Method and apparatus for performing spectral analysis to determine spectrum of sample

Abstract

The invention relates to a method and a device for performing a spectroscopic analysis for evaluating the spectrum of a sample (12), using a measuring device (11), in which primary radiation (15) is guided from a source (14) to the sample (12), in which secondary radiation (17) is emitted by the sample (12) or at least one layer (13) of the sample (12) as a result of an excitation of the sample (12) by means of the primary radiation (15), in which secondary radiation (17) is emitted from the sample (12) or at least one layer (13) of the sample (12). The spectrum of the secondary radiation (17) is detected by a detector (18), at least one detected spectrum is fed by the detector (18) into a computer-aided evaluation device (21) for evaluation, in which evaluation device the at least one detected spectrum is evaluated in at least one analytical neural network (22) of at least one first network structure (26), at least one neural network (22) for analysis is trained for quantitative analysis of a spectrum, the neural network (22) of the first network structure (26) being trained by a plurality of simulated spectra generated using a simulation method on the basis of a physical model (S = P (phi)), at least one second network structure (41) having a second neural network (46) for analysis being trained by a plurality of simulated spectra generated using a simulation method on the basis of a physical model (S = P (phi)), and a neural network (22, 46) for a qualitative analysis of the detected spectrum, and wherein a result relating to the concentration and / or identification of the at least one element of the sample (12) is output for the spectrum analyzed by the neural network (22, 46).

Description

Technical Field

[0001] The present invention relates to a method and a spectral analysis device for determining the spectrum of a sample. Background Art

[0002] In spectroscopic analysis, a sample's spectrum is determined using a spectrometer in a measuring device. This spectrum contains information about the sample's physical properties. These spectra are evaluated to determine, for example, the concentration of elements in a layer on or within the sample, as well as the presence of chemical elements. These processes must be performed quickly and with high reproducibility to allow reliable conclusions to be drawn from the measurements. Therefore, a fundamental goal is to improve the quantitative and / or qualitative analysis in such spectroscopic analysis and to reduce the time required for such analysis.

[0003] Previously, the determination of element concentrations in samples was performed, for example, using an iterative evaluation procedure. Consequently, a number of parameters were selected within a physical model and used as a basis. The measured spectrum was then compared with a theoretical spectrum derived from the physical model, and after iterative parameter optimization, a result was output representing the parameter set that best matched the measured and theoretical spectra. This iterative procedure was both time-consuming and expensive. Summary of the Invention

[0004] The present invention is based on the object of specifying a method and a device for performing a spectroscopic analysis to determine the spectrum of a sample in order to enable at least a rapid and precise quantitative analysis.

[0005] This object is achieved by a method for performing spectroscopic analysis to determine the spectrum of a sample, in which at least one detected spectrum is fed to and evaluated by at least one first network structure having an analytical neural network trained for quantitative spectral analysis. The first network structure is trained using a plurality of simulated spectra generated using a simulation method based on a known physical model S=P(ф).

[0006] become.

[0007] Furthermore, at least one second network structure having a second neural network is trained for qualitative analysis of the spectrum. Thus, in one process step, quantitative and qualitative analyses can be performed simultaneously, and the results of at least one element concentration and / or at least one element identification of the sample can be output with high accuracy / reliability.

[0008] The first network structure and the second network structure may be configured differently.

[0009] Preferably, at least one neural network for analyzing the network structure is trained to approximate the inverse function P of the physical model S=P(θ, Τ, λ, K) -1 (S) such that in a quantitative analysis at least one element concentration or layer thickness of the sample is output, wherein the spectrum is recorded as a function of the at least one element concentration or layer thickness, and / or in a qualitative analysis the absence or presence of at least one chemical element of the sample is determined and output. In order to carry out a quantitative analysis, it was previously necessary to analyze the spectrum using a physical model, whereby all relevant parameters had to be known. This model abstractly corresponds to the equation S=P(ф), whereby the spectrum S is a nonlinear function P of ф and ф represents all variables to be determined, such as, for example, the concentrations of all relevant elements and, if applicable, the thickness of the layer. The aim of the quantitative analysis is to determine ф for the measured spectrum under given measuring conditions of a known measuring instrument or measuring device. It was recognized that an inverse function P was required. -1 (S) to determine the variable ф without iteration. By training the analyzed neural network according to this inverse function, a rapid and accurate quantitative analysis of the concentration of at least one element in a sample and / or a qualitative analysis of the absence or presence of at least one element in a sample can be made possible.

[0010] Furthermore, it is preferably configured that the first network structure is trained using a plurality of simulated spectra generated using a simulation method based on an existing physical model S=P(θ, T, λ, K), particularly a Monte Carlo simulation method, and / or the first network structure is trained using a plurality of actually detected spectra. While training the neural network of the first network structure using a large number of simulated spectra requires a one-time increase in time and potentially increased computing power, after training the first network structure, the evaluation time for each detected spectrum can be significantly reduced.

[0011] Preferably, the simulated spectra are determined using at least: relevant parameters and / or predetermined parameters, such as the concentration of a chemical element or of at least one element of an alloy, element-specific physical constants, a layer thickness of at least one layer, different measuring conditions of a measuring device, and / or characteristic properties of different measuring devices, and / or device-specific data from one measuring device or different measuring devices.

