Intercomparison Exercise for Gases Emitted by a Cement Industry in Spain: A Functional Data Approach

ABSTRACT

This paper describes the results of an intercomparison exercise referring to the measurement of atmospheric pollutants emitted by cement plants. The research was conducted in 2008 in Catalonia, Spain. Thirteen Spanish companies accredited to make pollutant measurements and with suitably approved equipment and trained staff participated in the research. The aim of the research was to evaluate the technical competence of the accredited companies in conducting tests in situ. The results obtained from the application of the methodology described in international standards—on the basis of conventional statistical analyses—were compared with those obtained using functional data analysis. On comparing the two methods, it was concluded that the functional method, although more complex, has advantages over the conventional statistical method. This is because the functional approach compares curves rather than mean values. Furthermore, it does not presuppose a normal distribution of the data.

IMPLICATIONS

This work is of interest for companies accredited to make measurements of atmospheric pollutants. Gas emissions recorded for these companies are usually compared using a standard method that basically compares mean values for the whole measurement time interval. The authors propose to overcome the problems associated with this methodology by using a method that is based on the comparison of curves adjusted to the observed data. Advantages of the proposed method were confirmed in a real intercom-parison exercise conducted in Spain.

INTRODUCTION

Intercomparison exercises are used by bodies that accredit inspection companies and laboratories as part of the process for evaluating their competence in performing the tasks for which they are accredited. International standards for quality management systems, in particular International Organization for Standardization (ISO)/International Electrotechnical Commission (IEC) 17025,1 require accredited companies to participate in intercom-parison exercises as a way of ensuring the quality of their results.

The literature contains several examples of intercom-parison exercises referring to air quality and other parameters. Febo et al.2 described a 5-day intercomparison exercise aimed at evaluating techniques for measuring nitric acid and particulate nitrate that was carried out in the Area della Ricerca di Roma (Italy) on September 18–24, 1988. Sixteen teams from 11 European countries participated in the experiment, which intercompared the performance of several denuder and filter pack systems. The exercise revealed differences between the techniques analyzed. Tedeschi et al.3 described an intercomparison exercise conducted in Groupe Europeen de Recherches Gazières, in which 10 of the main European gas companies participated. The survey compared the performance of eight high-pressure gas flow laboratories in the autumn of 1998 to autumn of 1999. The aim was to identify to what extent the results obtained by the different laboratories were comparable and to assess possible ways of improving test performance. It was concluded that most of the companies participating in the intercomparison exercise produced very accurate results. It was also suggested that intercomparison exercises should be repeated at regular intervals to track possible variations and to improve the performance of the individual companies. In a laboratory setting, Schwab et al.4 compared six measurement methods and seven measurement instruments for gaseous ammonia at low part-per-billion (ppb) values. In a controlled setting, the laboratory intercomparison tested responses to concentration spikes and zero points and instrument time response. It was concluded that although sub-ppb measurement of gaseous ammonia was possible with existing research knowledge and commercial instruments, time response and accuracy were issues that needed to be carefully addressed to guarantee quality-assured data. Viant et al.5 described an international intercomparison exercise involving seven laboratories from the United States, Canada, the United Kingdom, and Australia that evaluated the efficacy of metabolomic environmental measurements based on nuclear magnetic resonance (NMR) spectroscopy. The measurements were made using the routine methods of the participating laboratories. Principal component analysis demonstrated that NMR-based metabolomics can generate data that are sufficiently comparable between laboratories, thereby supporting the continued evaluation of this approach to regulatory environmental studies.

In Spain in 2000, an agreement was signed between the Ministry of the Environment (General Sub-Directorate for Environmental Quality) and the Instituto de Salud Carlos III attached to the Ministry of Health that was aimed at optimizing and harmonizing the methods used by the Spanish atmospheric pollution networks. The purpose was to ensure quality control and quality assurance for pollution measurements in concordance with international, national, and, most importantly, European Union standards by carrying out intercomparison exercises aimed at analyzing the assessment methods used by the different atmospheric pollution measurement networks existing in Spain.6

This paper describes the results of an intercomparison exercise conducted in 2008 in Catalonia, Spain. Rather than merely explain how the intercomparison exercise was conducted and describe its results, the goal was to demonstrate the usefulness of functional data analysis as an alternative to the conventional statistical methods referred to in the standards currently in force.

MATERIALS AND METHODS

Data Collection

As a first stage in implementing the intercomparison exercise, a protocol was developed and sent to the participating companies before conducting the tests. The protocol, drawn up in accordance with the criteria established in Criterios Generales de Acreditación (CGA)-Entidad Nacional de Acreditación (ENAC)-Proveedores de programas de inter-comparaciones (PPI) revision 1,7 described the measurement points, the system for checking the representativeness of each measurement, the methodology for making simultaneous measurements, the scheduling for the exercise, etc.

