Application of the Ensemble Kalman Filter for Improved Mineral - - PowerPoint PPT Presentation

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Application of the Ensemble Kalman Filter for Improved Mineral - - PowerPoint PPT Presentation

Feb 22, 2023 40 likes •302 views

Application of the Ensemble Kalman Filter for Improved Mineral Resource Recovery C. Yksel, M.Sc. J. Benndorf, PhD, MPhil, Dipl-Eng. Department of Geoscience & Engineering, Delft University of Technology, Delft, the Netherlands 1

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Application of the Ensemble Kalman Filter for Improved Mineral Resource Recovery

  • C. Yüksel, M.Sc.
  • J. Benndorf, PhD, MPhil, Dipl-Eng.

Department of Geoscience & Engineering, Delft University of Technology, Delft, the Netherlands

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Mine Design Equipment Selection Reserve Estimation

The Flow of Information

Exploration and Data Collection Resource Modelling Production Scheduling and Operation Processing and Sale

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Uncertainty in Model-based Prediction

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Increasing Availability of Sensor Based Online Data:

  • Material characterization (geo-chemical, textural and physical properties)
  • Equipment performance, upstream and downstream (e.g. efficiency,

down-time)

  • Equipment location (e.g. GPS, UPS)

New Potential: Sensor Data

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Future Potential – Availability of Data Data Mining Content

How can we make best use of the available data?

  • Closing the Loop: A feed-back framework for Real-Time Resource Model

Updating

  • A Kalman Filter Approach
  • Using Online Data for Improved Production Control
  • Illustrative Case Study: Coal
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Towards Closed-Loop Management

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Towards Closed-Loop Management

Z*(x)

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Drillhole Data Prior Model (s) Model Based Prediction Updated Model (s) Sensor Observation (Production Data)

Towards Closed-Loop Management

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Interpolation (Kriging) Simulation Realisation 1&10 (Conditional Simulation)

(Benndorf 2013)

Resource Model

Generation of Prior Models

  • Best local estimation,
  • Minimization of error-variance estimate.
  • Represent possible scenarios about the deposit,
  • Represent structural behavior of data (in-situ variability),
  • Modelled by many different realizations,
  • Differences between realizations capture uncertainty

Seam Geometry and CV

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Closed-Loop Concept

True but un- known deposit Z(x) Exploration Data Set z(xi), i=1,…,n

Sampling

Estimated Deposit Model Z*(x) + Uncertainty

Modelling

Decisions e.g. Mine Planning A Model Based Prediction f(A,Z*(x))

Feed – Forward - Loop

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Closed-Loop Concept

True but un- known deposit Z(x) Exploration Data Set z(xi), i=1,…,n

Sampling

Estimated Deposit Model Z*(x) + Uncertainty

Modelling

Decisions e.g. Mine Planning A Model Based Prediction f(A,Z*(x))

Production Monitoring

Sensor Measurements Vj, j=1,…,m Difference f(A,Z*(x)) - Vj

Sequential Updating

Closing the Loop Feed – Back - Loop

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Linking Model and Observation

Production sequence – Matrix A

𝑏1,1 ⋯ 𝑏1,𝑛 ⋮ ⋱ ⋮ 𝑏𝑜,1 ⋯ 𝑏𝑜,𝑛

  • n mining blocks
  • each of the blocks contributes

to a blend, which is observed at a sensor station at time ti

  • m measurements are taken
  • ai,j proportion block i

contributes to the material blend, observed at time j by measurement li

1 2 . . . . . . n

Mining Blocks Observations

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𝒂∗ 𝒚 =𝒂∗0 𝒚 + 𝑳 (𝒘 − 𝑩𝒂∗0 𝒚 )

𝒂∗ 𝒚 … updated short-term block model (a posteriori) 𝒂∗

𝟏 𝒚

… prior block model based (without online sensor data) v … vector of observations (sensor signal at different points in time t) 𝑩 … design matrix representing the contribution of each block per time interval to the production observed at sensor station K … updating factor (Kalman-Gain)

Resource Model Updating

Sequential Model Updating - A Kalman Filter Approach

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Sequential Model Updating – A “BLUE”