[0012] Furthermore, it is preferably configured such that the second network structure for qualitative analysis is trained using a plurality of simulated spectra representing a plurality of intensity distributions of the energy spectrum of a chemical element, particularly wherein the plurality of intensity distributions deviate from one another. Preferably, the network structure is not trained for all existing chemical elements of the Periodic Table of Elements (PSE), but rather for a specific selection of elements required for spectrum evaluation. In particular, specific chemical elements can be selected for X-ray fluorescence analysis, such as those with an atomic number greater than 9. For other spectral analyses, correspondingly suitable chemical elements can be selected.

[0013] Preferably, the first network structure for quantitative analysis is configured in such a way that the detected spectrum is scaled using a scaling network with scaling factors to compensate for various possible excitation conditions, and the scaled spectrum is then fed to a prediction network, which outputs a result from the detected spectrum. This again enables a more accurate quantitative determination of the network.

[0014] A neural network is used for the prediction network and / or the scaling network, preferably a convolutional network (DenseNet), which can achieve shorter simulation times.

[0015] Preferably, a feature reduction method is used for quantitative and / or qualitative analysis of the detected spectra in order to generate pre-processed simulated spectra. This feature reduction method is then used to accelerate the training process.

[0016] Furthermore, it is envisaged that in a second network structure, starting from a plurality of spectra pre-processed using one of the feature reduction methods, such as a multi-layer network (MLP), a convolutional neural network (CNN), or a dense convolutional neural network (DenseNet), a network is trained. In particular, it has proven advantageous to establish the second network structure in which feature selection is performed as the feature reduction method and then a DenseNet is selected and trained.

[0017] In one of the feature reduction methods, it is preferably provided that the number of features to be evaluated of the generated spectrum (each number of features comprises, for example, 1024 features) is reduced to a number of features of 512, 256, 128, 64, 32, or 16. Spectral features are also understood to be frequencies or energies associated with the features of the spectrum, which are output as so-called channels, whereby a channel is equivalent to a feature, in particular when an A / D converter is used for the detector.

[0018] Another feature reduction method that may be used is mean compression, where the number of features in the recorded spectrum is reduced by averaging to a target spectrum with a reduced number of features.

[0019] Furthermore, the feature reduction method may be performed as feature selection, wherein the number of features or channels of the corresponding spectrum is reduced based on the original size of the generated spectrum.The generated spectrum is a spectrum generated by the above-mentioned simulation method.

[0020] Alternatively, a feature transformation may be performed, in particular using an autoencoder network, wherein the features of the respective spectra are weighted accordingly, the channels are weighted accordingly according to relevant and irrelevant features, and irrelevant features are eliminated.

[0021] Using the above-described feature reduction method, substantially similar performance results can be achieved in terms of the accuracy and precision of the results over the range in which the features of the spectrum are reduced, for example from 1024 features to a maximum of 32 features, with substantially similar performance results advantageously being within an evaluation range of 0.92 to 0.98 over an evaluation range of 0 to 1.

[0022] In feature selection as a feature reduction method, preferably, a watermelon model is selected, wherein, preferably, selection of features for selection is performed by Bayesian error rate estimation.

[0023] Furthermore, the analytical neural network is preferably trained using a model for network reduction. Preferably, the neural network is reduced in components such as neurons, filters, and / or parameters, particularly to eliminate redundant components. This also enables a reduction in required resources.

[0024] Furthermore, the analytical neural network is preferably trained using a model for quantization, wherein the data size is reduced, in particular the data size of the nodes of the neural network is reduced. Preferably, a bit size of 32 bits (32-bit floating point numbers) or less is selected.

[0025] The above-described feature reduction methods, which are preferably performed after training the neural network of the first network structure and / or the second network structure, can be used individually or in any combination or even cumulatively.

[0026] The feature reduction methods described above can reduce the size of the corresponding neural network used, thereby achieving the same or better evaluation results. At least one feature reduction method can achieve improved accuracy and reduced evaluation of measurements on samples, accompanied by significant reductions in data and computer costs.

[0027] Furthermore, it is preferably provided that the neural network of the meta-network is trained using simulated data from a plurality of known devices for the meta-learning procedure. Known devices are understood to be those that have already been calibrated, and preferably, known devices are understood to be those that have at least one characteristic property of the device that has already been determined. This makes it possible to minimize the calibration costs of the devices, in particular when manufacturing a large number of devices or measuring devices.

[0028] Furthermore, a meta-learning method is preferably used with a meta-network to calibrate an unknown measuring device or device for spectral analysis, wherein properties of the unknown measuring device and / or varying measurement conditions and / or measurement tasks are recorded, and simulated data and / or measured data of the unknown measuring device are used to additionally train the neural network of the meta-network. The duration of training the meta-network using the simulated data of the unknown measuring device is significantly reduced compared to the duration of training at least one neural network for the unknown measuring device. After training the meta-network to calibrate the unknown network, the device is ready for quantitative and / or qualitative analysis. An unknown device is preferably understood to be a device that has already been manufactured but not yet calibrated.

