# Near Real-Time Classification of Iron Ore Lithology by Applying Fuzzy Inference Systems to Petrophysical Downhole Data

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## Abstract

**:**

## 1. Introduction

^{TM}and AutoShuttle) and top-of-hole analytical instruments (Lab-at-Rig

^{®}) [1]. Logging-while-drilling and top-of-hole sensing technologies provide a wide range of near real-time data, whose timely analysis and interpretation is critical for real-time decision-making.

## 2. Materials and Methods

^{137}Cs (Caesium) with an energy of 662 keV, a long- and short-spaced detector which are shielded from the source so that they will only detect gamma rays scattered from interactions with the formation. The depth of investigation and vertical resolution depends on the detector spacing and is usually in the range of 50–60 cm. Different energy regions of the spectrum give different information about the surrounding rock mass (Figure 3). The gamma counts in the high energy region are indicative of Compton scattering and are used to calculate formation density (bulk density), the gamma ray counts in the low energy region (below ~100 keV) are influenced by photoelectric absorption interactions and give information about density as well as the formations average (or effective) atomic number Z, which can be used as a lithology indicator. By taking the ratio of high energy to low energy counts, the density information is eliminated and the resulting number, the spectral gamma-gamma ratio (SGG ratio, [18,19]), should only give information about the formations average atomic number:

_{1}, z

_{2},…, z

_{n}}, $c$ is the number of clusters, $m$ is the weighting exponent ($m$ ≥ 1), and V = {v

_{1}, v

_{2},…, v

_{C}} are the center values. U = {u

_{jk}∈ [0, 1]} is the membership matrix whose elements u

_{jk}represent the membership degree of the jth data point to the kth cluster. ${\Vert \Vert}_{2}$ is the Euclidian norm. The number of clusters c and the weighting exponent m need to be defined prior to clustering and fuzzy inference modelling.

_{2}O

_{3}%, three rules and one output variable, which is the desired class value. Three membership functions (Figure 5) per variable are defined from the initial fuzzy c-means clustering step of these two variables into three clusters c = 3, applying a weighting exponent of m = 1.6. The output functions are built based on predefined output classes, which represent the typical cut-off grades used by the iron ore industry:

- Class 1—waste BIF—Fe% < 50%, Al
_{2}O_{3}% < 3%; - Class 2—waste shale—Fe% < 55%, Al
_{2}O_{3}% > 3%; - Class 2.5—shaley ore—Fe% > 55%, Al
_{2}O_{3}% > 3%; - Class 3—low-grade ore—Fe% > 50% and < 58%, Al
_{2}O_{3}% < 3%; - Class 4—high-grade ore—Fe% > 58%, Al
_{2}O_{3}% < 3%

- if input 1 is in cluster 1 and input 2 is in cluster 1 then output is class 1;
- if input 1 is in cluster 2 and input 2 is in cluster 2 the output is class 2;
- if input 1 is in cluster 3 and input 2 is in cluster 3 then output is class 3.

_{2}O

_{3}% = 0 (standardized values). The untrained system yields a class value of 4.08, which represents high-grade ore, but the high value for aluminum suggests a high shale content and the sample should be classified as class 2 or 2.5. The value of 2.17 for the trained system represents a value in the correct range.

## 3. Results

#### 3.1. Data Set I

_{2}O

_{3}% as the first set of input variables. The top plot shows the initial and final training errors as well as the initial and lowest checking errors for the 50 consecutive runs; the middle plot shows the correlation between the prediction from FIS 1 and the desired output, and FIS 2 and the desired output class. The correlation is well above 97% in most cases for both systems and the errors are very low. A comparison between predicted and pre-defined class in the bottom plot confirms the successful prediction based on iron and aluminum input variables.

#### 3.2. Data Set II

_{2}O

_{3}% assay data to establish the predefined classes as before and tested two input variable combinations, namely (1) Fe% and Al

_{2}O

_{3}% and (2) SGG ratio and natural gamma. From the total of 1737 samples we selected 1000 for FIS training and applied the trained inference system to the total number of samples for prediction. We then selected the best-suited FIS based on the lowest checking error as before. Prediction results in Figure 12 show a match of 92% for the assay data and 87% for prediction from the SGG ratio and natural gamma log, indicating that iron grade can be successfully predicted from this data.

## 4. Conclusions

## Author Contributions

## Funding

## Acknowledgments

## Conflicts of Interest

## Appendix A

[FIS] = genfis3(Xin,Xout,type,n,fcm-op) Xin = matrix of input variables Xout = output variable type = ‘sugeno’ type used in this study n = number of clusters fcm-op = options for FCM clustering (e.g., weighting exponent, number of iterations, etc.)

