It is concluded that in order to obtain a reliable model (MOEsta vs. MOEdyn) at least 2 measurements are required at different positions on each piece of the batch.


Introduction
Acoustic non-destructive techniques (NDT) have proven to be an effective tool for estimating the physical or mechanical properties of timber elements from buildings or sawmills, such as density (ρ), modulus of elasticity (MOE) or strength (MOR) (Cavalli et al. 2016, Llana, et al. 2020a. Acoustic NDT applications include the characterisation or estimation of timber mechanical properties and the verification of the pathological state of a timber element (Carrasco andTeixeira 2012, Sousa et al. 2014). For obvious reasons NDT is often used instead of destructive techniques in the structural assessment of a building, to preserve historical heritage and before restoration. There are now several commercial alternatives that use different technologies to estimate or determine physical and mechanical parameters.
Essential parameters such as timber density can be estimated through semi-destructive methods such as needle penetration resistance or drill penetration resistance, among others (Osuna-Sequera et al. 2019). Other crucial parameters for determining the mechanical behaviour of timber during its service life are MOE and MOR (Cavalli et al. 2016). MOE and MOR can be estimated using non-destructive vibration or acoustic techniques (Íñiguez González et al. 2007, Llana et al. 2022. Acoustic techniques use different types of wave emission, such as ultrasound or pressure waves, and they may employ different emission frequencies (Llana et al. 2020b). The time it takes for a wave to travel from an emitting sensor to a receiver is called the Time-of-Flight (ToF). The dynamic modulus of elasticity can be determined from the relationship MOE dyn = (L ToF −1 ) 2 ρ, where L is the distance between the sensors in m, ToF in s, and ρ in kg m −3 (Wang 2013). In addition to the prediction of the aforementioned parameters, non-destructive techniques can locate possible problems or defects, such as decay, damage by xylophagous organisms, elevated moisture content or loss of density, etc (Cavalli et al. 2016, Riggio et al. 2016. Variations in the measurements performed with these techniques in pieces of a timber structure can also provide information to locate problems. It is therefore important to consider and study measurement variability in acoustic results. In timber from existing or new buildings, defects such as decay or knots, among others, can lead to relevant differences in ToF with non-destructive acoustic devices. Along pillars or beams, certain sections may be affected by the aforementioned defects, resulting in substantial variations in the same piece.
Several authors have carried out research and presented case studies of great use to the scientific community. Vössing and Niederleithinger (2018) compiled the state of the art of NDT and described the large arsenal of NDT and semi-destructive techniques (SDT) available for the detection of defects inside timber. Tannert et al. (2010) summarise the major issues related to the assessment of structural timber carried out by the The International Union of Laboratories and Experts in Construction Materials, Systems and Structures (RILEM) committee. Some more practical cases assessed the reliability of NDT, as shown by Ruy et al. (2018), who performed a study combining NDT and the Brazilian standard NBR 15521 (2007) with the results for the classification of round timber through longitudinal wave transmission velocity parallel to the grain in a total of 54 Eucalyptus sp. round logs. Three direct longitudinal measurements were taken in each piece, where possible, and the average of the three measurements was taken. However, when the velocity measurements differed by more than 10%, the lowest wave velocity value was chosen to preserve safety. More recent cases show the efficiency that can be achieved by combining different NDT techniques or using Visual Strength Grading (VSG) when applied to timber structural elements from existing buildings (Riggio et al. 2016, Branco et al. 2017, Yu et al. 2020. Additionally, various research works discuss the best measurement procedures and their influence when using available techniques , Osuna-Sequera et al. 2019, Nocetti et al. 2021. Arriaga et al. (2019) applied acoustic techniques and showed a correction coefficient (time-lag) for measurements at different piece lengths. For this purpose, the authors defined five sensor positions, direct (end-to-end), cross (face-to-face or edge-to-edge) and surface measurements on the same face or edge. Nocetti et al. (2021) studied the best geometrical approximation for irregular sections to obtain the static modulus of elasticity in timber pieces. Timber with an irregular geometric crosssection is often found in in-situ assessments of timber structures. Osuna-Sequera et al. (2019) used three non-destructive techniques (needle penetration resistance, screw withdrawal resistance metre, drilling chips extraction) for density estimation, reducing the number of measurements without loss of measurement accuracy for the in situ evaluation of timber pieces. On reflection, a lot of research has still to be carried out to improve the use of non-destructive acoustic techniques. The aim of this study is to detect the capability and reliability of different acoustic measurements to improve their applicability in building inspections and even for industrial applications. Research studies have illustrated the repercussions of pieces of different length, dimensions and cross-section, and the arrangement of sensors in recordings with several methods, acoustic NDT devices such as the Sylvatest Duo (CBS-CBT, La Rochette, France, Saint Sulpice, Switzerland) with conical 22 kHz sensors; the USLab (Agricef, Campinas, Brazil) with conical 45 kHz sensors; and the MicroSecond Timer (MST) (Fakopp Enterprise, Sopron, Hungary), and species (Oliveira et al. 2006, Arriaga et al. 2017, Osuna-Sequera et al. 2020. Furthermore, moisture content (MC) influence on NDT results has been studied and oriented to physical and mechanical properties estimation (Goken et al. 2018, Llana et al. 2018. As is well known, although many factors affect the mechanical properties of timber, there is a need to know the degree of variability that measurement with acoustic equipment gives rise to when estimating mechanical properties such as the dynamic modulus of elasticity or timber strength. A considerable amount of research relates linear models for wave velocity and dynamic modulus of elasticity (MOE dyn ) to the static modulus of elasticity (MOE sta ) (Teder et al. 2012) proposing different models for its estimation (Ross 2015, Llana et al. 2020a. However, there is a need to deepen our understanding of the suitability of measurement variability within a timber element. Although measurement precision is not commonly described in research works, this information is necessary and very useful when evaluating the reliability of these techniques when they are used to evaluate mechanical properties. In-situ assessment does not usually involve many repetitions of measurements on different parts of each timber element, accepting the one performed as true and representative of the whole piece. Knowledge of model variability and reliability is very important in general, especially when assessing the estimated values of individual members. In building assessments where timber structural elements are hidden in other elements such as floors, a low number of measurements is expected due to difficulty of access. In these cases, it is important to optimise the measurement method in order to obtain reliable results with a minimum number of measurements. The main purpose of this research is to carry out a preliminary study to analyse the influence of different lengths and positions of acoustic NDT measurements. These measurements (with stress wave and ultrasonic devices) take place in-situ for the estimation of the modulus of elasticity in beams, while also considering the number of measurements and repetitions required for reliable results. A mean static-dynamic MOE model for the estimation of properties using any distance and position is also defined.