[0029] For this method, a multi-layer network (MLP - Multilayer Perceptron), a convolutional neural network (CNN - Convolutional Neural Network), or a dense neural network (DNN - Dense Neural Network), in particular a dense convolutional network (DenseNet - Dense Convolutional Network) can be used to form the analytical neural network.

[0030] Furthermore, in order to perform the spectral analysis, preferably, in a first step, a qualitative analysis of the captured spectrum is performed using a second analysis neural network, and the results are output. This makes it possible to determine whether an element or elements to be analyzed are contained in the sample within a short processing time. In some cases, one such analysis may be sufficient. In this case, the process can be terminated. However, in most cases, a statement about the concentration of the element is required. In this case, the qualitative analysis is followed by a quantitative analysis using the first neural network. Due to the training of the neural network using a large number of simulated spectra, a very precise determination of the concentration of the element in the sample can be achieved within a very short evaluation time. Alternatively, quantitative and qualitative analyses can be performed simultaneously. As is known, only the first neural network can be used to perform the quantitative analysis.

[0031] The basic problem of the present invention is also solved by a device for performing spectral analysis to determine the spectrum of a sample, in particular, the device is a device for performing a method according to one of the above-mentioned embodiments, the device comprising a source for emitting primary radiation to the sample and a detector for detecting secondary radiation, wherein the secondary radiation is emitted after the sample is excited by the primary radiation, wherein a computer-aided evaluation device evaluates at least one detected spectrum by means of the detector, wherein at least one analytical neural network with at least one first network structure for quantitative analysis of the spectrum and at least one second analytical neural network with a second network structure for qualitative analysis of the spectrum are provided, as well as an output device which outputs the results of at least one spectrum analyzed by the at least one neural network regarding at least one element concentration and / or at least one element identification of the sample.

[0032] The problem underlying the present invention is also solved by a computer program for performing a spectroscopic analysis to determine the spectrum of a sample, in particular, the computer program being provided for an evaluation device of the aforementioned apparatus, the computer program being arranged on at least one computer-readable storage medium, which at least one computer-readable storage medium can be implemented in a computer-aided evaluation device and causes the evaluation device to perform a method according to one of the above-described embodiments. BRIEF DESCRIPTION OF THE DRAWINGS

[0033] The invention and other advantageous and further embodiments are described and explained in more detail below with reference to the examples shown in the accompanying drawings. According to the invention, the features derived from the description and the drawings can be used alone or in any combination. The drawings show:

[0034] Figure 1 Schematic diagram of an apparatus for performing spectral analysis;

[0035] Figure 2 Schematic diagram of the spectrum of the alloy determined by spectroscopic analysis;

[0036] Figure 3 Schematic diagram of using simulated spectra to train a neural network.

[0037] Figure 4 Schematic diagram of the first network structure of the neural network;

[0038] Figure 5 Used for Figure 4 Schematic diagram of the network structure shown in ;

[0039] Figure 6 A diagram showing a comparison between test loss before and after training a neural network;

[0040] Figure 7Schematic diagram showing the evaluation time of different network structures;

[0041] FIG8 is a table showing a comparison of evaluation times between a conventional measuring device and a measuring device supported by a neural network;

[0042] Figure 9 Schematic diagram of the second network structure used for qualitative analysis;

[0043] Figure 10 a schematic diagram of a network structure for a second network structure;

[0044] Figure 11 A schematic diagram showing the performance of feature reduction methods applied to neural networks;

[0045] Figure 12 Schematic representation of the spectrum with the full number of features;

[0046] Figure 13 Schematic representation of a spectrum with a reduced number of features;

[0047] Figure 14 Schematic diagram of the data size of a neural network;

[0048] Figure 15 Figure 14 Schematic diagram of the reduced data size of the neural network in;

[0049] Figure 16 Table showing time reduction of evaluation time for different feature reduction methods when using different neural networks;

[0050] Figure 17 A view of the steps used to train a neural network for high-performance spectral analysis, and

[0051] Figure 18 Schematic sequence of the meta-learning procedure for calibrating a measurement device. DETAILED DESCRIPTION

[0052] Figure 1A device 11 for performing spectroscopic analysis to determine the spectrum of a sample 12 is schematically shown. The device 11 includes a source 14 for generating primary radiation 15. The primary radiation 15 is directed toward the sample 12. A focusing element 16, such as an optical lens or a collimator, may be provided between the source 14 and the sample 12. The primary radiation 15 emits secondary radiation 17 in the sample 12 or in at least one layer 13 on the sample 12, which is detected by a detector 18. The device 11 includes a controller 19, by which at least the source 14 is controlled. The detector 18 converts the detected secondary radiation 17 into a spectrum and forwards the spectrum to an evaluation device 21. The evaluation device 21 is located, for example, in a spectrometer. The evaluation device 21 includes a neural network 22, which evaluates the data recorded by the evaluation unit 21. A display device 23 outputs the results determined based on the trained neural network 22.

