Improvements on electromagnetic fields exposure assessment in rolling stock

Transcription

1 Improvements on electromagnetic fields exposure assessment in rolling stock A. Gaggelli & E. Mingozzi TRENITALIA.p.A. Unità Tecnologie Materiale Rotabile, Italy Abstract Electromagnetic fields emissions have to be properly considered during exposure level assessments, especially within all the environments where they assume a very complex shape and specific features. uch electromagnetic areas may exist inside rolling stock. Even if they can be treated by general standards such as those issued by the International Commission on Non-Ionizing Radiation Protection (ICNIRP), by the European Council and by the Italian tate, a recent ICNIRP publication suggests processing these kinds of radiations more effectively. Through the present work, this concept has been applied to the exposure level assessment inside rolling stock. Different feasible implementations are compared, error analyses have been performed and practical hints are given. In addition, some results pertaining to real measurements on modern a train are discussed. Keywords: magnetic fields, exposure level, ICNIRP standard, numerical filtering, measurement technique. 1 Introduction At present days, the exposure level assessment is becoming a field more and more important. One of the most affordable and scientifically based standard is that issued by the International Commission on Non-Ionizing Radiation Protection (ICNIRP), namely the ICNIRP Guidelines [1]. It is worth noting that this kind of guidelines are appropriate in evaluating emissions inside involved environments, and some measurement techniques and analysis procedures have been developed to address this task in railways [ 4]. Nevertheless, considering the particular emissions present inside rolling stock, mainly due to traction systems, electrical motors and other power devices, 4 WIT Press, IBN

2 54 Computers in Railways IX a specific and more accurate approach has been suggested [5]. It proposes not to sum all the contributions at different frequencies, regardless the actual phase of each component [1], but it considers them as are, collecting all contributions by means of an [5]. In March 3, the ICNIRP issued a statement [6] that picked up this suggestion and declares the filtering approach is suitable on determining compliance of exposure to pulsed and complex non-sinusoidal waveforms below khz with its Guidelines [1]. Besides improving the accuracy of results, this method avoids most of the computations required to implement ICNIRP Guidelines [ 4], speeding up the analysis process. There are no more needs to pay attention to emissions stationary scale, time to frequency transformations are unnecessary and further computations useless; a simply filtering operation produces a precise exposure value. On the other hand, it is worth mentioning that a simple may be not sufficient to address the complete problem (three axial magnetic fields), hence other non-linear electronic circuits should be used in order to achieve exhaustive exposure level data. Because we analyze rolling stock emissions also for other EMC investigation [4], we need sampling and recording them in digital form. These two reasons make useful adopting the ICNIRP statement [6] by means of a digital filter. Digital filter development The goal is implementing the ladder network high-pass RC suggested in [6], through a numeric filter. The transfer function of the analog filter is jωτ H a ( jω) = g, (1) 1 + jωτ where τ = RC is the filter time coefficient, g the gain, ω = πf the angular pulsation and f the frequency. Considering workers reference limit, it is approximated by (1) if τ = µ s and g = 1/ 43. 4, whereas choosing τ = 194µ s and g = 1/ 8. 84, equation (1) describes general public reference limit [6]. Plots in Fig. 1 show workers and general public reference limit as represented by (1). Due the previously mentioned reasons it is suitable developing the RC highpass filter in a numeric form. The most immediate approach resorts to the discretization of the differential equation that relates the output voltage of the ladder network v ( ) with the input voltage v ( ), that is t 1 t d v ( t) =τ [ v1( t) v ( t) ]. () dt ubstituting the derivative operation in () with the following discrete expression 4 WIT Press, IBN

3 Computers in Railways IX 55 d dt [ v ( t) v ( t) ] 1 t= kt [ v ( k) v ( k) ] [ v ( k 1) v ( k 1) ] 1 T 1, (3) where v ( ) and v ( ) are respectively the input and output voltage at time t = kt 1 k k, and T is the sampling interval, we obtain the finite-difference equation v ) = f τ f τ f τ k v1 ( k) v1( k 1) + v ( 1+ f τ 1+ f τ 1+ f τ k ( 1), (4) where f = 1/ T is the sampling frequency. According the standard representation of such a time-discrete equation, the coefficients in (4) are collected in two elements array, f τ f τ f τ A = 1, B =. (5) 1+ f τ 1+ f τ 1+ f τ ura 5. Modulo della risposta in frequenza del filtro passa-alto RC. La traccia sa è relativa al caso dei lavoratori, la traccia blu al pubblico. -1 Magnitude Figure 1: Frequency response of the analog high-pass RC filters, continuous curve traces general public limit, dashed curve traces workers limit. The comparison between the frequency behavior of the and the above synthesized numeric one is depicted in Fig.. The sampling frequency is f = 48 Hz and the filter time coefficient is τ = µ s. 4 WIT Press, IBN

