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Optimizing stations location for urban noise continuous intelligent monitoring
Applied Acoustics 127 (2017) 250–259
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Applied Acoustics journal homepage: www.elsevier.com/locate/apacoust
Optimizing stations location for urban noise continuous intelligent monitoring Baoxiang Huang, Zhenkuan Pan ⇑, Huan Yang, Guojia Hou, Weibo Wei College of Computer Science and Technology, Postdoctoral Stations of System Science, Qingdao University, No. 308 Ningxia Road, 266071 Qingdao, China
a r t i c l e
i n f o
Article history: Received 15 August 2016 Received in revised form 12 June 2017 Accepted 12 June 2017
Keywords: Noise monitoring station PSO K-means IPKM algorithm
a b s t r a c t In most of urban noise monitoring systems, the optimization of number and locations of autonomous monitoring stations is a Non-deterministic Polynomial Complete (NPC) problem. It is also important for the implementation of intelligent measurement networks. This paper investigates an optimization method to achieve minimum stations for urban noise intelligent monitoring. First a mathematical model for monitoring stations selection has been developed. Next, a novel hybrid Immune PSO K-means (IPKM) clustering algorithm is proposed to solve the mathematical model. The IPKM algorithm can overcome the shortcomings (e.g. slow convergence speed) of the Particle Swarm Optimization (PSO) algorithm, and help K-means clustering algorithm escaping from local optima. Finally, the methodology has been applied to QingDao urban noise intelligent monitoring networks. For comparison, the K-means algorithm and IPKM algorithm are applied to the noise grid survey datasets of 1998–2014 years. The final optimized results illustrate the proposed method could perform relevant monitoring tasks with fewer monitoring stations. In addition, the importance of the proposed method is that it would be applicable for noise monitoring and noise control management problems. Ó 2017 Elsevier Ltd. All rights reserved.
1. Introduction Noise is among the most pervasive pollutants today [1,2]. According to statistical data, resident petition to reduce noise pollution is more common than those for air pollution [3]. The monitoring of noise effect is crucial to evaluate noise reduction measures for existing noise sources [4,5]. Measured data that comes from the noise monitoring system is useful for noise analysis and reduction [6,7]. In China, the environmental monitoring institutions should implement general noise grid survey at least once a year [8]. However, noise monitoring is manual monitoring which is arduous. Moreover, it is carried out only once in ten minutes every year. This kind of ‘‘short time measurements” cannot meet the new requirements and constraints of environmental noise management issues in complex urban context [9]. Longterm environmental monitoring [10] of noise levels can be done using autonomous measurement networks [11] as shown in Fig. 1. Intelligent measurement makes possible the advanced analysis of acoustic environment. Compared with manual monitoring, the noise automatic monitoring can really reflect the urban noise environment quality. Due to the high purchase of noise monitoring
⇑ Corresponding author. E-mail addresses: [email protected] (B. Huang), [email protected] (Z. Pan). http://dx.doi.org/10.1016/j.apacoust.2017.06.009 0003-682X/Ó 2017 Elsevier Ltd. All rights reserved.
device, the station number in intelligent measurement is severely limited [12]. At present, urban automatic noise monitoring system is being at the start stage in China. Then it is essential to identify how many measuring localization points are really required. At the same time, it is vital to find most appropriate locations for measurement stations to obtain adequate measurement results. Based on the historical noise grid survey datasets, the upper problem can be interpreted as classification of measured data of the grid points. It is ascribed to Non-deterministic Polynomial Complete (NPC) problem that can be solved by clustering techniques [13]. K-means clustering algorithm is a widely adopted clustering technique, and aims to divide n data points into K non-overlapping clusters, in which each point pertain to the cluster with high degree of similarity [14–16]. However, the K-means algorithm has two defects related to initial value. One is the number of clusters K that is needed to be initialized, and the other is the initial random seed points [13,17]. It is a good candidate for extension to work with evolutionary algorithm. The Particle Swarm Optimization (PSO) algorithm belongs to the modern evolutionary algorithms, and has high convergence speed for initial stage of a global search [18,19]. Unfortunately, search speed reduces obviously around global optimum because of degeneration [20]. In order to slowdown the degeneration of PSO, immune technology can be introduced into PSO algorithm to construct an Immune
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Fig. 1. Noise monitoring networks.
Technology PSO (ITPSO) algorithm [21]. At the same time, K-means algorithm can achieve faster convergence to optimum solution [22]. However, little research has been focused on optimizing urban noise monitoring stations with hybrid algorithm combining K-means and ITPSO algorithm. The purpose of this paper is to propose an optimizing method for urban noise intelligent monitoring stations with noise grid survey datasets. The organization of this paper is as follows: Section 2 analyzes optimization problem of noise monitoring station thoroughly, describes the relevant definitions, builds the mathematical model of optimization problem, and designs algorithm for proposed model. In Section 3, the methodology is applied to an illustrative case. The results are discussed in Section 4. Section 5 is the conclusion of the paper.
2. Methodology for optimizing the noise monitoring stations 2.1. Research program This study aims to identify the proper choice of intelligent measurement stations based on noise grid survey datasets. Traditional noise grid survey monitoring is relative subjective and random. For large monitoring area, if two grid survey points have the same value of noise indicators, it means that these two points have similar acoustic environmental features. Therefore, the number of monitoring stations can be reduced. The determination of the number and position of intelligent measurement nodes needs theoretical guidance, which includes mathematical model and quantitative analysis. Moreover, the method must guarantee monitoring the noise environmental features with the fewest number of monitoring stations. Also, the monitoring results should be consistent with the noise grid survey results. The overall research program is illustrated in Fig. 2. (1) Determine research scenario. According to the change of noise sources when historical monitoring data was taken, the research scenarios are divided into two types. It is note that noise grid survey for influenced area must be implemented if there are major changes. (2) Realize optimization process. Carry out noise grid survey data preprocessing combining with noise control zones, establish optimization model, and design algorithm for proposed model.
(3) Finally, output the optimization results and carry out spatial-temporal analysis. 2.2. Mathematical model The purpose of mathematical model is to minimize the number of monitoring stations with historical grid monitoring data. Assuming that there are n noise survey points fL1 ; L2 ; . . . ; Ln g, each grid monitoring point Li is a m-dimensional vector Li ¼ fLi1 ; Li2 ; . . . ; Lim g, every element Lik represents a specific noise indicator, such as LAeq . Furthermore, the grid survey points are located in corresponding noise control zone. Lki can be defined as the ith noise survey point of control zone k, where k ¼ 0; 1; . . . ; l. In the same way, each point is a m-dimensional vector Lki ¼ fLki1 ; Lki2 ; . . . ; Lkim g, i ¼ 0; 1; . . . ; nk , nk is the noise survey point number of acoustic control zone k. The total number of noise surP vey point is lk¼0 nk ¼ n. Consequently, the optimization results of stations can be achieved by partition n noise grid points into a minimum of clusters. Furthermore, in each cluster the noise indicators values of grid point have a high degree similarity, and are very dissimilar to data in other clusters. In order to describe the mathematical modeling of optimization problem, variables uj , ujopt , rj , rjopt , ukj , ukjopt , rkj , rkjopt are adopted. uj and ujopt are the jth comprehensive evaluation indicator average value of monitoring points before and after optimization, computational formula is Eq. (1). rj and rjopt are the jth noise indicator standard deviation of monitoring stations before and after optimization, computational formula is Eq. (2). ukj and ukjopt are the jth noise indicator average value of acoustic control zone class k before and after optimization, computational formula is Eq. (3). rkj , rkjopt are the jth noise indicator standard deviation of control zone class k before and after optimization, computational formula is Eq. (4). nk l X X uj ¼ Lkij
,
n; ujopt
k¼1 i¼1
rj
nk l X X ¼ Lkij xki
,
k¼1 i¼1
nk l X X xki
ð1Þ
k¼1 i¼1
vffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi ,ffi u l nk uX X k 2 n; ¼t ðLij uj Þ k¼1 i¼1
rjopt
vffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi , u l nk nk l X uX X X 2 ¼t xki ðLkij uj Þ xki k¼1 i¼1
k¼1 i¼1
ð2Þ
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Fig. 2. Overall research program.