Material
The material tested consisted of 20 Scots pine (Pinus sylvestris L.) timber pieces from a sawmill located in Cuenca, Spain. Nominal specimen dimensions were 200 × 200 × 4000 mm 3 (b × h × L, where b is width, h height and L length). The MC of the batch when NDT measurements (acoustic method) were performed was 11.4% with a coefficient of variability (CoV) of 7.9% during measurements, and the average density was 497 kg m −3 with a CoV of 6%. The average MC was measured according to European standard EN 13183-2 (2002) with a Gann Hydromette HT 85 T electrical resistance moisture metre (Gann, Gerlingen, Germany).

Marking of pieces and dimensions
Pieces were first marked on their ends with the letters A' and B'. Their faces and edges were marked counter-clockwise as F1, E2, F3 and E4, looking at the piece from the A' end. Eight cross-sections were then defined, denominated A, B, C, D, E, F, G and H as shown in Figure 1. Each cross-section was separated from the next by 50 cm, and the first and end ones were 25 cm from the nearest end. Three additional cross-sections (I, J and K) were located and their positions marked in the centre of the piece, separated by 100 cm.

Visual grading characteristics
Visual strength grading was carried out on the 20 timber pieces according to Spanish standard UNE-EN 56544 (2011). The main results obtained are shown in Table 1. Some authors (Piao et al. 2004, Nakijama and Murakami 2008, Teder et al. 2012, Vössing and Niederleithinger 2018, Osuna-Sequera et al. 2020) have defined density, knots and fibre deviation as the main parameters that affect mechanical properties such as modulus of elasticity, strength or hygroscopic properties, among others. Nevertheless, it is important to take all of the parameters into account to guarantee safety. Additionally, these authors found that pieces rejected in the visual strength grading process (VSG) fulfilled the required mechanical values to be graded as MEG (C22). The Concentrated Knot Diameter Ratio (CKDR) parameter was also recorded. This parameter has been used in several research works to quantify knottiness in timber pieces (Carballo et al. 2009, Hermoso et al. 2016).

