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

Abstract

The present invention relates to a method and an apparatus for performing a spectral analysis for evaluating a spectrum of a sample (12), comprising using a measurement device (11) to direct primary radiation (15) from a light source (14) onto the sample (12), secondary radiation (17) being emitted from the sample (12) or from at least one layer (13) of the sample as a result of excitation of the sample (12) by the primary radiation (15), a spectrum of the secondary radiation (17) being detected by a detector (18), the at least one detected spectrum being supplied by the detector (18) to a computer-aided evaluation device (21) for evaluation, and the at least one detected spectrum being coupled to at least one first network architecture trained for quantitative analysis of the spectrum. The method relates to a method for evaluating the detected spectra using at least one analytical neural network (22) of a first network architecture (26), wherein the neural network (22) of the first network architecture (26) is trained with a plurality of simulated spectra generated based on a physical model (S=P(ф)) using a simulation method, and wherein at least a second network architecture (41) is trained with a second analytical neural network (46) for qualitative analysis of the detected spectra, and results of at least one element concentration and / or at least one element identification of the sample (12) are output from the spectra analyzed by the neural networks (22), (46).

Description

[Technical Field]

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

[0002] In spectral analysis, a spectrometer in a measuring device is used to determine the spectrum of a sample, which contains information about the physical properties of the sample. These spectra are evaluated, for example, to determine the elemental concentrations or the presence of chemical elements in layers on or within the sample. To be able to draw reliable conclusions from the measurements performed, these processes must be carried out quickly and with high reproducibility. Therefore, a fundamental objective is to improve the quantitative and / or qualitative analysis of such spectral analysis, thereby reducing the time required for spectral analysis. [Background technology]

[0003] Traditionally, the determination of element concentrations in a sample has been performed, for example, by an iterative evaluation procedure, whereby several parameters in a physical model are selected and used as a basis. The measured spectrum is compared with the theoretical spectrum obtained from the physical model, and after iterative parameter optimization, a result is output showing the parameter set corresponding to the best match between the measured results and the theoretical spectrum. This iterative procedure is time-consuming and costly. Summary of the Invention [Problem to be solved by the invention]

[0004] The invention is based on the problem of proposing a method and a device for performing a spectral analysis for determining the spectrum of a sample in order to enable at least a rapid and accurate quantitative analysis. [Means for solving the problem]

[0005] This problem is solved by a method for performing spectral analysis to determine a spectrum of a sample, in which at least one detected spectrum is fed to and evaluated by at least a first network architecture having an analytical neural network trained for quantitative analysis of the spectrum, the first network architecture being trained with a plurality of simulated spectra generated based on a pre-existing physical model S=P(ф) using a simulation method.

[0006] Furthermore, at least a second network architecture is trained with a second neural network for qualitative analysis of the spectrum. In this way, both quantitative and qualitative analysis can be performed in one process step, and the results of the concentration of at least one element in the sample and / or the identification of at least one element can be output with high accuracy / reliability.

[0007] The first network architecture and the second network architecture may be of different structures.

[0008] The analytical neural network of at least one network architecture preferably comprises an inverse function P of the physical model S=P(T, λ, K). -1 A spectrum analyzer is trained to approximate (S), which in a quantitative analysis outputs at least one element concentration or layer thickness of the sample from which the spectrum was recorded, and / or in a qualitative analysis determines and outputs the presence or absence of at least one chemical element in the sample. Previously, performing quantitative analysis required analyzing the spectrum using a physical model, which required knowing all relevant parameters. This model corresponds abstractly to the equation S=P(ф), where the spectrum S is a nonlinear function P of ф, and ф represents all variables to be determined, such as the concentrations of all relevant elements and, if applicable, the layer thickness. The goal of quantitative analysis is to determine ф for a measured spectrum under given measurement conditions of a known measuring instrument or device. A non-iterative determination of the variable ф requires the inverse function P -1It has been recognized that (S) is necessary. By training a neural network analyzed with this inverse function, fast and accurate quantitative analysis of the concentration of at least one element in a sample and / or qualitative analysis of the presence or absence of at least one element in a sample is possible.

[0009] Furthermore, preferably, the first network architecture is trained using a simulation method, in particular a Monte Carlo simulation, with a plurality of simulated spectra generated based on an existing physical model S=P(θ, T, λ, K), and / or the first network architecture is trained using a plurality of actually detected spectra. Training the neural network of the first network architecture with a large number of simulated spectra requires a one-time increase in time and possibly an increase in computing power, but after training the first network architecture, the evaluation time for each detected spectrum can be significantly reduced.