[0053] The device 11 can be, for example, an X-ray fluorescence measuring device, wherein the source 14 is designed as an X-ray tube and the detector 18 includes an A / D converter to detect the energy of the secondary radiation 17, convert the energy into so-called channels, and output the channels. The index of these channels is proportional to the detected energy. The detected energy or output channel is referred to as a characteristic in the following text.

[0054] Alternatively, the apparatus 11 can be designed, for example, to perform laser-induced breakdown spectroscopy (LIBS), with the source 14 being designed as a laser source. The detector 18 is designed as a spectrometer for detecting the emitted light.

[0055] Figure 2 A schematic diagram of the spectrum of an alloy determined by apparatus 11 is shown. The elements contained in the alloy are represented in the spectrum by fluorescence lines of varying intensities I plotted along the Y-axis, and the energy of the corresponding fluorescence lines corresponding to the indices of the channels, each of which is plotted along the X-axis in feature M. The concentration / layer thickness of the chemical elements in layer 13 or sample 12 can be determined from the intensities. The chemical elements can be detected by assigning the intensities to the corresponding features.

[0056] The basis for the output of such a spectrum, which is achieved by the evaluation device 21, is an abstract physical model S=P(θ, T, λ, K), where θ represents the concentration of the chemical element, T represents the layer thickness on the object, λ represents the measurement conditions during the measurement by the device 11, and K represents a characteristic property of the device 11. In previous classical methods for determining, for example, the concentration of an element based on a physical model, the parameters are initially fixed, and after a measurement using the device 11, the recorded values ​​of the element concentration are optimized in an iterative process until the theoretical spectrum matches the measured spectrum as closely as possible in order to output the result.

[0057] This is accompanied by the problem that the evaluation time is long and the measurement conditions and measurement characteristics, as well as calibration if necessary, must be known. Based on this, the goal is to enable a fast and precise evaluation of the measurement results by using at least one neural network or neural networks. Furthermore, it should be possible to use at least one neural network on different end devices.

[0058] The use of an analytical neural network trained and constructed as follows makes it possible to capture complex nonlinear functions very accurately. It is also found that the inverse function P -1 (S) can be approximated by at least one neural network. This was not possible in previous spectral analysis.

[0059] Against this background, it is proposed to provide a neural network for the spectral analysis of the device 11 , which neural network at least accelerates the quantitative analysis and enables it to be performed with high precision.

[0060] For quantitative analysis of elemental concentrations, it is necessary to train the neural network using a large number of spectra, particularly simulated spectra. This training can be based on a physical model S=P(ф), where ф represents θ, T, and K, according to at least one simulation method, based on specific parameters of sample 12 and / or specific parameters of device 11. Training can also be based on randomly selected or set parameters. Training can also be performed using features from actual recorded spectra. Combinations are also possible. Using simulation methods, a large number of spectra can be generated. Advantageously, 80,000 to 150,000 spectra are used to train the neural network.

[0061] Figure 3 It is shown that, starting from a physical model (S=P(ф)) 24 , a large number of spectra are generated according to FIG. 25 , with the aid of which the neural network 22 of the first network structure 26 is trained.

[0062] The neural network 22 is based on neurons and includes an input layer, one or more hidden layers, and an output layer. For example, a single-layer network (MLP - Multilayer Perceptron) can be provided. Convolutional neural networks (CNN), dense neural networks (DNN), or other structures such as dense neural networks (DenseNet) can also be used.

[0063] Figure 4 Schematically shown is the structure of a first network structure 26. Starting from a captured spectrum 27, this is evaluated by means of a scaling network 28 and modified using a scaling factor 29, for example to compensate for different excitation conditions for generating the secondary radiation 17. A prediction network 32 is used to evaluate the spectrum 31 scaled by the scaling network 28, and a result 33 of the spectrum 27 obtained from the captured spectrum is output.

[0064] Figure 5 A schematic diagram shows a possible structure of a DenseNet (Densely Connected Convolutional Network) 35. Preferably, this DenseNet 35 is used in the scaling network 28 and / or the prediction network 32 of the first network structure 26. For example, the DenseNet 35 may include an input layer 36, a convolutional layer 37, and a subsequent so-called dense block 38. A further sequence of such layers occurs until the output layer 39, which is also selection-specific.

[0065] Dense block 38 in Figure 5 The dense block 38 comprises, for example, four consecutive folded layers 37, each layer 37 being in contact with the adjacent layer.

[0066] Figure 6 A schematic diagram is shown indicating the number of spectra that are beneficial for training the neural network 22 in order to achieve a low error rate in the output of the results. The error rate of failed tests is plotted along the Y-axis, and the number of spectra is plotted along the X-axis. A comparison is shown, in which the dotted line with dots represents the spectra after training the first network structure 26. The dotted line marked with a cross shows a comparison of failed tests and failed training. The comparison shows that if the size of the spectral training data is too small, this will lead to an increase in the error rate. In addition, it can be seen that in the range of greater than 80k (80,000 spectra), preferably in the range of 100k (100,000 spectra) to 160k (160,000 spectra), there is a lower loss and a lower error rate, and this range or number of spectra should be selected for training the neural network 22, in particular, for training the first network structure 26, so as to obtain satisfactory results for implementation in actual operation.

