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Radiation Measurements journal homepage: www.elsevier.com/locate/radmeas

A machine learning approach to glow curve analysis a

a,∗

a

Kevin Kröninger , Florian Mentzel , Robert Theinert , Jörg Walbersloh a b

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Technische Universität Dortmund, Lehrstuhl für Experimentelle Physik IV, Otto-Hahn-Str. 4a, 44227, Dortmund, Germany Materialprüfungsamt NRW, Marsbruchstr. 186, 44287, Dortmund, Germany

A R T I C LE I N FO

A B S T R A C T

Keywords: TL-DOS Thermoluminescence Glow curve analysis Fading time estimation Irradiation dose estimation Machine learning

We present a ﬁrst study of using artiﬁcial neural networks to estimate the fading time and irradiation dose using glow curve data from LiF thermoluminescent (TL) dosemeters. The resulting uncertainties in the inference process are compared to those obtained in previous studies without machine learning algorithms. The current study is based on measurement and simulated data using an eﬀective model of the kinetic parameters. We show that the resulting uncertainties of the estimated quantities can be signiﬁcantly reduced with the machine learning algorithm applied: fading times of up to 30 days can be predicted with an uncertainty of up to 10%, irradiation doses larger than 1 mSv can be estimated with an uncertainty of up to 10% for batch-calibrated dosemeters.

1. Introduction Personal dosimetry is an important aspect of radiation safety. A large variety of systems exist to measure and quantify irradiation doses, e.g. ﬁlm-badge dosemeters, electronic dosemeters and dosemeters based on the phenomenon of luminescence. For systems based on thermoluminescence, the time-resolved response of the dosemeter to heating is referred to as glow curve and it is characterized by a sequence of glow peaks. While the total number of photons of a glow curve gives information about the irradiation dose, we have shown in Ref. Theinert et al. (2018) that the relative peak heights can give further dosimetric information, in particular on the time between irradiation and readout. The estimation of this time span, also known as fading time, is of special dosimetric interest as its correct reconstruction provides the date of irradiation for single irradiation scenarios. The knowledge of the fading time also provides a non-destructive approach towards irradiation dose estimation under the impact of ambient temperature signal loss (see Ref. Theinert et al. (2018) for details). In comparison, the successfully used and well known method of post irradiation annealing for fading time correction (e. g. Ref. Walbersloh and Busch (2015)) results in a signiﬁcant loss of dosimetric information due to the preheating process involved. In this publication, we present a ﬁrst approach to irradiation dose estimation using artiﬁcial neural networks. The study is based on measurements conducted with thin-layer LiF:Mg, Ti thermoluminescent (TL) dosemeters of the TL-DOS system, ﬁrst described in Ref. Walbersloh and Busch (2015). The experimental setting and the data

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sets used are that described in Ref. Theinert et al., 2018. Instead of using the peak heights and their ratios directly to estimate the irradiation dose and the fading time, respectively, we train shallow neural networks to combine the information and correlate their output with either of these two quantities. In supervised machine learning, the availability of ground-truth data is a key to success. Since, however, the data set at hand is limited to a few well-deﬁned irradiation doses and fading times, an eﬀective model is developed which allows the simulation of glow curves. These simulations are used to optimize, test and validate the machine learning algorithm used in this study. The simulated data are also compared to measured data. The structure of this publication is as follows: the glow curve model and its simulation are described in Sections 2 and 3, the experimental setup and the data set used in this study are summarized in Section 4. Section 5 introduces the machine learning algorithms used for the inference problem at hand and the results of the studies are presented in Sections 6 and 7. Section 8 summarizes the studies and gives an outlook to possible improvements and further applications of machine learning in the analysis of glow curves. 2. Glow curve model Glow curves from LiF:Mg, Ti dosemeters in the range from 270 K to 570 K comprise of ﬁve glow peaks, P1 to P5, with individual half-lives ranging from minutes to years and they are typically modeled in temperature space, see e.g. Ref. Harvey et al. (2010) and references therein.

Corresponding author. E-mail address: ﬂ[email protected] (F. Mentzel).

https://doi.org/10.1016/j.radmeas.2019.02.015 Received 26 September 2018; Received in revised form 30 January 2019; Accepted 19 February 2019 Available online 26 February 2019 1350-4487/ © 2019 Elsevier Ltd. All rights reserved.