nk X ukj ¼ Lkij
, nk ; ukjopt
i¼1
rkj
nk X ¼ Lkij xki
,
i¼1
nk X xki
ð3Þ
i¼1
vffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi , u nk uX k nk ; ¼t Lij ukj
2.3. Main idea for solving the mathematical model
i¼1
rkjopt
vffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi , n u nk k X uX 2 t k k ¼ xi ðLij ukjopt Þ xki i¼1
ð4Þ
i¼1
Providing that average value and standard deviation don’t have obvious difference, the optimal goal is to use the least amount of stations to replace traditional grid survey. Then the optimization problem is modeled as Eq. (5).
min
On the other hand, xki ¼ 0 indicates that the ith noise survey point in control zone k is abandoned.
nk l X X xki k¼0 i¼1
8 jujopt uj j 6 1dB > > > > jrjopt rj j > 6 0:05 > > rj > > > > > jukjopt ukj j 6 1dB > > > > > jrkjopt rkj j 6 0:05 > > rkj > > < nu nv X X s:t: xki ðuÞ 6 xki ðv Þ; nu 6 nv ðu; v 2 f0; 1; . . . ; lg; u–v Þ > > > i¼1 i¼1 > > > > nk > X > > >1 6 xki 6 nk > > > > i¼1 > > > k > > > xi 2 f0; 1g : i ¼ 0; 1; . . . ; n; j ¼ 0; 1; . . . ; m; k ¼ 0; 1; . . . ; l
ð5Þ
P nk k where 1 6 i¼1 xi 6 nk constraints the number of monitoring stations in different acoustic zones. xki 2 f0; 1g limits the value is 0 or 1, if xki ¼ 1, the ith noise survey points in control zone k is selected.
The level of urban environmental noise is under the influence of various elements, including the frequency of noise source, complexity of propagation path, especially random factors [23,24]. So the measurement result is uncertain about the value of the membership function, thus urban environmental noise survey datasets can be assumed as fuzzy sets. For fuzzy sets partitioning problem, the K-means clustering algorithm is commonly employed with high convergence speed [25,26]. Here n noise survey grid points Li fall into K compact clusters, and each point Li is an m-dimensional vector Li ¼ fLi1 ; Li2 ; . . . ; Lim g. The partition process can be carried out in an easy and simple way. First it starts with an initial K partitions to obtain clustering centers ðc1 ; c2 ; . . . ; cK Þ. Next calculate the Euclidian metric distance between each noise grid point Li and kth centers. Assign Li to its nearest cluster centroid ck. Finally calcuP P late the sum of objective function of ¼ ni¼1 Kk¼1 min dðLi ; ck Þ2 . The K-means algorithm can achieve optimization results with small number of iterations. However, it severely depends on the initialization of the centers. The reason is its winner takes all partitioning strategy, the centers also tend to convergence to local optima. In order to conquer this disadvantage, K-means algorithm is extended with Immune Technology Particle Swarm Optimization (ITPSO). PSO is a population based stochastic optimization technique [27,28]. The swarm is composed of particles. Each particle is individual and on behalf of a noise grid survey point. In order to optimize the initial clustering centers for different noise control zones, clustering centers ðc1 ; c2 ; . . . ; cK Þ are selected as the particles in PSO. Each ci is the ith clustering center and is represented by a m-dimensional real-valued vector Lki ¼ fLki1 ; Lki2 ; . . . ; Lkim g, as shown
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in Fig. 3. Here assumed that a set of Nsarm particles forms a populaT tion as ½^c1 ; ^c2 ; . . . ; ^cN . In search space, that is noise control zones, particles cooperate to seek the best position based on movement and intelligence of swarms. Each particle moves in the light of good positions and velocity, and the velocity should be adjusted with historical behaviors of the particle itself and its neighbors. At each iteration, searching procedure can be implemented by Eq. (6).
V i ðt þ 1Þ ¼ x V i ðtÞ þ c1 rand1 ðPbesti Li ðtÞÞ þc2 rand2 ðGbest Li ðtÞÞ Li ðt þ 1Þ ¼ Li ðtÞ þ V i ðt þ 1Þ Li ðtÞ ¼ ½Li;1 ðtÞ; Li;2 ðtÞ; . . . ; Li;k ðtÞ1m
ð6Þ
Pbesti ¼ ½pbesti;1 ðtÞ; pbesti;2 ðtÞ; . . . ; pbesti;k ðtÞ1m Gbest ¼ ½gbest1 ðtÞ; gbest2 ðtÞ; . . . ; gbest k ðtÞ1m xmin x ¼ xmax xmaxtmax t
where t and t max are iteration number and maximum iteration number, respectively. Nkswarm is the particle number in kth noise control zone. m is the number of monitoring noise indicators. rand1 and rand2 are random numbers between 0 and 1. Pbesti is the best previous position recorded by the particle i. Gbest is the global optimal particle among the corresponding noise control zone. Constants c1and c2 are the learning factors in terms of acceleration, which pull each particle towards Pbesti and Gbest positions. The exploration property of the algorithm is controlled by inertia weight x; xmax is the maximum inertia weight and xmin is the minimum inertia weight. There is no overlapping and mutation calculation in PSO algorithm. As above mentioned, every particle determines its flight based on itself and its neighbors’ flying experience. It easily leads to lower accuracy in terms of the speed and direction regulation, and causes swarm degeneration during evolutionary process [29]. Immune technology is incorporated in PSO algorithm with crossover and mutation operators to properly curing the swarms. Consequently, the swarms can achieve non-dominated set of solutions. The antibodies operators extend the searching capacity and improve its adaptive nature. If new non-dominated solution is reproduced by performing crossover, mutation, immune selection and vaccination, then replace the inferior particles with immune memory particle in memory Cell. Memory Cell can be adopted for clonal selection with
mutation. On the other hand, some non-dominated solutions will be flushed when memory Cell is full. In next section, the details of optimized algorithm will be described. 2.4. Proposed IPKM algorithm As mentioned in Section 2.3, K-means clustering algorithm is efficient to handle optimization problems of urban noise stations. Combining with ITPSO, hybrid Immune PSO K-means (IPKM) clustering algorithm is designed. The IPKM can maintain the advantages of immune technology, PSO, and K-means. More specially, the hybrid algorithm has merits of non-independent on initialization, high convergence speed, and global optimization. The K-means algorithm is initialized as optimized results of ITPSO to improve simulation results. Fig. 4 illustrates the flowchart of the hybrid IPKM algorithm. Fitness function is the only criteria for particle search guidance of ITPSO algorithm. The objective function is partition basis of K-means clustering algorithm. To realize the integration of K-means and ITPSO, according to objective function of K-means, the fitness function of ITPSO is designed as Eq. (7).
