DEFECT DETECTION AND QUALITY ASSESSMENT OF HARDWOODLOGS: PART 1—ACOUSTIC IMPACT TEST AND WAVELET ANALYSIS1

Feng XuPhD Candidate

College of Information Science and TechnologyNanjing Forestry UniversityNanjing, Jiangsu, China

E-mail: xufeng@njfu.com.cn

Xiping Wang*†Research Forest Products Technologist, PhD

USDA Forest ServiceForest Products Laboratory

Madison, WIE-mail: xwang@fs.fed.us

Ed ThomasResearch Computer Scientist

USDA Forest ServiceNorthern Research Station

Princeton, WVE-mail: ethomas@fs.fed.us

Yunfei Liu*Professor

College of Information Science and TechnologyNanjing Forestry UniversityNanjing, Jiangsu, ChinaE-mail: lyf@njfu.edu.cn

Brian K. BrashawProgram Manager

E-mail: bbrashaw@fs.fed.us

Robert J. RossProject Leader

USDA Forest ServiceForest Products Laboratory

Madison, WIE-mail: rjross@fs.fed.us

(Received January 2018)

Abstract. The objective of this studywas to determine the technical feasibility of combining acoustic wave datawith high-resolution laser scanning data to improve the accuracy of defect detection and quality assessment in

* Corresponding author† SWST member1 This article was written and prepared by US Governmentemployees on official time, and it is therefore in the publicdomain and not subject to copyright.

Wood and Fiber Science, 50(3), 2018, pp. 291-309© 2018 by the Society of Wood Science and Technology

hardwood logs. This article (Part 1) focused on exploring the potential of an acoustic impact testing methodcoupled with advanced waveform analysis to detect internal decay of hardwood logs and classify logs in termsof log quality and potential board grade yields. Twenty-one yellow-poplar (Liriodendron tulipifera) logsobtained from the Central Appalachian region were evaluated for internal soundness using an acoustic impacttesting technique. These logs were then sawn into boards, and the boards were visually graded based onNational Hardwood Lumber Association grading rules. The response signals of the logs from acoustic impacttests were analyzed through moment analysis and continuous wavelet transform to extract time-domain andfrequency-domain parameters. The results indicated that the acoustic impact test coupled with wavelet analysisis a viable method to evaluate the internal soundness of hardwood logs. Log acoustic velocity alone was able toidentify the very low-end logs that have the most severe internal rot or other unsound defects but failed toidentify the logs with poor geometry that resulted in very low recovery. Time centroid, damping ratio, andcombined time- and frequency-domain parameters were found effective in predicting log quality in terms ofboard grade yields. Log segregation based on time-domain (time centroid and ρ/Tc2) and frequency-domain(damping ratio and Ed/ζ2) parameters showed a positive correlation with the board grade yields.

Keywords: Acoustic velocity, board grade, damping ratio, impact test, log defects, dynamic MOE, timecentroid, yellow-poplar.

INTRODUCTION

Internal defects in standing timbers and felledlogs cause the U.S. wood industry millions ofdollars in processing and reprocessing wood tokeep defective portions from being included inend products. The economic loss caused byheartwood decay and other internal defects ismost significant for hardwood trees and logs usedto produce high-value appearance-grade prod-ucts. For example, veneer logs typically cost 1.5-6 times that of Forest Service factory grade 1sawlogs (Wiedenbeck et al 2003). Because of theexceptionally high prices paid for high-qualitylogs, undetected defects in hardwood logs cancause a substantial monetary loss to timber buyersand wood manufacturers. Early detection of in-ternal defects in hardwood logs could providea significant benefit to the industry by allowingaccurate quality assessment and volume esti-mates, which would lead to optimal use of thehardwood resource.

Another important reason for early defect de-tection in hardwood logs is to remove logs fromthe processing stream that have little or noprofitability. This concept is commonly known asthe “break-even log” because processing a logwith quality lower than the break-even log resultsin a loss for the company. Ideally, to realize targetprofit maximization, logs that give no real fi-nancial return from processing should be sold toother processors that can economically process

these logs into products such as railroad ties,pallet lumber, pulp, or fuel.

Research in the field of nondestructive testing andevaluation of wood has resulted in an array oftools for detecting internal wood defects. Tech-nologies such as X ray, computed tomography,and nuclear magnetic resonance offer cross-sectional images with sufficient detail, but theyare not cost-effective for hardwood mills and aretoo slow to be considered suitable for on-lineimplementation (Wagner et al 1989; Chang 1992;Li et al 1996; Guddanti and Chang 1998;Bhandarkar et al 1999). As an alternative method,laser scanning has been investigated for detectingsurface defects regarded as degrade defects bythe visual grading rules. In addition, models weredeveloped to predict internal defects based onexternal features (Thomas et al 2006, 2008).However, a system based entirely on log surfaceinspection may incorrectly predict internal qual-ity. Some defects give the appearance of beingsolid or sound and effectively hide an unsound orrotten area, thereby reducing the accuracy ofpredicted internal product quality and value.

Acoustic wave methods use a mechanical impactto generate low-frequency stress waves thatpropagate longitudinally through a log and re-cord the reverberation of the waves within thelog. At the microstructure level, energy storageand dissipation properties of a log are con-trolled by orientation of wood cells and structural

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composition, factors that contribute to stiffnessand strength of wood. Such properties are ob-servable as frequency of the wave reverberationand rate of wave attenuation. Research has shownthat log acoustic measures can be used to predictthe stiffness and strength of structural lumber thatwould be produced from the log (Aratake et al1992; Aratake and Arima 1994; Ross et al 1997;Wang 2013). This research has opened the wayfor acoustic technology to be applied in mills forsorting and grading softwood logs for structuralquality. Commercial acoustic tools are now ac-cepted in the forest products industry for on-linequality control (structural lumber and veneer) andfield or in-plant segregation of incoming soft-wood logs (Harris et al 2002; Carter et al 2005;Wang et al 2007, 2013; Gaunt 2012; Wang 2013;Murphy and Cown 2015). However, research onthe use of the acoustic wave method for detectinginternal defects in hardwood logs has been foundto be very limited. In a mill study of assessing thestress level and potential wood quality of logsaffected by oak decline, Wang et al (2009)acoustically tested 400 black and scarlet oaklogs using an acoustic resonance tool. Principalcomponent and canonical correlation analysesrevealed that relationships do exist between logacoustic measurement and board grade yield, andbetween a linear combination of log acousticvelocity and diameter at breast height and a linearcombination of board defect measurements. But,no effort has been made to explore new acousticfeatures beyond acoustic velocity to assesshardwood logs in terms of internal defects andboard visual criteria.

