Evaluation of methods for feasible parameter set estimation of Takagi-Sugeno models for nonlinear regression with bounded errors

In data-driven modeling besides the point estimate of the model parameters, an estimation of the parameter uncertainty is of great interest. For this, bounded error parameter estimation methods can be used. These are particularly interesting for problems where the stochastical properties of the random effects are unknown and cannot be determined. In this paper, different methods for obtaining a feasible parameter set are evaluated for the use with Takagi-Sugeno models. Case studies with simulated data and with measured data from a manufacturing process are presented.

Approximating median absolute deviation with bounded error

The median absolute deviation (MAD) is a statistic measuring the variability of a set of quantitative elements. It is known to be more robust to outliers than the standard deviation (SD), and thereby widely used in outlier detection. Computing the exact MAD however is costly, e.g., by calling an algorithm of finding median twice, with space cost O ( n ) over n elements in a set. In this paper, we propose the first fully mergeable approximate MAD algorithm, OP-MAD, with one-pass scan of the data. Remarkably, by calling the proposed algorithm at most twice, namely TP-MAD, it guarantees to return an (ϵ, 1)-accurate MAD, i.e., the error relative to the exact MAD is bounded by the desired ϵ or 1. The space complexity is reduced to O ( m ) while the time complexity is O ( n + m log m ), where m is the size of the sketch used to compress data, related to the desired error bound ϵ. To get a more accurate MAD, i.e., with smaller ϵ, the sketch size m will be larger, a trade-off between effectiveness and efficiency. In practice, we often have the sketch size m ≪ n , leading to constant space cost O (1) and linear time cost O ( n ). The extensive experiments over various datasets demonstrate the superiority of our solution, e.g., 160000× less memory and 18x faster than the aforesaid exact method in datasets pareto and norm . Finally, we further implement and evaluate the parallelizable TP-MAD in Apache Spark, and the fully mergeable OP-MAD in Structured Streaming.

Error-Free Affine, Unitary, and Probabilistic OBDDs

We introduce the affine OBDD model and show that zero-error affine OBDDs can be exponentially narrower than bounded-error unitary and probabilistic OBDDs on certain problems. Moreover, we show that Las-Vegas unitary and probabilistic OBDDs can be quadratically narrower than deterministic OBDDs. We also obtain the same results for the automata counterparts of these models.

Optimal Identification and Metaheuristic PID Control of a Two-Tank System

In the modern optimization context, this paper introduces an optimal PID-based control strategy for a two-tank installation, namely ASTANK2. The process model was identified by using raw and spline smoothed measured data, respectively. Two PID controller configurations, a standard (regular) one (PID-R) and a non-standard one (PID-N), were considered for each type of model, resulting in four regulators. The optimal tuning parameters of each regulator were obtained by a searching approach relying on a combination of two metaheuristics. Firstly, an improved version of the Hill Climbing algorithm was employed to comprehensively explore the searching space, aiming to find fairly accurate tuning parameters. Secondly, an improved version of the Firefly Algorithm was proposed to intensively refine the search around the previously found optimal parameters. A comparative analysis between the four controllers was achieved in terms of performance and robustness. The simulation results showed that all optimal controllers yielded good performance in the presence of exogenous stochastic noise (bounded error tracking, setpoint tracking, reduced overshoot, short settling time). Robustness analysis is extensive and illustrates that the PID-R controllers are more robust to model uncertainties, whilst PID-N controllers are more robust to tracking staircase type references.