[0010] The simulated spectrum is preferably determined using relevant and / or predefined parameters such as at least the concentrations of the chemical elements or of at least one element of the alloy, element-specific physical constants, layer thickness of at least one layer, various measurement conditions of the measurement device and / or characteristics of various measurement devices and / or device-specific data from one or various measurement devices.

[0011] Furthermore, the second network architecture for qualitative analysis is preferably trained using a plurality of simulated spectra representing a plurality of intensity distributions of energy spectra of chemical elements, particularly those that are disparate from each other. The network architecture is preferably not trained on all existing chemical elements in the Periodic Table of Elements (PSE), but on a specific selection of elements whose spectra need to be evaluated. In particular, for X-ray fluorescence analysis, specific chemical elements can be selected, for example, elements with atomic numbers greater than 9. For other spectral analyses, suitable chemical elements can be selected accordingly.

[0012] The first network architecture for quantitative analysis is preferably configured to scale the detected spectrum with a scaling network having scaling factors to compensate for various possible excitation conditions, and then feed the scaled spectrum to a prediction network that outputs results from the detected spectrum, thereby enabling more accurate and quantitative determination of the network.

[0013] Neural networks, preferably convolutional networks (DenseNet), are used for the prediction and / or scaling networks, which can reduce simulation time.

[0014] Feature reduction methods are preferably used to generate preprocessed simulated spectra for quantitative and / or qualitative analysis of the detected spectra, which serve to accelerate the training process.

[0015] Furthermore, in the second network structure, it is envisioned to start from a plurality of spectra preprocessed using one of the feature reduction methods and train, for example, a multi-layer neural network (MLP), a convolutional neural network (CNN), or a dense convolutional neural network (DenseNet). In particular, it has been shown that implementing feature selection as the feature reduction method, followed by selecting and training DenseNet, is advantageous for setting up the second network structure.

[0016] In one feature reduction method, the number of features to be evaluated of the already generated spectra, each comprising, for example, 1024 features, can be reduced to preferably 512, 256, 128, 64, 32 or 16 features. Spectral features are understood to be frequencies or their associated energies that are output as so-called channels, particularly when an A / D converter is used in the detector, whereby a channel is equated with a feature.

[0017] Another feature reduction technique that may be used is mean compression, which averages the number of features in a recorded spectrum to produce a target spectrum with a reduced number of features.

[0018] Furthermore, the feature reduction method can be implemented as feature selection, which reduces the number of features or channels of each spectrum based on the original size of the generated spectrum. The generated spectrum was generated by the simulation method described above.

[0019] Alternatively, feature transformation can be performed, particularly using an autoencoder network, where each spectral feature or channel is weighted according to relevant and irrelevant features, and irrelevant features are removed.

[0020] Using the feature reduction method described above, within the range of reduced spectral features, e.g., from 1024 to 32 features, it is possible to achieve almost similar performance in the accuracy and precision of the results, which has the advantage of being 0.92-0.98 within the evaluation range of 0-1.

[0021] For feature selection as a feature reduction method, it is preferable to choose the watermelon model, where the selection of features to be selected is performed by Bayesian error rate estimation.

[0022] Furthermore, the analysis neural network is preferably trained using a network reduction model, where the neural network is preferably reduced by components such as neurons, filters and / or parameters, in particular to eliminate redundant components, thereby reducing the required resources.

[0023] Furthermore, the analysis neural network is preferably trained using a quantized model, which reduces the data size, especially for the nodes of the neural network, preferably choosing a bit size of 32 bits (32-bit floating point numbers) or less.

[0024] The aforementioned feature reduction methods are preferably implemented after training the neural networks of the first network architecture and / or the second network architecture, and can be used individually, in any combination, or even cumulatively.

[0025] The aforementioned feature reduction methods can reduce the size of the respective neural networks used, while still achieving comparable or better evaluation results. At least one feature reduction method can improve sample measurement accuracy and shorten evaluation times, while significantly reducing data and computational costs.

[0026] Furthermore, preferably, the neural network of the meta-network is trained with simulated data from a large number of known devices implementing a meta-learning procedure, where the known devices are devices that have already been calibrated, preferably devices for which at least one characteristic of the device has already been determined, thereby making it possible to minimize the costs of calibrating the devices, especially when manufacturing a large number of devices or measurement devices.