Acoustic waves and laser scanning methodsoperate under different principles. Each addressesthe weaknesses or inabilities of the other. Theobjective of this pilot study was to determine thetechnical feasibility of combining acoustic wavedata with high-resolution laser scanning data toimprove the accuracy of defect detection andquality evaluation in hardwood logs. The resultsof this research are reported in two parts. Part 1(this report) explores the capabilities and limi-tations of an acoustic impact testing methodcoupled with advanced waveform analysis to

detect internal defects of hardwood logs andclassify logs in terms of potential board qualityand grade yields. Part 2 will evaluate the effec-tiveness of using a combined acoustic and laserscanning system to rank hardwood logs andfurther improve the log segregation process.

MATERIALS AND METHODS

A random sample of 15 yellow-poplar (Lir-iodendron tulipifera) trees were harvested froma MeadWestVaco (Richmond, VA) leased andmanaged forest near Rupert, WV, in the CentralAppalachian region in late January of 2015. Eachtree was bucked to commercial lengths with threeto five logs being cut from each tree, resulting ina total of 52 logs. Each log was tagged with a treenumber and a log section code (A—butt log;B—2nd log; C—3rd log; D—4th log; and E—5thlog). All logs were transported to the United StatesDepartment of Agriculture (USDA) Forest Service,Forestry Sciences Laboratory located in Princeton,WV. Visual observation showed that these logsranged in quality level. Some logs had very ob-vious rot after bucking, some had deeply grownwounds with significant encapsulated decaypockets, and somewere very high quality. The logswere stored outside and exposed to winter weatherfor about 1 mo before the acoustic testing.

Acoustic Impact Test

One week before the acoustic impact test, the logswere moved into the heated laboratory building toallow the wood to thaw and reach room temper-ature. Each log was first put on a rack for physicaldiagramming of surface defect indicators and high-resolution laser scanning (detailed procedures areoutlined in Part 2 of this series). Each log was alsoweighed using a crane scale (LHS4000a, ADAMEquipment, Inc., Oxford, CT) by lifting the log upthrough a log loader. The crane scale has a capacityof 2000 kg and is accurate to the nearest 0.5 kg.Log density was determined based on the grossweight and the exact volume derived from the 3Dlaser scanning data.

Logs were then acoustically tested on the groundto obtain acoustic parameters for potential

Xu et al—DEFECT DETECTION AND QUALITY ASSESSMENT OF HARDWOOD LOGS 293

detection of internal defects. Acoustic impacttests were conducted in two different ways:1) using a resonance-based acoustic tool to di-rectly measure the acoustic velocity of each logand 2) using a laboratory impact testing system toobtain and record the response signals from eachlog following a mechanical impact. All acoustictests were conducted under conditions of 21°Cand 50% relative humidity (RH).

A hand-held resonance acoustic tool (HitmanHM200, Fiber-gen, Inc., Auckland, New Zealand)was used to directly measure the acoustic velocityof each log. Following a hammer impact, theHM200 tool immediately processes the receivedacoustic signals through the Fast Fourier Trans-form program built into the tool and calculateslog acoustic velocity (V) based on the resonantfrequency and log length:

V ¼ 2fnL=n; (1)

where fn is the nth harmonic frequency (Hz) of theresponse signal, L is the full length of a log (m),and n is the order of harmonic frequency.

To ensure the accuracy of log velocity mea-surement, three high-confidence (indication ofgood signals) velocity values were obtained fromeach log. The average velocity value was cal-culated for each log and used in data analysis.

To collect the response signals from each log, asensor probe (Fakopp spike sensor, Fakopp En-terprise Bt., Agfalva, Hungary) was inserted intothe end grain at the log end (close to the center). Theimpact acoustic waves were generated througha 5.44-kg sledge hammer blow on the opposingend, and the response signals were recorded throughthe data acquisition card (NI 5132) connected to thelaptop, with a sampling frequency of 20 kHz anda sampling length of 1000 points. Three replicatesignals were obtained from each log.

Sawing and Visual Grading

After acoustic testing, 21 logs were selected andsawn into 29-mm-thick boards using a portablesawmill. The reason of not sawing all 52 logs was

because we only had limited budget at the time ofthis study and the time window available for thesawing process was also limited. This subsampleof logs was systematically selected based onvisual assessment and resonant acoustic testingresults such that they represent the quality rangeof the 52 logs. The sawing was performed by anexperienced sawyer who worked to maximizethe yield and value of the lumber with respectto the National Hardwood Lumber Association(NHLA) rules (NHLA 2015). The general sawingstrategy was to open the log on the best face androtate the log when the face grade of the cantdropped. Some wood moisture samples werecut during the sawing process for determiningmoisture contents of the logs using the oven-drymethod.

The resulting boards were visually gradedaccording to NHLA rules (NHLA 2015). TheNHLA rules are based on the size and number ofcuttings (pieces) that can be obtained froma board when it is cut up and used in the man-ufacture of a hardwood product. Therefore, eachgrade provides a measurable percentage of clear,defect-free wood. The board grades determinedbased on NHLA rules include high grades(FAS—First and Second, F1F—FAS One Face,and Select), common grades (No. 1 Common,No. 2 Common, and No. 3 Common), and belowgrade (BG).

Extraction of Acoustic Parameters

In addition to the acoustic velocity directlymeasured on each log, physical and acousticparameters of the subsample of logs were ob-tained and evaluated for their potential to predictthe soundness of the logs and grade yields of theresulting boards. The predicting parameters weexamined included acoustic velocity (V), dynamicMOE (Ed), time centroid (Tc), and damping ratio(ζ), as well as two combined parameters of theresponse signals.

