Patent Publication Number: US-2023154314-A1

Title: Vehicle detection apparatus, method and program

Description:
This application is a National Stage Entry of PCT/JP2020/010715 filed on Mar. 12, 2020, the contents of all of which are incorporated herein by reference, in their entirety. 
    
    
     FIELD 
     The present invention relates to a vehicle detection apparatus, method and program. 
     BACKGROUND 
     Regarding detection using a response measured on a passing vehicle over a bridge, Non-Patent Literature (NPL) 1 discloses an automatic Vehicle Detection (AVD) algorithm that takes acceleration response data (time histories) of the bridge under traffic load and gives the automatic vehicle count. The AVD algorithm of NPL 1 gives information about traffic, such as total number of vehicles (vehicle count) that have passed during an interval of time. Time headway is difference in time between a leading vehicle and a following vehicle in a highway traffic situation. Time headway (T HW ) and distance headway (D HW ) are interrelated through vehicle speed (V) by T HW =D HW /V as illustrated in  FIG.  16 A  and  FIG.  16 B  which are cited from  FIG.  1    and  FIG.  2    of NPL1. AVD performs Vehicle Identification using a dictionary to identify a vehicle. AVD can distinguish between the two vehicles if the following condition holds: T HW &gt;=T HWmin , where T HWmin  is minimum time headway. Minimum time headway (T HWmin ) is predefined in AVD and its value is set to a value with which most trucks are going to follow each other. Any pair of trucks traveling so that T HW &lt;T HWmin  will be considered as a single vehicle. That is, AVD cannot discriminate individual ones of a pair of trucks travelling with T HW &lt;T HWmin . 
     Patent Literature (PTL) 1 discloses a finger-joint based detection system wherein a strain gauge is attached to a bottom side of a finger tip of the finger joint and deflection of the finger of the finger joint generated when a vehicle passes through the joint is converted to an electric signal. The strain gauges provided at appropriate intervals in a width direction of a bridge enables traffic amount survey for each lane. 
     PTL 2 discloses a measurement apparatus which detects a vehicle passing on a floor slab of a bridge, based on an acceleration signal (oscillation signal) transmitted from an accelerometer which is attached on a side of the floor slab. Vehicle detection is performed using an envelope of the oscillation signal in the following way. The measurement apparatus calculates an absolute value of a vertical acceleration and calculate the envelope (signal) of the calculated absolute value. When the vehicle enters a region close to the accelerometer, a magnitude of the envelop goes high at a start time during the vehicle passes while when the vehicle enters from an opposite direction, a magnitude of the envelop goes high at an end time when the vehicle leaves the bridge. 
     PTL 3 discloses a system wherein multiple sensors are arranged in each lane of a bridge to detect an axle interval(s) of a vehicle passing through a bridge. In an axle passing time group, a point where the passing time difference between axles is larger than a preset value is defined as a vehicle-to-vehicle separation and an axle interval(s) for each vehicle is detected. An active load strain, a time at which the k-th axle in the lane P has passed a reference position, a speed of the k-th vehicle on the lane P, and the lane P in which the vehicle is passing is acquired. By collating the axle intervals of a vehicle passing the lane of the bridge with reference to a database in which relationship between an axle interval(s) and a vehicle type is stored in advance, the type of the vehicle passing through the bridge is automatically detected substantially in real time.
     [PTL 1] Japanese Unexamined Utility Model Application Publication No. H04-112903   [PTL 2] Japanese Unexamined Patent Application Publication No. 2017-068781   [PTL 3] Japanese Unexamined Patent Application Publication No. 2006-084404   [NPL 1] Kanwardeep Singh Bhachu, J. David Baldwin, Kyran D. Mish, “Method for Vehicle Identification and Classification for Bridge Response Monitoring”, Proceedings of the IMAC-XXVIII Feb. 1-4, 2010, Jacksonville, Fla. USA   [NPL 2] 2.1. Gaussian mixture models, retrieved on 2020/01/08, Internet URL https://scikit-learn.org/stable/modules/mixture.html   [NPL 3] David M. Blei, Michael I. Jordan, “Variational inference for Dirichlet process mixtures”, 2006 International Society for Bayesian Analysis, 1, Number 1, pp. 121-144, retrieved on 2020/01/08, Internet URL http://www.cs.columbia.edu/˜blei/papers/BleiJordan2004.pdf   

