Feasibility analysis of a single-sensor-based approach for source identification of hazardous chemical releases☆

Zengqiang Chen *,Lian Ye ,Bo Dai3 ,Fang Wang

1 College of Information Engineering,Beijing Institute of Petrochemical Technology,Beijing 102617,China

2 School of Metallurgical and Ecological Engineering,University of Science and Technology Beijing,Beijing 100083,China

3 Office of Academic Affairs,Beijing Institute of Petrochemical Technology,Beijing 102617,China

ABSTRACT Source identification is critical for emergency responses to hazardous chemical releases,especially sudden releases of toxic gases.The timely arrangement of multiple sensors at the scene of a sudden accident is difficult.To overcome this limitation,a two-step source identification method based on a single sensor was developed.In the first step,the measured concentration was transmitted to the computing platform.First,a preliminary estimation of the release source was calculated from recently detected concentrations.Then,the preliminary result was used to predict the concentrations and to assess whether more measurements were needed.This data processing was conducted by the computing platform.In the second step,a new objective monitoring point was transmitted to the detector for the measurement of additional concentrations.These two steps were conducted repeatedly until the estimation adequately represented the release source.The fixed and mobile single sensor results were analyzed,and a comparison to multi-sensor results was also conducted.The results show that single-sensor source identification is attainable with a sufficient number of observations,and the number of valid concentration observations is required to be no less than the number of unknown parameters.To best estimate the release source,the movement strategy of the single sensor was based on the possible release source and the hazard partition of the gas plume.It is highly recommended that the single-sensor source identification method be used in unexpected incidents due to its flexibility and timely response.

Keywords:Safety analysis Emergency response Inverse problems Optimization Dispersion model

1.Introduction

Hazardous chemical accidents occurring in China and abroad are a significant safety problem for the public and society[1].To minimize casualties and loss,identification of the source of the accidental release is the primary initial task.Thus,efficient and timely identification of the release source of these contaminants plays an important role in emergency planning safety considerations[2].

During emergency responses involving hazardous materials,particularly when toxic gases are released,the contaminant source can be identified based on the concentration observations collected by sensors.There is no difficulty in identification of the release source when there are sufficient observations [3,4].Using the observed concentrations as input values,identification of the location and strength can be estimated with probability modeling methods or optimization modeling methods [5].Probability modeling methods are based on probability theory,such as Bayesian inference [6].Through observations at multiple points,coupled with prior assumptions of the model parameters,the posterior probabilities of the parameters are obtained by Bayesian inference.Following this,Monte Carlo (MC) sampling [7]or Markov Chain Monte Carlo (MCMC)sampling [8]is employed to achieve estimation of parameters.Recently,a Bayesian network based on probability theory was also used to identify the source dynamically[9].Since thousands of iterations are needed during the sampling process,these methods can be time-consuming [8].To solve this problem,an adjoint equation coupled with MCMC sampling was introduced [10-12],which dramatically improved the computational efficiency;hence,this approach has become a popular method for source identification.While considering the optimization modeling approaches,gas dispersion simulation models are coupled tightly with optimization techniques to determine the model input that best represents the observations collected by multiple sensors.These optimization techniques include the least squares method[13],the conjugate gradient method[14],artificial neural networks [15],simulated annealing [16],genetic [17-19]and evolutionary algorithms [20],the Petri net [21],etc.These approaches guarantee the tuning and update of the unknown parameters before an optimal solution is obtained.

Regardless of the approach,the implementation of source identification is based on concentration observations.Ideally,the setup of sensors will lead to the rapid and correct determination of the release point location and strength.Keats,Yee and Lien [22]employed the Bayesian approach to determine source parameters using an array of sensors,while an additional sensor was strategically designed to maximize the information.This informationdriven sensor placement helped reduce uncertain parameter estimations.Further research by Ucinski and Patan[23]added a mobile sensor in the monitoring network.As a result,performance of the monitoring network improved markedly,and the efficiency,accuracy and flexibility of observations increased.Hutchinson,Oh and Chen [24]have investigated the source term estimation methods for atmospheric dispersion events using static or mobile sensors.They concluded that the static sensors have been the dominant method of source term estimation.Good performance can be achieved with plenty of sensors.When there are lack of enough sensors,difficulties arised in source estimation.While the mobile sensors provide several benefits given by their mobility.However,there is limited research in source estimation using mobile sensors.