Data collection in the field consisted of simultaneous measurements of the different pollutants to be analyzed in this study by the accredited companies participating in the exercise. The 13 participating companies set up their measuring equipment at the exit outlet of an oven chimney flue in the cement plant. The flue had a diameter of 4.5 m and four internal outlets, each approximately 80 mm in diameter. The fact that it had four outlets enabled simultaneous sampling of the measurements of all of the participating companies, thereby satisfying the distance criteria established in the UNE-EN 13284-1 standard.8 Figure 1 shows the data collection procedure; a detail of one of the data collection points shows several probes operating simultaneously.

Figure 1. (a) View of the chimney where the intercomparison exercise was conducted. (b) Detail of one of the outlets where data were collected.

In the cement plant, milling products composed mainly of lime and, to a lesser extent, loam are placed in the clinker oven (an oven for the base product for manufacturing cement composed mainly of tricalcium silicate) and ceramic residues and lodes are added from industrial purification plants along with suitable proportions of clay, sand, and iron-bearing materials. Clinker size is in the range 0–100 μm. Oven temperatures are between 1400 and 1500 °C, and the fuel used is typically petroleum coke, a firing fuel, and a small proportion of dry lode from a purification plant.

The gases from the clinker oven exit through the chimney. Of the pollutants (listed in full below), only results for total organic carbon (TOC) are provided, given that the methodology used to detect outliers was the same for all of the gases). The TOC limit established by the standard is 50 mg/Nm,3 and all of the measurements made for this research were well below this value.

TOC was measured using the following equipment: PCF Elettronica volatile organic compound analyzer 2001, Bernath atomic 3006, Thermo FID 1850, Nira mercury 911, and especially Nira mercury 901, which was used by 7 of the 13 companies.

Measurements were made in all cases for the period of an hour, with data recorded each minute. All of the participating companies are recognized and approved as environmental control companies by the Catalan Autonomous Government's Department of the Environment and Housing, which means that they have homologated equipment and suitably trained staff to perform the measurements.

The pollutants measured and the techniques used for measurement were as follows:

•	Emissions of solid particles from a stationary emission source, in accordance with the UNE-EN 13284-1 standard.8
•	Emissions of sulfur dioxide from a stationary emission source, in accordance with the UNE-EN 14791 standard.9
•	Emissions of combustion gases (carbon monoxide [CO], oxides of nitrogen [NOx], and oxygen [O2]), in accordance with the UNE-EN 15058,10UNE-EN 14792,11 and UNE-EN 1478912 standards, respectively.
•	Emissions of combustion gases (CO, nitric oxide [NO], nitrogen dioxide [NO2], NOx, and O2) from a stationary emission source, in accordance with the American Society for Testing and Materials (ASTM) D-652213 standard for using an electro-chemical cell pack.
•	Emissions of TOC from a stationary emission source, in accordance with the UNE-EN 12619 standard.14

Comparison Based on European Standards

The interpretation of the results using the statistical method defined in international standards for the determination of pollutants was based on assuming that pollutant levels followed a Gaussian distribution and on determining a reference value. The procedure was as follows:

•	Elimination of outliers. The method for eliminating outliers was based on the recommendations of the International Union of Pure and Applied Chemistry (IUPAC) document entitled “Harmonized Protocol for the Proficiency Testing of Chemical Analytical Laboratories,”15 which describes how to establish the acceptance interval. According to this document, anomalous results are those outside of the interval (M − 1.5d, M +1.5d), where M is the median and d is the difference between the third and first quartile.
•	Capture of the consensus values from the remaining (nondiscrepant) values. A reference value (the mean of the accepted results) and a σ value (the standard deviation of the accepted results) were calculated from the values included in the acceptance interval.
•	Classification of the participants. The classification criterion for the participants applied the Z-score, which is used in aptitude tests to determine competence in performing specific tests. According to the ISO/IEC 43 guidelines,16 this parameter is calculated according to the following expression: 1 where V i is the mean value of the observations by participant i, V r is the reference value, and σ is the standard deviation of the sample.

The interpretation criteria are as follows:

•	zi ≤ 2 → satisfactory
•	2 ≤ zi ≤ 3 → uncertain
•	zi > 3 → unsatisfactory

This method has some well-known drawbacks: (1) it assumes that the data are distributed normally, (2) the limits used in the interpretation are heuristic, (3) the mean and standard deviation are affected by the outliers, and (4) it is not suitable for small samples. Furthermore, like other univariate and multivariate statistical methods used to detect outliers, it is not appropriate for functional data for the following reasons21: (1) the time correlation structure is ignored; (2) the infinite dimensionality of the functions means that methods for multivariate samples are greatly affected by the curse of dimensionality; (3) many of these methods are implicitly restricted to Gaussian or elliptical populations; and (4) outliers may not be detected for each time instant in a curve, yet the curve itself may be an outlier.

