A heuristic solution to the optimisation of flutter control in compression systems (and to some more binary quadratic programming problems) via ΔΣ modulation circuits

Abstract

An example of how circuit related techniques can help solving optimisatin problems originating from completely different domains is provided. It is shown that a specific class of Unconstrained Binary Quadratic Programming (UBQP) problems, including those arising in the optimisation of flutter control via blade mistuning, can be solved by means of ∆Σ modulators. This is done in steps, first restating the UBQP problem as a specific signal processing problem, and then attacking the latter via the design of a ∆Σ modulator with a suitably derived Noise Transfer Function. A (heuristically) optimal solution for the original problem is finally obtained from the modulator output stream. The method is validated by two numerical examples arising in the design of turbo-machines.

A Discrete Meta-Control Procedure for Approximating Solutions to Binary Programs

“…If λ * T j+1 a j = 0, binary values for u * j are determined by Equation (20). When λ * T j+1 a j = 0, the arc is singular, and we may reintroduce constraint (9), u j (1 − u j ) = 0, to force a binary solution.…”

“…In [19,20], circuit related techniques are used to transform unconstrained discrete quadratic programming problems and provide high quality suboptimal solutions. Our focus is on problems with linear objective functions, instead of quadratic, and linear equality constraints, instead of unconstrained.…”

Discontinuous piecewise‐linear discrete‐time dynamics – maps with gaps in electronic systems

“…Application to sigma-delta modulation and related electronic systems Sigma-delta (SD also known as delta-sigma) modulation is a technique very widely used throughout electronic systems (Norsworthy et al, 1996). It is first found used as a method of conversion between analogue and digital signals, but the technique is such a useful one that it has found use in many other systems, often well beyond the area of data conversion (Galton et al, 1998;Callegari and Bizzarri, 2010). Because of the simplicity and widespread applicability of the method, we will use the SD modulator and its variants as a vehicle to illustrate many of the methods of the previous section.…”

Optimal design of the noise transfer function of ΔΣ modulators: IIR strategies, FIR strategies, FIR strategies with preassigned poles

“…A/D, D/A and D/D conversion [1,2], frequency synthesis [3], waveform storage [4], signal processing [5] and more. Recently, it has been suggested that they may even be used as heuristic optimizers for special classes of optimization problems [6,7]. In all these applications, their attractiveness mainly derives from the ability to perform noise shaping.…”