Multiobjective Optimization for Air-Quality Monitoring Network Design

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Industrial & Engineering Chemistry Research

Multi-objective Optimization for Air-quality Monitoring Network Design Min Chen†, Sujing Wang‡,*, and Qiang Xu†,* †

Dan F. Smith Department of Chemical Engineering and ‡Department of Computer Science, Lamar University, Beaumont, TX 77710, USA Abstract For an industrial zone where petrochemical and chemical plants are heavily populated,

the design of an effective air-quality monitoring network (AQMN) is very important for local environmental and industrial sustainability. In this paper, a general methodology with multiobjective and deterministic optimization for AQMN design/redesign is developed. Generally, Gaussian dispersion model is employed to create spatial pollution distributions according to historical meteorological conditions and updated emission source profiles. After that, a multiobjective mixed-integer linear programming (MILP) model is developed to optimally design an AQMN, which allows the relocation of existing monitoring stations and/or the addition of new monitoring stations.

The optimization will maximize the detectable air-quality threshold

violation frequency (AQTVF) for potential pollution events in the studied industrial zone, as well as minimize the total budget cost for the AQMN implementation with considerations of existing monitoring station relocation, new station construction, and land uses with different prices at different locations. The Pareto frontier of AQTVF vs. total budget cost will be also provided for final decision making. The proposed methodology can be used to design a new AQMN from the scratch or to retrofit an existing AQMN to monitor regional air quality more effectively. Multiple case studies are employed to demonstrate its efficacy. Keywords: Multi-objective optimization; air quality monitoring; MILP; network design

1 Environment ACS Paragon Plus


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1. INTRODUCTION

Nowadays, petrochemical and chemical plants are trending to be built close to each other to form the so-called industrial zones. Benefits of such plant aggregations include but are not limit to: (1) it is convenient and economic to built, utilize, and share common infrastructures and utility supplies; (2) it enables cost-effectively exchanging material, energy, and information among different plants; (3) it makes viable and cost-effective to manage local resource and environment.1 BASF Ludwigshafen production base in German, Houston Ship Channel area in the U.S., and Shanghai Chemical Industry Park in China are typical examples of such chemical industrial zones. In spite of numerous benefits, however, heavily populated petrochemical and chemical plants in such an industrial zone will inevitably cause various emission sources concentrated in a restricted area, where the interaction or superimposition of pollutant emissions from different emission sources could induce adverse air-quality problems, such as the violation of National Ambient Air Quality Standards (NAAQS)2. Therefore, the design of an effective airquality monitoring network (AQMN) with multiple monitoring stations to real-time monitor regional air quality is every important for industrial and environmental sustainability in such a chemical industrial zone. It should be noted that chemical industrial zones are usually developing in a dynamic mode. With technology advancement, raw material and product portfolio change, as well as manufacturing capacity variations (e.g., expansion or reduction) for each individual plants in the region, emission profiles of plant emission sources may dynamically change with respect to time. This will cause the spatial distribution of potential air-quality events also changes dynamically, and thus may result in the original designed AQMN incapable of monitoring updated air pollution conditions timely and effectively. Sometimes, as Shindo and co-authors identified, the


