03 Lawday (jr/d) 18/10/00 9:58 am Page 447 The analytical use of stress waves for the detection of decay in standing trees G. LAWDAY1 AND P.A. HODGES2 1 Computing Department, Buckinghamshire Chilterns University College, Queen Alexandra Road, High Wycombe, Bucks HP11 2JZ, England 2 Forest Products Research Centre, Buckinghamshire Chilterns University College, Queen Alexandra Road, High Wycombe, Bucks HP11 2JZ, England Summary This paper describes the use of an innovative method to detect decay in trees. The criteria for the project required the decay detecting process to be non-invasive and to provide an estimation of the position and extent of decay. A measured impulse from a hammer blow was used to produce stress waves within the stem of a tree. The stress waves were detected by an accelerometer and the resulting amplitude-time signals were recorded on a portable oscilloscope. The time of flight and attenuation of the stress wave were determined and the signal was transformed on a computer hosting a commercial software package. Six measurements were taken between different coordinates positioned around the circumference of a tree stem that was suspected of containing decay. Analysis of the amplitude spectrum of the stress waves provided an indication of the presence of sound or decayed wood between each set of co-ordinates. Estimation of the position of decay in the stem was achieved by calculating a short-time Fourier transform on each temporal signal and mapping the path of the stress waves through sound wood. The information produced by the analysis of stress waves was confirmed by felling the tree. Introduction The hazard posed by a tree suffering from decay depends on the ratio of the infected to healthy tissue within the stem. Guidance notes (Minnesota Department of Natural Resources and the USDA Forest Service, 1996) suggest that a 25 mm ring of sound wood is required for every 150 mm of stem diameter at any point on the stem. If the proportion of decayed wood to sound wood exceeds this level then action may need to be taken to minimize the hazard posed by the tree. Visual appraisal and rudimentary assessment © Institute of Chartered Foresters, 2000 instruments have traditionally been used to detect decay in trees. Some systems are invasive, such as the use of an increment borer that provides a core sample for examination (Mattheck and Breloer, 1997). The deep holes produced by increment borers and drills can enable decay fungi to become established and help spread any compartmentalized infection to sound wood (Toole and Grammage, 1959). Aural assessment of decay in trees is considered to be non-invasive. This method relies on the tester’s ability to interpret the acoustic emission from a hammer blow and make a deduction Forestry, Vol. 73, No. 5, 2000 03 Lawday (jr/d) 18/10/00 9:58 am Page 448 448 F O R E S T RY based on the sound produced. This process can be considered as time-frequency signal analysis where the cochlea and auditory cortex of the inner ear sense fluctuations in air pressure. Several advanced acoustic techniques have been developed for the purpose of decay detection in trees. This equipment typically measures the time-of-flight of a pulse of ultrasound or a stress wave across a tree stem. Any deviation from the expected transit time is indicative of a peculiarity or degradation of a wave path. However, until recently, the interpretation of the data produced by these techniques has not been able to provide accurate information about the extent of decay within a stem. Waid and Woodman (1957) showed how the measurement of ultrasonic wave attenuation was a potential technique for the location and identification of incipient heart and butt rot in standing trees. The measurement method was based on observations of significant loss of transmission energy in diseased wood. Current ultrasonic tree testing tools exploit this phenomenon by measuring the increased transit time when ultrasonic waves circumvent decay within a tree trunk (Sandoz and Lorin, 1996). However, the system is limited to a time-of-flight value that provides insufficient detail to position or identify the type of decay. The work of Pellerin and Bozhang (1996) included the Fourier analysis of similar resonant stress wave signals and the mechanical properties of sound and decayed timber. Stress waves are generated in a material when it is disturbed with a force component parallel to the direction of wave propagation. The natural frequencies of longitudinal vibrations are independent of the area and cross section of the test piece, making the test very convenient for irregularly shaped objects. The authors associated the spectral components in stress wave signals with the mechanical properties of sound and decayed wood. Their approach to positioning the decay in trees was to perform multiple measurements on two axes of the timber and plot the results on a three-dimensional map of decay position and amplitude. The current work detailed in this paper is based on the signal analysis of stress waves set up in the stem of a standing tree. The evaluation method requires the velocity of stress waves in wood to be fairly constant. This was found to be the case by Hearmon (1948) who predicted that the velocity of plane waves in timber was in the order of 1300–1500 ms–1. It has been recognised that variations