A stability with optimality analysis of consensus-based distributed filters for discrete-time linear systems

In this paper we investigate how stability and optimality of consensus-based distributed filters depend on the number of consensus steps in a discrete-time setting for both directed and undirected graphs. By introducing two new algorithms, a simpler one based on dynamic averaging of the estimates and a more complex version where local error covariance matrices are exchanged as well, we are able to derive a complete theoretical analysis. In particular we show that dynamic averaging alone suffices to approximate the optimal centralized estimate if the number of consensus steps is large enough and that the number of consensus steps needed for stability can be computed in a distributed way. These results shed light on the advantages as well as the fundamental limitations shared by all the existing proposals for this class of algorithms in the basic case of linear time-invariant systems, that are relevant for the analysis of more complex situations

Investigation on the effect of the gas-to-metal ratio on powder properties and PBF-LB/M processability

Metal powders for the laser powder bed fusion process are usually produced via gas atomization. However, due to the tight particle size distribution required for this application, the yield of the atomization process is low, resulting in a high-powder cost. In this work, atomization process parameters were varied to increase the gas-to-metal ratio to reduce the particle size distribution produced, and therefore increase the yield of the process. As a result, eight powders were produced starting from scrap AISI 136L material at different gas-to-metal ratio values, and the atomization process yield was successfully increased by 50%. First, the eight powders were characterized in terms of powder size, shape distributions, and flowability. Later, all powders were used to produce tensile specimens. The powders produced at higher yield exhibited a larger number of fine particles but slightly lower circularity, particularly in the coarse fraction. Furthermore, powders produced at a high gas-to-metal ratio demonstrated enhanced flowing properties and higher packing density. Consequently, these powders exhibited superior tensile performance, with ultimate tensile strength (UTS) ranging from 651 to 673 MPa and elongation values between 63 and 66%

LTV stochastic systems stabilization with large and variable input delay

In this paper we propose a solution to the state-feedback and output-feedback stabilization problem for linear time-varying stochastic systems affected by arbitrarily large and variable input delay. It is proved that under the proposed controller the underlying stochastic process is exponentially centered and mean square bounded. The solution is given through a set of delay differential equations with cardinality proportional to the delay bound. The predictor is based on the semigroup generated by the closed-loop system in absence of delay, and its computation is described by a numerically reliable and robust method. In the deterministic case this method generates the same optimal trajectories as in the delay-less case

Projecting seismicity induced by complex alterations of underground stresses with applications to geothermal systems

Seismicity associated with subsurface operations is a major societal concern. It is therefore critical to improve predictions of the induced seismic hazard. Current statistical approaches account for the physics of pore pressure increase only. Here, we present a novel mathematical model that generalises adopted statistics for use in arbitrary injection/production protocols and applies to arbitrary physical processes. In our model, seismicity is driven by a normalised integral over the spatial reservoir volume of induced variations in frictional Coulomb stress, which—combined with the seismogenic index—provides a dimensionless proxy of the induced seismic hazard. Our model incorporates the classical pressure diffusion based and poroelastic seismogenic index models as special cases. Applying our approach to modeling geothermal systems, we find that seismicity rates are sensitive to imposed fluid-pressure rates, temperature variations, and tectonic conditions. We further demonstrate that a controlled injection protocol can decrease the induced seismic risk and that thermo-poroelastic stress transfer results in a larger spatial seismic footprint and in higher-magnitude events than does direct pore pressure impact for the same amount of injected volume and hydraulic energy. Our results, validated against field observations, showcase the relevance of the novel approach to forecast seismic hazards induced by subsurface activities

An adaptive POD approximation method for the control of advection-diffusion equations

We present an algorithm for the approximation of a finite horizon optimal control problem for advection-diffusion equations. The method is based on the coupling between an adaptive POD representation of the solution and a Dynamic Programming approximation scheme for the corresponding evolutive Hamilton-Jacobi equation. We discuss several features regarding the adaptivity of the method, the role of error estimate indicators to choose a time subdivision of the problem and the computation of the basis functions. Some test problems are presented to illustrate the method.Comment: 17 pages, 18 figure

A new distributed protocol for consensus of discrete-time systems

In this paper, a new distributed protocol is proposed to force consensus in a discrete-time network of scalar agents with an arbitrarily assignable convergence rate. Several simulations validate the performances and the improvements with respect to more standard protocols

Freeform optics measurements with the NANOMEFOS non-contact measurement machine

The NANOMEFOS non-contact measurement machine for freeform optics has been completed. The separate short metrology loop results in a stability at standstill of 0.9 nm rms over 0.1 s. Measurements of a tilted flat show a repeatability of 2-4 nm rms, depending on the applied tilt, and a flatness that agrees well with the NMi measurement

Influence of production batch related parameters on static and fatigue resistance of LPBF produced AlSi7Mg0.6

In laser powder bed fusion (LPBF), the influence material properties are often determined as a function of the inclination with respect to the build direction. In industrial production with variable component shapes and dimensions, the part orientation will often be a matter of the available space in the build volume. Additionally, build-to-build variability is an important factor that may impact the mechanical properties that are often not quantified. Such sources of variability are of great importance for highly demanding sectors such as aviation and aerospace, where lightweight Al-alloys are often used with the geometrical freedom given by the LPBF process. Hence, this work systematically investigates the influence of production batch-related parameters together with part inclination in the LPBF of AlSi7Mg0.6 alloy. Three builds were executed to quantify the impact of the batch, part position, and inclination on the static and fatigue resistance of the alloy in a completely randomized experimental design using an industrial LPBF machine. The results were analysed by the appropriate statistical methods both for discrete and functional data. The results showed that while the part orientation only influenced the static properties, the part position significantly affected the fatigue life demonstrated by the different low cycle fatigue life coefficients

Digital holography as 3D tracking tool for assessing acoustophoretic particle manipulation

The integration of digital holography (DH) imaging and the acoustic manipulation of micro-particles in a microfluidic environment is investigated. The ability of DH to provide efficient 3D tracking of particles inside a microfluidic channel is exploited to measure the position of multiple objects moving under the effect of stationary ultrasound pressure fields. The axial displacement provides a direct verification of the numerically computed positions of the standing wave’s node, while the particle’s transversal movement highlights the presence of nodes in the planar direction. Moreover, DH is used to follow the aggregation dynamics of trapped spheres in such nodes by using aggregation rate metrics