The acoustic parameters were extracted based onthe following procedures: 1) compute dynamicMOE of the logs based on log density and

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measured log velocity; 2) determine time centroid(Tc) of the response signals through first momentanalysis; 3) perform continuous wavelet trans-form (CWT) of the response signals and computethe wavelet ridge by maximizing the modulus ofwavelet skeleton at each time instant; 4) computeinstantaneous natural frequency (fi) and dampingratio (ζi) according to the wavelet ridge andskeleton.

Dynamic MOE (Ed). Modulus of elasticity ofa log is a global property that can be readilyestimated based on the one-dimensional waveequation:

Ed ¼ ρV2; (2)

where ρ is gross density of a log (green, at thetime of acoustic testing) and V is the measured logvelocity.

Time centroid (Tc). Time centroid, sometimesreferred to as “mean time,” represents the timewhen the bulk of the signal is received. Mathe-matically, Tc is obtained by dividing the first

moment of the signal by the zeroth moment of thesignal:

Tc ¼�N

i¼ 1jAijti�N

i¼ 1jAij; (3)

where N is the number of time samples, Ai is theamplitude of the ith time step, and ti is the time atthe ith time step.

In general, when a signal is excited and trans-mitted in a flawless medium, most of its energy istypically located in the beginning of the signalwaveform. Reflection and mode changes of thesignal often come from the boundaries and ma-terial flaws, causing skewing of the signal in thetime domain. As a form of the first momentanalysis, time centroid has been widely used tocharacterize the damage or deterioration of ma-terials (Tiitta et al 1998; Bayissa et al 2008).

Damping identification using a wavelettransform. Damping, often expressed by thedamping ratio, is the dissipation of vibration

Table 1. Dimensional and physical measures of the yellow-poplar logs.

Log no. Length (m)

Diameter (cm)

Weight (kg) Density (kg/m3) Sweep (cm) Debarked volume (m3)Large end Small end Avg.

1C 3.47 46.7 43.1 47.3 419.0 685.4 4.1 0.5192A 3.99 51.2 51.2 49.5 537.1 672.5 3.5 0.6823A 3.99 59.2 52.0 53.9 827.6 885.7 2.7 0.8013B 4.63 50.9 50.9 52.8 821.7 783.5 2.2 0.8973D 5.00 38.1 35.1 36.4 388.2 729.5 5.4 0.4414B 4.48 48.4 47.1 47.6 498.0 610.9 2.4 0.6924C 5.12 42.7 39.1 40.7 420.4 614.5 2.1 0.5744E 4.27 32.4 32.4 32.6 167.1 497.1 1.3 0.2735A 4.11 48.4 43.1 45.2 548.9 828.8 2.0 0.5595B 3.38 42.6 41.1 41.7 363.7 767.6 4.3 0.3995D 3.38 37.9 37.9 37.9 291.0 760.1 5.3 0.3195E 4.08 35.8 35.8 35.8 311.4 759.8 4.3 0.3398A 3.81 36.2 34.5 35.7 286.9 735.4 4.2 0.324

11A 3.60 53.4 51.6 54.0 675.1 785.9 3.9 0.73711B 2.90 52.9 52.9 52.1 643.8 810.1 3.1 0.55011C 3.47 51.1 46.1 48.2 522.6 800.3 6.3 0.55612D 5.03 43.4 38.4 40.5 548.4 827.0 4.6 0.55614B 5.18 59.9 58.5 57.9 1202.6 831.0 2.3 1.24614C 3.47 46.4 42.7 44.8 459.4 827.4 3.7 0.46915A 4.91 44.1 37.5 39.2 474.9 780.3 4.0 0.50915B 4.42 37.1 37.1 36.8 360.0 740.5 3.2 0.405

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energy in a material. Damping is an importantfactor in characterizing material properties. How-ever, the determination of damping is complex,depending on test procedures and data analysis.In this report, the damping ratio of the responsesignal was estimated through CWT. The theo-retical background of CWT and the proceduresto determine the instantaneous frequency anddamping ratio of the logs through wavelet anal-ysis are presented in the Appendix. Based on thewavelet ridge and skeleton computed for eachtime instant, instantaneous frequency fi and damp-ing ratio ζi of each log can be derived by solvingthe following equation:

8>>><>>>:

dlnBiðtÞdt

¼ 1BiðtÞ

dBiðtÞdt

¼ � 2πζi fi

dfiðtÞdt

¼ 2π fdi ¼ 2π fiffiffiffiffiffiffiffiffiffiffiffiffi1� ζ2i

q : (4)

Flowing signal processing, an average value foreach individual acoustic parameter (dynamicMOE, time centroid, and damping ratio) wasobtained for each log and used in subsequent dataanalysis.

Data Analysis

The research approach we adopted in this studywas a practical one, that is to saw the logs intoboards following acoustic impact test and laserscanning and use the board grade data as the logquality indication, which is the case in millproduction. One of the limitations of this ap-proach is that we were not able to obtain quan-titative data of actual internal defects on theboards and logs, thus a linear analysis was notpossible. To evaluate the effectiveness of theacoustic parameters as quality predictors, weanalyzed the characteristics of each possiblepredicting parameter and determined the re-lationships between the acoustic parameters(individual and combinations) of the logs and thegrade yield of the boards sawn from the logs. Forthis purpose, the 21 yellow-poplar logs wereranked and segregated into three acoustic classes(high, medium, and low quality sort) based on thefollowing sorting parameters: 1) acoustic velocity(V), 2) time centroid (Tc), 3) damping ratio (ζ), 4)combination of density (ρ) and time centroid(Tc), and 5) combination of dynamic MOE (Ed)and damping ratio (ζ). In general, the class

Table 2. Summary of the acoustic measures of the yellow-poplar logs.a

Log no. V (km/s) Ed (GPa) f (Hz) Tc (�10�2 s) ζ (�10�2) ρ/Tc2 (�106 kg/m3 s�2) Ed/ζ2 (�103 GPa)