Fitness ¼ 1=1 þ
n X K X
min dðLi ; ck Þ2
ð7Þ
i¼1 k¼1
At the tmaxth iteration, the best individual pbesti(tmax) of the ith particle can be achieved by solving maximization problem of Fit^i ðtÞÞ for t 6 t max ness, guaranteeing Fitnessðpbest i ðtmax ÞÞ P Fitnessðp iteration. Moreover, the global best gbest(n) can be obtained with Fitnessðgbest i ðt max ÞÞ P Fitnessðpbest i ðtmax ÞÞ, for i ¼ 1; 2; . . . N. Optimizing noise monitoring stations based on IPKM algorithm can be implemented in following steps. Step 1: Optimize the parameters with ITPSO. (1) Fix the number of clusters K, choose the number of particles Nsarm, fix the PSO parameters like learning factors (c1, c2), inertia weight (wmax,wmin), and the number of iterations tmax. (2) Copy the individuals (antibodies) to initialize swarms and memory Cell, assign position and velocity to each particle. (3) Set the iteration count t ¼ 1, start the iterative procedure.
Fig. 3. The representation of a particle.
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Fig. 4. Flowchart of hybrid algorithm IPKM.
(4) Calculate the fitness value with Eq.(7) for each particle, if pi ðf ðpi Þ < f ðgÞÞ, update the swarm’s best position: g so far. (5) Deliver dominate swarm to immune system for antibodies renewal, let non-dominate swarm fly for generation. (6) Select minimum distance as antigen according to Euclidian distance; select matching antibodies to share information by performing crossover and mutation in mating pool. Replace the previous antibodies. (7) Determine the global best gbesti and the individual best pbesti for each particle. Update the position and the velocity of each particle. (8) Check the termination criteria. If the current iteration number reaches tmax, the best particle labeled as ðcb1 ; cb2 ; . . . ; cbK Þ, stop iteration, go to next step; else perform crossover, mutation, immune selection and vaccination, reproduce new particle swarm. (9) Update t ¼ t þ 1 and loop to step 4). Step 2: K-means clustering for noise monitoring stations using optimized clustering centers. (1) Initialize the clustering centers c0 ¼ ðcb1 ; cb2 ; . . . ; cbK Þ as the best particles in Step1. Fix the iteration limit tkmax and the termination threshold e > 0. (2) Assign the iterative count t ¼ 1. Start iterative procedure. ðtÞ
(3) Calculate the distance measure by Eq. (8), dki , between kth cluster center and ith data set . ðtÞ dki
¼ kLi
ðtÞ ck k
vffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi uX u m ðtÞ 2 ¼ t ðLij ckj Þ
ð8Þ
j¼1
(4) Partition each noise grid survey data object Li to its nearest cluster centroid ck . (5) Recalculate and update the centroid average of noise survey grid point in the cluster according to Eq. (9). Where nk is number of noise indicator data items belonging to kth cluster.
P ðtÞ
ck ¼
Li 2k Li
(6) Calculate Pn PK i¼1
ð9Þ
nk the
value
of
objective
function
2 k¼1 min dðLi ; c k Þ , if the value has converged and
mathematical model is satisfied, output the final cluster ðtÞ
ðtÞ
ðtÞ
centroids ðc1 ; c2 ; . . . ; cK Þ. Otherwise set t ¼ t þ 1 and go to next step. Step 3: Optimizing localization of noise monitoring stations using the results of Step 2.
3. Study case: Application to noise action plan 3.1. Introduction to the study area The proposed methodology is validated by intelligent noise monitoring in Shinan district of Qingdao Environmental Protection Bureau. The study area is located in costal hilled terrain. The area of Shinan monitoring is 30.01 square kilometers, and is divided into noise control zone 0, noise control zone 1 and noise control zone 2 based on the prevalent land-use as shown in Table 1. The geographical location of study area is shown in Fig. 5(a). The 100 noise grid survey points are established by dividing study area into standard grids with the size of 500 m 500 m [30]. The acoustic zones and spatial distribution of the monitoring grids are also demonstrated in Fig. 5(b).
3.2. Spatial-time datasets Since 1998, Qingdao Environmental Protection Bureau carries out noise grid survey every year. At each survey point the A-weighted equivalent continuous sound level LAeq and the statistical value L10, L50, L90 are manual measured for each interval-time. Qingdao Environmental Protection Bureau provide us noise grid survey datasets, including noise survey dataset of 1998, 2002, 2004, 2006, 2008, 2010, 2012, and 2014. A description of the noise survey dataset is given in Table 2.
Table 1 Noise limits according to noise control standards in China. Acoustic zones
Description
Day
Night
Class Class Class Class Class
Particularly protected areas Residential area Mixed area Industrial area Both sides of road traffic area Both sides of railway area
50 55 60 65 70 70
40 45 50 55 60 60
0 1 2 3 4
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Fig. 5. (a) Geographical location of the study in this paper. (b) noise control zones and spatial distribution of grid noise monitoring stations in study area.
Table 2 Summary of manual noise survey datasets. Data
Number of Survey points
Survey date
Noise type
Dataset_1998 Dataset_2002 Dataset_2004 Dataset_2006 Dataset_2008 Dataset_2010 Dataset_2012 Dataset_2014
100 100 100 100 100 100 100 100
1998.5.7–1998.5.11 2002.5.15–2002.5.19 2004.5.8–2004.5.14 2006.5.9–2006.5.11 2008.4.24–2008.4.30 2010.4.16–2010.4.30 2012.5.8–2012.5.16 2014.4.16–2014.4.23
Industrial Industrial Industrial Industrial Industrial Industrial Industrial Industrial
noise; noise; noise; noise; noise; noise; noise; noise;
Noise indicator Traffic Traffic Traffic Traffic Traffic Traffic Traffic Traffic
In those noise datasets, LAeq is commonly used to describe the noise level in many countries. In a given situation and time period, LAeq is constant and contains the same acoustic energy as the actual time varying noise. Ln is the sound pressure level exceeded for n percent of the monitoring time. The commonly used values of n are 10, 50 and 90. Particularly, for 10% of the time, the sound or noise has a sound pressure level above L10. While for the rest time, the sound has a sound pressure level at or below L10. Sporadic or intermittent events are the main reason of these higher sound pressure levels. L50 is mid-point value of the noise recordings. L90 is background noise level. If the main source of noise is traffic noise, together with the collection of traffic characteristics in terms of classified traffic volume in the simultaneous basic with noise data in the same sampling time period.
noise; noise; noise; noise; noise; noise; noise; noise;
Noise Noise Noise Noise Noise Noise Noise Noise
of of of of of of of of
social social social social social social social social
activities activities activities activities activities activities activities activities
LAeq, LAeq, LAeq, LAeq, LAeq, LAeq, LAeq, LAeq,
L10, L10, L10, L10, L10, L10, L10, L10,
L50, L50, L50, L50, L50, L50, L50, L50,
L90, L90, L90, L90, L90, L90, L90, L90,
Road traffic density
r r r r r r r r
Vehicle Vehicle Vehicle Vehicle Vehicle Vehicle Vehicle Vehicle
type, type, type, type, type, type, type, type,
Vehicle Vehicle Vehicle Vehicle Vehicle Vehicle Vehicle Vehicle
volume volume volume volume volume volume volume volume
Fig. 6 demonstrates the spatial and temporal distribution of noise level LAeq. It is emphasis that noise survey is fulfilled only once every year and each survey points is measured for 10 min only. Meanwhile, the measurement is manual and not synchronous. Hence noise survey information is largely speculative. To reduce the influence of randomness, optimization of noise monitoring stations should select survey datasets as much as possible. 3.3. Optimization results with IPKM The Qingdao noise grid survey points are located in three categories of noise control zone, the number of noise monitoring stations in class 0, class 1 and class 2 are 8, 78, and 14 respectively,
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Fig. 6. Spatial and temporal distribution of noise level LAeq.