No matter estimated by static sensors or mobile sensors,the previous research on source identification is mainly based on observations collected by multiple sensors.Although such multipoint observations provide effective information on the contaminant dispersion,it is inconvenient and impractical for accidental releases.Rather,in such cases,contaminants can be detected at the accident site with a mobile sensor,which is advantageous at complex accident scenes.Zhang and Chen [25]use a single sensor to identify the contaminant sources in enclosed spaces.They indicated that identification of contaminant source location and strength based on a single sensor is possible if the sensor is appropriately placed in the downstream location of the contaminant source.Otherwise,multiple sensors are needed.Thus,the placement of the single sensor is very important.

However,publications on the identification of release sources with a single sensor are rare.This paper provides a framework for determining the release point location and strength with single-sensor time-series observations.A two-step source identification method based on data from a single sensor is proposed.Because only one concentration can be detected at a single point in time,all the recently detected concentrations are used to estimate the possible source.Then,the preliminary estimation of the source is used to estimate the concentrations and determine whether more observations are needed and also to guide the single-sensor movement.These two steps are repeated until the estimation acceptably represents the release source.Numerical studies are also conducted to verify the applicability of the source identification approach with synthetic concentrations and to further analyze the influence of the number of measurements and the location of the single sensor.The programming for this work was in MATLAB.

2.Methods

2.1.Single-sensor source identification system

The single-sensor source identification system consists of two parts,the detector and the computing platform(Fig.1).The detection equipment was used to detect the released gas concentration at the scene of the accident.The detected concentration was transmitted to the computing platform for data processing.The data processing was aimed to obtain a preliminary identification source,to assess whether more measurements were needed to determine the precise source,and to identify a new objective monitoring point.Then,the new objective monitoring point was transmitted to the detector.These processes were repeated until a precise source was identified by the single-sensor source identification system.

2.2.Source identification modeling

Identifying the location and strength of the release source from concentration measurements is known as an inverse problem.This inverse source identification was posed as an unconstrained optimization problem with unknown parameters (Q0,x0,y0,z0),where the objective function was constructed by the error between the detected and calculated concentrations as shown in Eq.(1).

Then,the single-sensor source identification was modeled as follows:

where θ is any feasible solution of (Q0,x0,y0,z0),Θ is the solution space that consists of all the feasible solutions,J(θ) is the objective function,Q0is the unknown strength,X0=(x0,y0,z0)is the unknown location,X is the monitoring point with the coordinates of (x,y,z),Ccal(X,t)|θis the calculated concentration at location(x,y,z)at time t when the value for the source is θ,and Cdet(X,t)is the detected concentration at location (x,y,z) at time t.

Fig.1.Single-sensor source identification system.A detector and computing platform are included in this system.Detected concentrations and new monitoring points are transmitted between these components.

The influence of different error functions,including the root mean square error(RMSE),the normalized root mean square error(NRMSE),the correlation function (CORR),and others,has been studied[26,27].However,none of these error functions have been found to be absolutely superior to the others.In this work,the sum of squared errors between the detected and the calculated concentrations was used.For the time-series observations Cdet(X1,t1),Cdet(X2,t2),...,Cdet(Xn,tn),the model was finally expressed as

Therefore,the θ to obtain the minimum of Eq.(3)was the optimal estimation of the release source.

2.3.Implementation of single-sensor source identification

The concentration detected by the detection equipment was transmitted to the computing platform.The measurements were used to obtain a precise release source.Unlike the multiple sensors for concentration observations used in other detection systems,in this system,there was only one concentration observed at each time point by a single sensor.The implementation of singlesensor source identification is shown in Fig.2.

As shown in Fig.2,when a concentration is detected,source identification modeling is conducted by the computing platform.A preliminary estimation of the source is obtained.Then,the result is used to determine whether more measurements are needed.If needed,a new objective monitoring point is determined and transmitted to the mobile detector.The implementation process includes the following steps.

