Relaxing high-dimensional constraints in the direct solution space method for early phase development

Early phase distributed system design can be accomplished using solution spaces that provide an interval of permissible values for each functional parameter. The feasibility property guarantees fulfillment of all design requirements for all possible realizations. Flexibility denotes the size measure of the intervals, with higher flexibility benefiting the design process. Two methods are available for solution space identification. The direct method solves a computationally cheap optimization problem. The indirect method employs a sampling approach that requires a relaxation of the feasibility property through re-formulation as a chance constraint. Even for high probabilities of fulfillment, \(P>0.99\), this results in substantial increases in flexibility, which offsets the risk of infeasibility. This work implements the chance constraint formulation into the direct method for linear constraints by showing that its problem statement can be understood as a linear robust optimization problem. Approximations of chance constraints from the literature are transferred into the context of solution spaces. From this, we derive a theoretical value for the safety parameter \(\varOmega\). A further modification is presented for use cases, where some intervals are already predetermined. A problem from vehicle safety is used to compare the modified direct and indirect methods and discuss suitable choices of \(\varOmega\). We find that the modified direct method is able to identify solution spaces with similar flexibility, while maintaining its cost advantage.     

An approach for robust PDE-constrained optimization with application to shape optimization of electrical engines and of dynamic elastic structures under uncertainty

We present a robust optimization framework that is applicable to general nonlinear programs (NLP) with uncertain parameters. We focus on design problems with partial differential equations (PDE), which involve high computational cost. Our framework addresses the uncertainty with a deterministic worst-case approach. Since the resulting min–max problem is computationally intractable, we propose an approximate robust formulation that employs quadratic models of the involved functions that can be handled efficiently with standard NLP solvers. We outline numerical methods to build the quadratic models, compute their derivatives, and deal with high-dimensional uncertainties. We apply the presented approach to the parametrized shape optimization of systems that are governed by different kinds of PDE and present numerical results.     

Investigating the flow of rod-like particles in a horizontal rotating drum using DEM simulation

Understanding the flow and mixing of rod-like particles is fundamental because of the widespread use of rods in the process industry. In this paper, discrete element method is used to investigate the flow and mixing of rod-like particles in a horizontal rotating drum, with rod-like particles being modeled by super-ellipsoids. The influence of the aspect ratio of the rod and the rotation speed of the drum on the flow of rod-like particles is studied. The investigation of spherical particles is also included in this paper to reveal the differences between rod-like and spherical particles. The simulation results show that the flow of rods is more intermittent than that of spheres and that there is more intermittent flow for rod-like particles with larger aspect ratios. Both the aspect ratio of the rod and the rotation speed of the drum considerably influence particle mixing. The mixing rate, as quantified by the slope of the variation in the mixing index with respect to drum revolution, increases as rotation speed and aspect ratio decrease. The study of particle orientation indicates that rod-like particles have a preferred orientation during rotation of the drum: the major axis of the rod inclines to be parallel to the end plate of the drum.     

Mobility in granular materials upon cyclic loading

We investigate the ability to move of large objects—referred to as intruders—embedded in a granular material and subjected to cyclic loadings. A discrete element method is used to simulate the dynamics response of intruders subjected to a vertical uplift cyclic force, exploring a wide range of loading magnitudes and frequencies. The analysis of the intruder and grains displacements over many cycles reveals three mobility regimes. In the first two regimes, called confined and failure the intruder either do not significantly move or consistently moves upward after each cycles. We introduce a physically based model considering an inertial drag force to rationalise the existence of these regimes depending on the loading frequency and magnitude. We further evidence a third intermediate regime of creep, where intruder trajectories exhibit long periods of confinement punctuated by shorter periods of sustained uplift motion. Finally, we observe unexpected failures at low loading magnitudes and specific frequencies, which we attribute to a process of elasto-inertial resonance. These results highlight the important differences in the mobility of intruders upon constant and cyclic loadings.     

Resolving force indeterminacy in contact dynamics using compatibility conditions

Contact dynamics (CD) is a powerful method to solve the dynamics of large systems of colliding rigid bodies. CD can be computationally more efficient than classical penalty-based discrete element methods (DEM) for simulating contact between stiff materials such as rock, glass, or engineering metals. However, by idealizing bodies as perfectly rigid, contact forces computed by CD can be non-unique due to indeterminacy in the contact network, which is a common occurence in dense granular flows. We propose a frictionless CD method that is designed to identify only the unique set of contact forces that would be predicted by a soft particle method, such as DEM, in the limit of large stiffness. The method involves applying an elastic compatibility condition to the contact forces, which maintains no-penetration constraints but filters out force distributions that could not have arisen from stiff elastic contacts. The method can be used as a post-processing step that could be integrated into existing CD codes with minimal effort. We demonstrate its efficacy in a variety of indeterminate problems, including some involving multiple materials, non-spherical shapes, and nonlinear contact constitutive laws.     