Fig. 7. Spatial distribution of optimized noise monitoring stations with IPKM algorithm.
n0 ¼ 8; n1 ¼ 78; n2 ¼ 14, thus the total number of noise survey point n ¼ 100, the noise comprehensive evaluation indicators includes LAeq ; L10 ; L50 ; L90 , so the number of variables m ¼ 4. The initial parameters of IPKM algorithm are fixed as inertia weight w ¼ 0:5, population size N swarm ¼ 50, learning factors c1 ¼ c2 ¼ 0:5, and number of iterations t max ¼ 1000. The spatial distributions of optimized noise monitoring stations obtained with the proposed method are shown in Fig. 7.
4. Discussion 4.1. Comparison of proposed method with K-means algorithm The advantages of the IPKM algorithm will be verified by comparison with K-means clustering algorithm. The spatial distributions of optimized noise monitoring stations obtained with K-means algorithm are shown in Fig. 8.
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Fig. 8. Spatial distribution of optimized noise monitoring stations with K-means algorithm.
4.2. Validation of optimized results
Fig. 9. The distribution of individuals during clustering process: (a) K-means algorithm, (b) IPKM algorithm.
Fig. 10. Comparison of IPKM and K-means on average fitness.
The distribution of individuals during the clustering process is shown in Fig. 9. The comparison between IPKM and K-means algorithm on the classification accuracy is illustrated in Fig. 10. The optimization result comparing IPKM algorithm with K-means algorithm are provided for Shinan district noise spatialtime datasets (1998, 2002, 2004, 2006, 2008, 2010, 2012), as shown in Table 3.
The 28 noise monitoring stations, which are the optimization result of IPKM algorithm, replace the monitoring result of original 100 stations should be validated. Using 2014 noise survey dataset to verify the accuracy, reliability and representation of the 28 noise monitoring stations, including absolute error, relative error and difference of sample mean for noise indicator (LAeq, L10, L50, L90) . F-test [31] and t-test [32] are employed to verify the optimization result. X1 and X2 stand for sample parameters before and after optimization, S1 and S2 are the standard deviation of parameters before and after optimization, n1, n2 is the number of sample respectively, in this case, n1 = 100, n2 = 28, SB and Ss are the bigger and smaller standard deviation of two samples respectively. The comparing result is illustrated in Table 4. From above validation, the comparison results can be reached that: (1) The absolute error of noise indicator (LAeq, L10, L50, L90) is not exceed ±1 dB(A), which satisfies the basic requirements of optimization. (2) The relative error of noise indicator (LAeq, L10, L50, L90) is not exceed 2%, which implies that the accuracy of optimization result is excellent. (3) The parameters mean value don’t have obvious difference in P < 0.05 probability level after strict t-test, this means that using 28 optimization stations replace original 100 stations has 95% confidence intervals. So IPKM algorithm is the successful method for the optimizing of urban noise monitoring stations. It should be noted that statistical values of noise measurements from reduced number of monitoring stations could compare with original number of stations. However, results cannot deduce that they were subject to exactly the same noise exposure. Notwithstanding its limitation, this study does clearly indicate the potential noise intelligent monitoring stations, which can be important
Table 3 Optimization results statistics comparison. Algorithms
The number of iteration mean value ± standard deviation
Optimized number of stations mean value ± standard deviation
Optimized number of stations
K-means IPKM
629.50 ± 441.680 516.80 ± 160.868
37.00 ± 2.6180 26 ± 1.3680
37 28
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Table 4 Comparison result for 2014 noise survey dataset. LAeq
Sample n1 (100) Sample n2 (28) jX 1 X 2 j jX 1 X 2 j=X 2 ð%Þ F = (SB/SS)2 Critical value F0.05 (100, 28) Verify result Homogeneity of variance Test method Critical value t 00:05 Actual value t 0 Verify result Conclusion
L10
L50
L90
X
S
X
S
X
S
X
S
53.048 53.092 0.044
2.456 0.547
54.891 55.046 0.155
2.639 1.034
51.502 51.621 0.119
2.693 0.987
49.328 49.414 0.175
2.533 1.329
0.08
0.28
0.23
1.53
21.664 2.04 F > F0.05 Not homogeneous t0 2.0080 0.8772 t0 < t00:05 No obvious difference
6.513 2.04 F > F0.05 Not homogeneous t0 2.0104 0.6451 t0 < t00:05 No obvious difference
7.445 2.04 F > F0.05 Not homogeneous t0 2.0071 1.021 t0 < t00:05 No obvious difference
3.632 2.04 F > F0.05 Not homogeneous t0 2.0089 0.8844 t0 < t00:05 No obvious difference
guidelines for implementation of urban continuous noise monitoring throughout the year. 5. Conclusion Optimizing localization of noise monitoring stations is very important for urban noise monitoring and has attracted much attention of many researches. With noise grid survey dataset, an optimization method was proposed to determine the number and location of monitoring stations. The mathematical model is solved with the proposed hybrid clustering algorithm IPKM. An illustrative case was carried out, in which the optimized results were compared with K-means algorithm. The major conclusions can be summarized as follows. (1) The optimization problem of number and locations of autonomous monitoring stations can be solved with clustering method with the noise grid measurement datasets. Assuming average value and standard deviation don’t have obvious difference, the mathematical model was constructed. Its optimal goal is to use the least amount of stations to replace traditional grid survey. (2) A new hybrid algorithm IPKM was proposed by integrating IT, PSO and K-means algorithms. The hybrid algorithm has better performance for multi-peak function optimization problem. Meanwhile, the integrated solving algorithm has advantage of non-independent on initialization, high convergence speed and global optimization, (3) The proposed method has been implemented and tested on noise survey dataset of Qingdao Shinan district and preliminary computational experience is very encouraging. It has been proved that IPKM algorithm can solve optimization problem of urban noise monitoring stations. (4) The proposed methodology can be extended to other environmental monitoring stations optimization problem from a theoretical point of view, such as atmospheric environmental monitoring.
Acknowledgements This work is supported by the China Postdoctoral Science Foundation under Grant No. 2015M571993, the National Natural Science Foundation of China under Grant Nos. 61602269, 11472144 and Qingdao Postdoctoral Application Research Funded Project. The authors appreciate Qingdao Environmental Protection Bureau for providing noise grid survey datasets.