Step 1:Preliminary estimation of the source.First,if a concentration at tkis detected,a time series of concentrations C(X1,t1),C(X2,t2),...,C(Xk,tk) can be used to identify the source.Step 2:Prediction,stopping observations,and sensor movement.With a single sensor,observations are obtained sequentially.Thus,it is vital to determine whether more observations are needed in terms of accuracy and time points.First,the preliminary result (Qk,Xk) from Step 1 is used to predict concentrations,and then these concentrations are compared with the observations to assess the necessity of the (k+1)th observation.If no more observations are needed,the observation is stopped and the optimal estimation is attained;otherwise,the optimization is further processed with incorporation of the observation at tk+1.The preliminary estimation could be used to guide the movement of the mobile single sensor when appropriate (shown in Fig.3).

Fig.2.The implementation process of single-sensor source identification.C(x,t)is the detected concentration at location x at time t.F(C)is the source identification model.(Qi,xi,yi) is the source identification result with the concentration detected at ti.C′ is the predicted concentration.

Fig.3.Detector movement guidance for estimation of the source location.The solid diamond is the current location of the sensor,and the solid circle is the estimated source location based on all the current detected concentrations.The arrow points to the estimated source location.

These two steps were carried out repeatedly until the estimation best represented the actual release source.

Recently,hybrid methods were studied to solve for source identification,such as the genetic algorithm coupled with the Nelder-Mead simplex method [28],the Tikhonov regularization method coupled with 1-step nonlinear partial swarm optimization [29]and particle swarm optimization [30],etc.

In our previous studies,the pattern search method(PS)coupled with a genetic algorithm(GA)was employed for source identification with multiple sensors[5].This hybrid method fully developed the GA’s global search and the PS’s local search performance.In the present study,the main approach has two steps and is based on a single sensor.The objective function,Eq.(3),was optimized via the HGAPS.The hybrid strategy [31]was that after every 50 generations,the PS method was employed to optimize the best GA result,and then the PS result was applied in further GA operations.

3.Results

Numerical studies were conducted to verify the feasibility and advantage of single-sensor source identification.To verify the feasibility of single-sensor source identification,a Gaussian model was employed[32]to model the concentration distribution.When the relative location of the source is(x0,y0,z0),the dispersion model is expressed as

Table 1 Release source identification results based on a single sensor

where (Q0,x0,y0,z0) are the unknown parameters,C(x,y,z,t) is the concentration at the location (x,y,z) at time t,u is the wind speed,and σx,σy,σzare the dispersion coefficients in the x,y,and z directions,respectively.

With a stability degree of D,the dispersion coefficients[26]are

In the calculation process,the dispersion coefficients were updated with the variation of the parameters.In the numerical study,the simulation parameters of the release source were set to Q0=2000 g,x0=50 m,y0=15 m,z0=10 m,u=5m·s-1.

In order to estimate the source successfully based on a single sensor,there must be enough monitoring data to be used in the source identification process.Thus,in the simulations the concentration is collected every 10 seconds.

The source identification modeling needs the concentration measured by a single sensor.This paper used Eq.(4)to generate the concentration field for the source identification.The observation of the single sensor versus time was also simulated by Eq.(4).Considering the error of the actual monitoring data,certain disturbance was added to the calculation data by Eq.(4)so that more close to the real situation.Thus,the calculation process was as follows.

First,when the detector detected the concentration C(X1,t1),a preliminary estimated result was obtained as (2355.48,45.92,23.25,12.31).Then,the obtained result was used to predict the concentration C′(X2,t2) at location X2.The relative error between the predicted concentration C′(X2,t2) and observed concentration C(X2,t2) was 29.75%,which is more than 5%.Thus,the concentration at t2was incorporated to get a more accurate result.These calculations were conducted by the computing platform.

Then,the new objective monitoring point was transmitted to the mobile detector.When the concentration C(X2,t2) is obtained,the C(X1,t1) and C(X2,t2) are incorporated,the estimated result is(2130.86,38.14,16.11,19.81),the relative error is 18.55% (＞5%).Thus,additional concentration measurements are needed.