Time-of-flight (ToF) measurement and wave velocity
Time-of-flight (ToF) measurements were carried out with the widely-used devices Sylvatest Trio (CBS-CBT, Lausanne, Switzerland) (SYL) and the MicroSecond Timer (Fakopp, Sopron, Hungary) (MST). Both devices have an emitter and a receiver sensor where wave travel time from the emitter to the receiver through the timber is measured (Time-of-Flight), Figure 2. In the case of SYL, the sensors are conical and have a frequency of 22 kHz, and the excitation is generated by a piezoelectric sensor with a specific ultrasonic frequency. On the other hand, the MST is considered a stress-wave device because its excitation is generated by a hammer. The accuracy of both devices is 1 μs.
Measurements in faces and edges were carried out with a distance between sensors of 1, 1.5, 2.5, 3.5 and 4 m end-toend (except in edge E4, where only 3.5 m measurements were taken), Figure 3. 1 m measurements were taken between AC, CE and FH cross-sections, 1.5 m between AD, CF and EH, 2.5 m between AF, BG, CH, 3.5 m between AH and end-to-end measurements between A' and B' ends, Figure 1. 9 readings were taken at each distance measured. Balmori et al. (2016) showed that surface measurements with the sensor positioned at 45 degrees gave better results than was the case with other arrangements. Due to this, sensors were positioned at 45 degrees from each face or edge where the measurement was carried out (Balmori et al. 2016, Arriaga et al. 2017, except in end-to-end measurements where measurements perpendicular to the end surface were taken.
Wave velocity may be calculated with the relation V = L/ ToF, where V is the wave velocity in m s −1 , L is the distance between two sensors using an acoustic NDT device in m and ToF is the Time-of-flight in s, Figure 2.

Modulus of elasticity (MOE)
The static modulus of elasticity (MOE sta ) was determined by a 4-point edgewise bending test according to EN 408 (2010) in   (2010) is MOE sta = I L 3 (56.35 Δw ΔF −1 ) −1 , where I is the moment of inertia of the piece in m −4 , L is the span in m, w is the deformation measured in mm and F is the force measured in N the test. MOE sta units in N mm −2 . The dynamic modulus of elasticity (MOE dyn ) was determined by the relation MOE dyn = ρ V² (Bucur 2006), where MOE dyn is the dynamic modulus of elasticity in N mm −2 , ρ is the global density in kg m −3 and V is the wave velocity in m s −1 .

Results and discussion
Visual grading characteristics Table 1 shows the data obtained on the defects found in the batch of timber according to Spanish standard UNE 56544 (2011). Some authors have studied defects in timber and their influence on measurements with non-destructive acoustic equipment. Esteban et al. (2010) analysed the effect of fissures on Scots pine timber beams from an eighteenth century building, concluding that there were no significant differences according to fissure size, load capacity and stiffness. Although wanes are very frequent in ancient and large cross-section pieces, they are considered to simply consist of a loss of cross-section area, without reducing strength (Arriaga et al. 2022). Resin and bark pockets are occasional defects along the length of a piece of timber that could compromise the integrity and safety of the functioning of a structure, so that certain limits are set for them in the Spanish UNE-EN 56544 (2011) standard used in this research. The most relevant singularities are knots and the slope of grain, due to their affect on the strength and stiffness of timber beams (Baño et al. 2013, Ross et al. 2010. A significant correlation was observed between the average ToF and CKDR per piece, Figure 4. The linear relationship has a r 2 = 56% and a StE = 30 μs with CKDR p-value = 0.0002. The formula was ToF = 341.27 CKDR + 465, where ToF is the 3.5 m average value of Time-of-Flight in μs and CKDR is the concentrated knot diameter ratio. Model measurements were considered with 3.5 m distance between sensors, as these measurements better represent the overall defects of the whole piece. The CKDR parameter was calculated as a global value of the piece. Therefore, the correlation between the average ToF value with fibre deviation was weaker (p-value = 0.2338) in a multiple regression, so that it was not considered. The relationship between the average value of each piece and its knottiness could be explained using this model. Due to this correlation, it is possible to explain why in different parts of the same timber beam there may be different average MOE dyn values. In this research, variability in different parts of the piece is studied in the following sections.

