Recognition of mineralogical and technological varieties of iron ore on the basis of ultrasound backscatter spectrograms

The research is aimed to the analysis and modeling of the process of propagation of ultrasonic waves in iron ore samples to assess its mineralogical varieties. The paper analyzes domestic and foreign experience in modeling of ultrasonic waves propagation; methods of mathematical and computer modeling were used, as well as methods of mathematical statistics and probability theory for analysis of the results. Scientific novelty consists in developing and substantiating a method for recognizing the mineralogical and technological varieties of iron ore of a developed deposit based on spectrograms of a backscattered ultrasonic probing signal. Practical valueconsists in developing a methodology for non-contact non-destructive mineralogical analysis of iron ore to improve the efficiency and quality of its further processing and preparation for metallurgical processing. results. As measurable characteristic estimates of textural and structural features of iron ore varieties the results of spectral analysis of the reversed radiant ultrasonic signal were used. To implement the measurement results classification procedure, Adaptive Neuro-Fuzzy Inference System is used. At the vector of parameters of membership functions of terms of input variables and the vector of coefficients of linear functions in the conclusions of the rules was formed based on the characteristics of the processed ore and the spectrograms of the backscattered ultrasonic signal. The average accuracy of recognition of magnetite, chlorite-carbonate-magnetite, hematite-magnetite, magnetite-cummngtonite-chlorite-siderite mineral varieties of iron ore of the studied deposit was 93%.


Introduction
Information about the mineralogical varieties of iron ore can be effectively used to improve the quality of its preparation for metallurgical processing [1].The technologies of mineralogical analysis that exist and are used in practice take a lot of time and require significant labor costs for preparatory operations.Ultrasonic measurement is a widely used tool for the detection, localization and characterization of materials with important applications in many fields [2].However, the solution of these problems is associated with great difficulties in relation to inhomogeneous media in which the ultrasonic wave is scattered by the microstructure of the material [3].The data obtained in this case directly from the results of raw measurements is difficult to analyze, since they depend on many interrelated characteristics of the medium under 1254 (2023) 012071 IOP Publishing doi:10.1088/1755-1315/1254/1/012071 2 study.In fact, the maximum information that can be experimentally obtained from each area of the material under study consists of the parameters of the transmitted and reflected probing signals.Thus, the actual problem is to substantiate the necessary and sufficient set of estimated characteristics of the process of propagation of ultrasound in randomly inhomogeneous media, as well as the development of effective methods for their processing for operational non-contact non-destructive mineralogical analysis of iron ore.

