Fuel cell stack prediction utilizing IHOS

A system for a vehicle, comprising:

• a fuel cell stack for providing electrical energy to the vehicle;
• and
• an electronic control unit connected to the fuel cell stack and configured to:
• obtain a first dataset having a plurality of data points associated with a plurality of sets of conditions and a plurality of operating states,
• generate a second dataset that includes data points that have a homotopic relationship from the first dataset,
• generate a first matrix that includes a plurality of sets of conditions based on the second dataset,
• generate a second matrix that includes a plurality of homotopic operating states based on the second dataset,
• generate an interpolation of homotopic operating states (IHOS) model that interpolates a behavior of operations of the fuel cell stack based on the first matrix and the second matrix, the HOS model having a plurality of reference rows of the plurality of sets of conditions associated with the plurality of homotopic operating states including a first reference row and a second reference row, the first reference row being a linear interpolation of the second reference row and having a first homotopic operating state that is a linear deformation of a second homotopic operating state of the second reference row,
• obtain a known set of conditions to predict or determine an unknown homotopic operating state,
• determine or predict the unknown homotopic operating state based on the known set of conditions and the HOS model, and
• control operation of the vehicle based on the determined or predicted homotopic operating state.

A method for real-time two-dimensional modeling of a fuel cell stack, comprising:

• obtaining a complex dataset having a plurality of data points, a data point of the plurality of data points being associated with a set of conditions of the fuel cell stack and an operating state of the fuel cell stack that results from the set of conditions;
• generating a homotopic dataset based on the complex dataset;
• generating a first matrix that includes a plurality of sets of conditions based on the homotopic dataset;
• generating a second matrix that includes a plurality of homotopic operating states based on the homotopic dataset;
• generating an interpolation of homotopic operating states (IHOS) model that interpolates a behavior of operations of the fuel cell stack based on the first matrix and the second matrix, the IHOS model having a plurality of reference rows of the plurality of sets of conditions associated with at least one homotopic operating state, each reference row being a linear interpolation of the other reference rows of the plurality of reference rows and having a homotopic operating state that is a linear deformation of a homotopic operating state of one other reference row;
• and
• controlling operation of the fuel cell stack using the IHOS model.