Aplicación de fragmentador de roca, Plasma FRAG BE, en sectores productivos de la Compañía Minera Cerro de Pasco cercanas a zonas urbanas para reducir impactos generados durante la fragmentación del macizo rocoso

La presente investigación se desarrolló en Compañía Minera Cerro de Pasco (CMCP) donde se busca aplicar el uso del Plasma como agente de fragmentación de macizo rocoso en sectores productivos de la mina cercanas a zonas de expansión urbanas. La finalidad del estudio consiste en comparar los valores de Velocidad Pico Partícula (VPP) entre el uso de Plasma Frag Be vs el ANFO a una distancia promedio igual en ambos casos. En tal sentido, se construye el modelo matemático Imperialist Competitive Algorithm (ICA) – linear, el cual permite estimar valores de VPP y a su vez modificar las variables de entrada como el burden, el espaciamiento, la longitud de taco, el factor de carga, la cantidad máxima de Plasma por disparo y la distancia entre el punto de fragmentación y la ubicación del sismógrafo. El modelo ICA-linear queda validado mediante la aplicación de 4 indicadores de rendimiento estadísticos los cuales son: el coeficiente de determinación, el error cuadrático medio, el error absoluto medio y el error porcentual absoluto medio cuyos resultados son 0.817, 5.001, 1.979 y 14% respectivamente. Los resultados de comparar los valores de VPP a una distancia promedio de 172 metros como se determinó según el estudio, en el caso del Plasma Frag Be los valores estimados son nulos, es decir no se registrarán valores a dicha distancia, mientras que en el caso del ANFO los registros muestran un valor promedio de 8.802 mm/s para la misma distancia mencionada, lo cual demuestra que los valores de VPP en el caso del uso del Plasma como fragmentador de macizo rocoso son considerablemente menores que cuando se utiliza ANFO.The present research was developed at Compañía Minera Cerro de Pasco (CMCP) where the aim is to apply the use of Plasma as a rock fragmentation agent in productive sectors of the mine close to urban expansion areas. The purpose of the study is to compare the values of Peak Particle Velocity (PPV) between the use of Plasma Frag Be vs ANFO at an equal average distance in both cases. In this sense, the Imperialist Competitive Algorithm (ICA) - linear mathematical model is built, which allows estimating PPV values and in turn modifying the input variables such as the burden, spacing, stemming, power factor, maximum charge of Plasma per delay and the distance from the blast-point to the seismograph. The ICA-linear model is validated by applying 4 statistical performance indicators which are: the determination coefficient, the mean square error, the mean absolute error and the mean absolute percentage error whose results are 0.817, 5.001, 1.979 and 14% respectively. The results of comparing the PPV values at an average distance of 172 meters as determined by the study, in the case of Frag Be Plasma the estimated values are zero, that is, no values will be recorded at that distance, while in the case of ANFO the records show an average value of 8,802 mm/s for the same distance mentioned, which shows that the PPV values in the case of the use of Plasma as a rock mass fragmentation device are considerably lower than when ANFO is used.Tesi

Development of new comprehensive relations to assess rock fragmentation by blasting for different open pit mines using GEP algorithm and MLR procedure

The fragment size of blasted rocks considerably affects the mining costs and production efficiency. The larger amount of blasthole diameter (ϕh) indicates the larger blasting pattern parameters, such as spacing (S), burden (B), stemming (St), charge length (Le), bench height (K), and the larger the fragment size.  In this study, the influence of blasthole diameter, blastability index (BI), and powder factor (q) on the fragment size were investigated. First, the relation between each of X20, X50, and X80 with BI, ϕh, and q as the main critical parameters were analyzed by Table curve v.5.0 software to find better input variables with linear and nonlinear forms. Then, the results were analyzed by multivariable linear regression (MLR) procedure using SPSS v.25 software and gene expression programming (GEP) algorithm for prepared datasets of four open-pit mines in Iran. Relations between each of X20, X50, and X80 with the combination of adjusted BI, ϕh, and q were obtained by MLR procedure with good correlations of determination (R2) and less root mean square error (RMSE) values of (0.811, 1.4 cm), (0.874, 2.5 cm) and (0.832, 5.4 cm) respectively. Moreover, new models were developed to predict X20, X50, and X80 by the GEP algorithm with better correlations of R2 and RMSE values (0.860, 1.3 cm), (0.913, 2.49 cm), and (0.885, 5.6 cm) respectively and good agreement with actual field results. The developed GEP models can be used as new relations to estimate the fragment sizes of blasted rocks

Identification of physical processes via data driven methods

Extracting governing equations from data can be viewed as reverse engineering of Nature- using data to identify the physical laws/models. This approach is crucial for fields where data is abundant ( such as geophysical flows, finance, and neuroscience) but the physical laws based on the first principles are not available. In recent years, the use of machine learning (ML) methods complemented the need for formulating mathematical models through the application of data analysis algorithms that allow accurate estimation of observed dynamics by learning automatically from the given observations. The neural networks and symbolic regression (SR) based approaches are the most popular ML frameworks used to learn the underlying physical process by only the observing data. While neural network approaches have shown great promise, its black-box nature makes it difficult to interpret the learned models. On the other hand, symbolic regression algorithms are capable of learning/finding an analytically tractable function in symbolic form. Hence to address the functional expressibility, a key limitation of the black-box machine learning methods, this study has explored the use of symbolic regression approaches for identifying relations and operators that accurately represent the underlying physical processes. This study demonstrates the use of an evolutionary algorithm called gene expression programming (GEP) and a sparse optimization algorithm called sequential threshold ridge regression (STRidge) in discovering physical models. The effectiveness of these algorithms is demonstrated on four different applications: (1) partial differential equation (PDE) discovery, (2) truncation error analysis, (3) hidden physics discovery and (4 ) discovering subgrid-scale closure models. This study shows the GEP and STRidge algorithms are able to distill various linear/nonlinear PDEs, truncation error terms and unknown source terms of 1D and 2D PDEs. Furthermore, the classical Smagorinsky model is identified for subgrid-scale (SGS) closure from an array of tailored features in solving the 2D Kraichnan turbulence problem. Our results demonstrate the huge potential of these techniques in distilling complex nonlinear physics models from only observing the data. Furthermore, this study reveals the importance of feature selection/feature engineering and embedding the prior knowledge about the unknown dynamical system in terms of invariances for identifying models

Feature engineering and symbolic regression methods for detecting hidden physics from sparse sensors

In this study we put forth a modular approach for distilling hidden flow physics in discrete and sparse observations. To address functional expressiblity, a key limitation of the black-box machine learning methods, we have exploited the use of symbolic regression as a principle for identifying relations and operators that are related to the underlying processes. This approach combines evolutionary computation with feature engineering to provide a tool to discover hidden parameterizations embedded in the trajectory of fluid flows in the Eulerian frame of reference. Our approach in this study mainly involves gene expression programming (GEP) and sequential threshold ridge regression (STRidge) algorithms. We demonstrate our results in three different applications: (i) equation discovery, (ii) truncation error analysis, and (iii) hidden physics discovery, for which we include both predicting unknown source terms from a set of sparse observations and discovering subgrid scale closure models. We illustrate that both GEP and STRidge algorithms are able to distill the Smagorinsky model from an array of tailored features in solving the Kraichnan turbulence problem. Our results demonstrate the huge potential of these techniques in complex physics problems, and reveal the importance of feature selection and feature engineering in model discovery approaches