Literature review
Measurement methods based on the evaluation of the characteristics of backscattered ultrasonic waves in the medium under study are widely used [4,5].In work [6] a new formulation is presented to derive the absolute backscatter coefficient from pulse echo measurements.The diffraction correction function for measuring the backscattering coefficient and the acoustic coupling function for the echo-pulse system are determined.The elements of these functions are presented for a flat disk transducer and a transducer with spherical focusing.Approximations of these functions are also given.For a flat disk transducer, the final formulation looks like a modification of the well-known Siegelmann-Reid formulation [7].For a focused transducer, the final correction is a weak function of frequency when the scattering volume is close to the focal region.
Velichko et al [8] proposed to use a set of measurement results to achieve a complete spatiotemporal separation of the data of the transmitter-receiver structure corresponding to different local areas of ultrasonic signal scattering.It is expected that access to local scattering data can provide valuable benefits for many applications.This method makes it possible to use the angular distribution of the scattering amplitude and phase of each local scattering region to detect small inclusions in various highly scattering materials.
To recognize the characteristics of the interaction of elastic vibrations with the medium in which they propagate, many methods have been proposed, for example, cepstral frequency coefficients (MFCC) are widely used, which describe the shape of the spectrum of an acoustic signal [9][10][11].The problem is that individual elements of the acoustic interaction signal are noise-like with a wide flat spectrum and may include strong signatures in the time domain.At present, only a few features in the time domain are known to characterize such diverse audio signals.In work [12] an empirical feature analysis is presented to characterize acoustic signals and it is proposed to use a tracking matching (MP) algorithm to obtain effective time-frequency responses.The MP-based method uses a dictionary for feature selection, resulting in a flexible, intuitive, and physically interpretable set of features.The MP-based function is used as an addition to the MFCC functions in order to provide a higher accuracy of recognition of the characteristics of the analyzed environment.
Traditional acoustic event recognition methods based on informative input characteristics or with internal sequencing methods tend to perform poorly in the presence of interfering acoustic noise.Since noise distortion may be unavoidable in practical situations, it is important to develop more robust analysis models and classifiers [13,14].Recent advances in this field use powerful machine learning techniques with multivariate input features such as spectrograms or auditory images.They increase reliability largely due to the discriminatory capabilities of internal classifiers.In work [15] new features derived from spectrogram characteristics are proposed, combined with the powerful classification capabilities of a convolutional neural network (CNN).The proposed method demonstrates high performance under noise conditions compared to current approaches to standard acoustic event analysis and recognition problems.
A number of works propose methods for classifying the parameters of acoustic signals based on the support vector machine (SVM) [16][17][18].Tran and Li [19] uses a parametric approach to the characterization of acoustic signals based on subband time envelope distribution (STE) and kernel techniques to determine the subband probabilistic distance (SPD) within SVM.It is shown that the generalized gamma model is well suited for characterizing acoustic events, and the determination of the probabilistic distance provides a closed-form solution for calculating the magnitude of the discrepancy, which significantly reduces computational costs.The results show that the proposed classification method is superior to traditional SVM classifiers with Mel-frequency cepstral coefficients (MFCC).
A promising biological method for classifying acoustic events, which combines spike coding with a spike neural network (SNN) [20].Peak encoding extracts key points that represent the local maximum components of the acoustic spectrogram and are encoded based on their local time-frequency information.Thus, both position information and spectral characteristics are extracted.The proposed method simultaneously increases the sparseness of the acoustic event spectrogram, producing a noise-tolerant representation, and also maximizes the distinguishability of the spike encoding input data in terms of their temporal information [21].
An important element of the analysis of the results of acoustic interaction is the method of its qualitative description.Mesaros et al [3] presents and discusses various metrics proposed for evaluating acoustic event detection systems used in real situations.An overview of the most common metrics in the field and how they are adapted and interpreted in the polyphonic case is presented.Each metric is defined based on segments and events, and the consequences of averaging based on instances and classes are analyzed using a case study.
Acoustic events can occur both as a result of the purposeful formation of a probing signal, and as a side effect [22][23][24].In work [25] a concept is presented that uses acoustic signals to classify instrument-tissue interactions during diathermy.This is done by training a CNN classification pipeline based on a logarithmic spectrogram of acoustic signals recorded directly from the operation area.The presented model achieved an accuracy of up to 89.90% on the data set obtained in the experimental setup.
Another use caseacoustic events, as a side effect, is a system toterrain classification implemented as a component of an autonomous mobile robotic system operating in unknown real conditions [26].Recently, several proprioceptive terrain classification techniques have been developed to improve reliability or act as a fallback to traditional approaches [27,28].However, they lack quality adaptation due to various factors including lack of accuracy, reliability, and slow execution times.Valada and Burgard [26] uses the sounds of vehicle interaction with the ground as a proprioceptive modality and proposes a recurrent model based on deep short-term memory that captures both the spatial and temporal dynamics of such an operation.The model has a new convolutional neural network architecture that allows for deep spatial features, and is supplemented with long-term memory to account for complex temporal dynamics.In addition, a training scheme is proposed that takes into account noise effects, which allows you to synthesize generalized models necessary for reliable operation in real conditions.
The tasks of analyzing the characteristics of rocks have much in common with the evaluation of suspension parameters.Heterogeneous mixtures of solids in liquids play an important role in various industries.Online methods for analyzing the concentration and size of solid particles in given suspensions are of great interest in chemistry, mining and processing industries, for example, for monitoring and controlling mineral processing processes [29].In work [30] a method for determining the concentration and size of particles using a parametric approach is proposed.This is achieved by selecting an analytical model for the spectra of the received echo signals and determining their quantitative parameters.It is shown that the values of amplitude, center frequency and bandwidth, which are obtained from the fitted model, have great potential for evaluating the characteristics of the suspension.
Thus, the development of methods for measuring characteristics, modeling, classification and recognition of randomly inhomogeneous media is an urgent scientific and technical problem.However, the complexity of solving this problem does not allow creating a universal theoretical and software-technical base for practical application in various industries.A promising approach in the implementation of the mineralogical analysis of iron ore is the use of the parameters of the backscattered ultrasonic signal propagating in the studied samples, and modern methods of their interpretation and analysis.