can occur between and within tree species with regard to this property (Bucur, 1995). However, for the following experiment it was assumed that a stress wave velocity of 1300 ms–1 provided sufficient accuracy. The adopted approach uses the Fourier transform, where a signal (expressed as a function of time) is transformed by spectral analysis. This technique was used to discover the spectral composition of the stress waves. Short-time Fourier transform analysis enables a signal to be divided into time slots and analysed. The spectral analysis of each time slot produces a dual density distribution of frequency and time, which can be shown graphically as a spectrogram. Interpretation of the spectrogram allows the extent and position of decay within the stem to be estimated. Further information on this method of time frequency analysis can be found in Cohen (1995). Method Tree measurement The work detailed in this paper relates to the examination of a mature ash tree (Fraxinus excelsior). Stress wave data were obtained from the standing tree using the equipment prior to the tree being assessed by the examination of bored samples. The tree was felled and the freshly exposed cross section enabled the accurate determination of the decay pattern and extent of infection. Measurements from the standing tree and subsequent cross-sections were taken approximately 1 m above ground level. Equipment A calibrated impulse hammer with a head mass of 1 kg was used to excite the wood and produce the stress waves. Detection of the resultant stress waves was undertaken with a piezoelectric accelerometer. Two short, large diameter metal screws were screwed into the tree to allow measurements to be taken between the reference co-ordinates. An accelerometer was attached to one, and the other was struck with the hammer. 03 Lawday (jr/d) 18/10/00 9:58 am Page 449 D E T E C T I O N O F D E C AY I N T R E E S U S I N G S T R E S S WAV E A N A LY S I S 449 The amplitude time signals were recorded on a portable storage oscilloscope so that both timeof-flight and wave attenuation could be determined. Subsequent transformation of the dataset was carried out on a personal computer using a commercial software package. Assessment procedure Four measurement positions around the circumference of the tree were selected and allocated a reference co-ordinate (A, B, C or D). The location of each co-ordinate was noted and the circumference of the tree was determined. A quantifiable impulse was applied at each of the co-ordinates and the resultant stress wave was recorded. Two methods were used to monitor the quality of the impulse. First, the response was measured in real time and, second, the recording oscilloscope could, if required, automatically average multiple measurements, thus minimizing the variability of the applied impulses. The equipment gave reproducible oscilloscope measurements of 20 mV per 4 N of applied force to provide the necessary degree of experimental replication. The oscilloscope sampling rate was set at 50 000 samples per second (Ss–1) and the average of 32 measurements was recorded between each pair of positions. A dataset of six readings was obtained by applying measured impulses between the screws at the different positions around the stem. The location of the co-ordinates, shown in Figure 1, enabled data to be collected along four chords and across the diameter of the stem. An increment borer was used to take a core boring of the wood in the radial direction from each co-ordinate position. The core borings were examined to determine the presence of any decay within the stem. Finally, the tree was felled to determine the exact extent of decay within the stem. Results and discussion Decay pattern within the tree The results of the boring trial shown in Table 1 indicated a central zone of decay surrounded by a ring of sound wood. However, upon visual assessment of the standing tree it was suspected that the biodeteriogen had entered the trunk via Figure 1. Transverse section of the tree under investigation with an area of decay shown crosshatched (not to scale). Dimensions in cm. Table 1: Depth of sound wood (cm) in the radial direction determined by boring from each co-ordinate position Co-ordinate A B C D Depth of sound wood (cm) 18 7 21 24 a side wound and that the extent of decay was greater than that deduced from the boring samples. The true pattern of decay, established upon felling the tree, is indicated by the crosshatched section shown in Figure 1. Approximately 38 per cent of the cross section of the tree was affected by decay at the assessment position. This extended from a canker at the surface, between co-ordinates B and D, into the heartwood. The decay zone did not extend to the chords set by co-ordinates B to C, A to C and A to D. 03 Lawday (jr/d) 18/10/00 9:58 am Page 450 450 F O R E S T RY Variations in stress wave velocity The velocity of each impulse between the co-ordinates is shown in Table 2. It should be noted that the distances given in this table were determined with reference to the positions of the metal interface screws. The distances allow for the reduced stress wave propagation path produced by the depth of penetration of these screws. The velocities were calculated by measuring the distance between each co-ordinate and recording the time of flight of the particular