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spatial-temporal structure of air pollution field may also change with the variation of the meteorological conditions after several years.3 Thereby, how to retrofit an existing AQMN to effectively and economically monitor local air quality with respect to updated emission profiles is also very important. Studies related to AQMN design/retrofit optimization have been reported. Mofarrah and Husain summarized necessities and objectives of AQMN as (1) planning and implementing air quality protection and air pollution control strategies; (2) ensuring that the air quality standard is achieved; (3) preventing or responding quickly to air quality deterioration; (4) evaluating the exposure population and other potential receptors; and (5) controlling emissions from significantly important sources.4 They also mentioned the minimization of network cost is also an objective of AQMN design. However, designing and redesigning AQMN under various economic constraints is rarely reported. Koda and Seinfeld presented a methodology based on the maximum sensitivity of the collected data to achieve the variations in the emissions of the sources of interest.5 Handscombe and Elson used spatial correlation analysis to design an AQMN in the greater London area.6 Tseng and Chang assessed relocation strategies of urban air quality monitoring stations.7 Silva and Quiroz applied an index of multivariate effectiveness to optimize an atmospheric monitoring network of Santiago - Chile’s capital.8 The research work of Ibarra-Berastegi focused on the prediction of hourly levels for multiple pollutants and built 216 specific models based on different neural networks in the area of Bilbao, Spain.9 Among these AQMN designing and redesigning, the cost criterion was mostly neglected, since the same installation cost for all the possible locations in the study areas was assumed.4 Though Tseng and Chang7 considered budget constraint of limiting the number of monitoring stations, they did not take into account



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the cost difference between constructing a new station and relocating an old station; meanwhile, they did not consider different land-use costs for monitoring stations. In this paper, a general methodology with multi-objective and deterministic optimization for simultaneous AQMN design/redesign has been developed. The two optimization objectives are to maximize the detection of air-quality threshold violation frequency (AQTVF) and minimize the total budget cost as well. It considers the cost associated with relocating old monitoring stations and building brand new monitoring stations, as well as the land price where the station is to be built or relocated. It also considers the spatial distance constraint between two monitoring station sites. In the developed methodology, Gaussian dispersion model is firstly employed to create spatial pollution distributions according to historical meteorological conditions and updated emission source profiles.10-15

Next, a mixed-integer linear programming (MILP) model is

developed to optimally design an AQMN, which allows the relocation of existing monitoring stations and the addition of new monitoring stations. The optimization will maximize the AQTVF detected by AQMN for potential pollution events in the studied industrial zone, as well as minimize the total budget cost for the AQMN implement with considerations of monitor relocation, new monitor construction, and land use at different prices in different locations. The Pareto frontier of AQTVF vs. the total budget cost will be also provided for final decision makings. The proposed methodology can be used to design a new AQMN from the scratch or to retrofit an existing AQMN to monitor regional air quality more effectively. Multiple case studies are employed to demonstrate its efficacy.

2. PROBLEM STATEMENT


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This study is to develop a systematic methodology for optimal design/redesign of AQMN in a chemical industrial zone subject to budget and spatial constraints. For clarity, the problem statement is summarized as below. Assumptions: (1) each emission source has a constant pollutant emission rate during its normal operating condition; (2) the emission transportation follows Gaussian dispersion model and there is no secondary consumption or generation during the pollutant air transportation; and (3) when the emitted pollutant reached ground through dispersion, it will be absorbed, i.e., there is no pollutant reflection from the ground during its transportation. Given information: (1) spatial locations of existing emission sources, existing monitoring stations, and candidate monitoring station areas with given land-use price; (2) current and future emission source data, including normal emission rate and stack parameters such as stack height and stack outlet temperature; (3) the pollutant concentration threshold for air-quality concerns; (4) minimum spatial-distance requirement between any two monitoring stations; and (5) historical meteorological data (e.g., local temperature, wind direction, and wind speed) in the studied region. Information to be determined: (1)

spatial distribution of AQTVF according to historical meteorological conditions and updated emission source data in the studied region;



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(2)

detailed optimal design of an AQMN under a fixed total budget; and

(3)

Pareto frontier of the maximum AQTVF vs. budget cost for decision-making support.

3. General Methodology

In this section, a general methodology framework for AQMN design is firstly introduced. After that, detailed simulation and optimization models will be respectively presented.

3.1 Methodology Framework This developed general methodology framework is shown in Figure 1. It includes five stages of work. Firstly, the historical meteorological data is collected and utilized to identify distribution functions of wind direction, wind speed and ambient temperature. Based on the obtained distribution functions, multiple meteorological scenarios with different wind direction, wind speed and ambient temperature will be sampled in the second stage. In the third stage, according to sampled meteorological scenarios, Monte Carlo simulations based on Ganussian dispersion model will be conducted, where the pollutant spatial distribution for each scenario will be obtained.