With repetitions of this process,a relatively accurate result can be obtained when the concentrations C(X1,t1),C(X2,t2),...,C(X4,t4)are used.The results based on the single-sensor time series are shown in Table 1.

By use of the concentrations C(X1,t1),C(X2,t2),...,C(X4,t4),unknown parameters(Q0,x0,y0,z0)were randomly initialized,with each concentration estimate containing information for all four unknown parameters.Then,the genetic operations were conducted to update the population.After every 50 generations,a local search was conducted via the pattern search method.The search process with HGAPS ended after 1000 generations.The optimization process of the strength Q0for location x0,y0,z0is shown in Figs.4 and 5.

Fig.4 shows the variation of the populations in the optimization process.The population variation improved rapidly and the difference between estimates decreased with successive iterations.In a further illustration,Fig.5 shows the variation of the optimal calculated values of the source strength Q0,and the location x0,y0and z0in the optimization process.From the figures,one can see that after 50 generations,the best estimate is close to the true value,which is due to the local search operations.Before a local search was conducted,the mean value varied with the iteration process.However,after 50 generations,the mean value was steady and close to the true value.

Fig.4.Variation of the populations in the optimization process.Q0 is the source strength,and x0,y0 and z0 are the coordinates of the location of the source.(a)-(d) are the variations of the population in each iteration.

Fig.5.Variation of the optimal calculated values of the unknown parameters.Q0 is the source strength,and x0,y0 and z0 are the coordinates of the location of the source.(a)-(d) are the variations of the optimal estimate in the population in each iteration.

Therefore,by analysis of the whole population and the variations of the optimal value,the true value can be closely estimated,which indicates that source identification based on a single sensor can be acceptably applied in accident responses.

Fig.6.Effect of the number of observations on the mean value and standard derivation of estimated source identifications.The red lines show the standard derivation of Q0,x0,y0 and z0.The blue lines show the mean value of Q0,x0,y0 and z0.

4.Discussion

4.1.Sensitivity analysis of the number of observations

Since source identification relies on monitoring data as input information,and the accuracy of the identification results is calibrated by sequential observations,the number of observations therefore plays an important role in the source identification.To analyze the sensitivity of source identification results to the number of concentration observations,200 simulationswereconducted for eachdatagroupsize of n observations.Among the data groups,the mean values and standard derivations varied with n,as shown in Fig.6.

Fig.6 shows a sensitivity analysis of the source identification results with respect to the number of observations.When the number of observations was less than 4,the identification results showed a large error,and the results were not stable,so the standard derivation was large.As the number of observations increased,the mean value of the 200 simulations dramatically improved and the standard deviation decreased.It can be seen in Fig.6 that the source identification estimates approximate the actual values when the number of observations is equal to or greater than the number of estimated parameters.As more observations were collected,there was no significant improvement in the identification results.Therefore,in an emergency response,the number of observations must be at least the number of the unknown parameters.

4.2.Influence of the sensor location

There is only one concentration observed at each time point by the single sensor.The single sensor can be at a fixed location or moved within the incident scene.Thus,for different t,the monitoring point can be the same or varied.Two different settings for contaminant observation,that is,fixed locations and mobile location,are shown in Fig.7.

When the monitoring point was fixed at one position(shown in Fig.7(a)),the time-series concentrations,Cdet(X,ti)(i=1,2,···,n),were at the same position X for each time point.If the monitoring point is not properly selected,the concentration measurement fails.Therefore,the effectiveness of a fixed,single sensor for determination of a gas release location and strength depends on the monitoring location with respect to the release point.In such cases,a better approach is to use a moveable single sensor for mobile monitoring.

Fig.7.Location of the single sensor.(a) Fixed location single sensor.(b) Mobile single sensor.The red star is the release point,and the solid circle is the sensor location.

Fig.8.Hazard partitions of an accidental release.Partition I contains lethal concentrations,partition II contains at least half the lethal concentration,partition III has harmful concentrations and partition IV is a safety area.