stress wave. Velocities in the region of 1300 ms–1 were determined between co-ordinates B to C, A to C and A to D. This finding was within the expected velocity range for sound wood as previously detailed by Hearmon (1948) and Bucur (1995). The velocities of the stress waves between positions B to D, C to D and A to B were considerably lower than 1300 ms–1. The lower stress wave velocities indicated the presence of decayed wood between these positions. This view was substantiated upon felling the tree when it was found that the chords between co-ordinates B to D, C to D and A to B passed through the decayed section of the stem. The concept that reduced stress wave velocity and increased time-of-flight can indicate the presence of decay has been used in the development of a number of decay-detecting instruments such as stress wave timers. However, such equipment cannot be used to determine the extent and position of the decay. Interpretation of the temporal signals and signal spectra The temporal waveforms shown in Figure 2 indicate the presence of sound and decayed wood within the stem of the tree. The reciprocal of the time of flight was used to give the resonant wave frequency. The waveforms measured for an impulse travelling between positions B to C, A to C and A to D are shown in Figures 2a, b and c. The resonant wave frequency of the stress wave between these co-ordinates was consistently centred at 2 kHz on the three waveforms. These results were typical of the response to sound wood when subjected to an impulse, as the chords between these co-ordinates were not located in the decayed section of the stem. The waveforms obtained for stress waves travelling along chords between positions B to D, C to D and A to B were different from the waveforms established for stress waves travelling through sound wood. The intricate waveform shown in Figure 2d relates to the measurements made between co-ordinates B to D on the circumference of the stem. The resonant wave frequency peaked at 2 kHz and indicates the presence of sound wood along this chord. However, unlike the readings determined for sound wood, resonant wave frequencies lower than 2 kHz were also present in this waveform. These were notably centred at approximately 1 kHz on the horizontal axis and this portion of the waveform was characteristic of the decayed wood that was found between the two positions. This waveform indicated that the stress wave was travelling through the decayed portion of the stem and also circumventing the region of decay. Another intricate waveform (shown in Figure 2e) was recorded for the impulse between position C and position D. The predominant resonant wave frequency was centred around 1 kHz on this waveform, which is lower than that expected for sound wood. Similarly, the waveform in Figure 2f shows that the spectrum had Table 2: Basic measurements made on the sample tree to calculate the velocity of stress waves between different positions Chord Distance (cm) Time-of-flight (s) A to D A to C B to C A to B B to D D to C 58 52 51 80 61 81 440 400 385 730 865 720 Calculated velocity (ms–1) 1318 1300 1325 1096 705 1125 03 Lawday (jr/d) 18/10/00 9:58 am Page 451 D E T E C T I O N O F D E C AY I N T R E E S U S I N G S T R E S S WAV E A N A LY S I S 451 Figure 2. Waveforms derived for the stress wave set up between (a) positions A and D, (b) positions A and C, (c) positions B and C, (d) positions B and D, (e) positions D and C and (f) positions A and B. 03 Lawday (jr/d) 18/10/00 9:58 am Page 452 452 Figure 2. Continued. F O R E S T RY 03 Lawday (jr/d) 18/10/00 9:59 am Page 453 D E T E C T I O N O F D E C AY I N T R E E S U S I N G S T R E S S WAV E A N A LY S I S Figure 2. Continued. 453 03 Lawday (jr/d) 18/10/00 9:59 am Page 454 454 F O R E S T RY shifted towards the lower frequencies (less than 2 kHz) in comparison with the waveforms determined for sound wood. However, taken in isolation, the waveform was not wholly indicative of the decayed portion between co-ordinates A and B. This result emphasises the need to compare the response with other measurements in order to make a decision regarding the presence of decay. A good correlation was made between the waveforms derived for stress waves between various positions on the circumference of the tree and the presence of decay between these positions. The waveform for sound wood was typically uncomplicated and exhibited a peak resonant wave frequency at 2 kHz. The waveform obtained for stress waves travelling through decayed wood tended to be more intricate and had resonant wave frequencies below 2 kHz. The amplitude spectrum was used to identify decay within a tree and the co-ordinate method described in this paper allowed the position of the decayed section to be approximately predicted. However, this method of signal analysis could not be used to position the decayed area accurately or be used to evaluate the extent of decay within a tree trunk. In order to be an effective diagnostic tool the analysis of the stress waves was developed further. Short-time Fourier transform analysis The spectrogram in Figure 3 shows a short-time Fourier transform (STFT) of the signal obtained between co-ordinates B and D. The chord between these positions was in the zone of decayed wood within the stem. This particular transform method enabled the resonant wave