[0067] Figure 7 A schematic diagram is shown in which various networks used for applications in the first network structure 26 are compared with each other. The mean error (MAE) of the detection is plotted along the Y-axis, and the response time (in seconds) of the output of the result is plotted along the X-axis. Obviously, when used in the first network structure 26, the use of the CNN structure and, in particular, the use of the DenseNet structure results in the shortest evaluation time compared to the MLP structure.

[0068] FIG8 shows an overview of the results of the evaluation of spectra measured on different samples 12 using different devices 11. A comparison is made between the previously known evaluation in the reference column and the application of the trained first network structure 26 for quantitative analysis in the new column. For this comparison, the mean absolute error rate MAE in percentage and the evaluation time in seconds are shown in each case. The differences between the average error rates are negligible. By using the first network structure 26, a significant reduction in evaluation time is achieved with an average duration of 0.049+ / -0.002 seconds. Compared with the reference, this is equivalent to a factor of at least 20 times. It is thus obvious that a significant reduction in evaluation time can be achieved by using the trained first network structure 26 of a large number of simulated spectra, in particular, a large number of simulated spectra between 80,000 spectra and 160,000 spectra. Compared with conventional quantitative analysis and the quantitative analysis supported by the first network structure 26, the mean absolute error (MEA) remains roughly the same.

[0069] By training the neural network using a plurality of actual detected spectra 27 and / or simulated spectra 27 including different pure elements, qualitative analysis of the spectra can be performed similarly to the quantitative analysis to identify the chemical element of the sample 12, whether the chemical element is present or absent.

[0070] For qualitative analysis related to element identification, preferably a second network structure 41 or an additional network structure 41 is provided for outputting results from the captured spectrum 27. This second network structure 41 is Figure 9 4. Based on the simulated spectrum 27, one or more feature reduction methods can be selected for evaluation. One of the feature reduction methods involves mean compression 42. Another feature reduction method can be feature selection 43. In addition, feature transformation 44 can be performed as a feature reduction method. Using one of these methods 42, 43, 44, a preprocessed spectrum 45 is determined. The preprocessed spectrum 45 is sent to a second neural network 46, for example, using a network structure MLP 47, CNN 48, or DenseNet 35, and then outputs a result 33, in which the identified chemical elements are indicated.

[0071] In the mean value compression 42 , it is preferably provided that, among the features to be evaluated of the spectrum 27 , the number of determined spectral features is reduced to a target spectrum by averaging.

[0072] In feature selection 43, the number of features can be reduced based on the complete spectrum. For example, the so-called watermelon model can be used. The watermelon model is based on Bayesian error rate estimation. First, the model uses kernel density estimation to approximate the true distribution of the data. Then, a Bayesian error rate estimate is calculated, and features are individually evaluated based on their independence or redundancy. Redundant features are identified.

[0073] During the feature transformation 44, preferably, the features of the respective spectrum 27 are weighted according to relevant features and non-relevant features, and non-relevant features in the spectrum are eliminated.

[0074] For example, the feature transformation 44 may be performed by Figure 10 The network structure shown in FIG. 3 is a so-called autoencoder 51. Starting from the input layer 36, the spectrum 27 is fed to an encoder 55, which has, for example, at least a first dense layer 56 and a second dense layer 57, and includes at least one further dense layer 58 between the encoder 55 and a subsequent decoder 59. At least one sealing layer 61, 62 may be provided in the decoder 59. The output layer 39 is then adjacent to the decoder 59.

[0075] These previously described procedures are used, for example, to train the neural network 22 using the first network structure 24 and / or the second network structure 41. After this training, the neural network 22 can be further optimized to reduce evaluation time and / or computing power.

[0076] Figure 11 A schematic diagram is shown in which the feature reduction method is plotted as a function of the number of features in the spectrum 27 and the different reduction methods. Along the Y-axis is plotted a factor indicating the accuracy output of the result using a factor FI from the detected spectrum ranging between 0 and 1, where 1 corresponds to 100% accuracy. Along the x-axis is plotted the number of features per spectrum 27. Line 61 shows the accuracy of the spectrum when the number of features is plotted according to the y-axis. Figure 11Performance curves when using the autoencoder 55. Line 62 shows the performance curve using the compression method 42, and line 63 shows the performance curve using the feature selection 43, whereby in particular the watermelon model was selected. All three feature reduction methods 42, 43, 44 are based on DenseNet 35 as the neural network 22. It can be seen that in all three cases, a high accuracy of >92% can be achieved within the range of reduction of the features of each spectrum from, for example, 1024 features to a maximum of 32 features. Compared to the case where the reduction method according to line 61 is used, the two reduction methods according to lines 62 and 63 can achieve a significantly improved accuracy of the determined spectrum. Therefore, feature selection is the preferred feature reduction method, and in particular, the watermelon model is the preferred feature reduction method, in particular the feature reduction method of the first network structure 26 and / or the second network structure 41, to reduce the evaluation time.