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Contents lists available at ScienceDirect
Applied Acoustics journal homepage: www.elsevier.com/locate/apacoust
Optimizing stations location for urban noise continuous intelligent monitoring Baoxiang Huang, Zhenkuan Pan ⇑, Huan Yang, Guojia Hou, Weibo Wei College of Computer Science and Technology, Postdoctoral Stations of System Science, Qingdao University, No. 308 Ningxia Road, 266071 Qingdao, China
a r t i c l e
i n f o
Article history: Received 15 August 2016 Received in revised form 12 June 2017 Accepted 12 June 2017
Keywords: Noise monitoring station PSO K-means IPKM algorithm
a b s t r a c t In most of urban noise monitoring systems, the optimization of number and locations of autonomous monitoring stations is a Non-deterministic Polynomial Complete (NPC) problem. It is also important for the implementation of intelligent measurement networks. This paper investigates an optimization method to achieve minimum stations for urban noise intelligent monitoring. First a mathematical model for monitoring stations selection has been developed. Next, a novel hybrid Immune PSO K-means (IPKM) clustering algorithm is proposed to solve the mathematical model. The IPKM algorithm can overcome the shortcomings (e.g. slow convergence speed) of the Particle Swarm Optimization (PSO) algorithm, and help K-means clustering algorithm escaping from local optima. Finally, the methodology has been applied to QingDao urban noise intelligent monitoring networks. For comparison, the K-means algorithm and IPKM algorithm are applied to the noise grid survey datasets of 1998–2014 years. The final optimized results illustrate the proposed method could perform relevant monitoring tasks with fewer monitoring stations. In addition, the importance of the proposed method is that it would be applicable for noise monitoring and noise control management problems. Ó 2017 Elsevier Ltd. All rights reserved.
1. Introduction Noise is among the most pervasive pollutants today [1,2]. According to statistical data, resident petition to reduce noise pollution is more common than those for air pollution [3]. The monitoring of noise effect is crucial to evaluate noise reduction measures for existing noise sources [4,5]. Measured data that comes from the noise monitoring system is useful for noise analysis and reduction [6,7]. In China, the environmental monitoring institutions should implement general noise grid survey at least once a year [8]. However, noise monitoring is manual monitoring which is arduous. Moreover, it is carried out only once in ten minutes every year. This kind of ‘‘short time measurements” cannot meet the new requirements and constraints of environmental noise management issues in complex urban context [9]. Longterm environmental monitoring [10] of noise levels can be done using autonomous measurement networks [11] as shown in Fig. 1. Intelligent measurement makes possible the advanced analysis of acoustic environment. Compared with manual monitoring, the noise automatic monitoring can really reflect the urban noise environment quality. Due to the high purchase of noise monitoring
⇑ Corresponding author. E-mail addresses: [email protected] (B. Huang), [email protected] (Z. Pan). http://dx.doi.org/10.1016/j.apacoust.2017.06.009 0003-682X/Ó 2017 Elsevier Ltd. All rights reserved.
device, the station number in intelligent measurement is severely limited [12]. At present, urban automatic noise monitoring system is being at the start stage in China. Then it is essential to identify how many measuring localization points are really required. At the same time, it is vital to find most appropriate locations for measurement stations to obtain adequate measurement results. Based on the historical noise grid survey datasets, the upper problem can be interpreted as classification of measured data of the grid points. It is ascribed to Non-deterministic Polynomial Complete (NPC) problem that can be solved by clustering techniques [13]. K-means clustering algorithm is a widely adopted clustering technique, and aims to divide n data points into K non-overlapping clusters, in which each point pertain to the cluster with high degree of similarity [14–16]. However, the K-means algorithm has two defects related to initial value. One is the number of clusters K that is needed to be initialized, and the other is the initial random seed points [13,17]. It is a good candidate for extension to work with evolutionary algorithm. The Particle Swarm Optimization (PSO) algorithm belongs to the modern evolutionary algorithms, and has high convergence speed for initial stage of a global search [18,19]. Unfortunately, search speed reduces obviously around global optimum because of degeneration [20]. In order to slowdown the degeneration of PSO, immune technology can be introduced into PSO algorithm to construct an Immune
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Fig. 1. Noise monitoring networks.
Technology PSO (ITPSO) algorithm [21]. At the same time, K-means algorithm can achieve faster convergence to optimum solution [22]. However, little research has been focused on optimizing urban noise monitoring stations with hybrid algorithm combining K-means and ITPSO algorithm. The purpose of this paper is to propose an optimizing method for urban noise intelligent monitoring stations with noise grid survey datasets. The organization of this paper is as follows: Section 2 analyzes optimization problem of noise monitoring station thoroughly, describes the relevant definitions, builds the mathematical model of optimization problem, and designs algorithm for proposed model. In Section 3, the methodology is applied to an illustrative case. The results are discussed in Section 4. Section 5 is the conclusion of the paper.
2. Methodology for optimizing the noise monitoring stations 2.1. Research program This study aims to identify the proper choice of intelligent measurement stations based on noise grid survey datasets. Traditional noise grid survey monitoring is relative subjective and random. For large monitoring area, if two grid survey points have the same value of noise indicators, it means that these two points have similar acoustic environmental features. Therefore, the number of monitoring stations can be reduced. The determination of the number and position of intelligent measurement nodes needs theoretical guidance, which includes mathematical model and quantitative analysis. Moreover, the method must guarantee monitoring the noise environmental features with the fewest number of monitoring stations. Also, the monitoring results should be consistent with the noise grid survey results. The overall research program is illustrated in Fig. 2. (1) Determine research scenario. According to the change of noise sources when historical monitoring data was taken, the research scenarios are divided into two types. It is note that noise grid survey for influenced area must be implemented if there are major changes. (2) Realize optimization process. Carry out noise grid survey data preprocessing combining with noise control zones, establish optimization model, and design algorithm for proposed model.
(3) Finally, output the optimization results and carry out spatial-temporal analysis. 2.2. Mathematical model The purpose of mathematical model is to minimize the number of monitoring stations with historical grid monitoring data. Assuming that there are n noise survey points fL1 ; L2 ; . . . ; Ln g, each grid monitoring point Li is a m-dimensional vector Li ¼ fLi1 ; Li2 ; . . . ; Lim g, every element Lik represents a specific noise indicator, such as LAeq . Furthermore, the grid survey points are located in corresponding noise control zone. Lki can be defined as the ith noise survey point of control zone k, where k ¼ 0; 1; . . . ; l. In the same way, each point is a m-dimensional vector Lki ¼ fLki1 ; Lki2 ; . . . ; Lkim g, i ¼ 0; 1; . . . ; nk , nk is the noise survey point number of acoustic control zone k. The total number of noise surP vey point is lk¼0 nk ¼ n. Consequently, the optimization results of stations can be achieved by partition n noise grid points into a minimum of clusters. Furthermore, in each cluster the noise indicators values of grid point have a high degree similarity, and are very dissimilar to data in other clusters. In order to describe the mathematical modeling of optimization problem, variables uj , ujopt , rj , rjopt , ukj , ukjopt , rkj , rkjopt are adopted. uj and ujopt are the jth comprehensive evaluation indicator average value of monitoring points before and after optimization, computational formula is Eq. (1). rj and rjopt are the jth noise indicator standard deviation of monitoring stations before and after optimization, computational formula is Eq. (2). ukj and ukjopt are the jth noise indicator average value of acoustic control zone class k before and after optimization, computational formula is Eq. (3). rkj , rkjopt are the jth noise indicator standard deviation of control zone class k before and after optimization, computational formula is Eq. (4). nk l X X uj ¼ Lkij
,
n; ujopt
k¼1 i¼1
rj
nk l X X ¼ Lkij xki
,
k¼1 i¼1
nk l X X xki
ð1Þ
k¼1 i¼1
vffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi ,ffi u l nk uX X k 2 n; ¼t ðLij uj Þ k¼1 i¼1
rjopt
vffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi , u l nk nk l X uX X X 2 ¼t xki ðLkij uj Þ xki k¼1 i¼1
k¼1 i¼1
ð2Þ
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Fig. 2. Overall research program.