     SUMMARY 
     The following analysis is made by the inventors of the present invention. 
     The AVD algorithm disclosed in NPL1 can identify or discriminate an individual vehicle where there is a vehicle (truck) travelling on a lane with a time headway T HW  between the vehicle (truck) and the other one(s) preceding/succeeding thereto being more than or equal to the time headway minimum. However, the AVD algorithm cannot well identify/discriminate vehicles in following traffic situations, as illustrated in  FIG.  17   . 
     (1) A plurality of vehicles passing on parallel lanes of a bridge (parallel traffic model). 
     (2) A plurality of vehicles passing one after other with combination of vehicle types, e.g., a truck and a car (serial traffic model). 
     (3) A plurality of vehicles passing with combination of parallel traffic model (1) and serial traffic model (2) (mixture traffic model). 
     When vehicles are passing on parallel lanes of a bridge, presence of a vehicle on each lane generates individual vehicle specific vibration. The AVD algorithm cannot identify/discriminate vehicles passing on parallel lanes of the bridge. Combined mixture of acceleration signals (oscillation signals) is measured as shown in  FIG.  18 B .  FIG.  18 B  shows a measurement result of an acceleration signal measured by an accelerometer in a parallel traffic model, wherein there are a vehicle 1 (4-axle truck) passing on lane 1 of a bridge and a vehicle 2 (2-axle car) passing on a lane 2 of the bridge, as illustrated in  FIG.  18 A . 
       FIG.  19 B  shows a measurement result of an acceleration measured by an accelerometer in a serial model. As illustrated in  FIG.  19 A , on a single lane 1, a small vehicle 2 (2-axle car) follows a large vehicle 1 (5-axle truck). The acceleration signal (oscillation signal) of the bridge induced by the small vehicle 2 is buried in the oscillation signal of the bridge induced by the large vehicle 1. The AVD algorithm disclosed in NPL 1 fails to identify the small vehicle 2 following the large vehicle 1 in serial traffic model with vehicle types combined. 
       FIG.  20 B  shows a measurement result of an acceleration measured by an accelerometer in a mixture traffic model wherein there are a vehicle 1 (3-axle truck) passing on lane 1 of a bridge and a vehicle 2 (2-axle car) following the vehicle 1 and passing on the lane 1, while there are a vehicle 3 (2-axle car) passing on lane 2 in parallel with the vehicle 1 in the lane 1 and a vehicle 4 (2-axle car) following the vehicle 3 and passing on the lane 2 as illustrated in  FIG.  20 A . It is noted that the measurement position of the acceleration signal (oscillation signal) below the bridge is same as proposed in the AVD algorithm disclosed in the Non-Patent Literature (NPL) 1, the signals shown in  FIGS.  17 ,  18  and  19    correspond to same location as defined in AVD algorithm. 
     The AVD algorithm disclosed in NPL 1 cannot identify/discriminate individual vehicles passing on two lanes of the bridge during multiple vehicles present on the bridge as illustrated in  FIG.  20 A . The AVD algorithm disclosed in NPL 1 cannot identify a vehicle(s) passing in mixture of the serial case and parallel case due to the aforementioned reason. 
     The AVD algorithm disclosed in NPL 1 uses a threshold-based dictionary. Creating a dictionary for combinations of vehicle types is time consuming and very complex. 
     Accordingly, it is one of objects of the present invention to provide a detection apparatus, a method, a non-transitory medium storing a program, each enabling to detect and identify vehicles passing on parallel lanes on a bridge. 
     According to one aspect of the disclosure, there is provided a detection apparatus comprising: 
     a signal acquisition part that acquires a plurality of oscillation signals from a plurality of sensors, respectively, each sensor provided for each lane of a bridge that includes a plurality of lanes running in parallel and capable of sensing oscillation of the bridge induced by an individual axle of a vehicle passing on the lane; 
     a signal separation part that receives, from the signal acquisition part, the plurality of the oscillation signals, applies blind source separation (BSS) to the plurality of the oscillation signals to estimate and separate a plurality of source oscillation signals, each source oscillation signal specific to each lane, and adjusts amplitude of an individual one of the plurality of the source oscillation signals to output a plurality of amplitude adjusted oscillation signals; and 
     a vehicle estimation part that receives the amplitude adjusted oscillation signal corresponding to the lane of interest from the signal separation part, and estimates, from the amplitude adjusted oscillation signal, a response oscillation due to a vehicle passing on the lane of interest to detect and count individual vehicles passing on the lane of interest. 
     According to a second aspect of the disclosure, there is provided a computer-based vehicle detection method comprising: 
     acquiring a plurality of oscillation signals from a plurality of sensors, respectively, each sensor provided for each lane of a bridge that includes a plurality of lanes running in parallel and capable of sensing oscillation of the bridge induced in the lane by an individual axle of a vehicle passing on the lane; 
     performing signal separation processing comprising:
         applying blind source separation (BSS) to the plurality of the oscillation signals to estimate and separate a plurality of source oscillation signals, each source oscillation signal specific to each lane; and   adjusting amplitude of an individual one of the plurality of the source oscillation signals to output a plurality of amplitude adjusted oscillation signals; and       

     performing estimation processing comprising:
         receiving the amplitude adjusted oscillation signal corresponding to the lane of interest output from the signal separation processing; and   estimating, from the amplitude adjusted oscillation signal, a response oscillation due to a vehicle passing on the lane of interest to detect and count individual vehicles passing on the lane of interest.       

     According to a third aspect of the disclosure, there is provided a recording medium storing therein a program for causing a computer to execute processing comprising: 
     acquiring a plurality of oscillation signals from a plurality of sensors, respectively, each sensor provided for each lane of a bridge that includes a plurality of lanes running in parallel and capable of sensing oscillation of the bridge induced in the lane by an individual axle of a vehicle passing on the lane; 
     performing signal separation processing comprising:
         applying blind source separation (BSS) to the plurality of the oscillation signals to estimate and separate a plurality of source oscillation signals, each source oscillation signal specific to each lane; and   adjusting amplitude of an individual one of the plurality of the source oscillation signals to output a plurality of amplitude adjusted oscillation signals; and       

     performing estimation processing comprising:
         receiving the amplitude adjusted oscillation signal corresponding to the lane of interest output from the signal separation processing; and   estimating, from the amplitude adjusted oscillation signal, a response oscillation due to a vehicle passing on the lane of interest to detect and count individual vehicles passing on the lane of interest.       