To perform Ganussian dispersion model simulation, additional input of

geographical data (e.g., all current emission source locations) and emission source data (e.g., emission rate, stack height and exit diameter, and outlet temperature) are needed. After the pollution distributions of each scenario are obtained, the distribution of potential AQTVF can be calculated in the fourth stage based on the statistics that pollution concentrations exceeds the airquality concern threshold at any spatial locations.


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Figure 1. Methodology framework.

In the final stage, the MILP model for an optimal AQMN design will be developed and solved. The objectives of such an AQMN design are to maximize the total AQTVF meanwhile minimize the total budget cost. In the optimization model, economic data such as costs for existing monitoring station relocation, new monitoring station construction, and land use at different prices in different locations will be considered. Meanwhile, spatial distance constraints that the space between any two monitoring stations must be larger than a designated minimum value should be kept. This is a multi-objective optimization problem. The Pareto frontier of the AQTVF vs. the total budget will be eventually obtained and used to support comprehensive decision makings.

3.2 Pollution Concentration Determination based on Gaussian Dispersion Model When the probability functions of wind direction, wind speed and ambient temperature ( f v (ξ v ) , f d (ξ d ) , and f T (ξ T ) ) are obtained based on historical meteorological data set, Monte Carlo simulations will be performed. It first generates multiple sets of parameters of wind direction ( ξ v ), wind speed ( ξ d ), and ambient temperature ( ξT ) according to their probability functions. Then, each set of parameters will be plugged into the Gaussian dispersion model to calculate a scenario of pollutant concentration distribution in the studied region. For simplicity, the studied region is represented as a mesh gridded area; and the pollutant concentration above each grid will be calculated and grouped together to characterize the pollutant distribution. The detailed calculation procedure is shown in the Appendix.



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Based on Gaussian dispersion model, when Ci , j (ξ v , ξd , ξT ) is obtained, the cumulative pollutant concentration at the j-th grid should be the summation of Ci , j (ξ v , ξd , ξT ) from all the emission sources i ∈ I , which can be expressed by Eq. (1).

C j (ξv , ξd , ξT ) = ∑ Ci , j (ξv , ξd , ξT ) , ∀ j ∈ J

(1)

i∈I

Note that C j (ξv , ξd , ξT ) is also a function of the meteorological scenario (ξ v , ξ d , ξT ) . The summation of each meteorological scenario will generate a cumulative pollutant concentration at any grid. Therefore, according to the threshold value designated for air-quality concern (say, C * ), each C j (ξv , ξd , ξT ) can be evaluated and classified as pollution violation or non-violation. Such that, the AQTVF at the j-th grid, NT j , can be accounted.

3.3 Determination of AQTVF at the j-th Grid According to obtained C j (ξv , ξd , ξT ) , the pseudo code to determine the AQTVF at grid j , denoted as NTj , is shown below. Set NT j = 0 for each grid j ( j ∈ J ) Numerate scenarios of (ξ v , ξ d , ξT ) For each scenario of (ξ v , ξ d , ξT ) , numerate j If C j (ξv , ξd , ξT ) > C * , then NT j = NT j + 1

End If Next Next 3.4 Optimization Design of AQMN


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All the grids in the studied region (see, Figure 2) are candidate sites of air-quality monitoring stations.

Through optimization, the detailed allocation of an AQMN will be

identified to maximize the detection of AQTVF in one hand; and in the other hand to minimize the total budget cost under the consideration of possible relocation of existing monitoring stations, new monitoring stations construction, and their land use costs in different geological locations. In addition, special constraints should be given to any pair of monitoring stations that their spatial distance should not be too close. Thus, this is a multi-objective optimization problem, which is modeled as the following.

Figure 2. Locations of existing chemical plants and land price distribution.

