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13 Optimize array performance for an affordable 70-element Develop a circular spiral baseline array that approximates array. or surpasses the Brel & Kjr array directivity for the truck Tailor array shape to optimize: application as used in the demonstration runs of 2005. Vertical directivity through vertical array aperture; Reduce the element number to 70 or 72, depending on the Horizontal directivity through combined array aperture numbers of spokes and circles in the array. and cross-range spreading loss during vehicle passby; To ensure comparable side lobe structure with a reduced Array height (vertical aperture) for assembly/disassem- number of elements, reduce array circular area proportion- bly in the field controlled by available facility; ately. This proportionate reduction provides comparable Side lobe suppression to minimize "false" source local- aperture area per element. izations at the high end of frequency range of interest. Deform the circular spiral array by expanding the vertical aperture using the chart of spot width vs. frequency (see The low frequency limit on array design was found to be Figure 4) developed for the study, to select a trial major axis 250 Hz, which should localize sources (potentially exhaust of the ellipse. Maintain element number and array area muffler related) to the upper or lower half of the cab area. while deforming. Degraded performance is unavoidable at lower frequencies, Selectively introduce tilt of the spokes and spiral angle, to given practicalities of array handling in the field. improve side lobe suppression as necessary. Figure 1 illus- The beamforming software package was developed to calcu- trates the essential geometry of an array of the type used in late both two-dimensional source image distributions pro- this study. jected in a vertical plane at the truck side and one-dimensional vertical sound source distributions determined at a distance of The notional array that is illustrated in Figure 1 represents 20 ft (6 m). All processing was done in the frequencytime one of the possible approximations to the array previously used domain in which the received signal is sectioned into roughly in the Caltrans demonstration tests (20). This array perfor- 15 time segments of 0.1 to 0.15 s duration. Within each time mance was the baseline for the current design study. The cir- segment, the spectrum of the sound at each array micro- cular array for this application, however, provides unnecessary phone was digitally computed in equivalent 1 Hz bands. localization in the horizontal direction and insufficient local- These spectral levels are used to compute either sound pres- ization in the vertical direction. Given the intrinsic horizontal sure levels or inter-element cross-spectral densities. The localization afforded by the passby itself, a deformed array was processed sound pressure levels are used to evaluate the ver- considered to optimize the effective localization vertically and tical profiles. The cross-spectral densities are used to localize horizontally for enhanced performance at low frequencies. in elevation (up and down) and cross-range (left or right) to Deformation of the parent circular array into an ellipse pro- give the two-dimensional source map in the vertical plane. To vides a means to tailor these arrays for truck passby. This facet do this step, the array is digitally steered to its left and to its right. of the array design represents one of the new products of the Because the arrival direction of the sound "looks" at the truck current project. The spiral angle and the spoke configuration both approaching and leaving the array zone, an adjustment in introduce spatial irregularity into the circular array, which Doppler shift is made at each frequency and for each arrival allows required side lobe suppression. angle of the sound from the truck. Additionally, a correction is All of the arrays shown in Figure 2 have the same area made for the range geometry spreading loss (i.e., 1/r2) at each of (i.e., AB = D2) and all have the same area density of ele- the time segments. The array is mathematically modeled as an ments. Figure 3 shows that the lobe structures of these acoustic lens that focuses on various points in the vertical plane arrays at 1000 Hz are virtually unaffected, as apparent from in order to "scan" for the sources. The narrow band images, the illustration. The projection of the lobe structure has a determined for 1 Hz band width, were summed to obtain shape outline that follows the outline of the array, but is images and sound levels in one-third octave frequency bands. rotated 90 degrees relative to it (i.e., an increase in array All microphone signals, the photocell signals, and a recording length along the x-axis results in a narrower beam in x; con- time code were simultaneously recorded to provide accurate versely, a reduction in array length along the y-axis results time resolution of the images at each moment of the passby. A in a wider beam in y). (In this example, x represents the ver- digital photograph of a truck was geometrically scaled to the tical axis and y represents the horizontal axis on a plane par- image plane dimensions using a pre-determined scale factor. allel to the array plane.) Figure 4 provides a chart that gives the approximate lobe width, here called "spot width," as it refers to the localization 3.2.2 Microphone Array Design in the truck side plane 20 ft (6 m) from the array plane. As The design strategy for the microphone array in this study shown, lengths on the order of 12 ft (3.7 m) are required to needed to accommodate many factors, among them: localize to within 5 ft (1.5 m).