Estimating Monotonic Functions and Their Bounds

A function estimator MSQUID is presented for fitting and bounding noisy data that are known to be monotonic. MSQUID augments a “backpropagation” neural network model with a set of constraints which restricts the model to monotonic functions. Model parameters are estimated using nonlinear, constrained optimization at little increase in computation over standard neural networks. It is proven that MSQUID can estimate any monotonic function and produces more accurate estimates than unconstrained optimization. These monotonic functions and their confidence bounds can be used in many fault detection and diagnosis systems.

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