Problem statement
The article presents the results of the development, justification and approbation of the method for recognizing the main mineralogical and technological varieties of iron ore of the developed deposit based on the spectrograms of the backscattered ultrasonic probing signal using the ANFIS neuro-fuzzy classifier.

Materials and results
In work [31] the characteristic of the mineral composition, as well as the size of mineral formations in the iron ore of magnetite deposits of the Kryvyi Rih basin is given.In the varieties of iron ore, the grains and aggregates that form them are distributed unevenly both in quantity and size.However, they differ with its physico-mechanical and chemical-mineralogical properties.Magnetite is one of the most common minerals in the Kryvyi Rih basin.
It is included in iron ores and ferruginous rocks as an important ore-forming mineral.Tables 1 and 2 show the characteristics of the mineral composition, as well as the size of individuals and aggregates of mineral varieties of hornfelses and jaspilites of the Skelevatsky magnetite deposit (Kryvyi Rih, Ukraine) [31].The characteristics are given in relation to the main iron-bearing mineral -magnetite and the main accompanying -quartz.
In mineral varieties, individual types of magnetite aggregates are unevenly distributed (table 2) and have different configurations (figure 1).
When ultrasonic waves propagate in a randomly inhomogeneous medium, with the characteristics given in table 1, their attenuation occurs due to the absorption and scattering of elastic vibrations on the mineral formations of iron ore.Fluctuations in the number and size of mineral inclusions in a controlled volume V of the medium under study affect the parameters of the ultrasonic signal measured by the detector D.  Let us determine the concentration of mineral inclusions of magnetite in the studied sample of iron ore through their number in volume V : Since the number of inclusions fluctuates, then N 1 is a random number with Poisson distribution: where < N 1 > is the average value of the number N 1 in the volume V , which can be determined through the average value of the concentration n 1 : Then the integral intensity of ultrasonic waves with wavelength λ, passing the distance Z in the medium, will be determined by the expression: where I λ is the intensity of the ultrasonic signal emitted into the medium under study; σ p (λ, R) is the attenuation cross section of ultrasonic vibrations with a wavelength λ on a mineral inclusion of size R i .
The detector reading D will be proportional to the value I • λ (Z), averaged over fluctuations in the number and size of inclusions, i.e. in proportion to the value: Denote by ξ random variable: To find the average value of the ξ apply the formula for the total mathematical expectation: In this expression M ξ k stands for conditional expectation.It is easy to show that: where: Here f (R) is a distribution function of mineral inclusions by size.Substituting expressions (2) and ( 9) into (7), we obtain In the same way, the influence of fluctuations in the concentration and size distribution of other mineral formations on the intensity of the ultrasonic signal propagating in the rock can be determined.In the expression (4) attenuation cross section of ultrasonic vibrations with wavelength λ is the sum of two terms: where σ c (λ, R) is the absorption cross section; σ s (λ, R) is the scattering cross section.
Let us consider in more detail the scattering of ultrasonic waves on mineral inclusions in iron ore.On figure 2 it is shown the types of ultrasound scattering depending on the ratio of its wavelength and the size of the scattering structure [32].
Specular scattering (figure 2, a) occurs when an object is much larger than the ultrasound wavelength.The ultrasonic wave can be reflected or refracted through the boundary between the object and its environment.Diffuse scattering (figure 2, b) occurs when the structure is much smaller than the ultrasound wavelength.Diffraction scattering (figure 2, c) occurs when the wavelength and size of the object are comparable.In this case, the incident wave scatters equally in all directions.
We will assume that the electrical transducer of ultrasonic waves combines the functions of transmission (generation) and reception of ultrasonic waves.In the transmission mode, the transducer surface is driven into oscillation by electrical excitation, and at the same time, a falling pressure field P in (r; w) is formed at the point r of the medium under study [6]: where P 0 (w) is the pressure amplitude on the transducer surface; D T (r; w) is the transducer directivity diagram; w = 2πf is the angular frequency of the acoustic wave.Using the electrical equivalent [6], can be written: where V s (r ∈ V ; w) is the received voltage signal from the scattering volume; V in (w) -electrical signal that excites the transducer; X T (w) = P 0 (w)/V in (w) -coefficient of electromechanical connection of the transducer in the transmission mode; X R (w) = V s (r; w)/P s (r; w) -coefficient of electromechanical coupling of the transducer in the receive mode.Since D s (r ∈ V ; w) can be obtained both analytically and numerically, the backscatter coefficient θ(w) can be calculated if the system response function |V in (w)•X T (w) • X R (w)| 2 is defined.In work [7] the response function of the system is measured by placing a reference plate with an ideal reflective surface at the location of the sample volume.There are techniques based on placing the reference plate at half this distance, as well as in the near field for a flat transducer and in the geometric focal plane for a focused transducer [4].
Assuming that the received signal is integrated over the surface of the receiver, and U R (r R ;w) is the relative sensitivity of the receiving element with coordinates r R , we can write: This expression defines the acoustic coupling function from the transducer surface (S Ractive transducer area) to the reference plane and back to the transducer surface [33].
Using the same electromechanical coupling coefficients, the output voltage of the converter due to the reflected wave: Taking into account ( 13) and ( 15), it is possible to determine the backscattering coefficient of ultrasonic waves: As follows from the above expressions, the parameters of the process of scattering of ultrasound on the structural inhomogeneities of the medium characterize its structural and textural properties.This allows them to be used to recognize the main mineralogical and technological varieties of iron ore in relation to certain of its deposits [34].