Technologies and logistics for phosphorus recovery from livestock waste

Phosphorus (P) runoff from livestock waste can trigger algal blooms that adversely affect aquatic life and human health. One strategy to mitigate this problem is to install nutrient recovery technologies that concentrate and mobilize nutrients from nutrient-rich regions to nutrient-deficient ones. We present supply chain design formulations to identify optimal types and locations for P recovery technologies. The formulations capture trade-offs in transportation costs, technology efficiency, investment/operational costs, revenue collected from different recovered products (struvite and nutrient cakes), and environmental impact. Our computational framework is used to analyze the impact of different scenarios for market prices of recovered products, recovery yields, and remediation costs. We find that transportation of waste alone (without any processing) can achieve significant reductions in environmental impact at low cost, but cannot achieve economic sustainability in the long run due to the lack of direct revenue streams. Mechanical separation technologies that recover P in the form of nutrient cakes are low-cost solutions that can achieve high environmental benefits and reduced transportation costs, but revenues are also limited due to low values of the cakes. Struvite crystallization in fluidized beds is found to be a highly attractive option under current struvite prices, but economic sustainability is strongly dependent on yield recoveries (which are currently highly uncertain).     

Analysis of bioenergy production at different levels of integration in energy-driven biorefineries

In this paper, a techno-economic and environmental assessment is performed to compare the stand-alone process and biorefinery ways to produce biodiesel, ethanol and butanol as potential cases for bioenergy production using fresh fruit bunches as raw material. Different levels of integration are considered (e.g., mass and energy integration, non-conventional technologies) along with the analysis of the process scale to determine the economic profitability and environmental impacts of the proposed cases. The results demonstrated that the biodiesel production based on the biorefinery concept has a positive effect on the profitability of the stand-alone process at different scales. The economic results were compared with data reported in the literature. Furthermore, the life cycle analysis of the proposed cases suggested that the deployment of the biorefinery concept at different levels of integration in the oil palm supply chain reduced the environmental impact of the biodiesel production, which was selected as the hotspot of the evaluated cases.     

K–La–MgO as heterogeneous catalyst for synthesis of 3-(2-hydroxyethyl)-1,3-oxazolidin-2-one from diethanol amine and carbon dioxide

Cost-effective valorization of carbon dioxide into bulk and specialty chemicals using catalysis will be attractive in the foreseeable future. 1,3-Oxazolidin-2-one derivatives are one of the important classes of heterocyclic compounds which have wide applications in pharmaceutical industries due to their biological activities such as antibacterial, antimicrobial, antiseptic. Various synthetic routes are employed to prepare these compounds which include phosgenation, oxidative carbonylation, etc., which make use of polluting chemicals and homogeneous catalysts. The heterogeneous catalytic processes to synthesize these derivatives are quite limited. Thus, developing a green route which is environmental friendly is highly desirable. The current work deals with development of a heterogeneous reusable catalyst and its application to synthesize 1,3-oxazolidin-2-one derivatives using carbon dioxide as a C1 source. The fact that no use of promoter or organic co-catalyst is made in the current process makes the synthesis route more favorable. Pure La–MgO and K–La–MgO with different K loading (1, 3, 5, and 7 wt%) synthesized by combustion route were screened for carbonylation of diethanol amine. 5% K–La–MgO was found to be the best catalyst. The catalyst was well characterized in virgin form and after use by various analytical techniques like TEM, SEM, XRD, CO₂ and NH₃-TPD, BET surface area analysis. With 5% K–La/MgO, 72% conversion of diethanol amine was achieved with 100% selectivity of the desired product at optimum conditions, i.e., 150 °C, 5 wt% K–La/MgO catalyst loading of 0.02 g/cm³ and 2.0 MPa CO₂ pressure. Reaction mechanism was proposed and kinetic model developed. The apparent activation energy was calculated as 18.76 kcal/mol. The catalyst was robust and recyclable. The process is clean and green.     

Delignification kinetics of empty fruit bunch (EFB): a sustainable and green pretreatment approach using malic acid-based solvents

Recently, the development of efficient and environmentally benign solvents has received great attention to replace current harsh organic solvents. In this context, low-transition-temperature mixtures (LTTMs) have emerged as favorable green solvents for biomass delignification. Palm oil biomass, empty fruit bunch (EFB) was pretreated with commercial l-malic acid and microwave hydrothermally extracted cactus malic acid-derived LTTMs at 60, 80, and 100 °C. The LTTMs applied in this study were derived from malic acid–choline chloride–water and malic acid–monosodium glutamate–water with a molar ratio of 2:4:2 and 3:1:5, respectively. Three first-order reactions were used to express the delignification kinetic model of EFB. The first term was based on the initial stage and assigned as infinite due to the fast rate of delignification which could not be detected. The second and third terms were proportional to bulk and residual delignification stages. A good agreement was obtained between the kinetic model and the experimental data obtained in this study with R²?≥?0.91. The activation energies for the delignification reactions using l-malic acid and cactus malic acid-based LTTMs in the bulk and residual stages were approximated as 36–56 and 19–26 kJ/mol and 34–90 and 47–87 kJ/mol, respectively.