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Fig. 2. The measured average relative values of Im for P3 are shown as a function of the fading time for irradiation doses between 1 mSv and 10 mSv. Also indicated is the parameterization with the corresponding uncertainty band.

Fig. 1. A typical glow curve for a dosemeter irradiated with 15 mSv and a fading time of less than 2 h. The individual peaks identiﬁed by a ﬁt of the model to the measurement data are also indicated. The bottom plot shows the difference between the measurement data and the ﬁtted glow curve. A 5%-uncertainty band is also shown.

As P1 has decayed completely for essentially all practical purposes, the glow curve is represented by the sum of peaks P2 to P5. The photon intensity of the individual peaks in our model are described as a function of the temperature by Equation (25) of Ref. Kitis et al. (2006). This function is based on Ref. Randall and Wilkins (1945), modiﬁed to take into account an exponential heating function and characterized by a well-deﬁned set of kinetic parameters according to Ref. Kitis et al. (2006). These are the maximal peak intensity, Im , the temperature of the peak maximum, Tm , and the parameter E which represents the width of the peak. The background is modeled by the sum of an exponential and a reciprocal term. Fig. 1 shows the ﬁtted glow curve from a dosemeter irradiated with a dose of 15 mSv and read out after a fading time of less than 2 h. The ﬁgure also shows the individual peaks P2 to P5 and the diﬀerence between the measurement data and the ﬁtted glow curve. A 5%-uncertainty band is shown to guide the eye and to give an impression about the agreement between the measurement data and the model.

Fig. 3. Simulated glow curves for diﬀerent fading times without background contributions.

times of zero days, three days and 25 days. As expected, the peak heights change signiﬁcantly with the fading time and with diﬀerent half-lives associated with the peaks. P2 vanishes over a time of 25 days. P3 increases ﬁrst and then decreases. The increase can be interpreted as clear sign of re-trapping being involved in the fading process. P4 and P5 increase monotonically over that time span. In order to take into account background and detector eﬀects, the predicted glow curves are transformed into the time regime by integrating the photon counts between discrete time points. Using ﬁxedwidth time intervals, the temperatures are computed using an exponential heating function. After the transformation, each bin is smeared by a Poisson term with an expected number of occurrences (λ) set equal to the integrated bin content. The re-transformation into the temperature space is done in the same form as for measurement data. The necessary steps are presented in detail in Ref. Theinert et al. (2017). Fig. 4 shows an example for glow curves from the simulation and the average measurement data set for an irradiation dose of 5 mSv and a fading time of 24 h. The uncertainty band shows the standard deviation of the measurement data and the Poisson-smeared simulation per temperature bin. The simulation and average measurement data curve show a reasonably good agreement, the maximum deviation observed is about 10%. The comparison in Fig. 4 is exempliﬁed, the simulation shows a very similar agreement for both the whole irradiation dose and fading time range included in the measurement data.

3. Eﬀective simulation of glow curves A ﬁrst approach towards glow curve simulation is developed as an eﬀective simulation based on a parameterization of the kinetic parameters: First, all glow curve data are ﬁtted with the model described in the previous section. Then the kinetic parameters Im , Tm and E for each peak are parameterized as a function of the irradiation dose and the fading time. Linear functions are used for the parameterization of Im as a function of the dose, the parameters Tm and E are kept constant. In contrast to that, all kinetic parameters, including E and Tm , were found to show a fading time dependence. This fading time dependence is parametrized using exponential functions with polynomial correction terms for all kinetic parameters. As an example, Fig. 2 shows the measured average relative values of Im for P3 as a function of the fading time from a batch of dosemeters irradiated with doses between 1 mSv and 10 mSv. Also indicated is the parameterization with the corresponding uncertainty band. The agreement between the parameterization and the measurement data is reasonable for all kinetic parameters. In this eﬀective model, the kinetic parameters are now purely a function of the irradiation dose and the fading time, and these two eﬀects are assumed to be independent. For each such pair of values, a glow curve can be predicted. The glow curves are binned with bin widths of 2.5 K. Fig. 3 shows three simulated glow curves for fading 35

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Fig. 4. Glow curves from the simulation and the average data set for an irradiation dose of 5 mSv and a fading time of 24 h. The uncertainty bands show the standard deviation of the measurement data and the simulated data per temperature bin.