[FIS,trainError,stepSize,chkFIS,chkError] = anfis(trainingData,options) FIS = trained FIS after last training epoch trainError = root mean square training error stepSize = training step size chkFIS = trained FIS at lowest checking error chkError = root mean square checking error options = options for anfis training (e.g., initial FIS, number of training epochs, checking data, etc.)

[output] = evalfis(input,FIS) output = predicted values input = input variables for prediction FIS = trained FIS for prediction

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**Figure 1.**Geological overview of the Pilbara region in Western Australia. The economically valuable banded-iron formations are hosted mainly by the Hamersley Group of the Mount Bruce Supergroup (after [17]).

**Figure 2.**Stratigraphy of the Hamersley Group illustrating the position of the important iron formations in relation to major uneconomic shale, carbonate or volcanic units. Shale interbeds, illustrated for the Dales Gorge member to the right, internally subdivide the iron formations. The 17 BIF macrobands (grey) are separated by the 16 shale bands (black) that are used for stratigraphic correlation (after [17]).

**Figure 3.**Sketch of the characteristics of a gamma ray spectrum recorded using a lithodensity tool with a

^{137}Cs source. The high energy region of Compton scattering is indicative of the formation density, the gamma counts recorded in the low energy region are influenced by photoelectric absorption and indicative of density and average atomic number (Z) of a formation.

**Figure 4.**Scatter plots of SGG ratio versus Fe%. Top plot shows the trend of the SGG ratio for the four different drillholes. The bottom plot shows the same data after shifting using drillhole (DH1) as a reference hole.

**Figure 5.**Membership functions for the two input variables before training of the fuzzy inference system. The yellow functions define membership to cluster 1 (SHALE), the green to cluster 2 (BIF), the red to cluster 3 (ORE).

**Figure 6.**Adjusted membership functions after training. The functions are spanning a considerably lower range than the initially defined functions in Figure 5 and thus reflect the desired output classes better.

**Figure 7.**Illustration of the fuzzy inference process regarding the rule evaluation and output value generation. The three rules and three membership functions per input variable are the result of initial fuzzy c-means clustering. All rules are evaluated simultaneously and a logical operator and method (AND/PRODUCT in this case) as well as the implication method applied to the rule evaluation results. The aggregated fuzzy output set is finally defuzzified by choosing value of the weighted average. In this example, the input value is high in iron and high in aluminum and its membership in terms of iron is to cluster one and partly to cluster 2 but in terms of aluminum it is to cluster 3. The minimum (implication method) is chosen to truncate the output function (which is a linear function in this case). The truncated outputs are aggregated into a single fuzzy set of which the weighted average value is chosen as he crisp output (class) value.

**Figure 8.**Results and parameters of the fuzzy inference system build from iron and aluminum input data. Top: training and checking errors for 50 consecutive runs; middle: correlation between prediction from the trained systems (FIS 1 is the last FIS from training (after 100 training epochs), FIS 2 is the system with the lowest checking error) and pre-defined classes indicating successful prediction (correlation above 97%); bottom: comparison of predicted and pre-defined classes from FIS 2.

**Figure 9.**Results and parameters of the fuzzy inference system build from iron and natural gamma log input data. Training and checking error are low, as in the case of predicting from Fe% and Al

_{2}O

_{3}%; correlation between predicted and pre-defined classes is high as well (>94%) showing that a substitution of the natural gamma log for the aluminum assay is feasible for predicting iron ore lithologies.

**Figure 10.**Results and parameters of the fuzzy inference system build from density and natural gamma log input data indicating that a substitution of density for iron content is not feasible for prediction of iron ore lithology.

**Figure 11.**Heat scatter (data density) cross-plot of Fe% and density. There are two apparent groups of iron concentration, which both have similar densities. A prediction of iron grade based on density is therefore not possible.

**Figure 12.**Comparison between predefined classes and predicted classes from elemental data (

**A**) and petrophysical logs (

**B**). Prediction based on elemental data shows an almost perfect match as would be expected, but prediction from SGG ratio and natural gamma shows a very good result as well.

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**MDPI and ACS Style**

Kitzig, M.C.; Kepic, A.; Grant, A.
Near Real-Time Classification of Iron Ore Lithology by Applying Fuzzy Inference Systems to Petrophysical Downhole Data. *Minerals* **2018**, *8*, 276.
https://doi.org/10.3390/min8070276

**AMA Style**

Kitzig MC, Kepic A, Grant A.
Near Real-Time Classification of Iron Ore Lithology by Applying Fuzzy Inference Systems to Petrophysical Downhole Data. *Minerals*. 2018; 8(7):276.
https://doi.org/10.3390/min8070276

**Chicago/Turabian Style**

Kitzig, Maria C., Anton Kepic, and Ashley Grant.
2018. "Near Real-Time Classification of Iron Ore Lithology by Applying Fuzzy Inference Systems to Petrophysical Downhole Data" *Minerals* 8, no. 7: 276.
https://doi.org/10.3390/min8070276