1C 3.34 7.65 521.7 1.74 3.59 2.26 5.932A 3.37 7.65 413.8 1.64 3.43 2.51 6.523A 3.04 8.18 382.2 1.47 3.61 4.10 6.273B 3.05 7.29 344.8 1.93 4.25 2.10 4.043D 3.27 7.81 331.5 2.08 4.26 1.68 4.314B 3.83 8.98 425.5 1.90 4.12 1.70 5.294C 3.78 8.79 372.7 1.88 4.41 1.73 4.514E 3.59 6.42 425.5 1.98 3.73 1.26 4.615A 3.65 11.05 447.8 1.41 3.16 4.14 11.045B 3.88 11.57 576.9 1.44 3.02 3.71 12.715D 3.76 10.72 560.8 1.75 3.16 2.50 10.765E 3.67 10.21 458.0 1.57 3.83 3.07 6.958A 2.91 6.22 389.6 1.80 3.88 2.27 4.1411A 3.38 8.98 480.0 1.48 4.17 3.60 5.1711B 2.93 6.95 560.8 1.21 3.75 5.50 6.0811C 3.32 8.85 476.2 1.51 4.53 3.49 4.3012D 3.23 8.64 319.2 2.04 4.27 1.98 4.7514B 3.30 9.06 317.5 1.69 4.06 2.91 5.5014C 2.98 7.35 428.6 1.88 4.14 2.34 4.2915A 3.63 10.28 387.1 1.53 3.16 3.31 10.2715B 3.73 10.31 419.6 1.70 4.13 2.54 6.06a V, acoustic velocity; Ed, dynamic modulus of elasticity; f, fundamental frequency; Tc, time centroid; ζ, damping ratio; ρ, log density.

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thresholds were evenly set across the determinedrange of each parameter. However, minor ad-justments were made when the observed datashowed distinct uneven distribution and also forrounding the values to even numbers whennecessary. The resulting sample size of each logclass ranged from 5 to 9 logs. It should bepointed out that the sample size of this study wasconsidered small, thus the ranges of the acousticparameters observed on the sample logs werelimited, and the parameter thresholds presentedin this article for segregating logs are indicativeand preliminary.

RESULTS AND DISCUSSION

Table 1 shows the dimensional and physicalmeasures of 21 selected yellow-poplar logs. Thelogs measured 2.9-5.18 m in length with an av-erage diameter ranging from 35.7 to 57.9 cm. It isnoted that on some logs, the small end is largerthan the average diameter. In most cases, this isbecause of a large knot being present at the end ofthe log. In other cases, abnormalities such as

gouges or multiple knots in the center of the logskew the average diameter.

Table 2 summarizes the acoustic measures of21 selected yellow-poplar logs. Acoustic impacttesting of the logs took place in early March, 1 moafter harvesting. The moisture contents of thesewood samples were found to be 45-60%, whichconfirmed that the logs were in green condition(well above the FSP of 30% MC) at the time ofacoustic testing. Therefore, all acoustic parame-ters discussed in this report are considered greenlog parameters.

Table 3 shows the sawing results (board volume,cant volume, board grade yield, and recoveryrate) of 21 selected logs. A total of 294 boardswere sawn from the sample logs, with the widthranging from 12 to 41 cm and length ranging from2.74 to 4.88 m. The board recovery rate rangedfrom 26.5% for log 5E to 64.6% for log 3A. Thehigh-grade boards are a combination of FAS,F1F, and Select grades. The below-grade boardswere also included in the table for the purpose oflog quality analysis.

Table 3. Sawing results of the yellow-poplar logs.

Log no.

Volume (m3) Grade yield (m3) Recovery (%)

Debarked Board Cant Higha 1C 2C 3C BG Totalb Board

1C 0.519 0.250 0.081 0.040 0.068 0.099 0.042 0 63.9 48.22A 0.682 0.373 0.076 0.326 0.019 0.017 0 0.012 65.8 54.73A 0.801 0.517 0.070 0.441 0.045 0 0.012 0.019 73.3 64.63B 0.897 0.467 0.083 0.139 0.286 0.014 0.014 0.014 61.3 52.13D 0.441 0.156 0.080 0.071 0.038 0.047 0 0 53.5 35.34B 0.692 0.371 0.090 0.076 0.132 0.097 0.066 0 66.6 53.54C 0.574 0.274 0.104 0.054 0.165 0.054 0 0 65.8 47.74E 0.273 0.085 0.066 0 0.017 0.028 0.040 0 55.5 31.15A 0.559 0.323 0.050 0.304 0.019 0 0 0 66.8 57.85B 0.399 0.205 0.059 0.144 0.061 0 0 0 66.4 51.55D 0.319 0.085 0.079 0 0.028 0.028 0.028 0 51.4 26.65E 0.339 0.090 0.097 0 0.024 0.066 0 0 55.2 26.58A 0.324 0.142 0.074 0.090 0.014 0.009 0 0.028 66.5 43.8

11A 0.737 0.378 0.080 0.208 0.135 0.012 0.024 0 62.1 51.311B 0.550 0.297 0.073 0.179 0.076 0.042 0 0 67.3 54.011C 0.556 0.264 0.140 0.054 0.085 0.109 0.017 0 72.7 47.612D 0.556 0.234 0.111 0.012 0.111 0.111 0 0 61.9 42.014B 1.246 0.684 0.074 0.453 0.137 0.094 0 0 60.8 54.914C 0.469 0.236 0.071 0.045 0.047 0.076 0.068 0 65.5 50.315A 0.509 0.231 0.102 0.127 0.035 0.068 0 0 65.5 45.515B 0.405 0.201 0.063 0.076 0.092 0.021 0 0.012 65.2 49.5a High includes grade First and Seconds, F1F, and Select.b Total, includes boards and cant.BG, below grade.

