BlastIQ™ Insights – Dig Analysis Dashboard

This Knowledge Base Article describes the use of the Dig Analysis Dashboard in BlastIQ™ Insights. 

 

Availability: This Dashboard is not supplied as part of the Standard BlastIQ™ Insights offering. It is supplied as an optional purchased add-on to the Standard Insights offering.

 

Summary

BlastIQ™ Insights enables users to compare and analyse diggability performance measures (such as Instantaneous Dig Rate) against blasting metrics (such as Energy Factor) for a selected blast via the Dig Regression Analysis Dashboard.

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Navigation

To Dashboard

To navigate to the Dig Analysis Dashboard:

  1. From the BlastIQ™ Insights toolbar, select Dashboards.
  2. From the Dashboards menu, expand Blast Analysis and select Dig Regression Analysis.

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Within Dashboard

The Dig Regression Analysis Dashboard is divided and arranged into six main areas:

  1. The Blast Selection drop-down menu.
  2. The Variable 1 Selection drop-down menu.
  3. The Variable 1 Map, displaying a plan view of the selected variable for the selected blast.
  4. The Variable 2 Selection drop-down menu.
  5. The Variable 2 Map, displaying a plan view of the selected variable for the selected blast.
  6. The Regression Plot/s comparing Variable 1 (x-axes) to Variable 2 (y-axes).

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To analyse a blast:

  1. Click on the “Select a blast” drop-down menu found across the top of the Dig Regression Analysis Dashboard to expand the selection list. Picture4.png

Blasts will appear in this list sorted by firing date (most recent first), then by Blast Name.

Unfired blasts are not available for selection on this Dashboard, only blasts that have been “fired” within BlastIQ™ Insights are available for selection and display within the Dig Regression Analysis Dashboard.  If a blast does not appear within the Blast Selection drop-down menu, check it’s “fired” status on the Blast Management page within BlastIQ™ Insights, and set accordingly.

  1. Select one blast from the list of available blasts to view the dig data for that blast.
  2. Select the first variable to compare, click on the “Select the first variable to compare” drop-down menu found at the upper-left of the Dashboard (just below the Blast Selection drop-down).Picture5.png

Choose one of the following available options:

      • Powder Factor
      • Energy Factor
      • Instantaneous Dig Rate

Note, other blasting and/or blast related metrics may be available for selection and analysis here, dependent on Customer data availability.

  1. Select the second variable to compare, click on the “Select the second variable to compare” drop-down menu found at the upper-right of the Dashboard (just below the Blast Selection drop-down).Picture6.png

Choose from the available options. 

Whatever variable was selected as Variable 1, will be inactive (greyed-out), and unavailable for selection as Variable 2 here.

 

Pan and Zoom functions are enabled within both the Variable 1 Map and Variable 2 Map these are accessed via the Plot Toolbar, visible in the top-right corner of each Plot when hovering the mouse anywhere over the Plot window.

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Each item within the Plot Toolbar enables the following action after selection:

  • camera.png Download Plot.  Save the current Plot View as an image file (.png format)
  • zoom.png Zoom. Utilise a click and drag action with the mouse to define the region of interest to Zoom in on.  Whilst holding the left-mouse-click and dragging, the region of interest will be highlighted within the view, upon release of the mouse-click, the view will update too the new zoomed extents.
  • pan.png Pan. Use a click (left-mouse button) and drag action to Pan the view.
  • zoom in.png Zoom In.  Click this to zoom in one level.
  • zoom out.png Zoom Out.  Click this to zoom out by one level.
  • reset.png Reset Axes. Click this to reset the view back to the original default view state (i.e. a view zoomed and centred on the selected blast).

Pan and Zoom functions are also enabled within the Regression Plot accessed via the Plot Toolbar, visible in the top-right corner when hovering the mouse anywhere over the Regression Plot window.

 

Interpretation

Variable Map

Both Variable Maps will render upon selecting the following:

  • A blast from the Blast Selection drop-down menu
  • Two blasting related variables, one from each of the Variable drop-down menus

The type of map shown in the Variable Map is dependent on the variable selected.  However, irrespective of the variable selected a form of heat-mapping will be utilised to graphically represent the variation across the blast plan in the variable of interest 

Choosing either Powder Factor or Energy Factor will result in the display of a choropleth style heat-map that utilises a Voronoi tessellation to represent each individual blast-hole region within the selected blast.  Each tessellation is colour filled using a continuous colour-scale.

heat-map.png

This plot allows users to visually interpret the explosive usage distribution within a Blast pattern, with darker coloured regions indicating areas of higher explosive usage (or energy) relative to the lighter coloured regions.

Hovering the mouse over a blast-hole tessellation region will reveal details of that blast-hole including the:

  • The blast-hole identifier
  • The Energy Factor or Powder Factor (dependant on the variable calculated for that blast-hole)

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Choosing Instantaneous Dig Rate will result in the display of a heat-map that utilises surface contouring to represent the digging variations observed within the selected blast.  The contour surface is colour filled using a continuous colour-scale.  The blast-holes, and blast boundary for the selected blast are also displayed.

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If multiple Excavator Types have been utilised in mining the selected blast, then multiple surfaces representative of the average Instantaneous Dig Rate will be rendered within the Plot.  Visibility of these surfaces can be toggled on and off by clicking the Excavator identifier in the Plot legend. 