3.4.1 Objective functions As aforementioned, the two objective functions are shown by Eqs. (2) and (3).

  max TNT =  ∑ BR j NT j + ∑ BN j NT j  BR j , BN j j∈J  j∈J 

[ (

)

(

(2)

)]

min TC = ∑ BN j C N + C Lj + BRj C R + C Lj − TCOL

BRj , BN j

j∈J

,

j ∉ BR j

(3)

where BR j and BN j are the binary integer variables. BR j = 1 represents an old monitoring station will be allocated in grid j; otherwise, BR j = 0. Similarly, BN j = 1 represents a new monitoring station will be allocated in grid j; otherwise, BN j = 0. Equation (2) suggests the first objective function is to maximize the number of violation detections via the designed AQMN. Equation (3) means the second objective function is to minimize the total budget costs, where

C N , C Lj , and C R are respectively new station construction cost, land use cost at location j , and



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old station relocation cost. The summation of first item in Eq. (3) are the total costs associated with new monitoring stations; while all the left items in Eq. (3) are the total costs associated with the old monitoring stations. Note that for all old monitoring stations, their previous land costs can be saved after their relocation. Thus, the total budget cost should minus the total land costs of all old monitoring stations (i.e., TCO L ), which should be given before optimization.

3.4.2 Budget constraint The total cost of the AQMN design should be subject to the available budget as shown in Eq. (4):

TC ≤ TC *

(4)

where TC * is the total available budget for the AQMN design.

3.4.3 Monitoring station relocation constraint After the design/redesign of an AQMN, the number of old monitoring stations previously used will not be changed.

∑ BR

j

=k

(5)

j∈J

where k is the number of old monitoring stations already existed in the studied domain. If k = 0 , which means there is no existing monitoring station in the area by far, the optimization problem is equivalent as designing a brand new AQMN.

3.4.4 Spatial distance constraint As constrained by Eq. (6), there should be no more than one monitoring station on each


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grid j, no matter it is a relocated monitoring station or a new constructed station. BR j + BN j ≤ 1 , ∀ j ∈ J

(6)

Meanwhile, for any pair of monitoring stations in the AQMN, their spatial direct distances are required to be larger than some threshold value. Thus, Eq. (7) should be hold.

(x

− x j ' ) + ( y j − y j ' ) ≥ D2 (BRj + BN j + BRj ' + BN j ' − 1) , ∀ j , j , ∈ J U j ≠ j ' 2

j

2

(7)

where D is the minimum threshold distance. Equations (7) ensures only when both two locations of j and j ' are occupied by a monitoring station (i.e. both ( BR j + BN j ) and ( BR j ' + BN j ' ) equal 1), their spatial direct distance can be constrained; otherwise, Eq. (7) will be relaxed. In summary, Eqs. (2) through (7) form the developed AQMN optimization model. It is a mixed-integer linear programming (MILP) model, which can be solved by the MILP solver CPLEX16.

4. CASE STUDY

To demonstrate the efficacy of the developed systematic methodology, a case study of an AQMN design for an industrial zone is employed. In this industrial zone, there are nine emission sources and three existing monitoring stations; meanwhile, different land use costs are given as shown in Figure 2 as the base case. In the case study, the spatial computational resolution is 100 m for both air-quality simulation and AQMN optimization. Also, as mentioned in the assumptions of Problem Statement, the Gaussian dispersion model only works on primary pollutants and does not consider chemical reaction and secondary formation of pollutants. Table 1 shows plume and stack parameters for the nine emission sources. The air-quality concern threshold C * for a pollutant is set as 75 ppb and the minimum threshold distance D between any



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pair of monitoring stations is 500 m. Based on historical meteorological data base, 8,760 scenarios of wind directions, wind speeds and ambient temperatures are sampled as shown in Figure 3, which are used for all the case studies.

Figure 3. Meteorological data distribution of (a) wind speed, (b) wind direction, and (c) ambient temperature for the case study.

