Signal Decomposition Using Masked Proximal Operators

We consider the well-studied problem of decomposing a vector time series signal into components with different characteristics, such as smooth, periodic, nonnegative, or sparse. We describe a simple and general framework in which the components are defined by loss functions (which include constraints), and the signal decomposition is carried out by minimizing the sum of losses of the components (subject to the constraints). When each loss function is the negative log-likelihood of a density for the signal component, this framework coincides with maximum a posteriori probability (MAP) estimation; but it also includes many other interesting cases. Summarizing and clarifying prior results, we give two distributed optimization methods for computing the decomposition, which find the optimal decomposition when the component class loss functions are convex, and are good heuristics when they are not. Both methods require only the masked proximal operator of each of the component loss functions, a generalization of the well-known proximal operator that handles missing entries in its argument. Both methods are distributed, i.e., handle each component separately. We derive tractable methods for evaluating the masked proximal operators of some loss functions that, to our knowledge, have not appeared in the literature.Comment: The manuscript has 61 pages, 22 figures and 2 tables. Also hosted at https://web.stanford.edu/~boyd/papers/sig_decomp_mprox.html. For code, see https://github.com/cvxgrp/signal-decompositio

Determining circuit model parameters from operation data for PV system degradation analysis: PVPRO

Physics-based circuit parameters like series and shunt resistance are essential to provide insights into the degradation status of photovoltaic (PV) arrays. However, calculating these parameters typically requires a full current–voltage characteristic (I-V curve), the acquisition of which involves specific measurement devices and costly methods. Thus, I-V curves of the PV system level are often not available. This paper proposes a methodology (PVPRO) to estimate these I-V curve parameters using only operation (string-level DC voltage and current) and weather data (irradiance and temperature). PVPRO first performs multi-stage data pre-processing to remove noisy data. Next, the time-series DC data are used to fit an equivalent circuit single-diode model (SDM) to estimate the circuit parameters by minimizing the differences between the measured and estimated values. In this way, the time evolutions of the SDM parameters are obtained. We evaluate PVPRO on synthetic datasets and find an excellent estimation of both SDM and the key I-V parameters (e.g., open-circuit voltage, short-circuit current, maximum power, etc.) with an average relative error of 0.55%. The performance, especially the extracted degradation rate of parameters, is robust to various measurement noises and the presence of faults. In addition, PVPRO is applied to a 271 kW PV field system. The relative error between the real and estimated operation voltage and current is less than 1%, suggesting that degradation trends are well captured. PVPRO represents a promising open-source tool to extract the time-series degradation trends of key PV parameters from routine operation data

Multifunctionality and mechanical origins: Ballistic jaw propulsion in trap-jaw ants

Extreme animal movements are usually associated with a single, high-performance behavior. However, the remarkably rapid mandible strikes of the trap-jaw ant, Odontomachus bauri, can yield multiple functional outcomes. Here we investigate the biomechanics of mandible strikes in O. bauri and find that the extreme mandible movements serve two distinct functions: predation and propulsion. During predatory strikes, O. bauri mandibles close at speeds ranging from 35 to 64 m·s(−1) within an average duration of 0.13 ms, far surpassing the speeds of other documented ballistic predatory appendages in the animal kingdom. The high speeds of the mandibles assist in capturing prey, while the extreme accelerations result in instantaneous mandible strike forces that can exceed 300 times the ant’s body weight. Consequently, an O. bauri mandible strike directed against the substrate produces sufficient propulsive power to launch the ant into the air. Changing head orientation and strike surfaces allow O. bauri to use the trap-jaw mechanism to capture prey, eject intruders, or jump to safety. This use of a single, simple mechanical system to generate a suite of profoundly different behavioral functions offers insights into the morphological origins of novelties in feeding and locomotion