     According to the disclosure, there is provided a computer-readable recording medium in which the program according to the above described third aspect of the disclosure is stored. The recording medium may be such as a semiconductor storage (such as read only memory (ROM), random access memory (RAM), electrically and erasable programmable read only memory (EEPROM)), Hard Disk Drive (HDD), Solid State Drive (SSD), Compact Disc (CD) or Digital Versatile Disc (DVD) etc. 
     According to a further aspect of the disclosure, there is provided a vehicle detection apparatus comprising: 
     a signal acquisition part that acquires a plurality of oscillation signals from a plurality of sensors, respectively, each sensor provided for each lane of a bridge that includes a plurality of lanes running in parallel and capable of sensing oscillation induced by a vehicle passing on the lane; 
     a vehicle estimation part that obtains a frequency spectrum of each frame of the oscillation signal by applying Fourier transform to the each frame extracted from the oscillation signal by a sliding window and calculates a sum of a normalized frequency vector, from the frequency spectrum of the each frame, for each lane, to generate a maximum vector with each element thereof being a max value of the sum of a normalized frequency vectors calculated for the plurality of lane, 
     generates a binary vector with columns, number of which is equal to number of the sums of normalized frequency vectors and with rows, an element of which corresponds to a time index and has a value 1 at an element position with a maximum value and 0 otherwise, 
     obtains time repeated vectors of the sum of a normalized frequency vectors and maximum vectors by multiplying a time value by a magnitude value of each of the vectors, 
     performs Gaussian mixture model-clustering on the time repeated vector to count number of clusters and finds start time and end time of presence of a vehicle in each lane, and 
     calculates a column-wise mean value of elements corresponding to the start time and the end time, in a row of the binary matrix to decide that the vehicle is present in a lane corresponding to a column of the binary matrix for which the column-wise mean value is calculated if the column-wise mean value is not less than a predetermined threshold value, 
     while if the column-wise mean value is less than a predetermined threshold value for all columns of the binary matrix, deciding that the vehicle is present in the plurality of lanes. There are provided a method, program, a non-transitory medium that correspond to the further aspect of the disclosure. 
     According to the present invention, it is made possible to detect and identify vehicles passing on parallel lanes on a bridge. Still other features and advantages of the present invention will become readily apparent to those skilled in this art from the following detailed description in conjunction with the accompanying drawings wherein only example embodiment of the invention are shown and described, simply by way of illustration of the best mode contemplated of carrying out this invention. As will be realized, the invention is capable of other and different embodiments, and its several details are capable of modifications in various obvious respects, all without departing from the invention. Accordingly, the drawing and description are to be regarded as illustrative in nature, and not as restrictive. 
    
    
     
       BRIEF DESCRIPTION OF DRAWINGS 
         FIGS.  1 A and  1 B  are diagrams illustrating an embodiment of the invention. 
         FIG.  2    is a diagram illustrating an arrangement of a vehicle detection system of the embodiment. 
         FIGS.  3 A to  3 C  are diagrams illustrating lane separation by BSS. 
         FIG.  4    is a flowchart illustrating an operation example of the embodiment. 
         FIGS.  5 A to  5 C  are diagrams illustrating an example of the embodiment. 
         FIGS.  6 A to  6 D  are diagrams illustrating an example of the embodiment. 
         FIG.  7    is a diagram illustrating an example of the embodiment. 
         FIGS.  8 A to  8 D  are diagrams illustrating an example of the embodiment. 
         FIGS.  9 A and  9 B  are diagrams illustrating an example of the embodiment. 
         FIG.  10    is a flowchart illustrating an operation example of the embodiment. 
         FIGS.  11 A to  11 C  are diagrams illustrating an example of the embodiment. 
         FIGS.  12 A to  12 C  are diagrams illustrating an example of the embodiment. 
         FIGS.  13 A and  13 B  are diagrams illustrating an example of the embodiment. 
         FIG.  14    is a diagram illustrating an arrangement of a vehicle detection system of the embodiment. 
         FIG.  15    is a diagram illustrating an operation example of the vehicle estimation part of another embodiment. 
         FIGS.  16 A and  16 B  are figures cited from NPL1. 
         FIG.  17    is a schematic diagram of traffic models. 
         FIGS.  18 A and  18 B  are a diagram and an example of an acceleration signal of parallel traffic model. 
         FIGS.  19 A and  19 B  are a diagram and an example of an acceleration signal of serial traffic model. 
         FIGS.  20 A and  20 B  are a diagram and an example of an acceleration signal of mixture traffic model. 
     
    
    