Table 1. Plume and Stack Parameters of Emission Sources

Figure 4(a) shows the original 3D AQTVF distribution in the studied industrial zone for the base case, where emission rates of nine emission sources are not updated yet. It can be seen under 8,760 metrological scenarios, the AQTVF distribution in the industrial zone is significantly different. Thus, the air-quality monitoring stations should be supposedly allocated in those high AQTVF spots. Figure 4(b) shows AQTVF contour on the x-y plane and the original AQMN design for base case. The coordinates of (12, 24), (16, 14), and (38, 34) have the largest AQTVF values, which account for the total of 674. Obviously, three existing monitoring stations are placed in those places.

Figure 4. (a) 3D distribution of AQTVF and (b) AQTVF contour and AQMN design for base case.

4.1 Case 1: AQMN Design under A Budget of 25 Units In the following case studies, an optimal AQMN design will be conducted under a given budget. Note that the given budget may possible cover the relocation cost CR for an existing


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monitoring station (25 units) and new construction cost CN for a new monitoring station (50 units), as well as the land use costs CL indicated in Figure 2. Meanwhile, new emission rates of nine sources in Table 1 should be followed for all the following case studies. In Case 1, the total available budget for AQMN design is 25 units. According to the developed methodology, the optimization results are presented in Figure 5. First of all, it shows the updated AQTVF contour based on new emission rates of nine sources under 8,760 metrological scenarios. Secondly, it shows the new AQMN design and locations. Three existing monitoring stations are involved in the new design without adding any new monitoring stations because of the small budget. Two of them are still kept in their current locations compared with the base case, which are monitoring stations in the coordinates of (12, 24) and (16, 14). One existing monitoring station is relocated from (38,34) to a new place at (21, 18) according to the optimization.

It happens that three monitoring stations are still allocated to three highest

AQTVF spots, which accounts for the AQTVF value of 1,608.

Figure 5. Updated AQTVF contour and optimal AQMN design under the budget of 25 units.

It is interesting to know that if the current three monitoring stations do not relocate, which means the total budget is 0, the AQTVF value will be 1,245. It is higher than the base case because new emission rates of nine sources are all increased (see Table 1), so that AQTVF distributions in the studied industrial zone are also increased in every grid correspondingly. However, from the Case 1, the AQTVF value could be further increased by 363 simply due to one monitoring station relocation enabled by 25 units of budget.



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4.2 Case 2: AQMN Design under A Budget of 55 Units Figure 6 shows the layout of a new AQMN under the budget of 55 units. Comparing to Case 1 (see Figure 5), it can be seen that three current monitoring stations are still kept in their locations but a new monitoring station is added at the coordinate of (21, 18). The AQTVF value of Case 2 is 1,921, which is a big increase based on Case 1. Note that the budget of 55 units could simultaneously support relocations of two existing monitoring stations to increase the AQTVF value. However, the optimization answers that the best AQMN design under 55 units of budget is to add a new monitoring station to an appropriate location instead of relocating two existing monitoring stations.

Figure 6. Optimal AQMN design under the budget of 55 units.

4.3 Case 3: AQMN Design under A Budget of 135 units When the available budget is 135 units, the obtained optimal AQMN design solution is shown in Figure 7. In this Case, two existing monitoring stations originally located at (12, 24) and (38, 34) are kept the same location; one existing monitoring station originally located at (16, 14) is moved a little down to (16, 13); meanwhile, two new monitoring stations are add at (17, 18) and (22, 18), respectively. The design in Case 3 can reach the AQTVF value of 2,640.

Figure 7. Optimal AQMN design under the budget of 135 units.