[0027] Furthermore, a meta-learning method is preferably used with a meta-network to calibrate an unknown measurement device for spectral analysis or instrumentation. In this case, the characteristics and / or changing measurement conditions and / or measurement tasks of the unknown measurement device are recorded, and the neural network of the meta-network is further trained using simulation data and / or measurement data of the unknown measurement device. The training time of the meta-network using simulation data for the unknown measurement device is significantly reduced compared to the training time of at least one neural network for the unknown measurement device. Once the meta-network that calibrates the unknown device has been trained, the device is ready for quantitative and / or qualitative analysis. An unknown device is preferably understood to be a device that has been manufactured but has not yet been calibrated.

[0028] In the method of the present invention, the analysis neural network can be formed using a multilayer 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).

[0029] Furthermore, spectral analysis is preferably performed by first performing a qualitative analysis of the acquired spectrum using a second analytical neural network and outputting the results. This allows for a quick determination of whether the sample contains the analyte or elements. In some cases, a single analysis may be sufficient. In this case, the process can be terminated. However, in most cases, a clear indication of the concentration of the element(s) is required. In this case, the qualitative analysis is followed by a quantitative analysis using the first neural network. By training the neural network with a large number of simulated spectra, a very accurate determination of the concentration of the element(s) in the sample can be made with very short evaluation times. Alternatively, both quantitative and qualitative analysis can be performed simultaneously. It should be understood that the first neural network can perform only quantitative analysis.

[0030] The problem underlying the present invention is further solved by an apparatus for performing a spectral analysis for determining the spectrum of a sample, in particular an apparatus for implementing a method according to one of the above-mentioned embodiments, comprising a light source for emitting primary radiation to the sample and a detector for detecting secondary radiation emitted after excitation of the sample by the primary radiation, wherein a computer-aided evaluation device evaluates at least one spectrum detected by the detector and provides at least one analytical neural network having at least one first network architecture for quantitative analysis of the spectrum and at least one second network architecture having a second analytical neural network for qualitative analysis of the spectrum, together with an output device for outputting the result of the at least one spectrum analyzed by the at least one neural network for the concentration of at least one element of the sample and / or the identification of at least one element.

[0031] The problem underlying the present invention is further solved by a computer program for performing a spectral analysis to determine the spectrum of a sample, which computer program is provided in particular for an evaluation device of the aforementioned instrument, which computer program is provided on at least one computer-readable storage medium, which computer program is executable in the computer-aided evaluation device and enables the evaluation device to perform the method according to one of the above embodiments.

[0032] The invention and other advantageous embodiments as well as further embodiments thereof are described and explained in more detail below with reference to examples shown in the drawings, in which the features taken from the description and the drawings can be used according to the invention individually or in any combination. [Brief explanation of the drawings]

[0033] [Figure 1] FIG. 1 is a schematic diagram of an apparatus for performing spectral analysis. [Figure 2] FIG. 2 is a spectrum diagram of the alloy determined by spectral analysis. [Figure 3] FIG. 3 is a schematic diagram of training a neural network using simulated spectra. [Figure 4] FIG. 4 is a diagram of a first network architecture of a neural network. [Figure 5] FIG. 5 is a schematic diagram of the network structure of the network architecture shown in FIG. [Figure 6] Figure 6 shows a comparison of the test loss before and after training the neural network. [Figure 7] FIG. 7 is a diagram showing the evaluation times of various network structures. [Figure 8-1] FIG. 8-1 is a table with a comparison of evaluation times between a conventional measurement device and a measurement device supported by a neural network. [Figure 8-2]FIG. 8-2 is a table with a comparison of evaluation times between a conventional measurement device and a measurement device supported by a neural network. [Figure 9] FIG. 9 is a schematic diagram of a second network architecture for qualitative analysis. [Figure 10] FIG. 10 is a schematic diagram of the network structure of the second network architecture. [Figure 11] FIG. 11 shows the performance of feature reduction methods applied to neural networks. [Figure 12] FIG. 12 is a schematic diagram of a spectrum with all the number of features. [Figure 13] FIG. 13 is a schematic illustration of a spectrum with a reduced number of features. [Figure 14] FIG. 14 is a schematic diagram of the data size of a neural network. [Figure 15] FIG. 15 is a schematic diagram of the reduced data size of the neural network of FIG. [Figure 16] FIG. 16 is a table showing the time reduction in evaluation time for various feature reduction methods when using various neural networks. [Figure 17] FIG. 17 is a diagram of the steps for training a neural network for high performance spectral analysis. [Figure 18] FIG. 18 is a schematic sequence diagram of a meta-learning procedure for calibrating a measurement device. DETAILED DESCRIPTION OF THE INVENTION

[0034] FIG. 1 shows a schematic diagram of an apparatus 11 for performing spectral analysis to determine the spectrum of a sample 12. The apparatus 11 includes a light source 14 that generates primary radiation 15. The primary radiation 15 is irradiated onto the sample 12. A focusing element 16, such as an optical lens or a collimator, may be provided between the light source 14 and the sample 12. The primary radiation 15 emits secondary radiation 17 within the sample 12 or within at least one layer 13 on the sample 12, which is detected by a detector 18. The apparatus 11 includes a controller 19 that controls at least the light source 14. The detector 18 converts the detected secondary radiation 17 into a spectrum and transmits it to an evaluation unit 21, which may be arranged, for example, in a spectrometer. The evaluation unit 21 includes a neural network 22 that evaluates the data recorded by the evaluation unit 21. A display unit 23 outputs the results determined based on the trained neural network 22.