[0077] Further feature reduction may include specifically reducing the number of features of the spectrum 27 . Figure 12 Shows something like Figure 2 The spectrum of the multiple spectra in the Figure 2 For example, the spectrum in plots 1024 features along the x-axis. Figure 13 In the spectrum shown in , the number of features of spectrum 27 has been reduced, for example from 1024 features to 32 features. For this feature reduction, for example, the above-mentioned feature selection can also be performed.

[0078] Furthermore, network reduction of the neural network 22 can be used to speed up the evaluation time. In such network reduction, the network structure can be examined in a first step to determine which neurons, filters, or parameters will impair the performance. In particular, redundant components can then be eliminated. In a second step, the parameter size and floating point operations (FLOPs) can be reduced within the network reduction method. For example, according to Figure 14 , a neural network 22 is shown symbolically in order to Figure 12 Verify the number of features in spectrum 27. Figure 15 In, with Figure 14 Compared with the neural network in FIG, a reduced neural network 22 is shown symbolically, which can be composed of Figure 14 Spectrum 27 training. According to Figure 14 The data size of the neural network 22 is, for example, 5.2 MB, and the calculation time is, for example, 540 ms. Figure 15 In FIG, the reduced neural network 22 has a data size of, for example, 0.1 MB and a computation time of, for example, 0.9 ms. This clearly demonstrates the advantage of network reduction.

[0079] Furthermore, the evaluation time of the neural network 22 can be reduced by network quantization. Typically, a bit size of 32 bits is used for floating point operations (floats). Network quantization aims to reduce the bit size of floating point operations to less than 32 bits and / or the bit size of integer representations (ints). Preferably, quantization can reduce the bit size to 16-bit floating point numbers (floats) or 8-bit integers (ints), or, for example, to 8-bit ints with 16-bit activation values. For example, by quantizing from 32-bit floats to 16-bit floats, the data size can be reduced by approximately 50%. The same applies to further bit reductions.

[0080] Figure 16 A further table is shown, which shows a performance comparison of various reduction methods. Data size (MB) and evaluation time (ms) are compared with each other, as well as accuracy with a factor (FI). Furthermore, the use of a CNN structure 48 on the one hand and a DenseNet structure 35 on the other hand are compared. The first row of the table, under "base", shows the neural network 22 of the first and / or second network structures 26, 41 without feature reduction and / or network reduction and / or network quantization.

[0081] Compared to the base, feature selection 43 has already achieved a significant reduction in data size by a factor of 5 in the CNN structure 48. The data size for the DenseNet structure remains unchanged. A 13.7-fold reduction in evaluation time can be achieved for the CNN structure 48, and a 16-fold reduction in evaluation time for the DenseNet structure 35. Compared to the base, when using feature selection, the accuracy of the results remains almost the same.

[0082] As can be seen from the table, network reduction methods and / or network quantization methods can also reduce data size and evaluation time. However, the accuracy of the results remains unchanged compared to the baseline.

[0083] Optional combinations of the three reduction methods listed, i.e. feature reduction, network reduction, and / or network quantization, can also be used in combination. If all three reduction methods are superimposed in order to optimize the neural network 22, the CNN structure 48 can reduce the data size by approximately 29 times and the evaluation time by 65 times. Using the DenseNet structure 35, the file size can even be reduced by 52 times, and the evaluation time can be reduced by 600 times. Therefore, it is obvious that, on the one hand, by feature reduction of the spectra for quantitative analysis and / or qualitative analysis, in particular, by feature selection of the spectra for quantitative analysis and / or qualitative analysis, and by using these spectra r to train the neural network 22, and preferably, by additional network reduction and / or network quantization of the neural network 22, not only the computational workload and therefore the cost can be reduced, but also the evaluation time can be significantly reduced.

[0084] Figure 17 A preferred embodiment for training the neural network 22 is shown. In particular, this embodiment is suitable for the production of a large number of devices, in particular for mass production, whereby the evaluation time is significantly reduced with high accuracy of the results. In a first step 71, the neural network 22 is trained by actually detected spectra and / or spectra simulated by simulation methods for qualitative and quantitative analysis. Preferably, the number of simulated spectra is several times greater than the number of actually detected spectra, in particular at least 100 times greater than the number of actually detected spectra. The training is based on Figure 9 In order to train the first network structure 26 on the chemical elements. In a further step 72, as Figure 4 and Figure 5 As shown, a similar procedure is performed as for the quantitative analysis in step 71. In particular, this provides for a pre-processed spectrum to be recorded from the determined spectrum 27 using a feature reduction method of feature selection 42, which is then trained using DenseNet.

[0085] Based on this, in another step 73, select Figure 12 and Figure 13 The feature selection 42 described in [ 42 ] is then used for feature reduction. Subsequently, in step 74, the preprocessed spectra of the first and / or second network structures 26 , 41 are used as a basis. Subsequently, network reduction is performed in step 75, and then network quantization is performed in step 76. In this way, a process-optimized method for performing spectral analysis can be created, particularly for large-scale production, in which a reduction in data size of up to 52 times and a reduction in evaluation time of up to 600 times can be achieved compared to conventional methods. At the same time, conventional measurement equipment with reduced computing power can be used.