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Acoustic Velocity

Acoustic velocity of the 21 selected yellow-poplar logs ranged from 2.91 to 3.88 km/s,which matches the velocity range of the 52logs bucked from the 15 randomly selected trees.We ranked the 21 selected logs by acoustic ve-locity in descending order and segregated theminto three groups based on the following velocityranges:

Group 1 (G1): 3.60 � V < 3.90 km/s (high-quality class)

Group 2 (G2): 3.30 � V < 3.60 km/s (medium-quality class)

Group 3 (G3): 2.90� V< 3.30 km/s (low-qualityclass)

The acoustic velocity class of the logs was thenassociated with the board grades determinedbased on the NHLA grading rules. Figure 1shows the distributions of board grade yield inrelation to log acoustic velocity classes. Three loggroups had almost the same volume recovery,

63.9% for G1, 63.6% for G2, and 64.6% for G3.Among the boards recovered, three log groupsshowed similar grade distribution, highest yieldfor the high-grade boards and decreasing yieldsfor 1 Common, 2 Common, 3 Common, and BGboards. The log acoustic class did not showa direct correlation with the board grade yield. Infact, the medium-velocity logs (G2) yielded themost high-grade boards (53.1%), and the low-velocity logs yielded 47.7% high-grade boards,even higher than the high-velocity logs (43.9%).In the BG level only, the log acoustic classshowed a positive trend; that is, BG boards in-creased as log velocity decreased. But, the BGboards only counted for 0.6-3% among all theboards. Therefore, acoustic velocity does notappear to be a meaningful predictor in log grouprating.

In physics, the velocity of stress waves propa-gating through a log depends on both stiffness andmass density of the log. The existence of smalldefects inside a log may not affect the globalstiffness of the log but could have a significant

Figure 1. Distribution of yellow-poplar board grade yields in relation to log acoustic classes segregated based on acousticvelocity.

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impact on the board grades according to thehardwood visual grading rules. In addition, it isunderstood that longitudinal waves traveling alongthe length of a material are not sensitive to thepresence of small sound defects because the wavescan bypass small defects without causing signif-icant changes in overall propagation path. Thiscould be amajor contributor to the poor correlationbetween log velocity class and board grade yield.

Conversely, the presence of significant internaldecay or major structural defects inside a logcould effectively decrease wood density, signifi-cantly impact wave propagation behavior, andthus result in abnormally low acoustic velocity(Wang et al 2009). Based on analysis of logvelocity distribution, five logs (8A, 11B, 14C,3A, and 3B) were identified as having unusuallylow velocities (2.91-3.05 km/s). The sawing re-sults confirmed that these logs either had internalrot, incipient decay, or missing wood (logs 3A,3B, 11B, and 14C) or had other structural defectsthat caused a significant downgrade in the sawnboards (log 8A). Therefore, acoustic velocity wasstill effective in identifying logs with severe in-ternal rot or other unsound defects.

Another important observation was that acousticvelocity failed to identify two small diameter logs(5D and 5E) that had a significant amount ofsweep (up to 5.3 cm) and resulted in the lowestboard recovery (26.5%) among the sample logs. Itappeared that wave propagation was not verysensitive to the longitudinal distortion, at least tothe extent of the sweep or crook observed in theyellow-poplar sample logs.

Time Centroid

Figure 2 shows the time signals (absolute am-plitude) and time centroid curves of the responsesignals from two yellow-poplar logs, one fromlog 5B (considered sound and good quality) andone from log 12D (considered a low-quality log).As we examined the time centroid curves (dotlines) of these two different logs, we found thatthe Tc of the good quality log (Fig 2a) exhibiteda steep slope in the beginning of the signal,

indicating a fast energy transmission. Then, the Tccurve became flat at the end of the signal, in-dicating that the energy gradually dissipated.However, the low-quality log (Fig 2b) showeddifferent characteristics in the Tc curve. The slopeof the curve remained almost constant, indicatingthat the signal energy was dissipated morequickly than that of the high-quality log.

The time centroids of the response signals ob-tained from the 21 selected logs are listed inTable 2. We ranked the logs by Tc in ascendingorder and segregated them into three groupsbased on the following evenly divided Tc ranges:

G1: 1.20 � Tc < 1.50 � 10�2 s (high-qualityclass)

G2: 1.50 � Tc < 1.80 � 10�2 s (medium-qualityclass)

Figure 2. Typical time signals and time centroid curves ofresponse signals received from yellow-poplar logs (a) Log5B; (b) Log 12D.

Xu et al—DEFECT DETECTION AND QUALITY ASSESSMENT OF HARDWOOD LOGS 299

G3: 1.80 � Tc < 2.10 � 10�2 s (low-qualityclass)

The lower the Tc value is, the greater the energy atthe beginning of the response signal, which thencorrelates to better quality with higher gradeyield.

Figure 3 shows the distributions of board gradeyield in relation to log time-centroid classes. Adirect correlation was found between board gradeyield and log time-centroid among the three logclasses. As the log time-centroid increased, theyield of high-grade boards decreased signifi-cantly, with a change from 74.2% for G1 to50.3% for G2 (α ¼ 0.05) and 21.8% for G3 (α ¼0.01). Meanwhile, the yields of the followingthree lower grades (1, 2, and 3 common) in-creased significantly (α ¼ 0.05). These two op-posite time-centroid trends reflected distinctdifferences between high-quality boards with noor few defects and common-grade boards withsome defects such as sound knots, unsound knots,or knot clusters and incipient decay.

Damping Ratio

To estimate damping ratio (ζ) of the responsesignals, a CWTwas performed to the time signalsusing the Morlet wavelet function. As examples,Fig 4 shows the response signal of a good qualitylog (log 5B) and the corresponding CWT anal-ysis, and Fig 5 shows the response signal ofa low-quality log (log 12D) and the corre-sponding CWT analysis. The wavelet modulusobtained is shown in Figs 4b and 5b (two-dimensional contour map) and Figs 4c and 5c(three-dimensional image). The wavelet ridge andskeleton were subsequently calculated from thewavelet modulus and are shown in Figs 4b and 5bas a red line and in Figs 4c and 5c as a black line,respectively. Figures 4d and 5d show the instan-taneous frequency, damping ratio, and dampingratio fitting curve (high-order polynomial fitting).

The instantaneous frequency we obtained was theinstantaneous natural frequency; therefore, thecorresponding damping ratio was the first-orderdamping ratio. For log 5B, a high-quality logproved by sawing results, the intrinsic frequency

Figure 3. Distributions of yellow-poplar board grade yield in relation to log acoustic classes segregated based on timecentroid (Tc).