Variability between faces and/or edges and distance measurements in each piece
The results reveal low variation in ToF when the same measurement is repeated at the same point 9 times for each sensor arrangement. The CoV was usually between 0% and 1%, reaching 5% in piece No. 2. This low variability shows that it is not necessary to repeat measurements at the same distance to obtain reliable ToF. Preliminary studies using two pieces of different grades selected by VSG and CKDR showed equivalent results (Osuna-Sequera et al. 2022).
The influence of timber quality on variability was analysed by comparing the variability of the measurements performed in pieces with different grades at different lengths and faces/ edges. In order to simplify the results, only pieces no. 1 and 12 (with the maximum and minimum knottiness in the batch and graded as MEG and rejected grade according to EN 56544 (2011), respectively) are shown. Although the other  pieces behaved in a similar way, the values shown are for the said two pieces. Figure 5 shows how piece no. 1, which has lower CKDR and high MOE dyn values, has less measurement variability independently of the face, edge and length between sensors considered. The exception is for the 3.5 m distance, which shows greater variability in the SYL measurements. On the contrary, in piece no. 12, which is the one with the highest CKDR value of the batch, the variation of measurements is higher in general. In both pieces, it can be seen that the variability of the results decreases when sensor distance increases. These results can be explained by the local influence of defects (knots and other features) included in the length of the piece measured. This will be less marked when the measured length increases, and it will also have less influence in pieces with a low CKDR.
Variability was found between some faces or edges of the pieces irrespective of the device used, which led to significantly different results between two measurements taken on the same part of the piece but on different faces or edges, Figure 6. This indicates that the measurements did not behave as volumetric measurements, but rather like surface measurements. It is important to consider this fact, as in an inspection of a timber building two measurements could be taken, one on one face and one on one edge, resulting in significant differences between the two measurements.
The differences between the MOE dyn in the same piece were very high in some cases, showing the importance of the location of in-situ measurements. In both pieces, an improvement of the MOE dyn variation between faces and edges and in the same position was observed when the distance between the sensors was increased (Figures 2 and 3). This behaviour can be explained by the fact that measurements are applicable to the piece as a whole when there is less distance between the sensors, and defects such as knots affect measurement variability more in the same face or edge.
In order to assess the variability between the MST and SYL devices a linear regression was carried out with both ToF measurements, including all positions at any distance between the sensors. This gives a coefficient of determination of R 2 = 0.99 and a standard error of the regression of StE = 16 μs, where the equation obtained is ToF SYL = ToF MST · 1.031-20.88, where ToF SYL and ToF MST are the ToF measured with the SYL and the MST in μs, respectively. This preliminary result makes it possible to simplify the study using only one device in some of the following analyses.
As an example, Figure 6 shows in piece No. 12 how 1 m measurements obtained with the MST and located at F1 could led to a MOE dyn from 8020 to 10349 N mm −2 and in 3.5 m measurements from 7603 to 7855 N mm −2 , respectively. In addition, mean and CoV values for piece No. 12 are 8548 N mm −2 and 12.3% for 1 m measurements and 7893 N mm −2 and 3.0% for 3.5 m measurements. Considering all of the differences in locations of 1 m, higher variability can be attained in ΔMOE dyn = 3863 N mm −2 than in locations of 3.5 m ΔMOE dyn = 673 N mm −2 . Variability also depends on the face or edge on which it was measured. These differences are more noticeable in pieces with greater knottiness. These results underline that in order to provide a value closer to the actual dynamic modulus of elasticity of the piece, the measurement taken must be sufficiently representative of the whole piece.
Experimental linear models for modulus of elasticity based on acoustic value variation at different distances A comparison was made between the linear models obtained separately between the MOE sta and the MOE dyn and wave velocity parameters considering twice times residual standard error (RSE) limits, Figure 7. These models are applied for the devices used and for each one of the distances between the sensors, to find the most suitable length to reliably estimate piece stiffness. The linear model with MOE dyn is considered when the density can be obtained, while wave velocity is used when it is not possible to obtain density. In both cases, the regressions showed higher coefficients of determination and lower standard error with increasing distance between sensors, Table 2. The best relationships are obtained for measurements at 2.5 m or more. The variability seen in the measurements at 1 and 1.5 m results from the variability of timber properties in local measurements in both cases (MOE dyn and wave velocity). Length and face/ edge independent linear regressions including all of the variability studied previously were carried out. Additionally, linear regressions were performed excluding 1 m measurements, where variability is higher and does not represent the piece as a whole. Mean statistical models avoiding 1 m measurements provide a better relationship, increasing up to 14% in the coefficient of determination (R 2 ) and decreasing standard error in the regression (StE) up to 11%.