[0035] The device 11 is, for example, an X-ray fluorescence fluorometer, the light source 14 being designed as an X-ray tube and the detector 18 comprising an A / D converter for detecting the energy of the secondary radiation 17 and converting it into so-called channels for output. The indices of these channels are proportional to the detected energy. The detected energies or output channels are referred to below as features.

[0036] Alternatively, the device 11 can be designed to perform, for example, laser-induced breakdown spectroscopy (LIBS), with the light source 14 being designed as a laser light source and the detector 18 being designed as a spectrometer that detects the emitted light.

[0037] FIG. 2 shows a spectrum of the alloy determined by the device 11. The elements contained in the alloy are represented in the spectrum by fluorescent lines of various intensities I plotted on the Y-axis and the corresponding fluorescent line energies corresponding to the channel indices plotted on the X-axis as feature quantities M. Through these intensities, the concentration / layer thickness of the chemical elements in the layer 13 or sample 12 can be determined. By assigning an intensity to each feature quantity, the chemical elements can be detected.

[0038] The basis for the output of such a spectrum by the evaluation device 21 is an abstract physical model S=P(θ,T,λ,K), where θ is the concentration of the chemical element, T is the layer thickness on the object, λ is the measurement conditions during the measurement by the device 11, and K is the characteristic of the device 11. In the conventional classical method of determining, for example, the element concentration based on a physical model, the parameters are initially fixed and, after the measurement by 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.

[0039] This leads to problems such as longer evaluation times and the need to know the measurement conditions and characteristics, as well as calibration, if necessary. The goal is to use at least one neural network or neural networks that allow for a fast and accurate evaluation of the measurement results. Furthermore, the at least one neural network must be able to be used with a variety of end devices.

[0040] As explained below, a trained and structured analytical neural network can capture complex nonlinear functions very accurately. -1 We also found that (S) can be approximated by at least one neural network, which is not possible with conventional spectral analysis.

[0041] Against this background, it is proposed to propose a neural network for spectral analysis of the device 11, which allows at least quantitative analysis to be accelerated and carried out with high precision.

[0042] For quantitative analysis of element concentrations, the neural network needs to be trained using a large number of spectra, in particular simulated spectra. This training may be based on a physical model S=P(ф) (where ф represents θ, T, K) based on specific parameters of the sample 12 and / or specific parameters of the instrument 11, based on at least one simulation method. Training may also be based on randomly selected or set parameters. Training may also be performed using features of actually recorded spectra. A combination of these is also possible. Using simulation methods allows the generation of a large number of spectra. Advantageously, the neural network is trained using 80,000 to 150,000 spectra.

[0043] FIG. 3 shows how, starting from a physical model (S=P(ф)) 24, a large number of spectra are generated according to FIG. 25, with which a neural network 22 of a first network architecture 26 is trained.

[0044] The neural network 22 is neuron-based and comprises an input layer, one or more hidden layers, and an output layer. For example, a single-layer network (MLP: Multi-Layer Perceptron) can be provided. Other architectures, such as a Convolutional Neural Network (CNN), a Dense Neural Network (DNN), or a Dense Neural Network (DenseNet), can also be used.

[0045] 4 shows a schematic structure of the first network architecture 26. Starting from a captured spectrum 27, the captured spectrum 27 is evaluated by a scaling network 28 and modified with a scaling factor 29, for example to compensate for various excitation conditions that generate the secondary radiation 17. The spectrum 31 scaled by the scaling network 28 is evaluated by a prediction network 32, which outputs a resulting spectrum 33 derived from the captured spectrum 27.

[0046] 5 shows a schematic diagram of a possible structure of a DenseNet (Densely Connected Convolutional Network) 35, which is suitable for use in the scaling network 28 and / or the prediction network 32 of the first network architecture 26. For example, the DenseNet 35 may comprise an input layer 36, a convolutional layer 37, followed by a so-called dense block 38. Optionally, further such layers may follow up to an output layer 39.