With a mobile single sensor,the concentrations are measured in different places at different times,forming the time-series of concentrations Cdet(Xi,ti)(i=1,2,···,n) (shown in Fig.7(b)).When a mobile sensor is used,the sensor must be moved when the concentration is not detected.For the sensor movement path,the monitoring points should be set around the central axis in the downwind direction.The gas plume can be partitioned into four areas[33],including the area with lethal concentrations,the area with at least half the lethal concentration,the area with harmful concentrations and the safe area.As shown in Fig.8,after the accidental release occurs,the concentration near the source is not steady,and there is a significant possibility of substantial errors in source identification based on the measured concentrations.As the hazardous chemical diffuses in the air,the concentrations tend to be stable (as shown in partitions II and III).After greater effects of diffusion and buoyancy in the atmosphere occur,the concentration is decreased to a safe range (as shown in partition IV).To consider the effect of measurements from different partitions on source identification,the concentrations in partition I and in combined partitions II and III were used to identify the release source.The results are shown in Fig.9.

As shown in Fig.9(a),the use of concentrations in partition I results in a large divergence in source identification estimates.However,the use of concentrations in the combined partitions II and III resulted in relatively stable estimates of source identification (shown in Fig.9(b)).Therefore,monitoring points should be set in the areas of partitions II and III to obtain more accurate identification of the release point.

Thus,in this study,based on the influence of the concentrations from different areas on source identification accuracy,the movement strategy for the sensor was as follows.

Step 1:The initial monitoring point was selected randomly.The observed concentration at this point was used to inversely identify the preliminary source location.Step 2:According to the concentration measurements and the calculations in step 1 the monitoring point was moved to the preliminary source location for the next measurements.The hazard partitions were determined.To obtain an accurate result quickly,the sensor was moved to the area of partitions II and III based on the distribution of the current possible release source,as shown in Fig.10.

Fig.9.Source identification results based on concentrations from different hazard partitions.(a) The identification of the source strength Q based on concentrations in partition I.(b) The identification of the source strength Q based on concentrations in partitions II and III.

Step 3:Repeat step 1 and step 2,the accident information is observed with mobile sensor flexibly.

4.3.Influence of sampling frequency

The determination of the sampling frequency is an empirical question.The released pollutants Diffused in the atmosphere and the concentration decreased with time.Therefore,to determine the sampling frequency,there are some aspects to be considered.First is the performance index of the sensor itself.Secondly,there must ensure that adequate monitoring data be collected before the pollutant dissipated.That is,the monitoring data should be collected in a specific time period.The influence of the sampling frequency to the identification results is showed in Fig.11.

As shown in Fig.11,one can see that when the sampling period is less than 30 seconds,the relative error of the results are in an acceptable range.When more than 30,errors increase significantly.That is because the concentration decreased with the dispersion,when the sampling period increases,the effective monitoring data is limited.And when the sampling period is too small,the cost of sampling increased.Therefore,in our simulation,10 s is chosen to be the sampling period.

4.4.Comparison of multi-sensor and single-sensor source identification

Contaminant concentrations of a toxic gas release based on multi-sensor measurements are depicted in Fig.12.

The construction of a multi-sensor array ensures that contaminant information is effectively detected.With a sensor array,concentrations can be observed even with changes in wind direction [2,3].

Fig.10.Movement strategy for the mobile sensor.The solid diamond is the current monitoring point,and the solid circle is the current possible release source.

To identify the release source with multiple sensors,the source identification model can be expressed as:

where N is the number of sensors,T is the number of time points,Ccal(Xi,tj)|θis the calculated concentration at Xiat time tjwhen the parameter value is θ,and Cdet(Xi,tj) is the detected concentration at Xiat time tj.For this method,all the sensors (N) were used for concentration observations,and assessments were made for each sensor as to whether the observation was valid at each time point.From Eq.(6),one can see that when N=1,Eq.(6)is equivalent to Eq.(3).That is to say,when there is only one sensor with valid measurements in a multi-sensor network,the sensor system is effectively reduced to a single sensor for concentration observations.

Comparisons of multi-sensor and single-sensor source identification are discussed below.