WOOD AND FIBER SCIENCE, JULY 2018, V. 50(3)300

Figure 4. Response signal of yellow-poplar log 5B (high-quality log) and CWT analysis. (a) time-domain signal and itsenvelope (red dotted line); (b) time-scale distribution of signal’s CWT and wavelet ridge (red line); (c) time-scale distributionof signal’s CWT (3D) and wavelet skeleton; and (d) instantaneous frequency (scale), damping ratio, and damping ratio fittingcurve of the signal.

Figure 5. Response signal of yellow-poplar log 12D (low-quality log) and CWT analysis. (a) time-domain signal and itsenvelope (red dotted line); (b) time-scale distribution of signal’s CWT and wavelet ridge (red line); (c) time-scale distributionof signal’s CWT (3D) and wavelet skeleton; and (d) instantaneous frequency (scale), damping ratio, and damping ratio fittingcurve of the signal.

Xu et al—DEFECT DETECTION AND QUALITY ASSESSMENT OF HARDWOOD LOGS 301

did not show much change within a finite du-ration of the analyzed signal (sampling points:300-900), indicating that the reflection and re-fraction of the acoustic signal that are typicallyassociated with internal defects in a material didnot occur. Consequently, a frequency conver-sion phenomenon was not observed. As a result,the damping ratio estimated from the instanta-neous frequency did not have much variation. Inthe case of log 12D, a low-quality log indicatedby sawing results, variation of the damping ratiowas found prominent as a result of existing in-ternal defects (decay, sound and unsound knots,and heavy distortion) revealed by the sawingresults.

Damping ratio increased with the existence ofinternal damage because the additional surfacescreated in damage areas increased the dissipationof the acoustic energy. This increase in dampingratio can be used as a measure of the extent ofinternal defects in a log. Therefore, we classifiedthe logs into three classes based on the followingdamping ratio ranges, which were approximatelyevenly divided across the range:

G1: 3.00 � ζ < 3.50 � 10�2 (high-quality class)G2: 3.50 � ζ < 4.10 � 10�2 (medium-quality

class)G3: 4.10 � ζ < 4.60 � 10�2 (low-quality class)

Figure 6 shows the distribution of board gradeyield in relation to log damping ratio classes. Forthe logs in the low damping ratio class G1 (high-quality sort), the high-grade boards accounted forabout 74.1% and low-grade boards (including 2common, 3 common, and BG) were only 12.6%.By contrast, for the logs in the high damping ratioclass G3 (low-quality sort), the high-grade boardsonly accounted for 28.5%, a significant decreasecompared with the G1 class; whereas the low-grade boards increased to 29.3%, a significantincrease compared with the G1 class. Similarly totime centroid, two opposite trends of board gradeyield in damping ratio classes reflect distinctdifferences in the quality of the resulting boards.As for medium-quality logs, all of their lumbergrade yields were located between that of high-quality and low-quality logs.

Combined Parameter ρ/Tc2

Wood density (ρ) is usually not considered afactor in hardwood visual grading, but it is rel-evant in assessing the soundness of hardwoodlogs. The existence of any significant internal rotin a logmay effectively decrease the gross densityof the log because of the loss of wood fibers.Wood density is also interrelated to acoustic wavepropagation based on the one-dimensional wavetheory, in which acoustic velocity is dependent onMOE and density. In this study, wood densitydata of the logs were combined with acousticmeasures for multiparameter analysis.

After examining various possible combinations,a new parameter, ρ/Tc2, derived from gross den-sity of a log and the time centroid of the responsesignal, was found to be an effective predictor oflog quality. Figure 7 shows the distribution ofboard grade yield in relation to log classes seg-regated based on the combined parameter ρ/Tc2.Similarly to time centroid log classification, theyellow-poplar logs were divided into three classesaccording to the following ρ/Tc2 ranges:

G1: 3.70 � ρ/Tc2 < 5.50 � 106 kg/m3 s�2 (high-quality class)

G2: 2.40 � ρ/Tc2 < 3.70 � 106 kg/m3 s�2

(medium-quality class)G3: 1.25 � ρ/Tc2 < 2.40 � 106 kg/m3 s�2 (low-quality class)

There was a clear trend of increasing yield ofhigh-quality boards as log class changed fromlow to high values of ρ/Tc2. For the high-qualitylog class G1 with ρ/Tc2 in the range of 3.70-5.50 � 106, the amount of high-grade boardsreached almost 80%; whereas 1 Common and 2Common had about 14.9% and 3.2%, respec-tively, 3 Common and BG accounted for only2.3% combined. For the low-quality log classG3 with ρ/Tc2 in the range of 1.25-2.40 � 106,high-grade boards only accounted for 23.8%,a significant decrease compared with that ofclass G1 (α ¼ 0.01); 1 Common accounted for39.7% and the lower grade boards (2 common,3 common, and BG combined) accounted for36.5%, a significant increase compared with the

WOOD AND FIBER SCIENCE, JULY 2018, V. 50(3)302

G1 class (α ¼ 0.01). As for the log class G2 withmedium ρ/Tc2, the grade yields of the resultingboards fell between the high and low ρ/Tc2classes.

Combined Parameter Ed/ζ2

Modulus of elasticity or stiffness of wood is animportant property in machine stress grading ofstructural timber. It is also a key property fordetermining the quality of laminated veneerlumber and other engineered wood products.Although it is not usually measured and moni-tored in hardwood log sawing process, thestiffness of a log, as a global parameter, can beaffected by the soundness (decay presence) orinternal structural defects (knots, cracks, graindistortions, etc.) of a log. In this study, dynamicMOE (Ed) of each log was determined usingacoustic velocity and log gross density. Theparameter Ed was then combined with dampingratio ζ to form a new parameter Ed/ζ2 as a qualitypredictor.