𝒇(𝒚)𝑢+1 = 𝒜(𝒚)𝑢+1 − 𝒜∗(𝒚)𝑢+1 𝑳 = 𝑫𝑢,𝑢𝑩𝑼(𝑩𝑫𝑢,𝑢𝑩𝑼 + 𝑫𝑤,𝑤)−𝟐

Estimation error: Estimation variance to be minimized: Updating factor:

𝑫𝑢+1,𝑢+1 = 𝐹 𝒇(𝒚)𝑢+1𝒇(𝒚)𝑢+1

𝑈

Resource Model Updating

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Sequential Model Updating – The Integrative Character

𝑳 = 𝑫𝑢,𝑢𝑩𝑼(𝑩𝑫𝑢,𝑢𝑩𝑼 + 𝑫𝑤,𝑤)−𝟐 Resource Model Updating

Model Uncertainty Extraction Sequence Sensor Precision

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Sequential Model Updating

Resource Model Updating

Main challenges:

  • Large grids
  • Industrial Case: 4,441,608 blocks
  • Non-linear relationships between model and observation
  • Non-Gaussian data
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Sequential Model Updating A Non-Linear Version – The Ensemble Kalman Filter

Resource Model Updating

(Reproduced after Geir Evensen 1993)

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Resource Model Updating

*Z Haiyan, J J Gomez-Hernandez, H H Franssen, L Li. 2011. An approach to handling non- Gaussianity of parameters and state variables. Advances in Water Resources, 844-864.

Sequential Model Updating To handle Non-Gaussian Data… N-Score-Ensemble Kalman Filter*

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Illustrative Case Study

Updating the Calorific Value in a Large Coal Mine

Case Study: Walker Lake Data Set (Exhaustive “true” data are available) Model based prediction:

  • Estimated block model (5200t/block)
  • Capacity Excavator 1: 500 t/h
  • Capacity Excavator 2: 1.000 t/h
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Illustrative Case Study

Updating the Calorific Value in a Large Coal Mine

Sensor Observations:

  • Artificial sensor data for a 10 minute average (representing 250 t)
  • Relative sensor error is varied between 1%, 5% and 10%
  • Sensor data obtained:
  • Model based prediction + dispersion variance + sensor error

CV in MJ/kg 8 9 10 11 True Block Grade True Block Grade + Dispesion Variance True Block Grade + Dispesion Variance + Sensor Error

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Illustrative Case Study

Prior Block Model based on Exploration Data Updated Block Model Integrating Sensor Data Differences

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Illustrative Case Study

Comparison to Reality

Kalman-Filter: 2 Excavators

Prior 10% 5% 1% MSE relative to Prior Relative Sensor Error 0.0 0.2 0.4 0.6 0.8 1.0 Prior 10% 5% 1% MSE relative to Prior Relative Sensor Error 0.0 0.2 0.4 0.6 0.8 1.0 Prior 10% 5% 1% MSE relative to Prior Relative Sensor Error 0.0 0.2 0.4 0.6 0.8 1.0

MSE-mined MSE- adjacent blocks MSE- 2 blocks away

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  • Significant improvement in prediction
  • Increased confidence in dispatch decisions
  • Less miss-classified blocks (ore/waste)
  • Less shipped train loads out of spec
  • Increased customer satisfaction and revenue
  • Magnitude of improvement depends on level of exploration,

variability and sensor error

Illustrative Case Study - Results

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  • EU - RFCS funded project RTRO-Coal

Current Work

Prior Model

with partners:

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Conclusions

  • Modern ICT provides online data, which can be the basis for (near-)

continuous process monitoring at different stages of the mining value chain

  • Utilizing these data for (near-) real-time decision making offers huge

potential for more sustainable extraction of mineral resource

  • Closed Loop Concepts offer:
  • Integration of prediction and process models with data gathering
  • Interdisciplinary and transparent project communication (breaking

the silos)

  • More complex use of data for increased resource efficiency
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Thank You for Your Attention

Source: RWE

Contact: Cansın Yüksel C.Yuksel@tudelft.nl