Comparison Using Functional Data Analysis

The sample used for this research was composed of discrete data for gas emissions collected at intervals of 1 min over the period of 1 hr. Because these observations can be considered as points representing continuous observations, they can be approximated using curves. Although the detection of differences between curves is easy if the intersection is empty, this is not always the case. In the case of the curves, outliers were detected from a definition of depth. The following sections describe how the data were smoothed to construct curves from the discrete observations, explain different depth measurements, and describe how outliers were detected from the depth measurements.

The Smoothing Process. It is quite normal to observe only the values x _i i = 1,…, n, in a functional model and not the of points x _i(t _j), , which, for simplicity sake, are assumed to be common to all of the functions in what follows below.

Moreover, observations may be subject to noise, and in this case they take from

(2)

where ε_ij is assumed to be random noise with zero mean, i = 1,…,n, j = 1,…,n _p.

The functional focus first requires the sample functions to be smoothed, which requires an estimation of each function x _i ∈ X ⊂ F, i=1,…,n.

The approach is based on assuming that F = span{φ₁,…,φ_nb}, where {φ_k} is a set of basic functions.17

If, for simplicity sake, any function in the sample is represented by x _i, i = 1,…,n, then this can be written as

(3)

The smoothing problem now consists of determining the solution to the following regularization problem:

(4)

where Z_j=X(t _j) + ε_j is the result of observing x in point t _j, where Г is an operator that penalizes the complexity of the solution and where λ is a regularization parameter. Adopted in this case is the operator where and where D ² is the second-order differential operator.

Bearing in mind the expansion defined in eq 3, the problem of eq 4 may be written as

(5)

where z = (z ₁,…,z _np)^T, c = (c ₁,…,c _nb)^T, is the matrix n _p × n _b with elements Φ_jk =Φ_k(t _j) and where R is the matrix n _b × n _b with elements:

(6)

The solution to this problem is given by c = (Φ^TΦ+ λR)⁻¹[Φ^Tz, in such a way that the estimated values for x in the observation points is obtained by x = Sz, where S = Φ(Φ^TΦ+λR)⁻¹[Φ^T, and where x = (x(t ₁),…,x(t _np))^T.

The selection of λ forms part of the problem and is usually done using crossvalidation.

Functional Data Depth Measurement

Depth measurement was originally included in multivariate analysis to measure the centrality of a point with respect to a points cloud. Depth information enables points to be ordered in a Euclidean space, from the center to the outside, in such a way that the points nearer the center are deeper.

Recently, the idea of depth has been extended to functional data.18–20 The aim of data depth for functional data is to measure the centrality of a given curve within a set of curves. Depth and outlyingness are inverse notions: Functional outliers are curves that are expected to be far away from the center of the data and correspond to curves of significantly low depth.21

The most frequently used depth measurements are as follows:

•	Fraiman–Muniz depth. Let F n,t(x i(t)) be the accumulative empirical distribution function18 for the values for the curves {x i(t)}i n =1 in an instant t ∈ [a,b] of time given by (7) where I(·) is the indicator function. Thus, Fraiman–Muniz functional depth (FMD) of a curve x i with respect to a set of curves x i,…,x n is given by (8) where D n(x i(t)) is the point depth given by (9)
•	H-modal depth. On the basis of the mode concept, the functional mode is defined as the curve that is most densely surrounded by the remaining curves in the sample. H-modal depth (MD)19 is expressed as (10) where is a kernel function, is a norm in a functional space, and h is the bandwidth parameter. One of the norms most frequently used in a functional space is L 2, given by (11)

Also Cuevas et al.20 recommend to use the infinite norm L ^∞:

(12)

Meanwhile, the different kernel functions K(·) can be defined, among them the truncated Gaussian kernel19:

(13)

Functional Outliers

A functional sample set may have elements that, although they do not incorporate error in themselves, may feature patterns different from the others. The depth measurement criterion described above is used to identify outliers in functional samples. Depth and outlier are inverse concepts; thus, an outlier for a functional sample will have considerably less depth. The curves with the greatest depths are sought to identify functional outliers.

One of the depth measurements described above, , was used to generate the outlier selection criterion. Selected was a cutoff in the absence of outliers in such a way that 5% of correct observations were wrongly identified as outliers (type I error):

(14)

Unfortunately, the distribution of the functional depth chosen was unknown (C is the first percentile), and so the value for C needed to be estimated. Of the different approaches to estimating this value,21 for the purpose of this research, a method was chosen based on the bootstrapping technique22 and applied to the curves in the original set with a probability proportional to their depth. The bootstrapping technique can be summarized in the following steps:

•	A new sample is extracted from the original sample by means of sampling with replacement; in other words, each extracted element is replaced after extraction and so may be selected again.
•	On the basis of the new sample, the population parameter of interest is estimated on the basis of the construction of a statistic.
•	The two steps above are repeated until many estimates are obtained.
•	Finally, the empirical distribution of the statistic is determined.