     DETAILED DESCRIPTION 
     The following describes an example embodiment with reference to drawings.  FIG.  1    is a schematic diagram illustrating the example embodiment of the present invention.  FIG.  1 A  is a schematic illustration of a side view, while  FIG.  1 B  is a schematic illustration of a plan view. Referring to  FIG.  1   , an expansion joint  14  is a joint provided between separate structures with different properties for accommodating movement, shrinkage, and temperature variations on reinforced and pre-stressed concrete, composite, and steel structures. An accelerometer is used as a sensor  12  for detecting acceleration (i.e., oscillation) of the bridge induced by a vehicle 1 passing on a lane of the bridge  10  to convert the oscillation to an electric signal. The sensor (accelerometer)  12  is provided below a concrete slab of the bridge  10  at least on an edge point of the bridge  10 . Acceleration data (oscillation signal) captured by the accelerometer is transmitted in digital data via wired or wireless communication to a vehicle detection apparatus not shown. 
       FIG.  2    is a schematic diagram illustrating an example of an arrangement of a vehicle detection apparatus of the example embodiment. Referring to  FIG.  2   , the vehicle detection apparatus  100  includes a signal acquisition part  102 , a signal separation part  104 , a vehicle estimation part  106 , and an output part  108 . The signal acquisition part  102  acquires acceleration data from the sensors s1 and s2 which are communicatively connected to the signal acquisition part  102 . The acceleration data includes an impulse response(s) of the lane, the impulse being given to the bridge  10  by axles of the vehicle passing over the bridge. The acceleration data (oscillation signals) from the sensors s1 and s2 are synchronized in time, that is, the acceleration data sampled by the sensors s1 and s2 at the same sampling time are received by the signal acquisition part  102 , as data of the same index in time series acceleration data vector. The signal separation part  104  receives, from the signal acquisition part  102 , respective acceleration data (oscillation signals) acquired by the sensors s1 and s2 and applies blind source separation (BSS) to acceleration data (oscillation signals) from the sensors s1 and s2 to separate each oscillation signal specific to each lane. The vehicle estimation part  106  detects and counts individual vehicles in each lane, based on the oscillation signal specific to each lane which has been separated by the signal separation part  104 . The vehicle estimation part  106  calculates time repletion feature from peaks of an amplitude of the oscillation signal separated to each lane and performs clustering on time repletion feature to detect presence of a vehicle(s) on each lane. The output part  108  outputs the detection result to a display apparatus in a storage apparatus, or via a communication network to a terminal or a computer system. The signal acquisition part  102 , signal separation part  104 , vehicle estimation part  106 , and output part  108  may be implemented by a processor that is included in the vehicle detection apparatus  100  and execute program instructions stored in a memory included in the vehicle detection apparatus  100 . 
       FIGS.  3 A- 3 C  are schematic illustration of the blind source separation (BSS) which separates a set of source signals from a set of mixed signals, without aid of information about the source signals or a mixing system. 
     BSS is used with an assumption that measured vibration responses can be separated to estimate individual vibration response of each lane. In  FIG.  3 A , two vehicles are passing in lane 1 and lane 2 on the bridge. The sensors s1 and s2 captures oscillation mixed signal y 1  and y 2  which are outputs of a mixing system which mixes actual source signals (oscillation signals) x 1  and x 2  of the lane 1 and lane 2 respectively, as illustrated in  FIG.  3 B  and  FIG.  3 C . 
         y   j ( n )=Σ i=1   2 Σ p=1   p   H   ji ( p ) x   i ( n−p+ 1)  (1)
 
     where x i  is a signal from actual source, y j  is a signal captured by the sensor (accelerometer) s j  (j=1,2), and H ji  is a mixing matrix from actual source to the sensor (accelerometer) s j .
 
Outputs of BSS are given as follows.
 
         {circumflex over (x)}   i ( n )=Σ j=1   2 Σ q=1   Q   W   ij ( q ) y   ij ( n−q+ 1)  (2)
 
     where {circumflex over (x)} i  (i=1,2) is a separated signal, and W ij  is a separation filter with Q taps. 
     In a case of p=1 and q=1, as illustrated in  FIG.  3 B  and  FIG.  3 C . 
         y   1 ( n )= H   11   x   1 ( n )+ H   21   x   2 ( n ) 
         y   2 ( n )= H   12   x   1 ( n )+ H   22   x   2 ( n ) 
         {circumflex over (x)}   1 ( n )+ W   11   y   1 ( n )+ W   21   y   2 ( n ) 
         {circumflex over (x)}   2 ( n )+ W   12   y   1 ( n )+ W   22   y   2 ( n )  (3)
 
       FIG.  4    is a flowchart of the embodiment. Referring  FIG.  4   , the signal acquisition part  102  acquires oscillation signals (time domain signals) from sensors s1 and s2 (S 101 ). The signal acquisition part  102  may cut off a DC component of the oscillation signal. 
     The signal separation part  104  calculates a sum of a normalized frequency spectrum (S 102 ). More specifically, the signal separation part  104  extracts waveform data (frame) using a sliding window of a time interval T (length of one frame) and perform FFT (fast Fourier transform) to the extracted waveform data to obtain a frequency spectrum, which is normalized by dividing each frequency component (amplitude) by a total sum value of frequency components (amplitudes) of the frequency spectrum. The signal separation part  104  calculates a sum of a normalized frequency spectrum for each frame of the waveform data acquired by the sensors s1 and s2. 
       FIG.  5    is a diagram for explaining the embodiment. It is assumed that a vehicle 1 (truck) with 3 axles is passing in the lane 1 and a vehicle 2 (car) with 2 axles is passing in the lane 2, as illustrated in  FIG.  5 A .  FIGS.  5 B and  5 C  show waveform data (oscillation signals) acquired by the sensors s1 and s2 provided in lane 1 and lane 2 where the vehicle 1 (3-axle truck) and vehicle 2(2-axle car) are passing, respectively. In  FIGS.  5 B and  5 C , a horizontal axis is a time and a vertical axis is an acceleration[m/s 2 ]. 
       FIG.  6 A  shows time series of a sum of the normalized frequency spectrum of lane 1 and  FIG.  6 B  shows time series of a sum of the normalized frequency spectrum of lane 2. In  FIGS.  6 A and  6 B , a sum of the normalized frequency spectrum for each frame are plotted along a time axis (horizontal axis). 
     The frequency component is normalized by a combined sum of the frequency spectrums of the oscillation signals (each frame). In case of  FIG.  6 A , the sum of normalized frequency of the frame acquired by the sensor s1 (lane 1) is given by the following equation: 
     
       
         
           
             
               
                 
                   
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     where spectrum (s1) is a vector having, as each element, an amplitude spectrum of each frequency bin in the frequency spectrum of the frame of the oscillation signal acquired by the sensor s1, 
     spectrum (s2) is a vector having, as each element, an amplitude spectrum of each frequency bin in the frequency spectrum of the frame of the oscillation signal acquired by the sensor s2, 
     sum of (spectrum (s1), spectrum (s2)) is a combined sum operation which adds each amplitude spectrum at each element of the vector spectrum (s1) and the vector spectrum (s2) to generate a scaler value (sum) by summing the added amplitude spectrums, 
     spectrum (s1)/sum of (spectrum (s1), spectrum (s2)) is an operation of dividing an amplitude spectrum of each element (frequency bin) in the vector spectrum (s1) by the sum of (spectrum (s1), spectrum (s2)) to obtain a normalized amplitude spectrum of each element (frequency bin) in the spectrum (s1), and sum ( ) is an operation of summing each normalized amplitude spectrum of each element (frequency bin) in the spectrum (s1). 
     In case of  FIG.  6 B , the sum of normalized frequency of the frame acquired by the sensor s2 (lane 2) is given, as with the expression (4), by the following expression: 
     
