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Detection and Classiﬁcation of Acoustic and Seismic Events using a Semi-Markov Energy Dynamical Model Sze Kim Pang, Geok Lian Oh, Shanguo Lu, Adrian Yap Cheng Lock ∗ Abstract also induce different characteristics of the measured energy level. We will show that the new dynamical model is able In acoustic and seismic remote sensing applications, the to describe these characteristics reasonably. intent is to detect and classify events based on the signal The paper is organised as follows. Section 2 presents received. Very often, the detector is just a simple energy de- the new energy dynamical model. Section 3 describes the tector. In this paper, we will like to explore using the energy Bayesian model for the event detection and classiﬁcation. proﬁle to detect and classify different types of event. The Section 4 develops the inference algorithm based on a parti- event detection and classiﬁcation will be treated jointly and cle ﬁlter. The results for simulation and real data are shown formulated as a Bayesian ﬁltering problem. We will develop in Section 5, followed by conclusions in Section 6. a new semi-Markov dynamical model for the acoustic and seismic energy level. A particle ﬁlter is then designed to ob- 2 Dynamical Model for Energy Proﬁle tain the posterior distribution of the quantities of interest, including the probability of an event, as well as the types of Here, a pair of acoustic and seismic sensor is used to event. We will demonstrate the results using both simulation measure the energy level of an event. Figure 1 and 2 shows as well as real data. an example of the acoustic and seismic energy proﬁle cap- tured. 1 Introduction 20 Event 1 10 Detecting and classifying events is an important appli- cation in many ﬁelds of work. There are applications in 0 Event 1 Acoustic Energy ZA (dB) Acoustic Event Detection (AED) [10], video analysis [13], Event 2 Event 2 t EEG analysis [2], information protection [5], neuron spike −10 Event 2 inference [15] etc. In some applications [11], the detection −20 and classiﬁcation are treated as two separate processes. This can potentially result in less optimal estimation. −30 In this paper, we will look at a remote sensing applica- tion, where a pair of acoustic and seismic sensor are used si- −40 multaneously to collect energy data of events. We will like to detect and classify different events based on the proﬁle −50 1300 1400 1500 1600 1700 1800 1900 2000 2100 2200 2300 of the energy data. One common approach would be to ex- Time (s) tract relevant event timing information, such as the rise time of the event, and feed it into a classiﬁer. Another approach could be to deﬁne a model, and use a Bayesian ﬁltering ap- Figure 1. This is an example of the acoustic A proach [15, 14, 9] to do event detection and classiﬁcation. energy proﬁle Et captured. Here, we will formulate the problem in the Bayesian ﬁl- tering framework. We will develop a new semi-Markov en- ergy dynamical model, based on a neuron spike model [15], The energy proﬁles show that besides the actual events, which can describe the changes in acoustic and seismic en- there are other noise events that can be potentially mistaken ergy level. In this model, the event start time is unknown, as as an actual event. Furthermore, the events may be closely well as the length of the event. Different types of event will spaced. It may not be easy to use heuristic rules to separate ∗ Sze Kim Pang, Geok Lian Oh, Shanguo Lu and Adrian Yap Cheng the two events. Lock are with the Sensors Division of DSO National Laboratories, 20 We will now develop a reasonable dynamical model for A Science Park Drive, Singapore 118230. (emails: {pszekim, ogeoklia, the acoustic energy proﬁle Et . First, the events resemble lshanguo, ychenglo}@dso.org.sg) some impulses with ﬁnite rise time. The rise time may be 1 40 A