[0047] 5 shows, in a schematic enlarged view, a dense block 38, which comprises, for example, four successive folded layers 37, each layer 37 being in contact with the adjacent layers.

[0048] FIG. 6 illustrates the number of spectra that are effective for training the neural network 22 to keep the error rate of the resulting output low. The Y-axis plots the error rate of failed tests, and the X-axis plots the number of spectra. For comparison, the imaginary line with circles represents the spectra after training the first network architecture 26. The imaginary line with crosses shows the comparison between failed tests and failed training. This indicates that the error rate increases when the training data size of the spectra is too small. Furthermore, since the loss and error rate are low within a range exceeding 80k (80,000 spectra), preferably within the range of 100k (100,000 spectra) to 160k (160,000 spectra), it is necessary to select a range of spectra or the number of spectra for training the neural network 22, particularly the first network architecture 26, to achieve satisfactory results in practical implementation.

[0049] 7 shows a schematic diagram comparing various networks for application in the first network architecture 26. The detection mean error (MAE) is plotted on the Y-axis and the response time (seconds) of the resulting output on the X-axis. It can be seen that the use of CNN architectures, and in particular the DenseNet architecture, results in the shortest evaluation times compared to MLP architectures when used in the first network architecture 26.

[0050] Figures 8-1 and 8-2 show an overview of the evaluation results for spectra measured on different samples 12 using different instruments 11. A comparison is made between known evaluations in the "Reference" column and the application of the trained first network architecture 26 to quantitative analysis in the "New" column. For comparison, the mean absolute error (MAE) (percent) and evaluation time (seconds) are shown for each case. The difference in mean error is negligible. Using the first network architecture 26 significantly reduces the average evaluation time to 0.049 + / - 0.002 seconds, which is at least 20 times faster than the reference. This clearly demonstrates that using the trained first network architecture 26 can significantly reduce evaluation time, especially with a large number of simulated spectra, such as 80,000 to 160,000 spectra. The mean absolute error (MEA) remains nearly identical when comparing conventional quantitative analysis with quantitative analysis supported by the first network architecture 26.

[0051] Qualitative analysis of the spectra to identify the presence or absence of chemical elements in the sample 12 can be performed similarly to quantitative analysis by training a neural network using several actually detected and / or simulated spectra 27 of various pure elements.

[0052] For qualitative analysis related to element identification, a second or further network structure 41 is preferably provided for outputting results from the captured spectrum 27. Such a second network structure 41 is shown in FIG. 9. Based on the simulated spectrum 27, one or more feature reduction methods can be selected for evaluation. One feature reduction method involves mean value compression 42. Another feature reduction method can be feature selection 43. Additionally, feature transformation 44 can be performed as a feature reduction method. Using any of these methods 42, 43, or 44, a preprocessed spectrum 45 is determined. This preprocessed spectrum 45 is fed to a second neural network 46, for example, having the network architectures MLP 47, CNN 48, or DenseNet 35, after which a result 33 is output indicating the identified chemical element.

[0053] In mean value compression 42, it is desirable that the number of determined spectral features of the spectrum 27 to be evaluated is reduced to the target spectrum by averaging.

[0054] 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, this model uses kernel density estimation to approximate the true distribution of the data. Then, a Bayesian error rate estimation is calculated, and features are individually evaluated for independence or redundancy. Redundant features are determined.

[0055] During feature transformation 44, the features of each spectrum 27 are preferably weighted by relevant and irrelevant features, and irrelevant features in the spectrum are removed.

[0056] The feature transformation 44 can be implemented, for example, by a network architecture as shown in Figure 10, a so-called autoencoder 51. Starting from the input layer 36, the spectrum 27 is fed to an encoder 55, which for example has at least first and second dense layers 56, 57, with at least one further dense layer 58 between the encoder 55 and a subsequent decoder 59, which may be provided with at least one occlusion layer 61, 62. An output layer 39 is then adjacent to the decoder 59.

[0057] These described procedures are used to train neural network 22, for example, using first network architecture 24 and / or second network architecture 41. After this training, neural network 22 can be further optimized to reduce evaluation time and / or computational power.