4 56 Computers in Railways IX 9 Magnitude [db] RC Phase [degree] RC (a) (b) Figure : Comparison between the high-pass RC (dashed curve) and the numeric one (continuous curve): a) magnitude, b) phase. 3 Numeric filter performance At first, the high-pass filter performance can be assessed applying it a simple monochromatic signal. Let us considering a three components magnetic induction radiation, with µt magnitude each and 1 Hz frequency (such a frequency value is far enough from the filter cut-off frequency). This signal lasts 14 s and it has been sampled at 48 Hz. The ICNIRP index quantity representative of the exposure level of this emission has been computed with the analytic formula (or exact), with the standard numeric procedure adopted by Trenitalia.p.A for the exposure level assessment according the ICNIRP Guidelines [], with the high-pass and with a high-pass. Taking into account for this test signal, the outcome values should be the same regardless from the method but, as reported in Tab. 1, there are some disagreements between the different filter implementations. Table 1: Comparison between the different methods of ICNIRP index evaluation. Method ICNIRP index value Error % ICNIRP Guidelines, exact ICNIRP Guidelines, numeric procedure [] ICNIRP tatement [6], with.8 4 ICNIRP tatement [6], with Moreover, the exhibits a lower accuracy with respect to the Butterworth one. Thus, it appears interesting to investigate on these differences, characterizing each filter and evaluating their performance. 4 WIT Press, IBN

5 4 Filter characterization, design and optimization Computers in Railways IX 57 It is quite evident that the frequency behavior of a numeric filter will trace that of the corresponding analog so much better how much greater the sampling frequency is. As the sampling frequency increases the sampling interval decreases, hence the discrete approximation (3) improves. For sake of simplicity, it could be put in evidence a graphical way. Figs. 3 collects three pictures, depicting the frequency response (in magnitude) of the numeric filters implementations RC numeric and Butterworth compared with the reference one analog for three different sampling frequencies: 48 Hz in Fig. 3a, khz in Fig. 3b and 4 khz in Fig. 3c. Of course, all the three filters have the same time coefficient τ = µ s, or 8 Hz cut-off frequency, and are representative of the general public ICNIRP limit Magnitude [db] Magnitude [db] fs=48 Hz -5 f s= khz -8 (a) (b) -5 - Magnitude [db] f s=4 khz (c) Figure 3: Magnitude plots of the three different filters: analog (continuous curve), RC numeric (dotted curve), Butterworth (dashed curve). a) 48 Hz sampling frequency; b) khz sampling frequency; c) 4 khz sampling frequency. 4 WIT Press, IBN

6 58 Computers in Railways IX From the comparison of the plots in Fig. 3 it can be proved that both of the numeric filters trace better the analog one as the sampling frequency rises. The first order Butterworth numeric filter has been designed, and its coefficient computed, by using MATLAB package. This filter exhibits superior performance with regard to the RC numeric. Both for f = khz and f = 4 khz, acts as the analog one. The comparison of the phase plots of the three filters yields the same conclusions. 4.1 Error analysis on the ICNIRP index A more striking estimator of the filters performance is definitely represented by what the real target is: the ICNIRP index value. On this basis, it can be effectively pointed out similarities and differences between the numeric filters and also with respect to the actual ICNIRP curve limit. Let us consider the ICNIRP general public limit and a sample sinusoidal emission with a certain frequency f and magnitude A M (peak value). We also assume this sinusoidal signal as one of three axial components of magnetic flux density. Taking into account only for this component in the ICNIRP index evaluation, as stated in [1], we have AM / I( =, (6) B ( where B L ( is the reference level (limit) at frequency f; B L ( can be obtained from the specific table in [1]. On the other hand, following the new computational approach suggested by the ICNIRP tatement of March 3 [6], the ICNIRP index is given by L ~ I ( = W ( /, (7) where W ( is the frequency response of the filter, just normalized to match the selected reference levels (general public or workers). In the case of general 6 1 public limit, the normalizing factor is 1/ 6.5 [ T ]. Considering the RC, from (1), we have A M = W a ( πfτ (πfτ ). (8) Computing ICNIRP index by means of the, it is immediate gathering an analytic expression for the relative error e I (. Recalling the expressions (7) and (8), follows 4 WIT Press, IBN

7 ~ I ( I( ei ( = = Wa ( BL ( 1. (9) I( The above relation (9) can be generalized for the case of numeric filters employed in the ICNIRP index evaluation. We achieve ~ I ( I( ei ( = = Wn ( BL ( 1, () I( where W n ( is the frequency response of the exploited numeric filter, properly 6 1 normalized by the coefficient 1/ 6.5 [ T ] (general public reference level). Comparing the ICNIRP reference limit to the corresponding one outlined by the, a mismatching between them is present around 8 Hz filter cut-off frequency with about 3% maximum error. ince this mismatching arises within a small frequency interval, it is not an inconvenience in exposure estimation because ICNIRP limits are widely precautionary, as asserted in [6]. In agreement with the former outcomes of this section, we can expect that the error tend to those given by (9) as the sampling frequency augments. This confirmation comes out from the plots of the relative error e I ( drawn in Fig. 4. It is easy showing that expression (9) and () hold also for the case of three spatial components, as a matter of fact and AxM + AyM + AzM / I( =, (11) B ( L Computers in Railways IX 59 I ~ ( = ( W ( A ) + ( W ( A ) + ( W ( A ) = W ( A xm xm + A ym + A zm ym / zm /. (1) Therefore, the relative error expression is ~ I ( I( ei ( = = W ( BL ( 1, (13) I( which assumes the same glance of the other one (single spatial component). 4 WIT Press, IBN