frequencies to be plotted against the time taken to receive the signal. The spectrogram shows spectral densities and times of flight for the stress wave travelling between these co-ordinates. The region at the higher frequencies on the spectrogram relates to the stress wave that circumvented the decayed portion of the stem. This was found to have a resonant wave frequency (shown on the vertical axis) centred at approximately 2 kHz. The region at the lower frequencies relates to the stress wave that travelled through the decayed part of the stem. This had a lower resonant wave frequency that was centred at approximately 1 kHz. The time taken to receive the signals is shown on the horizontal axis of Figure 3. Accurate determination of the time difference between the two spectral regions was determined on the computer using orthogonal cursors. This technique enabled interference terms to be ignored and detected each spectral density peak. A time displacement of 1.25 ms was found to exist between the spectral regions determined for sound wood (frequency 2 kHz) and for decayed wood (frequency 1 kHz). Since the stress wave velocity for sound wood has been found to be constant at 1300 ms–1, the path length of the stress wave that circumvented the decayed region could be calculated. The calculated path length for the stress wave to travel around the decayed portion was found to be 1.6 m. The circumference of the section of decayed wood on the cross section was measured after the tree was felled and found to be 1.56 m. Taking into account the co-ordinate positions in relation to the area of decay it is unlikely that the calculated path length of the stress wave would have exactly equalled the circumference of the decayed area. However, this information allowed the mapping of the stress wave path that goes around the decayed area. An assessment was then made regarding the extent and position of decay within the stem. The current mapping of decay relies on the intuitive use of the combined information derived from basic and advanced stress wave analysis. This is only satisfactory as the system is still at the development stage. Continuing research in the Computing Department at Buckinghamshire Chilterns University College will enable a mapping system to be developed that provides the operator with a visual picture of the predicted decay pattern that is overlaid on the cross-section of the stem. Conclusions Basic stress wave analysis was used to determine the presence of decay in trees. This process allowed the non-destructive evaluation of trees and could be used to indicate whether an invasive assessment technique is necessary. However, this technique only provided limited information regarding the position and extent of decay within the stem. Advanced stress wave analysis using 03 Lawday (jr/d) 18/10/00 9:59 am Page 455 D E T E C T I O N O F D E C AY I N T R E E S U S I N G S T R E S S WAV E A N A LY S I S 455 Figure 3. Spectrogram of the short-time Fourier transform for the stress wave set up between positions B and D. short-time Fourier transforms enabled the path length of stress waves in sound wood to be accurately predicted. Further interpretation of the data using short time Fourier transforms provides a good indication of the extent of decay in tree trunks and the possibility of accurately mapping the decayed regions. The technique exploited the attributes of living tree wood and the fundamental properties of elastic wave propagation. In particular, it was discovered that trees gave the same identifiable spectral component for sound wood in the radial and tangential direction. This spectral component became the discriminant for sound and decayed wood. The results showed that the selected method of undertaking stress wave measurement of a tree trunk gave sufficient information for the detection of a central region of decay. Six measurements allowed an estimation of the position and extent of the decayed portion of the stem. The accuracy of this novel decay detection process was confirmed by felling the tree and comparing the suspected decay pattern with the actual decay pattern. References Bucur, V. 1995 Acoustics of Wood. CRC Press, New York, 121 pp. Cohen, L. 1995 Time-Frequency Analysis. Prentice Hall, New Jersey. Hearmon, R. 1948 The elasticity of wood and plywood. Forest Products Research. Special Report No 7. HMSO, London. Mattheck, C. and Breloer, H. 1997 The Body Language of Trees. HMSO, London. Minnesota Department of Natural Resources and USDA Forest Service 1996 How to Recognize 03 Lawday (jr/d) 18/10/00 9:59 am Page 456 456 F O R E S T RY Hazardous Defects in Trees. USDA Forest Service NA-FR-01–96, Washington, DC, 20 pp. Pellerin, R. and Bozhang, S. 1996 Non-destructive evaluation of the degree of deterioration in wood: stress wave frequency spectrum analysis. In Proceedings of the 10th International Symposium on Nondestructive Testing of Wood, Lausanne, Switzerland, pp. 99–115. Sandoz, J. and Lorin, P. 1996 Tares internes de bois sur pied: detection par ultrasonics. Tech. For. 3, 231–240. Toole, E.R. and Grammage, J.L. 1959 Damage from increment borings in Bottomland hardwoods. J. For. 57, 909–911. Waid, J. and Woodman, M. 1957 A non-destructive method for detecting diseases in wood. Nature 80, 45–75. Received 30 June 1999
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