[0058] Figure 11 shows a plot of feature reduction methods as a function of the number of features in a spectrum 27 and as a function of various reduction methods. The Y-axis plots the coefficient, which indicates the resulting accuracy output from the detected spectrum by the coefficient FI, ranging from 0 to 1, with 1 corresponding to 100% accuracy. The X-axis plots the number of features per spectrum 27. Line 61 shows the performance curve using the autoencoder 55 from Figure 11. Line 62 shows the performance curve using compression method 42. Line 63 shows the performance curve using feature selection 43, which specifically selected the watermelon model. All three feature reduction methods 42, 43, and 44 were based on DenseNet 35 as the neural network 22. This shows that within the range of feature reduction per spectrum, e.g., from 1024 to 32, high accuracy (over 92%) can be achieved in all three cases. The two reduction methods according to lines 62 and 63 allow to significantly improve the accuracy of the determined spectrum compared to the reduction method according to line 61. Therefore, feature selection, in particular the watermelon model, is a preferred feature reduction method to reduce the evaluation time, in particular of the first network architecture 26 and / or the second network architecture 41.

[0059] Further feature reduction may consist in particular of reducing the number of features of spectrum 27. Figure 12 shows several spectra similar to those of Figure 2, plotted along the x-axis across, for example, 1024 features. In the spectra shown in Figure 13, the number of features of spectrum 27 has been reduced, for example, from 1024 features to 32 features. For this feature reduction, for example, feature selection as described above may be performed.

[0060] Furthermore, network reduction of the neural network 22 can be used to shorten evaluation time. In such network reduction, the network architecture can be checked in the first step to determine which neurons, filters, or parameters degrade performance. Redundant components, in particular, are removed. In the second step, the size of the parameters and the number of floating-point operations (FLOPs) can be reduced within the network reduction method. For example, FIG. 14 symbolically illustrates the neural network 22 for verifying the number of features of the spectrum 27 of FIG. 12. FIG. 15 symbolically illustrates a reduced neural network 22 compared to FIG. 14, which can be trained using the spectrum 27 of FIG. 14. The data size of the neural network 22 of FIG. 14 is, for example, 5.2 MB, and the calculation time is, for example, 540 ms. In FIG. 15, the reduced neural network 22 has a data size of, for example, 0.1 MB and a calculation time of, for example, 0.9 ms. This clearly demonstrates the benefits of network reduction.

[0061] Furthermore, the evaluation time of the neural network 22 can be reduced by quantizing the network. Typically, a bit size of 32 bits is used for floating-point arithmetic (float). Quantizing the network aims to reduce the bit size of floating-point arithmetic to a bit size and / or integer representation (int) smaller than 32 bits. Preferably, quantization can reduce the bit size to a 16-bit floating point or an 8-bit integer representation, or, for example, an 8-bit integer representation with a 16-bit significance. For example, quantizing from a 32-bit float to a 16-bit float can reduce the data size by approximately 50%. The same applies to further bit reductions.

[0062] 16 shows another table showing the performance comparison of various reduction methods. Data size (MB) and evaluation time (ms) as well as accuracy by factor (FI) are compared with each other. Furthermore, the application of the CNN architecture 48 on the one hand and the DenseNet architecture 35 on the other hand is compared. The first row of the table shows, as "base", the neural network 22 of the first network architecture 26 and / or the second network architecture 41, without feature reduction and / or network reduction and / or network quantization.

[0063] Feature selection43 can already achieve a significant data size reduction of 5x for CNN architecture48 compared to the base. The data size for the DenseNet architecture remains unchanged. Evaluation time reductions of 13.7x for CNN architecture48 and 16x for DenseNet architecture35 can be achieved. The accuracy of the results using feature selection remains almost unchanged compared to the base.

[0064] As can be seen from the table, the network reduction and / or network quantization methods can further reduce the data size and evaluation time, but the accuracy of the results remains the same as the baseline.

[0065] The three listed reduction methods, i.e., feature reduction, network reduction, and / or network quantization, can be used in combination if desired. When all three reduction methods are combined to optimize the neural network 22, the CNN architecture 48 can reduce data size by approximately 29 times and evaluation time by 65 times. Using the DenseNet architecture 35 can also reduce file size by 52 times and evaluation time by 600 times. It is therefore clear that feature reduction, particularly feature selection, of spectra for quantitative and / or qualitative analysis, on the one hand, and by training the neural network 22 with these spectra r, as well as preferably additional network reduction and / or network quantization of the neural network 22, not only reduces computational effort and thus costs, but also shortens evaluation time by a significant amount.

[0066] FIG. 17 illustrates a preferred embodiment for training the neural network 22. This embodiment is suitable for producing a large number of devices, particularly in mass production, thereby significantly reducing evaluation time while obtaining highly accurate results. In a first step 71, the neural network 22 is trained using actually detected spectra and / or spectra simulated by a simulation method for qualitative and quantitative analysis. Preferably, the number of simulated spectra is a multiple of the number of actually detected spectra, particularly at least 100 times greater. Training is based on the second network structure 41, described in more detail in FIG. 9, for training the first network architecture 26 for chemical elements. In a next step 72, quantitative analysis is performed using a procedure similar to step 71, as shown in FIGS. 4 and 5. In particular, this allows for recording preprocessed spectra from the spectra 27 determined using the feature reduction method of feature selection 42, which are then trained using DenseNet.