APPLICATION AND RESULTS

The sample of 13 functions corresponded to measurements made by 13 different companies accredited to assess gas emissions by a cement plant in Catalonia, Spain. These emissions were measured for a time interval of 1 hr with data recorded each minute. Given that the procedure for comparing observations is identical for each gas measured, whether using the conventional statistical method or the functional data analysis method, only the results for TOC will be shown. For the rest of the gases, the discussion is analogous.

Figure 2a shows the mean values obtained by the 13 companies. The horizontal lines indicate the values that define outliers according to the IUPAC criterion. It can be observed that the mean values for each company fell within the limits marked by the outliers. The lower part of Figure 2 shows the Z-score values. Thus, on the basis of the IUPAC criterion, the measurements made by the 13 companies are equivalent; that is, from a statistics point of view, they all come from the same population.

Figure 2. (a) Mean values for the observations of 13 companies and upper and lower lines defining outliers. (b) Z-score values calculated according to ISO/IEC 43.

It is important to note that the conventional inter-comparison method assumes that gas concentrations are normally distributed. The normality hypothesis is thus taken for granted and is generally not tested. However, in this case, the Shapiro–Wilkes normality test23 was applied, with the results showing that two of the companies failed the normality test (for a level of significance of 5%) once outliers had been eliminated in the set of observations made by each company.

The functional analysis of the outliers was conducted using the H-modal depth measurement described above. Figure 3a shows the result for this technique, with one functional outlier detected (Figure 3b). One thousand splines were used as basis functions with 10⁻⁶ as the mean quadratic error obtained. It can be observed that the range of concentrations for the set of 13 curves is approximately 6.5–10.5 mg/m³. The curves, although complex, are similarly shaped and maximums and minimums largely coincide. The lags indicate that not all of the equipment began measuring at exactly the same instant. The curve detected by the functional method as an outlier is evidently above the other curves.

Figure 3. (a) Representation of the curves for the gases measured. (b) Outliers detected using the H-modal functional approach.

In addition to the Z-score vectorial analysis, an analogous sample analysis was performed from a functional focus so as to identify the curves that deviated from the mean and the degree of deviation in terms of the number of standard deviation units. If curve deviation is graphically represented with respect to the mean and the result compared with the standard deviation, it can be observed (Figure 4) that the curve that turned out to be an outlier according to the functional analysis was slightly above the line corresponding to 2 standard deviations. More specifically, 25% of the measurements deviated from the mean by more than 2 standard deviations. Even so, the Z-score method failed to detect this set of measurements as a possible outlier. To test the incapacity of the Z-score to detect outliers, some of the measurements for this curve were artificially modified to have 41% of the total with deviations more than 2 standard deviations, again the method failed to detect the curve as an outlier. Therefore, it would seem that the conventional method for comparing observations is overly simplistic because it only uses the mean value of the observations over time and fails to take temporal variations into account.

Figure 4. Functional sample showing how the outlier detected using functional analysis deviates, at particular points in time, more than 2 standard deviation (std) units with respect to the mean of all of the curves.

Following the same methodology, another functional outlier was detected for the NO_x, although it does not correspond to the same company. Again, this outlier was not detected by the Z-score method.

CONCLUSIONS

Functional data analysis and the conventional method described in international standards were compared in terms of their capacity to detect differences in gas concentration measurements made by accredited companies.

A study of outliers enables an assessment of measurements that correspond to a stochastic distribution process that is different from the other measurements.

The application of the two techniques to the case described gave rise to different results. The conventional method failed to detect any outliers, whereas the functional method identified 1 of the 13 companies as providing measurements different from the others. It was graphically proven that there were several time instants (corresponding to 25% of the total measuring time) in which the measurements carried out for that company differed from the mean by more than 2 standard deviations.

An additional advantage of functional data analysis is that it does not require the assumption of a normal distribution for the emission measurements. It would seem that the Z-score method is not appropriate for functional measurements such as those measured over time because one of its main drawbacks is that it oversimplifies the comparison process to reducing it to a comparison of mean values.

The authors consider these results to be sufficiently significant for research to continue for further examples that support using the functional approach rather than the Z-score method. The ultimate outcome would be the replacement of the conventional method for detecting outliers with the proposed functional method, which could be supported by the development of software with a graphic interface that would automatically make the calculations. People with only basic mathematical knowledge could therefore rapidly perform the intercomparison studies.