A Tsamp A 30 Et − Et−1 = − A A (Et−1 − Eb ) + AA It k τd A 20 Event 1 +σP Tsamp ǫA t (3) Seismic Energy ZS(dB) Event 1 t 10 Here, the impulse train It will last a randomn time length Event 2 Event 2 Event 2 of τk . k ∈ {1, 2} here refers to the type of event. For sim- 0 plicity of the model, in this paper, the impulse train time −10 length τk is chosen to be some integer multiples of the ob- servation sampling time Tsamp . In more general case, the −20 impulse train time length is a continuous time variable [3]. The length of the impulse train is a randomn quantity. This −30 can be used to model different classes of event, as well mod- 1300 1400 1500 1600 1700 1800 1900 2000 2100 2200 2300 elling the variation of event length. This results in a semi- Markov model [3, 9], as we will see in the subsequent sec- tion. For the observation model, we use a additive standard Figure 2. This is an example of the seismic A A Gaussian noise νt with standard deviation σZ as follows S energy proﬁle Et captured. A A A A Zt = Et + σZ νt . (4) different for differnt types of event, and it can potentially be We assume that the events are mutually exclusive, i.e. at random. Second, different types of event may give rise to any one time instance, there can only be one type of event different sizes of impulse. Third, the reduction of energy af- happening. Furthermore, we also introduce independent ter an event resembles an exponential decay with some time shot noise into each of the sensors to model more impul- A A constant τd to a baseline level of Eb . Here we assume sive disturbances when no event occurs, i.e. that the exponential decay is affected only by the surround- ing environment where the sensor is located. Hence, if the A A Tsamp A A A A surrounding is full of buildings, then we will expect the de- Et − Et−1 = − (Et−1 − Eb ) + Bt γt + τdA cay time to be longer due to more reverberation. Fourth, A we model the dynamics to have some Gaussian noise un- σP Tsamp ǫA t (5) certainty. A A A model that has been used in literature for modelling where γt is a Bernoulli randomn variables, Bt is the ran- neuron spikes [15] has very similar properties. This is given domn amplitude of the shot noise and PShot is the probabil- by ity of a shot noise. A A Tsamp A A γt A ∼ B(γt |PShot Tsamp ) (6) Et − Et−1 = − A A (Et−1 − Eb ) + AA nt τd A Bt A ∼ U(Bt |bA , bA ) (7) l u A +σP Tsamp ǫA , t (1) where U(·|a, b) is a continuous uniform distribution be- where AA is the amplitude of the impulse, σP is the stan- A tween a and b. A Figure 3 and 4 show an example of the output of the dard deviation of the process noise, ǫt is a standard Gaus- sian variable and Tsamp is the observation sampling time. acoustic energy proﬁle dynamical model for two different Here, for each neuron spike, the event is modelled by nt , types of event. It shows the relationship for the event nt , A which is a Bernoulli random variable with probability of the impulse train It and the energy proﬁle Et . event PEvent , i.e. A similar set dynamic and observation equations can be developed for the seismic sensor, nt ∼ B(nt |PEvent Tsamp ) . (2) S S Tsamp S Et − Et−1 = − S S (Et−1 − Eb ) + AS It k While the above model generally describe the energy τd S proﬁle, it is not able to describe the ﬁnite rise time of events +σP Tsamp ǫS t (8) shown in Figure 1 and 2. However, if we now instead of S Zt = + S Et S S σZ νt (9) using a single impulse nt , but consider the event as a result S S Tsamp S S S S of a series of smaller impulses or a impulse train It , it can Et − Et−1 = − S (Et−1 − Eb ) + Bt γt be better at modelling the energy proﬁle. The new model τd S with ﬁnite rise time can be written as +σP Tsamp ǫS t (10) 2 Figure 5 and 6 plot the generated observations from the 1 dynamical and observation models with empirically ﬁtted Event nt parameters (Table 1) against the actual acoustic and seismic 0.5 energy data. Visually, it shows that there is a reasonable ﬁt 0 between the data and the model. 