[0086] Figure 18 A schematic diagram of a meta-learning method 64 with a meta-network 65 is shown. In particular, this meta-learning method 64 is used for calibration of a device 11 or a measuring device manufactured in a factory. Furthermore, in order to correct any drift that may have occurred during operation of the measuring device, it is often necessary to recalibrate the device 11 after a period of operation.

[0087] In the meta-learning procedure 64, the goal is to use information learned from different tasks so that the meta-network can quickly adapt to new, unknown tasks, particularly within the device 11. In a first step 66, spectra 27 are recorded from a sample 12 under different measurement conditions using a known measurement device 11. These spectra 27 are evaluated by the first network structure 26 of the neural network 22. Spectra are then determined and / or simulated spectra are generated from further samples 12 using another known measurement device 11, taking into account not only the various measurement conditions but also the various characteristic properties of the measurement device 11. These spectra from at least one known device 11 are used in step 66 to train the meta-network 65. An agnostic meta-learning model (MAML—Model-Agnostic Meta-Learning) can be used for this purpose. Thus, the meta-network 65 is trained for the calibration of the device 11.

[0088] To calibrate the unknown measuring device 11, in step 67, the meta-network 65 is first trained using the measurement conditions and / or measurement properties of the unknown measuring device 11. Subsequently, the unknown measuring device 11 is calibrated by the meta-network 65. Advantageously, calibration of the unknown measuring device 11 can be performed without measuring the sample 12. Alternatively, at least one measurement can be performed on the unknown measuring device 11. In this case, the meta-network 65 is additionally trained, thereby achieving an improved calibration of the unknown measuring device 11.

[0089] After a predetermined or longer period of operation of the measuring device 11, recalibration may be required according to step 68. The measurement data of the measuring device 11 to be recalibrated is recorded so that the meta-network 65 is trained again using the measurement data. Due to the additional training of the meta-network 65 by the measuring device 11 to be recalibrated, the meta-network 65 can be further trained and recalibrated more quickly and more efficiently.

[0090] Preferably, the meta-learning procedure 64 is divided into two processes, namely training before calibrating the unknown measurement device 11 and training after calibrating the then-known measurement device 11. The meta-learning procedure 64 can achieve substantial cost savings for the industry and customers.

Claims

1. A method for performing spectroscopic analysis to evaluate the spectrum of a sample (12), - using a measuring device (11), -in, primary radiation (15) is directed from a source (14) to the sample (12), wherein, due to the excitation of the sample (12) by means of the primary radiation (15), secondary radiation is emitted by the sample (12) or at least one layer (13) of the sample (12), - wherein the spectrum of the secondary radiation (17) is detected by a detector (18), wherein at least one detected spectrum is fed by the detector (18) to a computer-assisted evaluation device (21) for evaluation, wherein the at least one detected spectrum is evaluated in at least one analytical neural network (22) of at least one first network structure (26), wherein the neural network (22) is trained for quantitative analysis of the spectrum, - wherein the neural network (22) of the first network structure (26) is trained by a plurality of simulated spectra generated on the basis of a physical model (S=P(ф)) using a simulation method, wherein at least one second network structure (41) having a second analytical neural network (46) is trained for qualitative analysis of the detected spectrum, - wherein the concentration and / or identity of at least one element of the sample (12) is output as a result of the spectrum analyzed by the neural network (22, 46).

2. The method according to claim 1, characterized in that At least one neural network (22, 46) of the network structure (26, 41) is trained to approximate the inverse function P -1 (S), so that: in a quantitative analysis, the concentration of at least one element of the detected spectrum of the sample (12) is determined and output; and / or in a qualitative analysis, the absence or presence of at least one chemical element of the detected spectrum of the sample (12) is determined and output.

3. The method according to claim 1, characterized in that The neural network (22) of the first network structure (26) is trained by a plurality of simulated spectra generated on the basis of a physical model (S=P(θ, Τ, λ, K)) using a simulation method, in particular a Monte Carlo simulation method, and / or the first network structure (26) is trained using a plurality of actually detected spectra.

4. The method according to claim 3, characterized in that The simulated spectrum is determined using predetermined parameters, in particular, the simulated spectrum is determined using the concentration of a chemical element or the concentration of at least one element of an alloy, element-specific physical constants, the layer thickness of at least one layer, different measurement conditions of the measuring device (11), and / or characteristic properties and / or device-specific data from one measuring device (11) or different measuring devices (11).

5. The method according to claim 1, wherein The neural network (46) of the second network structure (41) is trained using a plurality of spectra of at least one chemical element, in particular the neural network (46) of the second network structure (41) is trained using mutually different intensity distributions of energy spectra of at least one chemical element determined by X-ray fluorescence analysis, preferably the at least one chemical element having an atomic number greater than 9.

6. The method according to any one of the preceding claims, characterized in that A scaling network (28) is used for quantitative analysis of the detected spectra in the first network structure (26), wherein the at least one detected spectrum of the sample (12) is adjusted with a scaling factor (29), preferably to compensate for one or more excitation conditions, in particular different excitation conditions, and the scaled spectrum is subsequently sent to a prediction network (32) and the prediction network (32) outputs the result of the spectrum.