nk X ukj ¼ Lkij
, nk ; ukjopt
i¼1
rkj
nk X ¼ Lkij xki
,
i¼1
nk X xki
ð3Þ
i¼1
vffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi , u nk uX k nk ; ¼t Lij ukj
2.3. Main idea for solving the mathematical model
i¼1
rkjopt
vffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi , n u nk k X uX 2 t k k ¼ xi ðLij ukjopt Þ xki i¼1
ð4Þ
i¼1
Providing that average value and standard deviation don’t have obvious difference, the optimal goal is to use the least amount of stations to replace traditional grid survey. Then the optimization problem is modeled as Eq. (5).
min
On the other hand, xki ¼ 0 indicates that the ith noise survey point in control zone k is abandoned.
nk l X X xki k¼0 i¼1
8 jujopt uj j 6 1dB > > > > jrjopt rj j > 6 0:05 > > rj > > > > > jukjopt ukj j 6 1dB > > > > > jrkjopt rkj j 6 0:05 > > rkj > > < nu nv X X s:t: xki ðuÞ 6 xki ðv Þ; nu 6 nv ðu; v 2 f0; 1; . . . ; lg; u–v Þ > > > i¼1 i¼1 > > > > nk > X > > >1 6 xki 6 nk > > > > i¼1 > > > k > > > xi 2 f0; 1g : i ¼ 0; 1; . . . ; n; j ¼ 0; 1; . . . ; m; k ¼ 0; 1; . . . ; l
ð5Þ
P nk k where 1 6 i¼1 xi 6 nk constraints the number of monitoring stations in different acoustic zones. xki 2 f0; 1g limits the value is 0 or 1, if xki ¼ 1, the ith noise survey points in control zone k is selected.
The level of urban environmental noise is under the influence of various elements, including the frequency of noise source, complexity of propagation path, especially random factors [23,24]. So the measurement result is uncertain about the value of the membership function, thus urban environmental noise survey datasets can be assumed as fuzzy sets. For fuzzy sets partitioning problem, the K-means clustering algorithm is commonly employed with high convergence speed [25,26]. Here n noise survey grid points Li fall into K compact clusters, and each point Li is an m-dimensional vector Li ¼ fLi1 ; Li2 ; . . . ; Lim g. The partition process can be carried out in an easy and simple way. First it starts with an initial K partitions to obtain clustering centers ðc1 ; c2 ; . . . ; cK Þ. Next calculate the Euclidian metric distance between each noise grid point Li and kth centers. Assign Li to its nearest cluster centroid ck. Finally calcuP P late the sum of objective function of ¼ ni¼1 Kk¼1 min dðLi ; ck Þ2 . The K-means algorithm can achieve optimization results with small number of iterations. However, it severely depends on the initialization of the centers. The reason is its winner takes all partitioning strategy, the centers also tend to convergence to local optima. In order to conquer this disadvantage, K-means algorithm is extended with Immune Technology Particle Swarm Optimization (ITPSO). PSO is a population based stochastic optimization technique [27,28]. The swarm is composed of particles. Each particle is individual and on behalf of a noise grid survey point. In order to optimize the initial clustering centers for different noise control zones, clustering centers ðc1 ; c2 ; . . . ; cK Þ are selected as the particles in PSO. Each ci is the ith clustering center and is represented by a m-dimensional real-valued vector Lki ¼ fLki1 ; Lki2 ; . . . ; Lkim g, as shown
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in Fig. 3. Here assumed that a set of Nsarm particles forms a populaT tion as ½^c1 ; ^c2 ; . . . ; ^cN . In search space, that is noise control zones, particles cooperate to seek the best position based on movement and intelligence of swarms. Each particle moves in the light of good positions and velocity, and the velocity should be adjusted with historical behaviors of the particle itself and its neighbors. At each iteration, searching procedure can be implemented by Eq. (6).
V i ðt þ 1Þ ¼ x V i ðtÞ þ c1 rand1 ðPbesti Li ðtÞÞ þc2 rand2 ðGbest Li ðtÞÞ Li ðt þ 1Þ ¼ Li ðtÞ þ V i ðt þ 1Þ Li ðtÞ ¼ ½Li;1 ðtÞ; Li;2 ðtÞ; . . . ; Li;k ðtÞ1m
ð6Þ
Pbesti ¼ ½pbesti;1 ðtÞ; pbesti;2 ðtÞ; . . . ; pbesti;k ðtÞ1m Gbest ¼ ½gbest1 ðtÞ; gbest2 ðtÞ; . . . ; gbest k ðtÞ1m xmin x ¼ xmax xmaxtmax t
where t and t max are iteration number and maximum iteration number, respectively. Nkswarm is the particle number in kth noise control zone. m is the number of monitoring noise indicators. rand1 and rand2 are random numbers between 0 and 1. Pbesti is the best previous position recorded by the particle i. Gbest is the global optimal particle among the corresponding noise control zone. Constants c1and c2 are the learning factors in terms of acceleration, which pull each particle towards Pbesti and Gbest positions. The exploration property of the algorithm is controlled by inertia weight x; xmax is the maximum inertia weight and xmin is the minimum inertia weight. There is no overlapping and mutation calculation in PSO algorithm. As above mentioned, every particle determines its flight based on itself and its neighbors’ flying experience. It easily leads to lower accuracy in terms of the speed and direction regulation, and causes swarm degeneration during evolutionary process [29]. Immune technology is incorporated in PSO algorithm with crossover and mutation operators to properly curing the swarms. Consequently, the swarms can achieve non-dominated set of solutions. The antibodies operators extend the searching capacity and improve its adaptive nature. If new non-dominated solution is reproduced by performing crossover, mutation, immune selection and vaccination, then replace the inferior particles with immune memory particle in memory Cell. Memory Cell can be adopted for clonal selection with
mutation. On the other hand, some non-dominated solutions will be flushed when memory Cell is full. In next section, the details of optimized algorithm will be described. 2.4. Proposed IPKM algorithm As mentioned in Section 2.3, K-means clustering algorithm is efficient to handle optimization problems of urban noise stations. Combining with ITPSO, hybrid Immune PSO K-means (IPKM) clustering algorithm is designed. The IPKM can maintain the advantages of immune technology, PSO, and K-means. More specially, the hybrid algorithm has merits of non-independent on initialization, high convergence speed, and global optimization. The K-means algorithm is initialized as optimized results of ITPSO to improve simulation results. Fig. 4 illustrates the flowchart of the hybrid IPKM algorithm. Fitness function is the only criteria for particle search guidance of ITPSO algorithm. The objective function is partition basis of K-means clustering algorithm. To realize the integration of K-means and ITPSO, according to objective function of K-means, the fitness function of ITPSO is designed as Eq. (7).