Fig. 7. Illustration of the temperature-space features.

Fig. 8. Linear correlation coeﬃcients between the diﬀerent features.

an example of a quantity derived from measured and simulated glow curves, namely the intensity of P3 divided by that of P4 . The agreement between simulation and measurement data is reasonable.

Fig. 5. A measured peak ratio Im3/ Im4 as a function of the fading time compared to the simulation results.

4. Data sets and simulations The measurement data set used comprises of glow curves from 1,600 measurements for which the TL dosemeters have been irradiated with doses ranging from 0.5 mSv to 10 mSv and with fading times between 30 min and 41 d. The dosemeters were not individually calibrated, but batch-wise. Details of the experimental setup and the measurement data set can be found in Ref. Theinert et al. (2018). For the simulated data set, a total of 100,000 glow curves have been simulated. The dose values and fading times for which the glow curves are calculated are randomly distributed between 1 mSv and 15 mSv and between 0 d and 41 d, respectively. 5. Machine learning Machine learning algorithms are known since decades and have been applied in a variety of scientiﬁc ﬁelds. With the ever-increasing computational power of modern computer systems, the development and application of machine learning algorithms also outside the scientiﬁc realm has recently experienced a very strong boost. Artiﬁcial neural networks are one such class of algorithms. They are characterized by a set of input variables (features), one or several output nodes and a set of hidden layers with a variable number of nodes connecting the input and output layers. The simplest variant of an artiﬁcial neural

Fig. 6. Illustration of the time-domain features.

The statistical ﬂuctuations of the simulated glow curves including detector eﬀects are smaller than the standard deviation observed for the data. This is the case for the majority of data sets because the dosemeters were not calibrated individually and the intrinsic variation of the sensitivity is less than 5% for doses larger than 1 mSv. Fig. 5 shows 36

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Fig. 9. Two-dimensional scatter plot of two features illustrating the sensitivity of the approach to the fading time.

Fig. 11. Estimated total uncertainty of the reconstructed fading time (red line). Also shown are the uncertainty from non-linearities (dashed green line) and the statistical uncertainties (dashed blue line and markers). The uncertainty estimate from our previous studies (dashed orange line) is also shown, together with the 50% and 100% uncertainty ranges. (For interpretation of the references to colour in this ﬁgure legend, the reader is referred to the Web version of this article.)

Fig. 10. Predicted fading time as a function of the true fading time for the measurement data (blue markers) and for the simulation data (red line) including the uncertainty band. (For interpretation of the references to colour in this ﬁgure legend, the reader is referred to the Web version of this article.)

network is a perceptron introduced in the 1950's (Rosenblatt, 1958) to model information processing of the brain. For the current study, we use the Multilayer-Perception implementation of fully connected neural networks from the scikit-learn package (Pedregosa et al., 2011) to infer on the irradiation dose and the fading time. A fully connected neural network consists of layers of neurons where every neuron is connected with all neurons in both the previous and in the following layer. The ﬁrst layer consists of the input features. The output of each node is a function, the so-called activation function, of its total input. A weighted linear combination of the outputs of the nodes of a layer is the input for the next layer of neurons. The weights of those linear combinations are randomly initialized and need to be adjusted to match the given data set to predict new data. This adjustment process is called training and uses data with a known

target result, in our case the fading time and the irradiation dose. During training, the weights are updated iteratively with a technique known as backpropagation that is most commonly used for the training of neural networks (Hecht-Nielsen, 1989). In each training iteration, a loss is computed as measure of the deviation of the predicted to the real target values. We use the mean squared error as loss function. The algorithm used to minimize the cost function during training is the Limited-Memory BFGS optimizer (Liu and Nocedal, 1989). The large amount of neuronal interconnections results in a large amount of trainable parameters. Neural network trained on too few input samples are analogous to a high order polynomial ﬁt to few data 37