       
         
           
             
               
                 
                   
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     The signal separation part  104  detects a first peak in the sum of the normalized frequency spectrum of each of lane 1 and lane 2 (S 103 ).  FIG.  6 C  shows a sum of normalized frequencies of the lane 1 (sensor s1) where a first peak designated by a small circle indicates that a first vehicle has entered in the lane 1.  FIG.  6 D  shows a sum of normalized frequencies of the lane 2 where a first peak designated by a circle indicates that a second vehicle has entered in the lane 2. Using a peak(s) of the sum of normalized frequencies, the signal separation part  104  determines a region boundary between a first vehicle region that is a time interval during when a vehicle enters in one of the lanes and there is no vehicle entering in the other lane and a mixed signal region is a time interval during when there are vehicles entering in both lanes. The signal separation part  104  selects a first vehicle region from a time-stamp of the first peak of  FIG.  6 C  until the time-stamp of the first peak of  FIG.  6 D  (S 104 ). 
       FIG.  7    shows the first vehicle region and mixed signal region which are mapped to the oscillation signal (time domain signal) of lane 1 ( FIG.  5 B ) acquired by the sensor s1. The signal separation part  104  stores the time domain signals of lane 1 and lane 2 ( FIG.  5 B  and  FIG.  5 C ) in a semiconductor memory (e.g., RAM (Random Access Memory or EEPROM(Electrically Erasable Programmable Read-Only Memory)), or a storage unit (e.g., HDD (Hard Disk Drive) or SSD(Solid State Drive)) provided in the vehicle detection apparatus. 
     The signal separation part  104  applies BSS to time domain signals ( FIG.  5 B  and  FIG.  5 C ) including the first regions and the mixed signal region to obtain estimated source signals ({circumflex over (x)}1 and {circumflex over (x)}2 in  FIG.  3 C ). (S 105 ). 
       FIG.  8 A  and  FIG.  8 B  show the estimated source signals {circumflex over (x)}1 of lane 1 and {circumflex over (x)}2 of lane 2 which have been estimated by the BSS. 
     The signal separation part  104  calculates an amplitude ratio α by dividing a sum of power spectrum of the first vehicle region of measured time domain signal by a sum of power spectrum of the first vehicle region of time domain signal estimated by BSS. 
     
       
         
           
             
               
                 
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     The signal separation part  104  multiplies the amplitude ratio α to the estimated signals {circumflex over (x)}1 and {circumflex over (x)}2 to obtain amplified estimated signals α·{circumflex over (x)}1 and α·{circumflex over (x)}2. 
       FIG.  8 C  and  FIG.  8 D  show respectively amplified estimated signals α·{circumflex over (x)}1 and α·{circumflex over (x)}2 of lane 1 and lane 2 which are obtained by multiplying the amplitude ratio α to the estimated source signals {circumflex over (x)}1 and {circumflex over (x)}2 of lane 1 and lane 2 shown in  FIG.  8 A  and  FIG.  8 B . 
     The following describes an example of the operation of the vehicle estimation part  106  which can detect and count vehicles passing one after other with combination of vehicle types, e.g., a truck and a car (serial model), in a single lane of interest (one of lane 1 and lane 2) individually, based on one of amplified estimated signals α·{umlaut over (x)}1 and α·{circumflex over (x)}2. 
       FIG.  9 A  illustrates a serial case where a vehicle 1 (3-axle truck) and a vehicle 2 (2-axle car) following the vehicle 1 are present on the lane 1 of the bridge  10 . The vehicle 2 is preferably spaced apart from the vehicle 1 by a time interval of e.g., about 0.5 second or more.  FIG.  9 B  illustrates estimation of the number of vehicles based on clustering using a Gaussian mixture model with Dirichlet process prior. The number of Gaussian probability density function(s) obtained by the clustering and taking a value greater than a predetermined threshold value is counted as the number of vehicles. 
       FIG.  10    is a flow chart illustrating an operation example of the vehicle estimation part  106  which detects the number of vehicles passing a lane. 
     It is assumed that the vehicle estimation part  106  receives from the signal acquisition part  102 , the oscillation signal, i.e., the amplified estimated signal of a lane of interest, as shown in  FIG.  11 A . 
     The vehicle estimation part  106  is configured to detect a vehicle (s) passing serially on a single lane (e.g., lane 1) from the oscillation signal of lane 1 captured by the sensor s1. 
     The vehicle estimation part  106  calculates a normalized frequency spectrum (S 201 ).  FIG.  11 B  shows a normalized frequency spectrum of the signal shown in  FIG.  11 A . More specifically, the vehicle estimation part  106  applies short-time(term) FFT (Fast Fourier Transform) (STFT) to the oscillation signal shown in  FIG.  11 A . That is, using a sliding window of a predetermined length (length of one frame), each shifted by predetermined value, each frame is extracted from the oscillation signal. The neighboring frames have overlapping portion. FFT is applied to each frame to obtain a frequency spectrum of each frame. Discrete Fourier transform (DFT) may as a matter of course be used in place of FFT. 
     Let&#39;s X t =[x 0 , x 1  . . . x N−1 , x N  . . . ] be time series of sampled values x k  (where k is non-negative integer) of the oscillation signal with a shift of the sliding window=m, frames X j  (j=1,2,3 . . . ) with length N (N&gt;m) are extracted by the sliding window from the oscillation signal and FFT is applied to each frame to obtain a frequency spectrum Y(ω) j  of the j-th frame X j  (j=1,2,3 . . . ), 
         X   1 =[ x   0   , . . . ,x   N−1 ]→ Y (ω) 1   =FFT ( X   1 )
 
