A Novel Approach to Optimizing Material Processing Yield

Material Processing Systems function like assembly lines but maintain a continuous flow of materials through multiple interconnected steps. Optimizing these systems typically focuses on maximizing the total yield by balancing the two key performance indicators of throughput and quality. This requires identifying the optimal operating parameters that will maximize yield given variations in raw materials and environmental conditions.

Previous solutions to optimization problems have traditionally involved two high-level steps. First, predictions are made on how each operating parameter will impact yield. Then, those predictions are used to formulate an optimization algorithm that recommends setpoints. These solutions have typically taken the following approach:

1. A predictive model is built that maximizes accuracy by including as many variables as possible and using black box algos (e.g., gradient boosted trees, neural nets, etc.).
2. These black box algos are then used to make predictions across a range of ore types and setpoints. Setpoints are then chosen with the highest prediction for each ore type (sometimes using heuristic or evolutionary solvers to expedite).

However, there are several challenges unique to material processing systems that these previous methods fail to address:

Challenges in predicting impact of each variable on yield:

• Each step influences others, causing upstream or downstream effects that complicate analysis. For example, a bottleneck downstream can reduce upstream throughput.
• Controlling certain variables (such as torque and RPM) indirectly controls others (such as power), requiring selective management of variables.
• Some steps are influenced by uncontrollable factors, such as ambient temperature.
• Human operators respond in real time to changes, potentially biasing data and skewing analytical insights. (E.g., every time yield drops by a lot, operators press a setpoint that improves yield by a little, making it look like the setpoint is associated with dropping yields).
• Physical relationships between variables must be respected to avoid unsafe or nonsensical outcomes (i.e., you can’t use black box algos).
• Variables interact in complex, non-linear ways, complicating model development.

Challenges in formulating the optimization problem:

• Objective functions must be continuous to avoid wild changes in recommended setpoints given small changes in incoming ore.
• The system must consistently produce the same results under the same conditions, limiting the use of heuristic or evolutionary methods.
• Recommendations must provide a range of options rather than fixed points, thereby forcing operators to adjust dynamically to maintain safety.

To address these challenges, our patented process includes:

• Causal Diagram Development: Collaborate with process experts to map out the causal relationships between variables through diagrams. These diagrams can range from simple to complex, showing layers of cause and effect.
• Encoding Prior Knowledge: Integrate expert insights about expected relationships, including the direction and strength of effects, and the functional forms of these relationships (e.g., quadratic, convex).
• Applying Do-Calculus: Use Judea Pearl’s Do-calculus to identify essential variables for predictive modeling, ensuring that models focus on causation rather than correlation.
• Probabilistic Programming: Accurately estimate relationships between variables by developing models using probabilistic programming, strengthened by strong priors based on expert input and historical data.
• Convex Stochastic Optimization: Formulate a convex stochastic optimization problem to determine optimal setpoint bands, maximizing yield while accommodating real-time adjustments and safety.

Incorporated into our solution for natural resource processing, our novel approach enables us to yield uplift than with past approaches. We can do this by correctly characterizing how physical processes change given changes in raw materials (e.g., copper ore). We can, therefore, continuously adjust to the correct recipe as the ore changes – and the more time spent at the best recipe for a given ore type, the higher the uplift.