8 6 Computers in Railways IX Relative error [%] (a) f s=48 Hz Relative error [%] (b) f s= khz -5 - Relative error [%] (c) f s=4 khz Figure 4: Relative error plots of the ICNIRP index yielded by the three filters: analog (continuous curve), RC numeric (dotted curve), Butterworth (dashed curve). a) 48 Hz sampling frequency; b) khz sampling frequency; c) 4 khz sampling frequency. 4. Filter selection and optimization tarting from the above considerations, it results that the immediate solution in designing a numeric filter, that is the straight discretization of RC analog differential equation, is not the best choice. The synthetic shows higher performance compared to the previous one. For this reason we adopt a first order high-pass with an adequate sampling frequency. Obviously, the filter sampling frequency is related to that of its input signal. If the input signal sampling frequency is high enough there are no troubles with the filters behavior. A bit more attention should be paid if the frequency extension of the input signals is not large enough. As shown in Figs. 3, good filter performance needs a sampling frequency that could be greater than input signal sampling frequency. We can overcome this problem by pre-processing the input signal (up-sampling), 4 WIT Press, IBN

9 Computers in Railways IX 61 then applying it the numeric filter and finally down-sampling the filtered signal. This way of proceeding may represent an optimization in the application of the present technique and allows us using a numeric filter accurate as needed. 5 Application to real data Both RC numeric and s are used for the analysis of current measured magnetic flux density emissions inside rolling stock. The results herein reported are related to an area next to a power drive system of a modern double deck commuter train belonging to Trenitalia.p.A fleet. The frequency span of these emissions is bounded in the range (5, 8) Hz they are and sampled at 48 Hz. By using the same sampling frequency 48 Hz in the filters design procedure, namely the RC numeric and Butterworth, the obtained ICNIRP index curves are depicted in Fig. 5a. The main distinction between them is an offset, which is due to the different behavior of the numeric filters, as aforementioned. Designing the two filters with a 4 khz sampling frequency and applying the upsampling/down-sampling hint to measured/filtered data, similar results are produced in both cases. To emphasize the residual differences, in Fig. 5b we plots the percentage relative error between them. The two ICNIRP index curves are very close, since maximum of the plot in Fig. 5b is 1.3%. Also, the overall root mean square error normalized to the entire number of samples is worth.8-7. ICNIRP index (general public) Relative error % Time [s] (a) Time [s] (b) Figure 5: a) ICNIRP index computed by the (background plot) and the (foreground plot); b) relative error between the outcomes of the RC numeric and Butterworth numeric filters. 4 WIT Press, IBN

10 6 Computers in Railways IX 6 Conclusion In this communication, the most recent ICNIRP tatement to assess exposure levels in environments with low-frequency pulsed and complex non-sinusoidal electromagnetic fields has been applied. Certain railways environments and rolling stock areas exhibit such features. An analysis technique has been developed, comparing performance of different solutions and pointing out some critical aspects. This method not only results exposure levels much closer to real emissions with respect to the overestimations produced by the general approach [1] but also it meaningfully reduces the processing time during the ICNIRP index computation. References [1] ICNIRP, Guidelines for limiting exposure to time-varying electric, magnetic, and electromagnetic fields (up to 3 GHz), Health Physics, 74(4), pp , [] Trenitalia.p.A., Caratterizzazione dei campi magnetici a bordo di rotabili ferroviari (5 Hz khz), Int. norm TI.UTMR.CEM1.1, 3. [3] Gaggelli, A., Puliatti, G. & Violi, A. G., A measurement and analysis technique for evaluating exposure to low frequency electromagnetic fields. Proc. of 8 th Int. Conf. on Computer Aided Design, Manufacture, and Operation in the Railway and Other Advanced Mass Transport ystems, COMPRAIL VIII, Lemnos, Greece, pp ,. [4] Bellan, D. et al., Measurement and analysis of low-frequency magnetic field emissions in rolling stock. Proc. of the European ymposium on Electromagnetic Compatibility, orrento, Italy, pp ,. [5] Jokela, K., Restricting exposure to pulsed and broadband magnetic fields. Health Physics, 79(4), pp ,. [6] ICNIRP, Guidelines on determining compliance of exposure to pulsed and complex non-sinusoidal waveforms below khz with ICNIRP guidelines. Health Physics, 84(3), pp , 3. 4 WIT Press, IBN