Analysis of the minimum number of measurements required for reliable estimations
In order to find the minimum number of measurements given the previous variability results, an analysis of the reliability of the data obtained from the 20 pieces was carried out by developing the model that best explains the relationship between MOE sta and MOE dyn . The parameters R 2 and StE from several of the previously obtained linear models by experimentation are analysed as a function of the number of measurements made on each piece. For this purpose, an algorithm developed in R data software (R Core Team 2013) was used to simulate several technical inspection situations of timber pieces to predict a range of scenarios in building inspection. The algorithm randomly selects data without replacement depending on the input data (measurements measured at 1, 1.5, 2.5, 3.5 m and end-to-end). The variability of the R 2 and StE parameters generated by random technical assessments with the algorithm is shown in Figure 8, depending on the distance between sensors considered on each piece and the number of measurements. In this work, there were 20 assessments for each number of measurement repetitions evaluated. The results presented in Figure 8 correspond to measurements carried out with MST experimental models. Linear regressions carried out with SYL showed similar results to the ones obtained with MST.
The results show how the quality of the linear regression improves as the number of measurements increases, with any distance between sensors and random faces or edges. Measurements taken at 1 m distance between sensors showed the worst relationship and variability. A statistical model was fitted to relate the dependence between the variables R 2 and StE with the number of measurements. The best fit was with an x-inverse model. The equations for each case are shown in Table 4.
Analysis of Variance and Least Significant Difference multiple range tests with a 95% confident interval were carried out to find homogeneous groups for R 2 and StE while varying the distance between sensors and the number of Table 4. Summary of the inverse x-model equations of the dependence between R 2 and the standard error of the regression as a function of the number of measurements ( Figure 5). Notes: Equations are shown according to the distance between the sensors (1 m, 1.5 m, 2.5 m and 3.5 m). StE is the standard error of regression, R 2 is the coefficient of determination.  (Table 3). For the R 2 and StE parameters, one measurement results in three homogeneous groups, 1 m, 1.5 m and the last group with 2.5 m and 3.5 m measurements together. When two measurements are used to calculate the MOE dyn , only two homogeneous groups emerge, with 1 m measurements in one group and all of the others in another. It is therefore reasonable to consider at least two measurements to group 1.5, 2.5 and 3.5 m measurements in a general linear regression to obtain satisfactory variability, where any of these distances between sensors could be considered. In the case of 2.5 and 3.5 m measurements, at least two measurements should be taken to ensure that R 2 and StE CoV are less than 10% through the iterations of Figure 8. The reduction of variability in the linear models generated therefore depends on the distance between the sensors from indirect measurements to the second measurement onwards, with measurements taken at 1.5, 2.5 and 3.5 m. It is recommendable to take at least 2 measurements in different positions in this case, with the exception of 1 m measurements, to achieve acceptable variability. The 1.5, 2.5 and 3.5 m distances between sensors are therefore considered the best options for reliable results.

Conclusions
The variability of repeated measurements in the same point of the beam is negligible, with a CoV between 0% and -1% for all the distances between sensors and for both of the devices assessed.
An increase in MOE variability was found at shorter distances between the sensors compared to measurements with a larger distance between them on each piece. Lower quality pieces exhibit higher variability in MOE dyn measurements, and variability in the measurements on adjoining faces in the same position was found in some cases. This behaviour corresponds to surface features influencing wave transmission rather than fully volumetric wave transmission. In addition, variability at short sensor distances (1, 1.5 m) is higher than it is at longer ones (2.5, 3.5 m) in the same piece. Thus where measurements are taken in timber in-situ assessment could greatly influence the result.
Several MOE sta vs. MOE dyn linear regression models were obtained for the different measurement lengths and devices, showing that variability increases when the distance between sensors is reduced, making it possible to obtain R 2 and StE that show the level of accuracy obtained in each situation.
Based on the experimental linear regression models obtained and the use of an algorithm that simulates several possible in-situ assessments using different distances between sensors, it can be concluded that it is necessary to carry out measurements with a minimum of 1.5 m between sensors and in at least two different positions. The use of 1 m measurements gives more variable results and would not be recommendable in order to obtain the representative stiffness in 4 m timber pieces.

Disclosure statement
No potential conflict of interest was reported by the author(s).

Funding
The technical support offered by Ramón García Lombardero for measurements was greatly appreciated.