Figure 8 shows the distribution of board gradeyield in relation to log Ed/ζ2 class. Similarly, theyellow-poplar logs were divided into threeclasses according to the following Ed/ζ2 ranges:

G1: 6.50 � Ed/ζ2 < 12.80 � 103 GPa (high-quality class)

G2: 4.80 � Ed/ζ2 < 6.50 � 103 GPa (medium-quality class)

G3: 4.00 � Ed/ζ2 < 4.80 � 103 GPa (low-qualityclass)

The data show a clear trend of increasing yield ofhigh-quality boards as log class changed fromlow to high values of Ed/ζ2. For the high-qualitylog class G1, high-grade boards reached 69.0%,whereas 1 Common and 2 Common had 14.3%and 13.7%, respectively. 3 Common and BGaccounted for only 3.1% combined. For the low-quality log class G3, high-grade boards onlyaccounted for 25.0%, a significant decreasecompared with the G1 class (α ¼ 0.05); 1Common accounted for 41.0% and the lowergrade boards (2 Common, 3 Common, and BG

Figure 6. Distributions of yellow-poplar board grade yield in relation to log acoustic classes segregated based on dampingratio (ζ).

Xu et al—DEFECT DETECTION AND QUALITY ASSESSMENT OF HARDWOOD LOGS 303

combined) accounted for 33.9%, both a signifi-cant increase compared with the G1 log class. Asfor the log class G2 with medium Ed/ζ2, gradeyields of the resulting boards fell between thehigh and low Ed/ζ2 classes.

CONCLUSIONS

Acoustic impact test coupled with advancedwaveform analysis was investigated as a newmethod for segregating hardwood logs in terms ofinternal soundness and potential board gradeyields. The acoustic parameters examined in-cluded log acoustic velocity, time centroid,damping ratio, and two combined parameters,ρ/Tc2 and Ed/ζ2. Based on the results obtainedfrom this study, the following conclusions can bedrawn:

1. Log classes based on acoustic velocity did notshow a clear direct correlation with boardgrade yields, but acoustic velocity was able toidentify the very low-end logs that had themost severe internal rot or other unsounddefects.

2. Acoustic velocity was not sensitive to longi-tudinal distortion of hardwood logs andtherefore failed to identify logs with signifi-cant sweep or crook that resulted in very lowboard recovery.

3. Log classes based on time-domain (timecentroid and ρ/Tc2) and frequency-domain(damping ratio and Ed/ζ2) parameters showedpositive correlations with the board gradeyields. The mechanism of each parameterassociated with various unsound defects oflogs are not yet fully understood, but eachparameter has its strengths and weaknesses.Given the inherent great variability of internaldefects in hardwood logs, all acoustic pa-rameters resulting from impact testing shouldbe considered in defect diagnosis to make anoptimal sorting decision.

4. Because of the small sample size of this study,the distinction of log classes with the groupthresholds presented in this article is indica-tive and preliminary. A production trial witha larger sample size is needed to furthervalidate the effectiveness of the acoustic

Figure 7. Distributions of yellow-poplar board grade yield in relation to log acoustic classes segregated based on ρ/Tc2.

WOOD AND FIBER SCIENCE, JULY 2018, V. 50(3)304

parameters and to determine practical logsorting criteria that will result in optimal useof the hardwood resource.

ACKNOWLEDGMENTS

This project was conducted under the cooperativeresearch agreement (14-JV-11111133-089) be-tween the Natural Resources Research Institute ofthe University of Minnesota Duluth and theUSDA Forest Service, Forest Products Labora-tory. Mr. Feng Xu’s participation in this projectwas supported by the Priority Academic ProgramDevelopment of Jiangsu Higher Education In-stitutions and the Nanjing Forestry UniversityInnovation Grant for Outstanding PhD Disser-tations (grant no. 163070682). We thank NealBennett and Deborah Conner for their technicalassistance during the project.

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APPENDIX: DETERMINATION OF INSTANTANEOUS

FREQUENCY AND DAMPING RATIO BASED ON

CONTINUOUS WAVELET TRANSFORM

CONCEPT OF CONTINUOUS WAVELET TRANSFORM

Wavelet transform (WT) is a localized decom-position in time-scale (frequency) domain, and itsessence is to represent or approximate a signal byusing a family of basic functions, allowing localfeatures of the signal to be better represented. TheCWT of a finite energy signal xðtÞ 2 L2ðRÞ can bedefined as follows (Mallat 1999):

W ½x�ða; bÞ¼ 1ffiffiffia

pðþ‘

�‘

xðtÞwp

�t� b

a

�dt; (1)

where wpð$Þ is the complex conjugate of the basicwavelet function w($), and a and b are thetranslation and scale/dilation parameters, re-spectively (Grossmann and Morlet 1984; Slavicet al 2003). The wavelet coefficientsW[x](a,b) arenormalized by the factor 1=

ffiffiffia

p. This normali-

zation ensures that the integral energy given byeach wavelet wa,b($) is independent of the di-lation a.

WOOD AND FIBER SCIENCE, JULY 2018, V. 50(3)306

The most common wavelet for analyzing tran-sient free vibration signals is the Morlet wavelet(Kronland-Martinet et al 1987; Staszewski 1997).In this report, the modified Morlet wavelet wasused to estimate the damping ratio of the acousticsignals. A modified Morlet is defined as

wðtÞ¼ 1ffiffiffiffiffiffiπfb

p e j2πfcte�t2/fb ; (2)

where fb is the wavelet bandwidth parameter andfc is wavelet center frequency. The center fre-quency fc of the Morlet wavelet is approximatelybounded by 2πfc � 5 to fulfill the condition ofadmissibility (Kronland-Martinet et al 1987). TheFourier transform of the Morlet wavelet is

wðaf Þ¼ e�π2fbðaf � fcÞ2 : (3)

ASYMPTOTIC ANALYSIS

For a certain class of wavelets, referred to as theanalytic wavelets, the analysis procedure can bemuch simplified if the signal is the asymptoticfunction. The characteristic of an analytic func-tion f(t) is that its Fourier transform values are allzeros in terms of the negative frequencies, namely

f ðωÞ¼ 0; "ω< 0: (4)

A common monochromatic signal can be de-scribed as a function of an instantaneous am-plitude A(t) and a phase w(t) as follows (Delpratet al 1992; Ulker-Kaustell and Karoumi 2011):

xðtÞ¼AðtÞcosðfðtÞÞ: (5)

The instantaneous angular frequency can be de-fined as the time derivative of the phase

ωðtÞ¼ _fðtÞ: (6)