The scheme of functioning of the system for recognition of mineralogical and technological varieties of iron ore is shown in figure 3. The functioning algorithm includes the processing of ultrasonic signals and annotations, as well as training the recognition system [3].Acoustic characteristics are extracted from the measurement results, and at the training stage, a correspondence is found between them and the characteristics of the iron ore samples indicated in the annotations.The testing chain includes processing test signals as for training, testing the system, and, if necessary, post-processing the output of the system to obtain a representation similar to annotations.
In practice, there are three main methods for analyzing acoustic signals in the clock and frequency domains.The watch area has parameters that are taken from the statistics of the output.In the frequency domain, Four's transformations are performed for frequency spectroscopy and cepstral analysis [35].Let's look at the possibility of victorious results in the Figure 3. Scheme of functioning of the system for recognition of mineralogical and technological varieties of iron ore.spectral analysis of the turning pink ultrasonic signal for the task of recognizing the mineralogy and technological diversity of the flood.
Spectrograms are two-dimensional visualizations of spectral sequences with time on the abscissa and frequency on the ordinate.The color intensity of each pixel is related to the amplitude of the corresponding frequency.When ultrasonic waves propagate in a rock, due to their multiple reflection and scattering on mineral formations, a spectral characteristic of the medium in which they propagate is formed.Thus, the spectrogram of a backscattered probing signal is a spatial (in a certain area) amplitude-frequency characteristic of the medium under study or its acoustic structural-textural image.
To obtain spectrograms in accordance with the methodology used in the works [25,26], a short-time Fourier transform (STFT) was performed for each window segment of the recorded probing signal: where x[n] is the signal consisting of N f samples, w[n − j] is the window function in frame n − j, p are iteration variables, 2πk is the frequency.In this expression, X(i; j) is the matrix representation of the spectrogram of the received signal with f (k) = kf s /N f ; x[n] is the recorded raw received signal with sample length N f and sampling rate f s .The sliding window step size was set to 512 samples, resulting in a window overlap of 50%.
To compensate for the Gibbs effect during STFT by smoothing out discontinuities at the beginning and end of the received signal, the Hamming window function was used: Then the power spectrum log is calculated: In order to reduce the effect of disturbing noise effects, the spectrograms are normalized by dividing by the maximum amplitude.S(i; j) = S log (i, j)/ max S log (i, j). ( Then the average spectrum over the entire data set is calculated and subtracted from the normalized spectrogram. On figure 4 it is shown spectrograms of various mineral varieties of iron ore: the x-axis represents time, (ms); y-axis -frequency scale, (Hz); pixel intensity -amplitude, (dB).
As shown in work [36], due to the peculiarities of acoustic interaction, spectrograms provide qualitative characteristics of the classification of research objects.
To implement this procedure, ANFIS (Adaptive Neuro-Fuzzy Inference System) is usedthe editor of the Matlab package.In the task of recognizing the main varieties of iron ore of the developed deposit, the vector of parameters of the membership functions of the terms of the input variables and the vector of coefficients of linear functions in the conclusions of the rules are formedbased on the characteristics of the processed ore and the spectrograms of the backscattered ultrasonic signal.ANFIS -the editor automatically synthesizes a neuro-fuzzy network from experimental data, which can be considered as one of the varieties of fuzzy inference of the typeTakagi-Sugeno.In the process of approbation of the used recognition method, we evaluatedadding the number of epochs of learning, types and number of functions of occurrence of input fuzzy terms in the ANFIS-model for the accuracy of classification.
To study the influence of the number of training epochs of the ANFIS model, the following constant parameters were adopted: the number of input functions of the membership of fuzzy terms -3; type of input membership functions -bell-shaped ('gbellmf'); the type of output membership functions is linear ('linear') -the only possible option for fuzzy Sugeno-type derivation.Classification accuracy and time spent on model training were calculated.The results of this experiment are shown on figure 5.
With the number of epochs 20 spent 6.9512 s for training.During training for 50 epochs -11.7630 s were spent.At the same time, the accuracy increases from 0.9410 to 0.9524.A conclusion was made regarding the expediency of further researching the model by training it for 20 epochs.
In the process of researching the influence of the types of membership functions of the input fuzzy terms of the ANFIS model, the following constant parameters were adopted: the number of learning epochs -20; the number of input functions belonging to fuzzy terms is 3; type of output membership functions -linear ('linear').The type of input membership functions that were investigated is given in table 3. The results of the study of the influence of the types of membership functions of the input fuzzy terms of the ANFIS model on the classification accuracy and the time spent on training the model are shown in figure 6.
Among the tested membership functions, the best results were shown by the bell-shaped In the process of studying the influence of the number of membership functions of the input fuzzy terms of the ANFIS model on the classification accuracy and the time spent on training, the following constant parameters were adopted: the number of training epochs -20; type of input membership functions -bell-shaped ('gbellmf'); type of output membership functionslinear ('linear').Variable parameters: the number of fuzzy terms of the input membership functions (2,3,4,5).
The results of calculations of the influence of the number of membership functions of the input fuzzy terms of the ANFIS model on the classification accuracy and the time spent on training are given in the table 4. The option with four membership functions is selected.Therefore, a model trained for 20 epochs out of 4 was further investigated bell-shaped membership functions of the input fuzzy terms of the ANFIS model.
The average accuracy of recognition of magnetite, chlorite-carbonate-magnetite, hematitemagnetite, magnetite-kummngtonite-chlorite-siderite mineral varieties of iron ore, the characteristics of which are given in tables 1 and 2 was 93%.