(1) Identification mode.With multiple sensors,the total number of sensors (N) was used for concentration observations,and assessments were conducted for each sensor as to whether the observation was valid at each time point.The release source was identified from one time point when there was an adequate number of valid observations.In contrast,with a single sensor,more than one measurement time point was always required to obtain sufficient data for source identification.For single-sensor source identification,only one valid concentration can be detected at one time,and the measurements and calculations are conducted multiple times to obtain a precise result.

Fig.11.Influence of the sampling frequency to the identification results.The solid diamond is the relative error of Q0 with sampling period.The solid triangle is the relative error of x0 with sampling period.The solid cycle is the relative error of y0 with sampling period.The solid square is the relative error of z0 with sampling period.

Fig.12.Placement of multiple sensors.The red star is the release source,and the solid circles are the sensor locations.

(2) Accuracy and efficiency.The results after an adequate number of concentrations were measured for source identification with single and multiple sensors are shown in Fig.13.

The source identification results and parameter errors for single-and multi-sensor systems are shown in Table 2.

According to Fig.13 and Table 2,one can see that the source identification results are very close to the true values for both of the tested models.That is,with sufficient concentration data,both models can accurately identify the release source.

In further analysis,the computational efficiency of the two models was compared.

When there was adequate monitoring data at a single time point,multi-sensor source identification only needed to conduct measurements at one time point.Using a Thinkpad T450 laptop to run the Matlab program,the calculation time was approximately 8.37 s.However,the single-sensor source identification steps had to be conducted multiple times since only one measurement can be taken at one time point.With each new concentration measurement,the calculation was repeated.Using the same laptop,the processing time for single-sensor identification was 25.97 s.Thus,considering computational speed,the multi-sensor source identification system can more quickly determine an accurate source location.

(3) Application in emergency response.Due to the extensive distribution of sensors,the multi-sensor system provided sufficient observations for source identification in a relatively short time when the sensor placement was timely.However,especially in emergencies,it is not practical to install a multi-sensor system for source identification in a timely manner.In contrast,the single-sensor system,and in particular a mobile single sensor,can enter accident scenes with ease,and thus,source information can be timely and effectively detected.Therefore,for unexpected incidents,a mobile single-sensor source identification system is more highly recommended for use in emergency response.

Fig.13.Comparison of results based on single-sensor and multiple-sensor detection systems.The dashed lines and solid lines are the results from single-sensor and multiplesensor systems,respectively.

Table 2 Source identification results and errors for multiple-sensor and single-sensor detection systems

4.5.Limitations and applications

The source identification method presented was developed based on a single sensor.In the simulations,the observed concentrations is calculated with the Eq.(4),while in real application the concentrations should be collected by the sensor.Thus the accuracy of the dispersion model determines the accuracy of the source identification results.In addition,the Gaussian dispersion model is based on the assumption that the pollutants dispersion scenarios is open without obstacle.This assumption excludes the application of the method in situations the dispersion scenarios is closed or some complex scenario with obstacle.Therefore,in the future research,the dispersion model must be studied further.

This work assures that there is only one release source.This assumption excludes the application of the method when there are multiple sources.Thus,the case of multiple sources requires a dedicated research in the future.

5.Conclusions

A two-step source inversion model based on a single sensor was proposed for the identification of release sources.The performance and applicable conditions for the proposed model were carefully analyzed,and then two models,a single-sensor and a multisensor model,were compared.Through the present research,the following conclusions were obtained.

First,the proposed single-sensor model was successfully used to identify the release source.To accurately identify the source,the sampling of concentration was required at least 4(the number of unknown parameters).

Second,source identification was successfully determined with the use of a mobile single sensor with a certain movement strategy,which,combined with the flexibility offered by the mobile sensor,led to the high recommendation of this method for use in emergency response.

Third,the multi-sensor and single-sensor models were nearly equally accurate,but the single-sensor model needed more processing time.

Thus,these results show that the single-sensor method provides greater flexibility and is suitable for more timely use in emergency responses to unexpected accidents.Further,it is highly recommended to use a mobile single sensor,especially for application in emergency response analysis.

Acknowledgements

The authors are grateful to the American Journal Experts for their valuable copyediting of the language usage,spelling,and grammar.