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Additionally, feature engineering is used for this study to reduce the number of input parameters while keeping a maximum of information about the glow curve. Using all available features like the time or temperature resolved photon counts results in a large amount of trainable features and is not necessary. Instead, a lower number of features which are highly correlated to the irradiation dose and the fading time is derived from the glow curve using the presented glow curve model. The extracted features are presented in the next paragraph. The variables used as input to the neural network are calculated from two sources, the recorded glow curve in the time domain and the ﬁtted glow curve in temperature space. For the former glow curve they include three time intervals t(i/4)N with i = [1,2,3]. They denote the time points up to which 25%, 50% and 75% of the total photon count N within the region of interest (RoI), in which the signal is signiﬁcantly larger than the background, has been recorded. Also, the time point tmax , at which the global mode of photon counts Imax occurs, is used as feature. All these time points are normalized to the length of the RoI tRoI = tRoI;up − tRoI;low . The four respective photon intensities I(i/4)N and Imax are also used as input features. For the latter glow curve they include the ﬁt parameters Tm, i , Ei and Im, i with i = [2,3,4,5] for the observed glow peaks as well as the peak integrals Ni and several peak ratios. Figs. 6 and 7 illustrate these two feature sets, respectively. These variables characterize the glow curves. The features are preprocessed by scaling the individual feature distributions to mean values of 0 and standard deviations of 1. The scaled variables are then decorrelated using principal-component analysis (Jolliﬀe and Cadima, 2016).

Fig. 12. Predicted irradiation dose as a function of the true dose for the measurement data (orange markers) and for the simulation data(blue markers). The bottom plot shows the relative diﬀerence between the prediction and the true dose. (For interpretation of the references to colour in this ﬁgure legend, the reader is referred to the Web version of this article.)

6. Fading time estimation The three features with the largest sensitivity to the fading time are the peak ratio (Im2 + Im3)/(Im4 + Im5) , the 25%-quantile of the glow curve, t(1/4N )/ IRoI and the peak ratio Im3/ Im5 . Some of the features used show a correlation, e.g. the diﬀerent peak heights and the total number of photons recorded. Fig. 8 shows a matrix of the linear correlation coeﬃcients of the input features used and the network output prediction. This linear correlation with the predicted values can be interpreted as a measure of a single feature's importance for the prediction. The coeﬃcients can be positive and negative and their absolute values can range from small values (|ρ| = 0.05) to rather large values (|ρ| = 0.89). The feature space is thus decorrelated to help the shallow neural network distinguish between diﬀerent fading times. The sensitivity of the features chosen can be demonstrated by twodimensional scatter plots. Fig. 9 shows such scatter plots for four different fading times of zero days, two days, 16 days and 41 days. While the projections onto the individual variables (diagonal plots) already shows a reasonable discrimination power, the two-dimensional scatter plots (oﬀ-diagonal plots) make the potential of these features to discriminate between diﬀerent fading times even more visible. The output of the neural network is a single ﬁgure that is an estimate of the true fading time and which shows no residual dependence on the irradiation dose. Fig. 10 shows the predicted fading time as a function of the true fading time for the measurement data and for the simulation data including the corresponding uncertainty band. The data are averaged over all doses and the same neural network is used for both measurement and simulated data. Measurement and simulated data up to true fading times of about 32 days are consistent with a linear trend with a slope of unity. A negative bias is observed for larger fading times is visible and accounted for as systematic uncertainty. Fig. 11 shows the estimated uncertainty of the reconstructed fading time. The method of uncertainty calculation is presented in detail in Ref. Theinert et al. (2018). The measurement data is used only for the uncertainty calculation, no simulation data is included. The latter are only used to test the linearity of the estimator. The total uncertainty of the fading time estimation (red line)

Fig. 13. Estimated total uncertainty of the reconstructed dose (black line). Also shown are the systematic and statistical uncertainty as well as the 5% and 10% uncertainty ranges.

points. The excess of model complexity results in precise reproduction of known data but fails to generalize on unseen, new data. This is called over-ﬁtting (Piotrowski and Napiorkowski, 2013) and its monitoring is of high importance in machine learning. As a ﬁrst step to reduce the probability of over-ﬁtting considering the size of our data set being relatively small in terms of machine leaning, we choose a neural network accordingly. We minimize the training parameters by using a shallow neural network that features one hidden layer with one more node than there are input nodes, and it only has one output node. Another method to observe generalization of the trained network is called cross-validation and is a commonly used tool (Stone, 1974). For this technique, the training data is split up into n equally sized folds, n = 8 folds are used in our study, resulting in training and validation data set fractions of 87.5% and 12.5%, respectively. The weight-adjustment is performed on n − 1 folds. The last fold is used as validation data set. The average performance of n individually trained networks on each of the validation sets respectively, is used to provide a more reliable measure of the network performance on new data. A ﬁnal evaluation is performed on an additional test set that was not part of the training process. Simulated data are used for the training and testing process for the estimation of the irradiation dose, and they are solely used for comparison for the estimation of the fading time.

