Optimal Stabilization of Linear Stochastic System with Statistically Uncertain Piecewise Constant Drift

The paper presents an optimal control problem for the partially observable stochastic differential system driven by an external Markov jump process. The available controlled observations are indirect and corrupted by some Wiener noise. The goal is to optimize a linear function of the state (output) given a general quadratic criterion. The separation principle, verified for the system at hand, allows examination of the control problem apart from the filter optimization. The solution to the latter problem is provided by the Wonham filter. The solution to the former control problem is obtained by formulating an equivalent control problem with a linear drift/nonlinear diffusion stochastic process and with complete information. This problem, in turn, is immediately solved by the application of the dynamic programming method. The applicability of the obtained theoretical results is illustrated by a numerical example, where an optimal amplification/stabilization problem is solved for an unstable externally controlled step-wise mechanical actuator.

Ore crushing in the high-pressure roller-press as a modelling object under stochastic properties of feed materials

The results of improving ore crushing in a high-pressure roller-press are presented. Application of a roller-press enables higher crushing efficiency due to both power saving and reduction of sizes of ore crush products to release mineral aggregates. Ore disintegration by compressive strain prevails among currently applied crushing methods. Disintegration occurs not only due to the compressive, but also to the shear strain. Considering smaller power consumption of the shear strain than that of the compressive strain, it is concluded that roller-press application is quite efficient. Simulation of crushing by using the Bond law frequently applied in practice is under consideration. It is essential to consider the stochasticity of the ore flow to be crushed. Presentation of this flow as a random figure by transforming it by the Bond crushing law results in a probabilistic characteristic of the crushing result. This characteristic enables finding properties of the crush product and probabilistic formulation of the problem of improving the crushing process by setting a relevant functional. To apply the results obtained to practical uses, the crushing process is simulated. The theoretical results are confirmed by setting the stochastic properties of the input ore flow by means of Rosen-Rammler’s law followed by statistical substantiation of the conducted calculations in Mathcad. After stimulation and considering stochastic properties of the feed ore flow, the solution of the optimal stabilization problem reveals that stabilization is achieved, while dispersion in relation to the stabilization goal reduces sharply almost five-fold

Stabilization Study of a Contaminated Soil with Metal(loid)s Adding Different Low-Grade MgO Degrees

Low-grade magnesium oxide (LG-MgO) was proposed as ordinary Portland cement (OPC) or lime substitute (CaO) for metal(loid)s remediation in contaminated soils. Some metal(loid)s precipitate at pH ≈ 9 in insoluble hydroxide form thus avoiding their leaching. LG-MgO avoids the re-dissolution of certain metal(loid)s at 9.0 < pH < 11.0 (pH-dependents), whose solubility depends on the pH. A highly contaminated soil with heavy metal(loid)s was stabilized using different LG-MgO by-products sources as stabilizing agents. Two of the three studied LG-MgOs were selected for the stabilization, by mixing 5, 10, and 15 wt.%. The effect of using LG-MgO not only depends on the size of the particles, but also on those impurities that are present in the LG-MgO samples. Particle size distribution, X-ray fluorescence (XRF), X-ray diffraction (XRD), thermogravimetric analysis, citric acid test, specific surface, bulk density, acid neutralization capacity, batch leaching tests (BLTs), and percolation column tests (PCTs) were techniques used to deeply characterize the different LG-MgO and the contaminated and remediated soils. The remediation’s results efficacy indicated that when the medium pH was between 9.0 and 11.0, the concentration of pH-dependent metal(loid)s decreases significantly. Although around 15 wt.% of a stabilizing agent was appropriate for the soil remediation to ensure an alkali reservoir that maintains optimal stabilization conditions for a long period, 5 wt.% of LG-MgO was enough to remedy the contaminated soil. When evaluating a polluted and decontaminated soil, both BLTs and PCTs should be complementary procedures.