[0067] Based on this, feature selection 42 shown in Figures 12 and 13 is selected for feature reduction in a further step 73. Subsequently, in step 74, the preprocessed spectra of the first network architecture 26 and / or the second network architecture 41 are used as a basis. Subsequently, network reduction is performed in step 75, and network quantization is performed in step 76. In this way, a process optimization method for performing spectral analysis, especially in large-scale production, can be created, which can reduce data size by up to 52 times and evaluation time by up to 600 times compared to conventional methods. At the same time, conventional measurement equipment can be used with reduced computing power.

[0068] 18 shows a schematic diagram of a meta-learning method 64 using a meta-network 65. Such a meta-learning method 64 is particularly useful for calibrating factory-manufactured devices 11 or measurement devices. Furthermore, it is often necessary to recalibrate the device 11 after a period of operation to correct for drift that may occur during operation of the measurement device.

[0069] The meta-learning process 64 aims to train the meta-network 65 with information from various tasks so that it can quickly adapt to new, unknown tasks, particularly to devices 11. In a first step 66, spectra 27 are recorded from a sample 12 under various measurement conditions using a known measurement device 11. These spectra 27 are evaluated by the first network architecture 26 of the neural network 22. Next, spectra are determined from additional samples 12 using additional, known measurement devices 11, and / or simulated spectra are generated, taking into account not only the various measurement conditions but also the various characteristics of the measurement device 11. These spectra from at least one known device 11 are used to train the meta-network 65 in step 66. For this purpose, model-agnostic meta-learning (MAML) can be used. In this way, the meta-network 65 is trained for the calibration of the device 11.

[0070] To calibrate the unknown measurement device 11, first, in step 67, the meta-network 65 is trained with the measurement conditions and / or measurement characteristics of the unknown measurement device 11. The unknown measurement device 11 is then calibrated by the meta-network 65. Advantageously, the calibration of the unknown measurement device 11 can be performed without measuring the sample 12. Alternatively, at least one measurement can be performed with the unknown measurement device 11. In this case, further training of the meta-network 65 improves the calibration of the unknown measurement device 11.

[0071] After the measurement device 11 has been in operation for a predetermined period of time, it may need to be recalibrated, per step 68. Measurement data from the measurement device 11 to be recalibrated is recorded, and the meta-network 65 is retrained using these measurement data. Further training of the meta-network 65 with the measurement device 11 to be recalibrated allows the meta-network 65 to be further trained, resulting in faster and improved recalibration.

[0072] The meta-learning process 64 is preferably split into two processes: training before calibrating the unknown measurement device 11, and training after calibrating the now known measurement device 11. The meta-learning process 64 allows for significant cost savings for industry and customers.

Claims

1. 1. A method for performing spectral analysis to evaluate a spectrum of a sample (12), comprising: A measuring device (11), Primary radiation (15) is directed from a light source (14) to the sample (12); As a result of excitation of the sample (12) by the primary radiation (15), secondary radiation is emitted by the sample (12) or by at least one layer (13) of the sample (12), The spectrum of the secondary radiation (17) is detected by a detector (18); the at least one detected spectrum is provided by the detector (18) to a computer-aided evaluation device (21) for evaluation, and the at least one detected spectrum is evaluated with at least one analytical neural network (22) of at least one first network architecture (26) trained for quantitative analysis of the spectrum; the neural network (22) of the first network architecture (26) is trained with a plurality of simulated spectra generated from a physical model (S=P(φ)) using a simulation method; at least a second network architecture (41) is trained with a second analytical neural network (46) for said qualitative analysis of said detected spectrum; The concentration and / or identity of at least one element of the sample (12) is output as a result from the spectrum analyzed by the neural network (22), (46). method.

2. The neural network (22), (46) of the at least one network architecture (26), (41) is configured with an inverse function P －１ 2. The method of claim 1, wherein the method is trained to approximate (S) such that, in the quantitative analysis, the concentration of the at least one element in the detected spectrum of the sample (12) is determined and output, and / or in the qualitative analysis, the presence or absence of at least one chemical element in the detected spectrum of the sample (12) is determined and output.