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particular shallow neural networks, for the analysis of glow curve data from LiF thermoluminescent dosemeters. The data set used was composed of measured data from irradiated dosemeters and simulated data based on an eﬀective glow curve model and a parameterization of the kinetic parameters. We have demonstrated that it is possible to estimate the fading time in the clinically relevant time interval of 30 days with an uncertainty of up to 10% and to estimate the irradiation dose for doses larger than 1 mSv with an uncertainty of less than 10%. The study thus shows that it is possible to overcome the problem of fading without using an additional preheating step (Walbersloh and Busch, 2015; Lee et al., 2015), and that information about the time of the irradiation can be estimated. This is a signiﬁcant advantage over other passive dosemeters, e.g. ﬁlm-badge dosemeters. The applicability of the approach followed here for the clinical routine will be investigated in ﬁeld tests. This includes an individual calibration of the dosemeters. In further studies, we will also exploit the potential of machine learning algorithms to give further information about the irradiation, e.g. the type of radiation and the distinction between a single irradiation (accident scenario) and continuous irradiation (missing radiation protection scenario).

increases almost linearly and ranges up to three days for a true fading time of 30 days. It is computed as the squared sum of a statistical (dashed blue line) and a systematic uncertainty(dashed green line). The statistical uncertainty is estimated with a quadratic ﬁt to the standard deviations of the results (blue markers). In the given measurement data set, they are largest for the measurement data with an irradiation dose of 0.5 mSv. The shown systematic uncertainties in Fig. 11 represent therefore an upper limit for the whole irradiation dose range. The systematical uncertainty is estimated using the ﬁt of a quadratic function as well but to the absolute value of the diﬀerence of predicted and true fading time. The 50% and 100% uncertainty ranges are indicated to guide the eye. The result from our previous studies using a single peak ratio feature for fading time estimation (Ref. Theinert et al., 2018) is included (orange dashed) for a comparison of methods. It is clearly shown that the uncertainties are signiﬁcantly reduced with the neural network method presented within this study. Especially the divergence of uncertainties for longer fading times described in Ref. Theinert et al. (2018) can be eliminated with the new approach. 7. Irradiation dose estimation

References

Neural networks, as well as other machine learning algorithms, can sometimes be sensitive to discretely distributed input data. The presented measurement data contains samples with only four diﬀerent irradiation doses. Therefore, the training is performed on the empirically simulated data for the irradiation dose estimation to minimize the impact of discrete input values on the prediction. For performance evaluation, both a 15% split of the simulation data and the measurement data are used as test set. Furthermore, the successful transfer on the measurement data veriﬁes the possibility to use simulated glow curves for training purposes. The features with the largest sensitivity to the irradiation dose are those related to the number of photons, e.g. the total number of photons counts or the number of counts in the individual peaks. The output is again a single quantity which estimates the dose which shows no residual dependence on the fading time. Fig. 12 shows the predicted irradiation dose as a function of the true dose, both, for measurement and simulated data, averaged over all fading times. The bottom plot shows the relative diﬀerence between the prediction and the true dose which is consistent with zero over the full dose range. The deviation from perfect linearity measured in the measurement data is accounted for as systematic uncertainty. The estimated total uncertainty of the reconstructed irradiation dose is shown in Fig. 13. Again, the measurement data are averaged over all fading times. The statistical and systematic uncertainties are also shown which both have a similar impact on the total uncertainty. The 5% and 10% uncertainty ranges are indicated to guide the eye. The total uncertainty does not exceed 10% for irradiation doses larger than 1 mSv. The statistical uncertainty is assumed to be reduced signiﬁcantly with an individual calibration of the dosemeters.

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8. Conclusions and outlook We have presented a study of using machine learning algorithms, in

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