Fitness ¼ 1=1 þ
n X K X
min dðLi ; ck Þ2
ð7Þ
i¼1 k¼1
At the tmaxth iteration, the best individual pbesti(tmax) of the ith particle can be achieved by solving maximization problem of Fit^i ðtÞÞ for t 6 t max ness, guaranteeing Fitnessðpbest i ðtmax ÞÞ P Fitnessðp iteration. Moreover, the global best gbest(n) can be obtained with Fitnessðgbest i ðt max ÞÞ P Fitnessðpbest i ðtmax ÞÞ, for i ¼ 1; 2; . . . N. Optimizing noise monitoring stations based on IPKM algorithm can be implemented in following steps. Step 1: Optimize the parameters with ITPSO. (1) Fix the number of clusters K, choose the number of particles Nsarm, fix the PSO parameters like learning factors (c1, c2), inertia weight (wmax,wmin), and the number of iterations tmax. (2) Copy the individuals (antibodies) to initialize swarms and memory Cell, assign position and velocity to each particle. (3) Set the iteration count t ¼ 1, start the iterative procedure.
Fig. 3. The representation of a particle.
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Fig. 4. Flowchart of hybrid algorithm IPKM.
(4) Calculate the fitness value with Eq.(7) for each particle, if pi ðf ðpi Þ < f ðgÞÞ, update the swarm’s best position: g so far. (5) Deliver dominate swarm to immune system for antibodies renewal, let non-dominate swarm fly for generation. (6) Select minimum distance as antigen according to Euclidian distance; select matching antibodies to share information by performing crossover and mutation in mating pool. Replace the previous antibodies. (7) Determine the global best gbesti and the individual best pbesti for each particle. Update the position and the velocity of each particle. (8) Check the termination criteria. If the current iteration number reaches tmax, the best particle labeled as ðcb1 ; cb2 ; . . . ; cbK Þ, stop iteration, go to next step; else perform crossover, mutation, immune selection and vaccination, reproduce new particle swarm. (9) Update t ¼ t þ 1 and loop to step 4). Step 2: K-means clustering for noise monitoring stations using optimized clustering centers. (1) Initialize the clustering centers c0 ¼ ðcb1 ; cb2 ; . . . ; cbK Þ as the best particles in Step1. Fix the iteration limit tkmax and the termination threshold e > 0. (2) Assign the iterative count t ¼ 1. Start iterative procedure. ðtÞ
(3) Calculate the distance measure by Eq. (8), dki , between kth cluster center and ith data set . ðtÞ dki
¼ kLi
ðtÞ ck k
vffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi uX u m ðtÞ 2 ¼ t ðLij ckj Þ
ð8Þ
j¼1
(4) Partition each noise grid survey data object Li to its nearest cluster centroid ck . (5) Recalculate and update the centroid average of noise survey grid point in the cluster according to Eq. (9). Where nk is number of noise indicator data items belonging to kth cluster.
P ðtÞ
ck ¼
Li 2k Li
(6) Calculate Pn PK i¼1
ð9Þ
nk the
value
of
objective
function
2 k¼1 min dðLi ; c k Þ , if the value has converged and
mathematical model is satisfied, output the final cluster ðtÞ
ðtÞ
ðtÞ
centroids ðc1 ; c2 ; . . . ; cK Þ. Otherwise set t ¼ t þ 1 and go to next step. Step 3: Optimizing localization of noise monitoring stations using the results of Step 2.
3. Study case: Application to noise action plan 3.1. Introduction to the study area The proposed methodology is validated by intelligent noise monitoring in Shinan district of Qingdao Environmental Protection Bureau. The study area is located in costal hilled terrain. The area of Shinan monitoring is 30.01 square kilometers, and is divided into noise control zone 0, noise control zone 1 and noise control zone 2 based on the prevalent land-use as shown in Table 1. The geographical location of study area is shown in Fig. 5(a). The 100 noise grid survey points are established by dividing study area into standard grids with the size of 500 m 500 m [30]. The acoustic zones and spatial distribution of the monitoring grids are also demonstrated in Fig. 5(b).
3.2. Spatial-time datasets Since 1998, Qingdao Environmental Protection Bureau carries out noise grid survey every year. At each survey point the A-weighted equivalent continuous sound level LAeq and the statistical value L10, L50, L90 are manual measured for each interval-time. Qingdao Environmental Protection Bureau provide us noise grid survey datasets, including noise survey dataset of 1998, 2002, 2004, 2006, 2008, 2010, 2012, and 2014. A description of the noise survey dataset is given in Table 2.
Table 1 Noise limits according to noise control standards in China. Acoustic zones
Description
Day
Night
Class Class Class Class Class
Particularly protected areas Residential area Mixed area Industrial area Both sides of road traffic area Both sides of railway area
50 55 60 65 70 70
40 45 50 55 60 60
0 1 2 3 4
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Fig. 5. (a) Geographical location of the study in this paper. (b) noise control zones and spatial distribution of grid noise monitoring stations in study area.
Table 2 Summary of manual noise survey datasets. Data
Number of Survey points
Survey date
Noise type
Dataset_1998 Dataset_2002 Dataset_2004 Dataset_2006 Dataset_2008 Dataset_2010 Dataset_2012 Dataset_2014
100 100 100 100 100 100 100 100
1998.5.7–1998.5.11 2002.5.15–2002.5.19 2004.5.8–2004.5.14 2006.5.9–2006.5.11 2008.4.24–2008.4.30 2010.4.16–2010.4.30 2012.5.8–2012.5.16 2014.4.16–2014.4.23
Industrial Industrial Industrial Industrial Industrial Industrial Industrial Industrial
noise; noise; noise; noise; noise; noise; noise; noise;
Noise indicator Traffic Traffic Traffic Traffic Traffic Traffic Traffic Traffic
In those noise datasets, LAeq is commonly used to describe the noise level in many countries. In a given situation and time period, LAeq is constant and contains the same acoustic energy as the actual time varying noise. Ln is the sound pressure level exceeded for n percent of the monitoring time. The commonly used values of n are 10, 50 and 90. Particularly, for 10% of the time, the sound or noise has a sound pressure level above L10. While for the rest time, the sound has a sound pressure level at or below L10. Sporadic or intermittent events are the main reason of these higher sound pressure levels. L50 is mid-point value of the noise recordings. L90 is background noise level. If the main source of noise is traffic noise, together with the collection of traffic characteristics in terms of classified traffic volume in the simultaneous basic with noise data in the same sampling time period.
noise; noise; noise; noise; noise; noise; noise; noise;
Noise Noise Noise Noise Noise Noise Noise Noise
of of of of of of of of
social social social social social social social social
activities activities activities activities activities activities activities activities
LAeq, LAeq, LAeq, LAeq, LAeq, LAeq, LAeq, LAeq,
L10, L10, L10, L10, L10, L10, L10, L10,
L50, L50, L50, L50, L50, L50, L50, L50,
L90, L90, L90, L90, L90, L90, L90, L90,
Road traffic density
r r r r r r r r
Vehicle Vehicle Vehicle Vehicle Vehicle Vehicle Vehicle Vehicle
type, type, type, type, type, type, type, type,
Vehicle Vehicle Vehicle Vehicle Vehicle Vehicle Vehicle Vehicle
volume volume volume volume volume volume volume volume
Fig. 6 demonstrates the spatial and temporal distribution of noise level LAeq. It is emphasis that noise survey is fulfilled only once every year and each survey points is measured for 10 min only. Meanwhile, the measurement is manual and not synchronous. Hence noise survey information is largely speculative. To reduce the influence of randomness, optimization of noise monitoring stations should select survey datasets as much as possible. 3.3. Optimization results with IPKM The Qingdao noise grid survey points are located in three categories of noise control zone, the number of noise monitoring stations in class 0, class 1 and class 2 are 8, 78, and 14 respectively,
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Fig. 6. Spatial and temporal distribution of noise level LAeq.