         X   2 =[ x   m−1   , . . . ,x   N+m−2 ]→ Y (ω) 2   =FFT ( X   2 )
 
         X   3 =[ x   2m−1   , . . . ,x   N+2m−3 ]→ Y (ω) 3   =FFT ( X   3 )
 
     The vehicle estimation part  106  calculates a normalized frequency spectrum by dividing each frequency component (amplitude) by a total sum of amplitudes of the frequency components of the frequency spectrum. The total sum of amplitude spectrum q j  for j-th frame X j  is given by 
     
       
         
           
             
               
                 
                   
                     S 
                     j 
                   
                   = 
                   
                     
                       ∑ 
                       
                         i 
                         = 
                         1 
                       
                       
                         
                           N 
                           2 
                         
                         - 
                         1 
                       
                     
                       
                     
                       
                         q 
                         j 
                       
                       ( 
                       i 
                       ) 
                     
                   
                 
               
               
                 
                   ( 
                   7 
                   ) 
                 
               
             
           
         
       
     
     where q j (i) is an amplitude of i-th frequency bin of the frequency spectrum Y(ω) j  of the j-th frame X j . 
         q   j ( i )=√{square root over (Re( y   j ( i )) 2 +Im( y   j ( i )) 2 )}  (8)
 
     where y j (i) (i=1, . . . , N/2−1) is an i-th frequency component (bin) of the frequency spectrum Y(ω) j . Re( ) and Im ( ) are real part and imaginary part of complex y j (i) where y j (0) (i=0) is a DC component, an imaginary part of which is zero and a real part of which is assumed to be zero, and an index i=N/2 corresponds to the Nyquist frequency bin. 
     The normalized frequency spectrum Q for the j-th frame X is given as 
     
       
         
           
             
               
                 
                   
                     Q 
                     j 
                   
                   = 
                   
                     
                       ( 
                       
                         1 
                         
                           s 
                           j 
                         
                       
                       ) 
                     
                     [ 
                     
                       
                         
                           q 
                           j 
                         
                         ( 
                         1 
                         ) 
                       
                       , 
                       … 
                         
                       , 
                       
                         
                           q 
                           j 
                         
                         ( 
                         
                           
                             N 
                             2 
                           
                           - 
                           1 
                         
                         ) 
                       
                     
                     ] 
                   
                 
               
               
                 
                   ( 
                   9 
                   ) 
                 
               
             
           
         
       
     
     The vehicle estimation part  106  calculates a frame-wise sum of a normalized frequency spectrum (S 202 ). 
     The frame-wise sum f(j) of a normalized frequency spectrum for j-th frame X j  (j=1, 2, . . . ) is given as 
     
       
         
           
             
               
                 
                   
                     f 
                     ⁡ 
                     ( 
                     j 
                     ) 
                   
                   = 
                   
                     
                       ∑ 
                       
                         i 
                         = 
                         1 
                       
                       
                         
                           N 
                           2 
                         
                         - 
                         1 
                       
                     
                       
                     
                       
                         q 
                         j 
                       
                       ( 
                       i 
                       ) 
                     
                   
                 
               
               
                 
                   ( 
                   10 
                   ) 
                 
               
             
           
         
       
     
       FIG.  11 C  shows frame-wise sum for each frame. In  FIG.  11 C , values of the frame-wise sum f(j) (j=1,2,3, . . . ) are plotted, where a horizontal axis is a time axis (i.e., index j=1,2,3, . . . ) and a vertical axis is the value of the frame-wise sum: f(j).  FIG.  11 C  is a plot of the following vector (frame-wise sum vector), 
         F =( f (1), f (2), f (3), . . . )  (11)
 
     The vehicle estimation part  106  performs amplitude transformation of the vector F to scale in pre-defined range (S 203 ).  FIG.  12 A  shows a result of amplitude transformation of the frame-wise sum vector shown in  FIG.  11 C . In the example of  FIG.  12 A , the vector F in  FIG.  11 C  is transformed to a vector F_scaled of a range between 0 and 100, though not limited thereto. 
       scaled_min=0, 
       scaled_max=100, 
         F _min=min( F ), 
         F _max=max( F ). 
     The amplitude transformation is calculated as: 
         F _scaled=scale* F +scaled_min− F _min*scale  (12)
 
       where 
       scale=(scaled_max−scaled_min)/( V _max− V _min)  (13)
 