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4.4 Pareto Frontier of the AQMN Design Similar to Cases 1 through 3, when a new budget is given, a new AQMN design will be obtained with an associated AQTVF value and actual cost value. All pairs of AQTVF value and actual cost value can be plotted in Figure 8. Since AQTVF value and cost value are two optimal objective functions, those points (solutions) connected by dot line represents the Pareto frontier of the multi-objective optimization problem. Table 2 summarizes the details of those solutions on the Pareto frontier. Those solutions are supposedly the optimal solution candidates that should be considered when decision makers need to balance between AQTVF value and AQMN design cost. Note that the other solutions below the Pareto frontier are inferior solutions that are not cost effective. Therefore, the proposed methodology can provide technical supports for costeffective decision makings to effective AQMN designs for chemical industrial zones.

Figure 8. Pareto frontier of AQTVF vs. budget amount for new AQMN designs.

Table 2. Summary of Solutions on the Pareto Frontier in Figure 8

5. CONCLUDING REMARKS

This paper developed a general methodology with multi-objective and deterministic optimization for AQMN design/redesign in chemical industrial zones. It contains five stages of work. Generally, Gaussian dispersion model is employed to create spatial pollution distributions according to historical meteorological conditions and updated emission source profiles. After that, a mixed-integer linear programming (MILP) model is developed to optimally design an



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AQMN, which allows the relocation of existing monitoring stations and the addition of new monitoring stations.

The optimization will maximize the AQTVF detected by AQMN for

potential pollution events in the studied industrial zone, as well as minimize the total budget cost for the AQMN implement with considerations of existing monitoring station relocation, new station construction, and land use at different prices in different locations. The Pareto frontier of AQTVF vs. total budget cost will be also provided for cost-effective decision makings on AQMN designs for chemical industrial zones.

AUTHOR INFORMATION Corresponding Author *Tel.: 409-880-7798. Fax: 409-880-2197. E-mail: [email protected]. (S.W.) *Tel.: 409-880-7818. Fax: 409-880-2197. E-mail: [email protected]. (Q.X.)

ACKNOWLEDGEMENTS

This work was supported in part by Lamar University Graduate Student Scholarship and Texas Air Research Center headquartered at Lamar University.

APPENDIX

(1) Meteorological data scenario generation

ξ v ~ f v (ξ v )

(A-1)

ξ d ~ f d (ξ d )

(A-2)

ξT ~ f T (ξT )

(A-3)


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where ξ v , ξ d , ξT represent the generated random variables of wind speed, wind direction, and ambient temperature according to their probability functions of f v (ξ v ) , f d (ξ d ) and f T (ξ T ) , respectively.

(2) Spatial coordinate calculation The direct distance ( d i , j ) between emission source i and grid j can be calculated as:

d i, j =

(x j − xi )2 + (y j − y i )2

(A-4)

where xi , yi and x j , y j are respectively the coordinate values of emission source i and grid j. Next, the azimuth angle ( θ i, j ) from emission source i and grid j is calculated as:

θ i, j

°   y j − yi  ° 180  − 270 arctan     π − x x   j i   y j − yi  180 °   arctan  = 90 ° −  x j − xi  π    180 °  0 ° 

if x j − x i < 0

(A-5)

if x j − x i > 0 if x j − x i = 0，y

j

− yi < 0

if x j − x i = 0，y

j

− yi > 0

When d i , j and θ i, j are calculated, the relative spatial coordinates of Xi,j , Yi,j, and Zi,j (the relative distance along the elevated direction) from source i to grid j can be calculated by Eqs. (A-6) through (A-8).

X i , j (ξ d ) = d i , j cos (θ i , j − ξ d )

(A-6)

Y i , j (ξ d ) = d i , j sin (θ i , j − ξ d )

(A-7)

Z i, j = H i − Z j

(A-8)



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where the wind field direction angle ξ d can be calculated from the wind azimuth angle ( θ A ) based on Eq. (A-9). Figure 9 gives an illustration for the calculation of ξ d , θ A , Xi,j ,and Yi,j..

θ −180 ° ξ d =  A ° θ A +180

if θ A ≥180 °

(A-9)

if θ A 1/2

Multiobjective Optimization for Air-Quality Monitoring Network Design

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