350 400 450 500 550 600 650 700 750 1 Impulse Train It 0.5 Model Parameter Symbol Value Time interval between measure- Tsamp 0.5s 0 350 400 450 500 550 600 650 700 750 ments S Seismic Decaying Time Con- τd 8.0s A 0 Energy Et stant −20 S Seismic Energy Ambient Level Eb −15.0 dB −40 1 S Seismic Process Noise σP 0.70dB 2 350 400 450 500 550 600 650 700 750 1 Time (s) S Seismic Observation Noise σZ 1.25dB 2 S S Seismic Shot Noise Amplitude bl , bu 5dB to 10dB Range A Figure 3. These ﬁgures show the relation- Acoustic Decaying Time Con- τd 9.6s ships between the event nt , impulse train It stant A A and energy level Et for two closely spaced Acoustic Energy Ambient Level Eb −36dB Event 1. 1 A Acoustic Process Noise σP 0.75dB 2 1 A Acoustic Observation Noise σZ 2dB 2 A A Acoustic Shot Noise Amplitude bl , bu 5dB to 15dB Range 1 Event 1 Parameters Event nt Mean Impulse Train Time τ1 8s 0.5 Seismic Impulse Level AS 1 3.5dB 0 Acoustic Impulse Level AA 1 4.75dB 350 400 450 500 550 600 650 700 750 1 Event 2 Parameters Impulse Train It Mean Impulse Train Time τ2 17s 0.5 Seismic Impulse Level AS 2 0.5dB Acoustic Impulse Level AA 2 0.75dB 0 350 400 450 500 550 600 650 700 750 A 0 Energy Et Table 1. Parameters for the Energy Proﬁle Dy- −20 namical Model −40 350 400 450 500 550 600 650 700 750 Time (s) Figure 4. These ﬁgures show the relation- 3 Bayesian Framework ships between the event nt , impulse train It A and energy level Et for a single Event 2. We now deﬁne a suitable Bayesian framework to do the event detection and classiﬁcation using the seismic and acoustic energy observations introduced in the previous sec- 3.1 Dynamical Model tion. We ﬁrst deﬁned all the state variables. Let nt ∈ {0, 1} S A represents whether there is an event at time t. Et and Et We are now ready to deﬁne the full dynamical model represent the seismic and acoustic energy state respectively. p(St |St−1 ). We choose to expand the model according to Let θt ∈ {0, 1, 2} represents the type of event. Event type Eq. (11). 0 here refers to the ambient condition where no event is happening. Let τt be the randomn length of the current The dynamical model is moderately complex, as it has to event, and Ct be the corresponding time sample at which take into account the semi-Markov nature of each event, as the current event happened. Also, let the joint state be well as dealing with different types of possible events. Now A S St = {nt , Et , Et , θt , Ct , τt }. we give more details on each of the transition models. 3 p(St |St−1 ) A S A S = p(nt , Et , Et , θt , Ct , τt |nt−1 , Et−1 , Et−1 , θt−1 , Ct−1 , τt−1 ) = p(nt |nt−1 , Ct−1 , τt−1 )p(Ct |Ct−1 , τt−1 , nt )p(θt |θt−1 , Ct−1 , τt−1 , nt ) A A S S ×p(τt |τt−1 , Ct−1 , nt , θt )p(Et |Et−1 , θt )p(Et |Et−1 , θt ) (11) 20 40 Event 1 Actual Observations Actual Observations 10 Generated Observations 30 Generated Observations Event 1 0 20 Acoustic Energy ZA (dB) Event 1 Seismic Energy ZS(dB) Event 1 Event 2 Event 2 t t −10 Event 2 10 Event 2 Event 2 Event 2 −20 0 −30 −10 −40 −20 −50 −30 1300 1400 1500 1600 1700 1800 1900 2000 2100 2200 2300 1300 1400 1500 1600 1700 1800 1900 2000 2100 2200 2300 Time (s) Figure 5. This ﬁgure plots the actual acoustic Figure 6. This ﬁgure plots the actual seismic energy and the synthetic energy proﬁle dy- energy and the synthetic energy proﬁle dy- namical model output together. This shows namical model output together. This shows that the energy proﬁle dynamical model is that the energy proﬁle dynamical model is ﬂexible enough to model different types of ﬂexible enough to model different types of events. events. 