     The vehicle estimation part  106  creates a new vector (time-repeated vector) from the vector F_scaled by repeating time value by its magnitude value (S 204 ).  FIG.  12 B  shows an example of the new vector (time-repeated vector), where a vertical axis is a time axis and a horizontal axis is a repetition index. More specifically, the vehicle estimation part  106  repeats time occurrence by its magnitude. The vehicle estimation part  106  repeats x (time value) by y (scaled amplitude) times, i.e., (time value)*(scaled amplitude at the corresponding time). For example, in  FIG.  13 A , at time: 0 (index 0 of F_scaled), scaled amplitude (value of an element 0 of F_scaled) is 2, so time-repeated vector V starts with a time value 0 repeating 2 times, next, at time: 1 (index 1 of F_scaled), scaled amplitude (value of an element 1 of F_scaled) is 10, so repeating a time value 1 by 10 times. After the multiplication for all time value is iterated, we have a new time-repeated vector V as shown in  FIG.  12 B . In  FIG.  12 B , a time axis (horizontal axis) is an index of each element of the time-repeated vector V and a vertical axis is a value of each element of the time-repeated vector V. 
     Assuming that each vehicle is estimated based on a Gaussian Mixture model, transforming the signal to time-repeated feature makes it easy to perform clustering and vehicle detection by Gaussian Mixture Modelling. A vehicle occurrence time in the oscillation signal is not known. To detect the vehicle occurrence time, repeating time value by a scaled amplitude times is adopted, which generates more density at a peak location of the amplitude. This operation results in an expected distribution (such as Gaussian probability distribution) at each vehicle occurrence, as shown in  FIG.  12 C , which is a histogram (time axis histogram) of the time-repeated vector created by the vehicle estimation part  106 . 
     The vehicle estimation part  106  performs clustering based on learning (unsupervised model training) of a mixture of Gaussian probability distributions (S 205 ). The Gaussian mixture model is a probabilistic model that assumes all the data points are generated from a mixture of a finite number of Gaussian probability distributions with unknown parameters. The Gaussian Mixture Model may be learned from train data. Though not limited thereto, in the embodiment, Variational Bayesian Gaussian Mixture model, a variant of the Gaussian mixture model with variational inference algorithms, such as Variational Bayesian DPGMM (Dirichlet Process Gaussian Mixture Model) is used, which is an infinite mixture model with the Dirichlet Process, as a prior distribution on the number of clusters. Regarding Variational Bayesian DPGMM, reference may be made to NPL2 or NPL3.  FIG.  13 A  shows a clustering result of the time repeated vector V using Variational Bayesian DPGMM. In  FIG.  13 A , a horizontal axis is a time axis and a vertical axis is a scaled version of probability density value. 
     The vehicle estimation part  106  counts the number of clusters, each of which has a value of a probability density function greater than a predetermined threshold value (S 206 ), as shown in  FIG.  13 B . The predetermined threshold value is defined to identify a response oscillation of the bridge induced by a vehicle passing on the lane of the bridge. 
     The vehicle detection apparatus  100  may be implemented on a computer system as illustrated in  FIG.  14   . Referring to  FIG.  14   , a computer apparatus  200 , such as a server, includes a processor (Central Processing Unit)  202 , a memory  204  including, for example, a semiconductor memory (for example, Random Access Memory (RAM), Read Only Memory (ROM), Electrically Erasable and Programmable ROM (EEPROM), and/or a storage device including at least one of Hard Disk Drive (HDD), SSD (Solid State Drive), Compact Disc (CD), Digital Versatile Disc (DVD) and so forth, a display apparatus  206  that display the result of detection of the number of a vehicle(s) passing on each lane, and a communication interface  208 . The communication interface  208  (such as a network interface controller (NIC)) may well be configured to communicatively connect to sensor(s) provided under lanes of a bridge. A program  210  including program instructions (program modules) for executing processing of the signal acquisition part  102 , the signal separation part  104 , the vehicle estimation part  106  and the output part  108  of the vehicle detection apparatus  100  shown in  FIG.  2    is(are) stored in a memory  204 . The processor  202  is configured to read the program  210  (program instructions) from the memory  204  to execute the program (program instructions) to realize the function and processing of the vehicle detection apparatus  100 . 
     In the above embodiments, detection of the number of vehicles passing on a single lane of a bridge is described, but the present invention is not limited to the number of vehicles. The present invention can be applied to detection of weight of a vehicle passing on a single lane of a bridge, a load weight of a vehicle, a deterioration/fatigue diagnostic of a bridge, etc. 
     In the above embodiments, accelerometers are used as sensors to detect impulse response (oscillation) of the bridge. However, in the present invention, a sensor is not limited to detection of impulse response (oscillation) of the bridge. That is, the present invention is applicable to an oscillation signal detected by an acoustic sensor such as a piezoelectric transducer, microphone, etc. 
     The following describes a further example embodiment. In this embodiment, the vehicle estimation part  106  is configured to realize vehicle detection in parallel traffic model ( FIG.  18 A ). In this embodiment, without using BSS, the vehicle estimation part  106  can detect presence/absence of vehicle(s) passing on a lane(s) of the bridge 0. In this embodiment, the vehicle detection apparatus  100  includes the signal acquisition part  102 , the vehicle estimation part  106 , and the output part  108 . The signal separation part  104  can be omitted. 
       FIG.  15    is a flow chart illustrating an operation example of the vehicle estimation part  106  in this embodiment. The signal acquisition part  102  acquires oscillation signals (time domain signals) from sensors s1 and s2 (S 301 ). 
     The vehicle estimation part  106  calculates a sum of a normalized frequency spectrum (S 302 ). More specifically, the vehicle estimation part  106  extracts waveform data (frame) using a sliding window of a time interval T (length of one frame) and perform FFT (fast Fourier transform) to the extracted waveform data to obtain a frequency spectrum, which is normalized by dividing each frequency component (amplitude) by a total sum value of frequency components (amplitudes) of the frequency spectrum. 
     The vehicle estimation part  106  obtains sum of normalized frequency vectors from sensors s1 and s2, by using respectively the equation (4) and (5) which define the sum of normalized frequency for each frame (S 303 ). The sum of normalized frequency vector (s1) is constituted by a time series vector including, as elements thereof (where total N elements are assumed), the sums of normalized frequency (each given by the equation (4)) e.g., for frames 1, 2, . . . , N (or time instant 1 to N). The sum of normalized frequency vector from the sensor s2 is constituted by a time series vector including, as elements thereof (where total N elements are assumed), the sums of normalized frequency (each given by the equation (5)), e.g., for frames 1, 2, . . . , N (or time instant 1 to N). 
     Then, the vehicle estimation part  106  obtains s1s2_maximum vector by selecting a maximum amplitude value at each time-instant (each element) from the sum of normalized frequency vector (s1) and the sum of normalized frequency vector (s2). The s1s2_maximum vector has N elements (S 304 ). 
         s 1 s 2_maximum vector=max(sum of normalized frequency vector( s 1),sum of normalized frequency vector( s 2))  (14)
 