7. The method according to claim 6, characterized in that The prediction network (32) and / or the scaling network (28) are constructed using a neural network, in particular a dense convolutional network (DenseNet), which includes at least one dense block (DenseBlock) with convolutional layers, wherein, preferably, each layer in the dense block is in contact with other layers.

8. The method according to any one of claims 3 or 5, characterized in that At least one feature reduction method is applied to the generated simulated spectrum for quantitative analysis and / or qualitative analysis of the generated spectrum.

9. The method according to claim 8, characterized in that Based on the plurality of simulated spectra and / or detected spectra, pre-processed spectra are generated using the at least one feature reduction method, and the neural network is trained using the pre-processed spectra.

10. The method according to claim 8 or 9, characterized in that The number of features to be evaluated of the spectrum is reduced from 1024 to 512, 256, 128, 64, 32, or 16 features by one of the feature reduction methods.

11. The method according to any one of claims 8 to 10, characterized in that - the feature reduction method is performed as mean compression, wherein the number of features of the detected spectrum and / or simulated spectrum is reduced to a target spectrum by averaging, and / or - the feature reduction method is performed as feature selection, wherein the features of the corresponding spectrum are reduced in number starting from their original size and are reduced to the pre-processed spectrum, and / or The feature reduction method is performed as a feature transformation, preferably using an autoencoder network, wherein the features of the respective spectra are weighted according to relevant and irrelevant features and the irrelevant features are eliminated.

12. The method according to claim 11, characterized in that The feature selection is performed using a watermelon model, wherein, preferably, the feature selection is performed by Bayesian error rate estimation.

13. The method according to any one of the preceding claims, characterized in that After simulation of the spectrum and / or reduction of the spectrum for quantitative analysis and / or selection of chemical elements for qualitative analysis, the analytical neural network (26, 46) is trained using at least one further model for reducing evaluation time.

14. The method according to claim 13, characterized in that After the simulation of the spectrum and / or the reduction of the spectrum for quantitative analysis and / or the selection of the chemical elements for qualitative analysis, the analytical neural network (22, 46) is trained using a model for network reduction, wherein the neural network (22, 46) is reduced by components such as neurons, filters, and / or parameters, in particular by redundant components.

15. The method according to claim 14, characterized in that Filter reduction is performed on a neural network (22, 46) including folded layers, and / or neuron reduction is performed on a neural network (22, 46) including dense layers.

16. The method according to claim 13, characterized in that After the simulation of the spectrum and / or the reduction of the spectrum for quantitative analysis and / or the selection of the chemical elements for qualitative analysis, the analytical neural network (22, 46) is trained using a model for quantification, wherein the data size, in particular the data size of the nodes of the neural network (22, 46) is reduced, preferably to a bit size of less than 32 bits (32-bit floating point numbers).

17. The method according to any one of the preceding claims, characterized in that The measuring device (11) is trained by a neural network of a meta-network (65) with the aid of simulated data of a plurality of known measuring devices in order to perform a meta-learning procedure (64) for an unknown measuring device (11).

18. The method according to claim 17, characterized in that In order to calibrate an unknown measuring device (11) for spectral analysis, a meta-learning method (64) with a meta-network (65) is used, wherein properties of the measuring device (11) to be calibrated and / or changing measurement conditions and / or measurement tasks are recorded, and the meta-network (65) is supplemented by training with simulated data and / or measured data of the unknown measuring device (11).

19. The method according to claim 17 or 18, characterized in that The meta-network (65) is enabled by training at least for the quantitative analysis of the unknown measuring device (11).

20. The method according to any one of the preceding claims, characterized in that The analyzing neural network (22, 46, 65) is designed at least as a multi-layer network (MLP), a convolutional neural network (CNN) or a dense neural network (DNN), in particular a dense convolutional network (DenseNet).

21. The method according to one of the preceding claims, characterized in that In a first step, a qualitative analysis is performed to examine the sample (12), and a quantitative analysis of the sample (12) is performed for further analysis of the sample (12).

22. The method according to any one of the preceding claims, characterized in that The source (14) is formed as an X-ray tube and emits X-ray radiation.

23. A measuring device for performing spectroscopic analysis to determine a spectrum of a sample, - having a source (14) for emitting primary radiation (15) towards the sample (12); - a detector (18) for detecting secondary radiation (17) emitted after excitation of the sample (12) by means of primary radiation (15); - having a computer-assisted evaluation device (21) which evaluates at least one detected spectrum of the detector (18); wherein at least one analytical neural network (22) having at least one first network structure (26) is provided for quantitatively analyzing the spectrum; wherein at least one second network structure (41) having a second analytical neural network (46) is provided for qualitative analysis of the spectrum, and - having an output device that outputs the results of at least one spectrum analyzed by at least one of the neural networks (22, 46) regarding the concentration and / or identity of at least one element of the sample (12).

24. A computer program for performing spectroscopic analysis to determine a spectrum of a sample (12), wherein The computer program is provided on at least one computer-readable storage medium, which can be executed on a computer system and causes the computer system to perform the method according to any one of claims 1 to 22 .

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