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

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

5. 2. The method according to claim 1, characterized in that the neural network (46) of the second network architecture (41) is trained with a plurality of spectra of at least one chemical element, in particular intensity distributions of the energy spectra of the at least one chemical element that differ from one another, determined by X-ray fluorescence analysis, preferably the at least one chemical element having an atomic number greater than 9.

6. 6. The method according to claim 1, wherein a scaling network (28) is used for the quantitative analysis of the detected spectra in the first network architecture (26), preferably to adjust the at least one detected spectrum of the sample (12) with a scaling factor (29) in order to compensate for one or more, in particular different, excitation conditions, and wherein the scaled spectrum is then fed to a prediction network (32), which outputs the spectral result.

7. 7. The method according to claim 6, characterized in that the prediction network (32) and / or the scaling network (28) are constructed as neural networks, in particular as dense convolutional networks (DenseNet) comprising at least one dense block with convolutional layers (DenseBlock), preferably each layer in said block being in contact with the other layers.

8. 6. The method of claim 3 or claim 5, characterized in that at least one feature reduction method is applied to the generated simulated spectra for quantitative and / or qualitative analysis of the generated spectra.

9. 9. The method of claim 8, characterized in that, starting from a plurality of simulated and / or detected spectra, preprocessed spectra are generated using said at least one feature reduction method, and said neural network is trained using these preprocessed spectra.

10. 10. The method of claim 8 or claim 9, wherein the number of spectral features to be evaluated is reduced from 1024 to 512, 256, 128, 64, 32 or 16 features by the one feature reduction method.

11. 11. The method according to any one of claims 8 to 10, the feature reduction method is performed as a mean compression, in which the number of features of the detected spectrum and / or the simulated spectrum is reduced to a target spectrum by averaging; and / or the feature reduction method is performed as a feature selection in which the reduction of the number of features of each spectrum is reduced to preprocessed spectra starting from their original size; and / or the feature reduction method is preferably implemented using an autoencoder network as a feature transformation, whereby a weighting of the features of each spectrum is performed by relevant and irrelevant features, and the irrelevant features are removed; A method characterized by:

12. 12. The method of claim 11, wherein the feature selection is performed using a watermelon model, and the selection of the features is preferably performed by Bayesian error rate estimation.

13. 13. The method according to claim 1, wherein the analytical neural network (26), (46) is trained with at least one further model for reducing the evaluation time after the simulation of the spectra for the quantitative analysis and / or for reducing the spectra for the qualitative analysis and / or for selecting the chemical elements for the qualitative analysis.

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

15. 15. The method according to claim 14, characterized in that filter reduction is performed on the neural network (22), (46) with a convolutional layer and / or neuron reduction is performed on the neural network (22), (46) with a dense layer.

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

17. 17. The method according to claim 1, wherein the measurement device (11) is trained by a neural network of a meta-network (65) with simulation data from several known measurement devices performing a meta-learning procedure (64) for the unknown measurement device (11).

18. 18. The method according to claim 17, characterized in that the meta-learning method (64) using the meta-network (65) is used to calibrate an unknown measurement device (11) for spectral analysis, the characteristics and / or the changing measurement conditions and / or the measurement tasks of the measurement device (11) to be calibrated are recorded, and the meta-network (65) is further trained by simulation data and / or measurement data of the unknown measurement device (11).

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

20. 20. The method according to claim 1, wherein the analysis neural network (22), (46), (65) is constructed as at least a multi-layer neural network (MLP), a convolutional neural network (CNN) or a dense neural network (DNN), in particular a dense convolutional network (DenseNet).

21. 21. The method according to one of claims 1 to 20, characterized in that the qualitative analysis is carried out in a first step of examining the sample (12) and that a quantitative analysis of the sample (12) is carried out for further analysis of the sample (12).

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

23. 1. A measurement device for performing spectral analysis to determine a spectrum of a sample, comprising: a light source (14) for emitting primary radiation (15) onto the sample (12); a detector (18) for detecting secondary radiation (17) emitted after excitation of the sample (12) by the primary radiation (15); a computer-aided evaluation device (21) for evaluating the at least one detected spectrum of the detector (18), At least one analytical neural network (22) having at least a first network architecture (26) is provided for quantitatively analyzing the spectrum; at least a second network architecture (41) is provided for said qualitative analysis of said spectrum, said second network architecture (41) having a second analytical neural network (46); an output device for outputting the results of at least one spectrum analyzed by said at least one neural network (22), (46) for the concentration and / or identification of said at least one element in said sample (12); Measuring device.

24. 23. A computer program for performing a spectral analysis to determine a spectrum of a sample (12), said computer program being provided on at least one computer-readable storage medium executable on a computer system, causing said computer system to perform the method of any one of claims 1 to 22.

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