1. p(nt |nt−1 , Ct−1 , τt−1 ) event occurs, i.e. nt = 1, Ct is set to the current time t. p(nt |nt−1 , Ct−1 , τt−1 ) 3. p(θt |θt−1 , Ct−1 , τt−1 , nt ) 0 if t < Ct−1 + τt−1 ; = B(nt |PEvent Tsamp ) Otherwise. p(θt |θt−1 , Ct−1 , τt−1 , nt ) (12) θt−1 if t < Ct−1 + τt−1 ; = rand(0.5, 0.5) if t ≥ Ct−1 + τt−1 , nt = 1; Here, the current event happened at τt−1 and it lasts 0 if t ≥ Ct−1 + τt−1 , nt = 0. a length of Ct−1 time samples. If the current event is (14) active, i.e. t < Ct−1 +τt−1 , then there is no possibility of a new event happening. Otherwise, at each time If the current event is active, the current type of event step, the probability for a new event is given by the θt remains unchanged from θt−1 . If there is currently Bernoulli process Eq. (2). no event happening, θt is kept at 0. This represents the ambient condition. When a new event occurs, i.e. 2. p(Ct |Ct−1 , τt−1 , nt ) nt = 1, θt is set to the event 1 or 2 with equal proba- p(Ct |Ct−1 , τt−1 , nt ) bility (as indicated by the discrete random distribution rand(0.5, 0.5)). Ct−1 if t < Ct−1 + τt−1 ; = t if t ≥ Ct−1 + τt−1 , nt = 1; 4. p(τt |τt−1 , Ct−1 , nt , θt ) 0 if t ≥ Ct−1 + τt−1 , nt = 0. p(τt |τt−1 , Ct−1 , nt , θt ) (13) τt−1 if t < Ct−1 + τt−1 ; If the current event is active, the time of the current = Ud (·|τθt − τr , τθt + τr ) if t ≥ Ct−1 + τt−1 , nt = 1; 0 if t ≥ Ct−1 + τt−1 , nt = 0. event Ct remains unchanged from Ct−1 . If there is no new event happening, Ct is kept at 0. When a new (15) 4 If the current event is active, the current length of event where Z1:t = [Z1 · · · Zm · · · Zt ] are the observations and τt remains unchanged from τt−1 . If there is no event δ(·) denotes the Dirac delta function. The weight wt,p , of happening, τt is kept at 0. When a new event occurs, the particle p, is updated according to i.e. nt = 1, τt is drawn from a discrete uniform dis- tribution Ud (·|·, ·) between τθt − τr and τθt + τr . τθt p(Zt |St,p )p(St,p |St−1,p ) wt,p = wt−1,p × (20) is the mean value of the length of the event θt . This q(St,p |St−1,p , Zt ) models the random nature of the length of the different type of events. For simplicity of the model, the ran- The choice of the importance density q(St,p |St−1,p , Zt ) is domn length τt will be some discrete multiples of the an important issue in particle ﬁlter design. It can be shown observation time Tsamp . that the optimal importance density (in the sense of mini- A A S S mizing the variance of the importance weights), conditioned 5. p(Et |Et−1 , θt ) and p(Et |Et−1 , θt ) upon St−1,p and Zt is p(St,p |St−1,p , Zt ) [1]. However, the A S The acoustic and seismic energy level Et and Et can optimal importance density is generally not tractable. There be determined from Eq. (3), (5), (8) and (10), condi- are other suboptimal choices. For example, a popular choice tional on the type of event θt . is to use the prior model density p(St,p |St−1,p ). When sub- stituted into Eq. (20), we obtain 3.2 Observation Model wt,p = wt−1,p × p(Zt |St,p ) (21) The observation models will be based on Eq. (4) and A S (9). Let Zt = {Zt , Zt }. We will assume that conditional The simple and general algorithm above forms the basis of on the state St the observation of the acoustic and seismic most particle ﬁlters. However, it will result in the variance sensors are independent, i.e. of the importance weights increasing over time [1]. This will adversely affect the accuracy and lead to the degen- eracy problem where, after a certain number of recursive A A S S p(Zt |St ) = p(Zt |Et )p(Zt |Et ) (16) steps, all but one particle will have negligible normalized weights. This will result in a large computational effort de- voted to updating particles whose contribution to the ap- 4 Inference Algorithm proximation of p(St |Z1:t ) is almost zero. A practical mea- sure of the degeneracy of the particle weights is the effective Assuming a Markovian state transition, the standard state sample size Nef f introduced in [7]: update and prediction equations are given by −1 p(Zt |St )p(St |Z1:t−1 ) Np p(St |Z1:t ) = (17) Nef f = wt,p 2 (22) p(Zt |Z1:t−1 ) p=1 p(St |Z1:t−1 ) = p(St |St−1 )p(St−1 |Z1:t−1 ) dSt−1 (18) It is easy to see that 1 ≤ Nef f ≤ Np . A small Nef f indi- cates a degeneracy problem. When this occurs (for example with Z1:t = [Z1 · · · Zm · · · Zt ]. when Nef f drops below some threshold Nthr ), a step called resampling [4] has to be performed. Resampling eliminates 4.1 Particle Filter sample with low weights and multiplies samples with high importance weights. This involves mapping a random mea- The ﬁltering distribution of the dynamical and observa- Np 1 Np sure {St,p , wt,p }p=1 into a random measure {St,p , Np }p=1 tion probability model above is complex and non-linear. with uniform weights. Sequential Monte Carlo methods such as particle ﬁlters There are several methods available when implementing [12] can be used to do the inference. A particle ﬁl- the remapping step. The ﬁrst introduction of resampling ter represents the required posterior density function by [4] uses random sampling of the particles based on their a set of random samples (or particles) with associated Np weights. However, a complete random selection is not nec- weights {St,p , wt,p }p=1 . These particles are then propa- essary and it increases the Monte Carlo variation of the par- gated through time to give predictions of the posterior dis- ticles. Other methods such as stratiﬁed sampling [6] and tribution function at future time steps. As the number of residual sampling [8] may be applied. Systematic resam- samples tends to inﬁnity, this Monte Carlo characterization pling [6] is another efﬁcient method. It is simple to im- becomes an equivalent representation to the functional de- plement, it has order Np computational complexity and it scription of the posterior density function. The posterior minimizes the Monte Carlo variation. ﬁltered density at time t is approximated by In this paper, we make use of a particle ﬁlter to perform Np the inference. We use the prior p(St |St−1 ) as the impor- p(St |Z1:t ) ≈ wt,p δ(St − St,p ) (19) tance function. For the resampling step, we use the system- p=1 atic resampling method. 5 4.2 State Regeneration Parameter Symbol Value Number of Particles NP 2000 In the particle ﬁlter above, the simulation of the current Probability of an Event PEvent 0.0025 event time length τt is not efﬁcient. This is due to the fact Probability of a Shot Noise PShot 0.05 that the end of the current event Ct +τt is typically well into Effective Sample Size Thresh- Nthr 1800 the future. In the particle ﬁlter, once τCt is sampled at the old start of the event at time Ct , the state is never regenerated Single sided range for event τr 4 and the particles can attain low weights at some point in length the future. The use of resampling also serve to deplete the posterior representation of the particles. This can be address by regenerating the values τCt :t . Table 2. Parameters for the Event Detection We will adopt the same approach as described in Godsill and Classiﬁcation Algorithm and Vermaak [3]. We will regenerate the values τCt :t only if does not affect any of the current or previous likelihood computation. After resampling, for each particle, we will 1 regenerate the values τCt :t if t < Ct + τθt − τr . This is Event nt given by 0.5 0 0 200 400 600 800 1000 Time (s) A S p(τCt :t |n0:t , E0:t , E0:t , θ0:t , C0:t , τ0:(Ct −1) , Z1:t ) Impulse Train It 1 A S = p(τCt :t |n0:t , E0:t , E0:t , θ0:t , C0:t , τ0:(Ct −1) ) 0.5 (if t < Ct + τθt − τr ) 0 0 200 400 600 800 1000 t Time (s) = p(τt′ |τt′ −1 , Ct′ −1 , nt′ , θt′ ) 2 Event Type θt t′ =C t 1 t 0 = Ud (τCt |τθCt − τr , τθCt + τr ) δ(τt′ − τCt ) 0 200 400 600 800 1000 Time (s) t′ =C t +1 (23) 5 Results Figure 7. This is the ground truth for Simula- tion Scenario 1. In this section, we will demonstrate the joint detection and classiﬁcation results of the models described above. 