     For instance, let&#39;s assume sum of normalized frequency vector (s1)=[sa1, sa2, . . . , saN] where sa1, sa2, . . . , saN are sums of normalized frequency vector (s1) at time-instant 1, 2, . . . N and sum of normalized frequency vector (s2)=[sb1, sb2, . . . , sbN] where sb1, sb2, . . . , sbN are sums of normalized frequency vector (s2) at time-instant 1, 2, . . . N and sa1sb2&gt;sb1, sa2&lt;sa2, . . . and saN&lt;sbN, then 
         s 1 s 2_maximum vector=[ sa 1, sb 2, . . . , sbN ]  (15)
 
     The vehicle estimation part  106  generates a new binary matrix B with the number of rows equal to the number of elements in s1s2_maximum vector (N elements) and the number of columns equal to 2 (corresponding to sums of normalized frequency vectors (s1) and (s2)), where, at each time-instant, i.e., in each row, a value 1 represents element position with the maximum value and 0 otherwise (S 305 ). In the case of the equation (15), the N*2 binary matrix is given as 
     
       
         
           
             
               
                 
                   
                     B 
                     T 
                   
                   = 
                   
                     [ 
                     
                       
                         
                           0 
                         
                         
                           
                             1 
                             ⁢ 
                                
                             … 
                             ⁢ 
                                
                             1 
                           
                         
                       
                       
                         
                           1 
                         
                         
                           
                             0 
                             ⁢ 
                                
                             … 
                             ⁢ 
                                
                             0 
                           
                         
                       
                     
                     ] 
                   
                 
               
               
                 
                   ( 
                   16 
                   ) 
                 
               
             
           
         
       
     
     where a superscript T indicates a transpose of the matrix B. 
     The vehicle estimation part  106  creates a time-repetition vector by repeating a time value by a corresponding magnitude value of the s1s2_maximum vector (S 306 ). Similarly, the vehicle estimation part  106  also repeats the rows in the matrix B by repeating each row corresponding to a magnitude value of the s1s2_maximum vector. 
     Then, the vehicle estimation part  106  applies Gaussian Mixture model-based clustering (S 307 ) and counts the number of clusters (S 308 ), as explained in steps  205  and  206  in  FIG.  10    on the time-repeated vectors, that is, counts the number of estimated Gaussian distributions (the number of vehicles). 
     Assuming, for example, ±3σ value (where σ is a standard deviation) from a mean value of the Gaussian distribution, as start time and end time of a vehicle impulse, the vehicle estimation part  106  obtains start time and end time of each vehicle present in each lane (S 309 ). In order to detect in which lane the vehicle is present, the vehicle estimation part  106  calculates a column-wise mean of sliced number of rows from the binary matrix B, that corresponds to the start and end time of each vehicle. Assuming b ij  is a value (1 or 0) of i-th row and j-th column of the binary matrix B (where j=1 or 2) (S 310 ). 
     
       
         
           
             
               
                 
                   
                     
                       the 
                       ⁢ 
                           
                       column 
                       ⁢ 
                           
                       wise 
                       ⁢ 
                           
                       mean 
                       ⁢ 
                           
                       value 
                       ⁢ 
                           
                       
                         ( 
                         for 
                       
                       ⁢ 
                           
                       jth 
                       ⁢ 
                           
                       column 
                     
                     ) 
                   
                   = 
                   
                     
                       
                         ( 
                       
                       
                         1 
                         
                           end_time 
                           - 
                           start_time 
                         
                       
                       
                         ) 
                       
                     
                     ⁢ 
                     
                       
                         ∑ 
                         
                           i 
                           = 
                           start_time 
                         
                         end_time 
                       
                         
                       
                         
                           b 
                           
                             i 
                             ⁢ 
                             j 
                           
                         
                       
                     
                   
                 
               
               
                 
                   ( 
                   17 
                   ) 
                 
               
             
           
         
       
     
     When the column-wise mean value of the sliced number of rows of the binary matrix B is greater than or equal to a pre-defined threshold (S 311 : “Yes” branch), the vehicle estimation part  106  estimates that the vehicle is detected in that a lane corresponding to the column of the matrix B for which the column-wise mean value is calculated (corresponding to the sensors s1 or s2) of the matrix B (S 312 ). When the column-wise mean value in both the columns of the matrix B is less than the pre-defined threshold (S 311 : “No” branch), the vehicle estimation part  106  estimates that presence of a vehicle is detected in both of the lanes under which the sensors s1 and s2 are arranged (S 313 ). It is noted that the above described embodiments are not limited to two lanes running in parallel on the bridge but can be applied to detection of vehicles passing on three or more lanes on the bridge. 
     Each disclosure of the above-listed PTLs 1-3 and NPLs 1-3 is incorporated herein by reference. Modification and adjustment of each example embodiment and each example are possible within the scope of the overall disclosure (including the claims) of the present invention and based on the basic technical concept of the present invention. Various combinations and selections of various disclosed elements (including each element in each Supplementary Note, each element in each example, each element in each drawing, and the like) are possible within the scope of the claims of the present invention. That is, the present invention naturally includes various variations and modifications that could be made by those skilled in the art according to the overall disclosure including the claims and the technical concept.