Conclusions and further research
As measurable characteristic estimates of textural and structural features of iron ore varietiesthe results of spectral analysis of the reversed radiant ultrasonic signal were used.
To implement the measurement results classification procedure, ANFIS (Adaptive Neuro-Fuzzy Inference System) is used -the editor of the Matlab package.At the vector of parameters of membership functions of terms of input variables and the vector of coefficients of linear functions in the conclusions of the rules was formedbased on the characteristics of the processed ore and the spectrograms of the backscattered ultrasonic signal.
The average accuracy of recognition of magnetite, chlorite-carbonate-magnetite, hematitemagnetite, magnetite-cummngtonite-chlorite-siderite mineral varieties of iron ore of the studied deposit was 93%.
Due to the variety of physical-mechanical and chemical-mineralogical characteristics of rocks, the proposed method for recognizing the mineral varieties of iron ore requires tuning the ANFIS model on samples of a particular deposit.To increase the possibility of its more universal use, it is necessary to increase the number of characteristic parameters used to build the model.It is also advisable to consider more advanced methods for building and training the used model, for example, convolutional neural networks (CNN), transfer learning, etc.

Figure 1 .
Figure 1.Distribution and configuration of magnetite aggregate types in various varieties of iron ore.

Figure 2 .
Figure 2. Types of ultrasound scattering in an inhomogeneous medium.

Figure 4 .
Figure 4. Spectrograms of various mineral varieties of iron ore.

Figure 5 .
Figure 5.The influence of the number of epochs of ANFIS model training on classification accuracy and time spent on training.

Figure 6 .
Figure 6.The influence of the types of membership functions of the input fuzzy terms of the ANFIS model on the accuracy of classification and the time spent on training.

Table 1 .
Characteristics of the mineral composition, as well as the size of individuals and aggregates in iron ore.

Table 3 .
Type of studied input membership functions.

Table 4 .
The influence of the number of membership functions of the input fuzzy terms of the ANFIS model on the classification accuracy and the time spent on training.