If variation of the amplitude A(t) is much smallerthan that of the phase w(t), ie if the followingcondition can be met

�� _fðtÞ�������_AðtÞAðtÞ

����; (7)

then, the signal x(t) is called an asymptoticsignal. In this condition, the associated analyticsignal of x(t) can be approximated by the fol-lowing form:

ZxðtÞ�AðtÞe jfðtÞ: (8)

If the signal is asymptotic and wavelet function isanalytic, the relationship between the CWT of thereal-valued signal x(t) and that of its analyticsignal Zx(t) can be denoted by

W ½x�ða; bÞ¼ 12W ½Zx�ða; bÞ: (9)

An approximation of the CWT is proposedas follows by using Taylor’s formulae aroundt ¼ b (Carmona et al 1998; Le and Paultre2013):

W ½x�ða; bÞ¼ 12W ½Zx�ða; bÞ

¼ 12

ffiffiffia

pð‘

�‘

AðtÞe jfðtÞwp

�t� b

a

�dt

�ffiffiffia

p2

AðbÞe jfðbÞwp�a _fðbÞ�: (10)

WAVELET RIDGE AND SKELETON OF CWT

Assuming that a signal consists of only a fre-quency component, the maximum modulus of itsCWT is concentrated along a curve in thetime–frequency plane, which is referred to aswavelet ridge ar(b). The maximum moduluscorresponding to the points located in the curve iscalled wavelet skeleton W[x](ar(b), b). Becausethe wavelet used in this study is analytic, a defi-nition of the wavelet ridge and its skeleton aregiven as follows:8>><>>:

arðbÞ¼ ωw0

_fðbÞ

W ½x�ðarðbÞ; bÞ�ffiffiffia

p2

AðbÞe jfðbÞwp�arðbÞ _fðbÞ

�;

(11)

Xu et al—DEFECT DETECTION AND QUALITY ASSESSMENT OF HARDWOOD LOGS 307

where ωw0is the angular frequency at which the

modulus of the mother wavelet obtains the localmaximum. Thus, the amplitude of the asymptoticsignal A(b) can be determined by the modulus ofwavelet ridge using the following equation:

AðbÞ¼ jW ½x�ðarðbÞ; bÞj��� ffiffia

p2 e

jfðbÞwp�arðbÞ _fðbÞ

����¼ 2jW ½x�ðarðbÞ; bÞjffiffiffi

ap ��wp

�arðbÞ _fðbÞ

���: (12)

If a signal x(t) consists of multiple frequencycomponents, ie xðtÞ¼�

kxkðtÞ, because of the

linearity property of CWT, its CWT can be pro-cessed by

W ½x�ða; bÞ¼W

��kxkðtÞ

ða; bÞ

¼�kW ½xk�ða; bÞ: (13)

By appropriately selecting the mother waveletparameters, each particular component of x(t) canbe extracted from the multicomponents and eachmodulus of CWT of the point on the ridge is localmaximum in the case.

ESTIMATION OF INSTANTANEOUS FREQUENCY AND

DAMPING RATIO

For a linear n-degree-of-freedom system, whenthe kth point of the system is impacted by a unitimpulse force, the response at the ith point can berepresented as

hlkðtÞ¼ �n

i¼ 1

flif

ki

mi fdie�2πζi fitsinð2πfditÞ; (14)

where fli and f

ki are the ith-order modal shape of

the testing point l and k, respectively,mi is the ith-order modal mass, ζi is damping ratio of the ith-order modal shape, fi is the ith-order undampedfrequency, and fdi ¼

ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi1� ζ2i

qfi is the ith-order

damped frequency.

To facilitate the expression, the response signal canbe expressed as

xðtÞ¼ �n

i¼ 1Aie

�2πζi fitsinð2πfditÞ; (15)

where Ai ¼flif

ki

mi fdiis a constant only related to the

testing point and modal order i.

When the modified Morlet wavelet transform isapplied to the response function x(t), the fol-lowing equation can be obtained according toEqs (3), (10), and (15)

W ½x�ða; bÞ�ffiffiffia

p2�n

i¼1AðbÞe jfðbÞwp

�a _fðbÞ�

¼ffiffiffia

p2�n

i¼1Aie

�2πξi fibe�π2fbðafi� fcÞ2e jð2πfdibÞ;

(16)

where e�π2fbðafi � fcÞ2 is a dilated version of Fourier

transform of the Morlet wavelet. For a fixedvalue of the dilatation parameter a ¼ ai ¼ fc /fi,e�π

2fbðafi � fcÞ2 , wavelet modulus can reach themaximum (skeleton) on the wavelet ridge. In thiscase, the ith-order mode associated with aidominates the wavelet transform, whereas allthe other terms contribute nothing to the waveletmodulus and therefore are negligible. Thus, thewavelet transform of each separated mode i canbe represented as

W ½x�ðai; bÞ¼ffiffiffiffiai

p2

Aie�2πζi fibe jð2πfdibÞ: (17)

For an idiomatic expression, we substitute t forb in Eq (17); thus, the equation can be re-written as

W ½x�ðai; tÞ¼ffiffiffiffiai

p2

Aie�2πζi fite jð2πfditÞ

¼BiðtÞe jfiðtÞ: (18)

WOOD AND FIBER SCIENCE, JULY 2018, V. 50(3)308

The instantaneous amplitude BiðtÞ and theinstantaneous phase fiðtÞ of the CWT coefficientW ½x�ðai; tÞ can be defined as8<

:BiðtÞ¼

ffiffiffiffiai

p2

Aie�2πζi fit

fiðtÞ¼ 2πfdit: (19)

The following equation can be obtained by takingthe derivatives of Eq (19):

8>>><>>>:

dlnBiðtÞdt

¼ 1BiðtÞ

dBiðtÞdt

¼�2πζi fi

dfiðtÞdt

¼ 2πfdi ¼ 2πfiffiffiffiffiffiffiffiffiffiffiffiffi1� ζ2i

q : (20)

The instantaneous frequency fi and damping ratioζi of the system can be derived by solvingEq (20).

Xu et al—DEFECT DETECTION AND QUALITY ASSESSMENT OF HARDWOOD LOGS 309