40 5.1 Simulation Scenario 1 20 Seismic ZS t 0 In this scenario, we will use the dynamical model to gen- erate a set of observations. Figure 7 shows the ground truth −20 of the events. There are 8 events, with 4 of them closely 100 200 300 400 500 600 700 800 900 1000 Time (s) spaced between 750s and 820s. Figure 8 shows the syn- 20 thetic seismic and acoustic observations generated using dy- namical model described in Section 2, and the parameters in 0 Acoustic ZA t Table 1. −20 Figure 9 shows the results of the detection and classiﬁ- cation using the particle ﬁlter described in Section 4, with −40 parameters in Table 2. The event probability shows that all 100 200 300 400 500 600 700 800 900 1000 Time (s) the 8 events are detected, even with the 4 targets closely spaced between 750s and 820s. The classiﬁcation also ac- curately recognised all the 8 events. Figure 8. This is the set of synthetic seis- 5.2 Real Data Set 1 mic and acoustic observations for Simulation Scenario 1. Here we will use the same method to analyse a set of real data. In this set of data, there are a total of 16 events. This can be seen in the manually-tagged ground truth in Figure 6 1 40 Event Probability 0.8 20 Seismic ZS t 0.6 0.4 0 0.2 −20 0 100 200 300 400 500 600 700 800 900 1000 500 1000 1500 2000 2500 3000 Time (s) Time (s) Classification Probabilities 1 20 0.8 0 Acoustic ZA t 0.6 0.4 −20 0.2 −40 0 100 200 300 400 500 600 700 800 900 1000 500 1000 1500 2000 2500 3000 Time (s) Time (s) Figure 9. These ﬁgures show the Event Prob- Figure 11. This is the set of seismic and ability and Classiﬁcation Probabilities (Blue acoustic observations for Real Data Set 1. for Ambient, Red for Event 1 and Green for Event 2). 1 Event Probability 0.8 0.6 10. Figure 11 shows the actual observations by the seismic 0.4 and acoustic sensors. 0.2 Figure 12 shows the result of the detection and classiﬁ- 0 cation. Almost all the events are detected at probability of 500 1000 1500 2000 2500 3000 Time (s) 0.8 and above. The classiﬁcation of events are all correct, Classification Probabilities 1 except for an unusual deviation of Event type 1 at around 0.8 2750s. 0.6 0.4 1 0.2 Event nt 0.5 0 500 1000 1500 2000 2500 3000 Time (s) 0 0 500 1000 1500 2000 2500 3000 Time (s) Impulse Train It 1 0.5 Figure 12. These ﬁgures show the Event Probability and Classiﬁcation Probabilities 0 0 500 1000 1500 Time (s) 2000 2500 3000 (Blue for Ambient, Red for Event 1 and Green 2 for Event 2). Event Type θt 1 0 0 500 1000 1500 2000 2500 3000 also developed a complete Bayesian model for the joint Time (s) event detection and classiﬁcation. This is based on a ﬂexi- ble semi-Markov model formulation, which generalises the sojourn time of typical Markov models. We have also de- Figure 10. This is the ground truth for Real signed a particle ﬁlter to do the inference. Both the synthetic Data Set 1. and real data results show good detection and classiﬁcation performances. Further work includes looking at other type of events that can be modelled by the same type of dynami- cal model. 6 Concluding Remarks References In this paper, we have developed a new Energy Dynami- cal Model that can be used to model different types of event [1] Arnaud Doucet, Simon J. Godsill, and C. An- observed by a pair of acoustic and seismic sensor. We have drieu, On Sequential Monte Carlo Sampling Methods 7 for Bayesian Filtering, Statistics and Computing 10 [13] Nicolas Thome, Serge Miguet, and Sbastien Ambel- (2000), 197–208. louis, A Real-Time, Multiview Fall Detection Sys- tem: A LHMM-Based Approach, IEEE Transactions [2] Themis P. Exarchos, Alexandros T. Tzallas, Dim- on Circuits and Systems for Video Technology (2008), itrios I. Fotiadis, Spiros Konitsiotis, and Sotirios 1522–1532. Giannopoulos, EEG Transient Event Detection and Classiﬁcation Using Association Rules, IEEE Trans- [14] O. Urfaloglu, Ercan E. Kuruoglu, and A. 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