Fig. 7. Spatial distribution of optimized noise monitoring stations with IPKM algorithm.
n0 ¼ 8; n1 ¼ 78; n2 ¼ 14, thus the total number of noise survey point n ¼ 100, the noise comprehensive evaluation indicators includes LAeq ; L10 ; L50 ; L90 , so the number of variables m ¼ 4. The initial parameters of IPKM algorithm are fixed as inertia weight w ¼ 0:5, population size N swarm ¼ 50, learning factors c1 ¼ c2 ¼ 0:5, and number of iterations t max ¼ 1000. The spatial distributions of optimized noise monitoring stations obtained with the proposed method are shown in Fig. 7.
4. Discussion 4.1. Comparison of proposed method with K-means algorithm The advantages of the IPKM algorithm will be verified by comparison with K-means clustering algorithm. The spatial distributions of optimized noise monitoring stations obtained with K-means algorithm are shown in Fig. 8.
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Fig. 8. Spatial distribution of optimized noise monitoring stations with K-means algorithm.
4.2. Validation of optimized results
Fig. 9. The distribution of individuals during clustering process: (a) K-means algorithm, (b) IPKM algorithm.
Fig. 10. Comparison of IPKM and K-means on average fitness.
The distribution of individuals during the clustering process is shown in Fig. 9. The comparison between IPKM and K-means algorithm on the classification accuracy is illustrated in Fig. 10. The optimization result comparing IPKM algorithm with K-means algorithm are provided for Shinan district noise spatialtime datasets (1998, 2002, 2004, 2006, 2008, 2010, 2012), as shown in Table 3.
The 28 noise monitoring stations, which are the optimization result of IPKM algorithm, replace the monitoring result of original 100 stations should be validated. Using 2014 noise survey dataset to verify the accuracy, reliability and representation of the 28 noise monitoring stations, including absolute error, relative error and difference of sample mean for noise indicator (LAeq, L10, L50, L90) . F-test [31] and t-test [32] are employed to verify the optimization result. X1 and X2 stand for sample parameters before and after optimization, S1 and S2 are the standard deviation of parameters before and after optimization, n1, n2 is the number of sample respectively, in this case, n1 = 100, n2 = 28, SB and Ss are the bigger and smaller standard deviation of two samples respectively. The comparing result is illustrated in Table 4. From above validation, the comparison results can be reached that: (1) The absolute error of noise indicator (LAeq, L10, L50, L90) is not exceed ±1 dB(A), which satisfies the basic requirements of optimization. (2) The relative error of noise indicator (LAeq, L10, L50, L90) is not exceed 2%, which implies that the accuracy of optimization result is excellent. (3) The parameters mean value don’t have obvious difference in P < 0.05 probability level after strict t-test, this means that using 28 optimization stations replace original 100 stations has 95% confidence intervals. So IPKM algorithm is the successful method for the optimizing of urban noise monitoring stations. It should be noted that statistical values of noise measurements from reduced number of monitoring stations could compare with original number of stations. However, results cannot deduce that they were subject to exactly the same noise exposure. Notwithstanding its limitation, this study does clearly indicate the potential noise intelligent monitoring stations, which can be important
Table 3 Optimization results statistics comparison. Algorithms
The number of iteration mean value ± standard deviation
Optimized number of stations mean value ± standard deviation
Optimized number of stations
K-means IPKM
629.50 ± 441.680 516.80 ± 160.868
37.00 ± 2.6180 26 ± 1.3680
37 28
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Table 4 Comparison result for 2014 noise survey dataset. LAeq
Sample n1 (100) Sample n2 (28) jX 1 X 2 j jX 1 X 2 j=X 2 ð%Þ F = (SB/SS)2 Critical value F0.05 (100, 28) Verify result Homogeneity of variance Test method Critical value t 00:05 Actual value t 0 Verify result Conclusion
L10
L50
L90
X
S
X
S
X
S
X
S
53.048 53.092 0.044
2.456 0.547
54.891 55.046 0.155
2.639 1.034
51.502 51.621 0.119
2.693 0.987
49.328 49.414 0.175
2.533 1.329
0.08
0.28
0.23
1.53
21.664 2.04 F > F0.05 Not homogeneous t0 2.0080 0.8772 t0 < t00:05 No obvious difference
6.513 2.04 F > F0.05 Not homogeneous t0 2.0104 0.6451 t0 < t00:05 No obvious difference
7.445 2.04 F > F0.05 Not homogeneous t0 2.0071 1.021 t0 < t00:05 No obvious difference
3.632 2.04 F > F0.05 Not homogeneous t0 2.0089 0.8844 t0 < t00:05 No obvious difference
guidelines for implementation of urban continuous noise monitoring throughout the year. 5. Conclusion Optimizing localization of noise monitoring stations is very important for urban noise monitoring and has attracted much attention of many researches. With noise grid survey dataset, an optimization method was proposed to determine the number and location of monitoring stations. The mathematical model is solved with the proposed hybrid clustering algorithm IPKM. An illustrative case was carried out, in which the optimized results were compared with K-means algorithm. The major conclusions can be summarized as follows. (1) The optimization problem of number and locations of autonomous monitoring stations can be solved with clustering method with the noise grid measurement datasets. Assuming average value and standard deviation don’t have obvious difference, the mathematical model was constructed. Its optimal goal is to use the least amount of stations to replace traditional grid survey. (2) A new hybrid algorithm IPKM was proposed by integrating IT, PSO and K-means algorithms. The hybrid algorithm has better performance for multi-peak function optimization problem. Meanwhile, the integrated solving algorithm has advantage of non-independent on initialization, high convergence speed and global optimization, (3) The proposed method has been implemented and tested on noise survey dataset of Qingdao Shinan district and preliminary computational experience is very encouraging. It has been proved that IPKM algorithm can solve optimization problem of urban noise monitoring stations. (4) The proposed methodology can be extended to other environmental monitoring stations optimization problem from a theoretical point of view, such as atmospheric environmental monitoring.
Acknowledgements This work is supported by the China Postdoctoral Science Foundation under Grant No. 2015M571993, the National Natural Science Foundation of China under Grant Nos. 61602269, 11472144 and Qingdao Postdoctoral Application Research Funded Project. The authors appreciate Qingdao Environmental Protection Bureau for providing noise grid survey datasets.
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