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When “toggled off” the legend item will become “greyed-out”.

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This plot allows users to visually interpret the variations in digging performance within a Blast pattern, with darker coloured regions indicating areas of higher digging rates (better digging performance) relative to the lighter coloured regions.

Hovering the mouse over a blast-hole will reveal details of the average Instantaneous Dig Rate including:

  • The blast-hole identifier
  • The average Instantaneous Dig Rate calculated within the vicinity of that blast-hole

inst dig rate details.png

Regression Plot

A Regression Plot will render upon selecting the following:

  • A blast from the Blast Selection drop-down menu
  • Two blasting related variables, one from each of the Variable drop-down menus

A separate Regression Plot will be displayed for each Excavator Type utilised in the mining of the selected blast. 

Each Regression Plot consists of a scatter plot displaying each blast-hole within the selected blast (as a single data-point) in relation to the two selected VariablesVariable 1 will be plotted on the x-axis and Variable 2 on the y-axis.

regression plot.png

Hovering the mouse over a blast-hole sample point on the Regression Plot will reveal details of that sample point including:

  • The blast-hole identifier
  • The Variable 1 value for that blast-hole (e.g. Energy Factor)
  • The Variable 2 average value calculated within the vicinity of that blast-hole (e.g. Instantaneous Dig Rate)

regression plot details.png

A Linear Model is also fitted to these blast-hole sample points and displayed on the Regression Plot as a solid-black line. 

Hovering the mouse over the line of best-fit will reveal the linear equation coefficients (slope and intercept).

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A Confidence Region (bounded by two orange-solid lines) and Prediction Band (bounded by two black-dashed lines) are also displayed for this fitted linear model.  The Confidence Region represents the uncertainty in the fitted linear model based upon the supplied sample data.  The Prediction Band represents the uncertainty in the value of a new data-point (observed from the same population from which the given data-set was sampled).

The Regression Plot and fitted Linear Model allows users to identify correlations (including the strength of those correlations) that may exist between the selected blasting variables.  When a reasonable correlation between two selected variables is present, a user could then apply this Linear Model to inform further decisions about how to improve blasting.

Calculation of Powder Factor and Energy Factor

The Powder Factor and Energy Factor variables are both indicators of the ratio of explosives (total weight (in kg or lb) and total energy (in MJ or kcal) respectively within the blast-hole) used per volume of rock. 

In the Dig Analysis Dashboard the volume of rock per blast-hole is determined as follows:

V = A(Zc - Zg)

where:

V = blast-hole volume

A = Area of blast-hole tessellation region

Zc = blast-hole collar elevation (best available)

Zg = blast-hole grade elevation

The “best available” blast-hole collar information is used in this calculation, this means that when actual collar coordinates (X, Y, and Z) are available, these are used.  However, if actual collar coordinates are unavailable within the BlastIQ™ system, and evidence exists that the hole has been drilled (e.g. any blast-hole measure has been recorded against the hole), then the adjusted design collar coordinates will be used (where available), alternatively the design collar coordinates will be used, to ensure a volume estimate can be made to facilitate calculation of either a Powder Factor or Energy Factor.

Calculation of Dig Rate Surface and Average Instantaneous Dig Rate Values

In the Dig Analysis Dashboard, the actual Instantaneous Dig Rate measures obtained from the Customer’s Fleet Management System data are averaged to provide a single estimate at each blast-hole location based upon all the dig rate measures observed within the vicinity of that blast-hole.

Inverse Distance Weighting is used to provide this single point estimate at each blast-hole location.  The same Inverse Distance Weighting technique is also used to estimate dig rates across a consistent regular grid of points, contours are then extracted from these grid point estimates to create the surface contour heat-map.

Inverse Distance Weighting is a method for assigning a value to an unknown point using a weighted average of nearby values available at known points.  Weights are assigned using the inverse distance from the unknown point to the known point.

The Inverse Distance Weighted Average is calculated as follows:

formula.png

where:

u(x) = weighted average at unknown point

xi = value at known point

n = total number of known points

wi = Inverse Distance Weighting function

formula_2.png

where:

wi = weight

d = distance from known point to unknown point

p = power parameter

Note, the following constraints are applied when determining the weighted average dig rates within this Dashboard:

  • The maximum number of known points (n) used in this calculation is capped at 20, if there are more than 20 known points, we use the 20 nearest points.
  • Known points with a distance (from the unknown) greater than 5.0m are ignored, e.g., only dig measures observed within 5 metres of the blast-hole are used for estimation of dig rate at that blast-hole location.
  • A minimum number of 3 known points (within 5m) are required to perform the estimate.
  • 1.8 is used as the power parameter.

Linear Regression Model Determination

Fitting of the linear model is performed by minimising the sum of the squared errors between the predicted and measured values for Variable 2.

The linear model is of the form:

y = mx + c

where:

y = the dependent variable, Variable 2

x = the independent variable, Variable 1

m = the slope (or gradient) of the fitted line

c = the intercept

The linear coefficients (m and c) are determined as follows:

formula_3.png

where:

x1 = value at known point

y1 = value at known point

n = total number of known points

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