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Search indexed NASA NTRS and DOE OSTI research on propulsion, heat transfer, battery materials and energy systems. Follow report and document links to the original sources.

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All sourcesNASA NTRSDOE OSTI
DOE OSTI2023

Ciel

Compiler optimizations can alter the numerical results of scientific computing applications. When numerical results differ significantly between compilers, optimization levels, and floating-point hardware, these numerical inconsistencies can impact programming productivity. Ciel is a framework that helps programmers identify locations in the source code that are affected by compiler optimizations in CPU and GPU code. Ciel uses a floating-point precision enhancement strategy, guided by a recursive bisection search algorithm with increasing search granularity, to identify the program expressions that induce numerical inconsistencies due to compiler optimizations.

Miao, Wenjun↗
DOE OSTI2023

MLIR loop optimizations for High-Level Synthesis: a case study

High-Level Synthesis (HLS) tools simplify the design of hardware accelerators by automatically generating Verilog/VHDL code starting from a general purpose software programming language. They include a wide range of optimization techniques in the process, most of them performed on a low-level intermediate representation (IR) of the code. Introducing optimizations on a higher level of abstraction could significantly contribute to the automated design process results; for example, polyhedral techniques for the manipulation of loops could have a significant impact on the generated accelerators when applied on a specialized IR. We use loop pipelining as a case study to explore the introduction of compiler-based transformations on top of an existing HLS process. We leverage the Multi-Level Intermediate Representation (MLIR) framework and an external scheduler to implement the required transformations, and couple them with existing HLS tools to evaluate the improvements that loop pipelining brings to the performance of generated accelerators. The proposed approach can be integrated with other high-level transformations on the MLIR representation, combining different techniques to obtain pre-optimized inputs for HLS that do not have to rely on a specific backend tool.

Curzel, Serena↗
DOE OSTI2019

Multi-Stage Stochastic Programming to Joint Economic Dispatch for Energy and Reserve With Uncertain Renewable Energy

To address the uncertain renewable energy in the day-ahead optimal dispatch of energy and reserve, a multi-stage stochastic programming model is established in this paper to minimize the expected total costs. The uncertainties over the multiple stages are characterized by a scenario tree and the optimal dispatch scheme is cast as a decision tree which guarantees the flexibility to decide the reasonable outputs of generation and the adequate reserves accounting for different realizations of renewable energy. Most importantly, to deal with the “Curse of Dimensionality” of stochastic programming, stochastic dual dynamic programming (SDDP) is employed, which decomposes the original problem into several sub-problems according to the stages. Specifically, the SDDP algorithm performs forward pass and backward pass repeatedly until the convergence criterion is satisfied. At each iteration, the original problem is approximated by creating a linear piecewise function. Besides, an improved convergence criterion is adopted to narrow the optimization gaps. The results on the IEEE 118-bus system and real-life provincial power grid show the effectiveness of the proposed model and method.

economic dispatch↗
DOE OSTI2025

Mixed-Integer Linear Programming Formulation with Embedded Machine Learning Surrogates for the Design of Chemical Process Families

In previous work, we introduced process family design. The main idea is to design a platform of common elements, and, allowing us to capture additional cost savings, simultaneously design a family of processes, and reducing both engineering and deployment timelines. We formulate this as an optimization problem, specifically a nonlinear generalized disjunctive program (GDP). We have proposed two approaches for reformulating and solving this problem: one based on full-discretization of the design space and one that uses Machine Learning (ML) surrogates to replace the nonlinear process models. Using ML surrogates to predict required system costs and performance indicators allows us to reformulate the nonlinearities in the GDP generate an efficient MILP formulation. In this work, we apply the ML surrogate approach to two case studies. One case study involves designing a family of carbon capture systems to cover a set of different flue gas flow rates and inlet CO 2 concentrations, where we consider the absorber and stripper as common unit module types. The second case study focuses on a water-desalination process, where we design a family of these processes for a variety of salt concentrations and flow rates. In both of these case studies, we demonstrate a scalable optimization approach that enables the design of multiple processes simultaneously, reducing the time-to-market and overall costs by maximizing the cost savings due to both economies of scale and economies of numbers.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2018

Instrumentation for Hanford Direct-Feed Low-Activity Waste Real-Time, In-Line Process Monitoring - 18339

The direct-feed low-activity waste (DFLAW) process will utilize facilities in the Hanford tank farms to stage tank waste feed, a new facility to pretreat the tank waste feed, and facilities in the Hanford Waste Treatment and Immobilization Plant (WTP) to immobilize the low-activity waste (LAW) and disposition effluents from the vitrification process. Process sampling is used extensively throughout the DFLAW process to qualify waste feeds, control the process, and demonstrate compliance with regulatory and contractual commitments. The U.S. Department of Energy's Office of River Protection (ORP) has started a program to evaluate the potential benefits of replacing some sample collection requirements with realtime, in-line monitoring (RTIM). The program will identify, develop, and evaluate technologies that can reduce the number of samples required for WTP operation. Potential benefits of RTIM include elimination of process holds for sample analysis, a reduction in worker exposure to radiation and chemical hazards, decreased secondary waste volume, reducing the cost for sample collection and analysis, an improvement in product quality, and timely indication of process anomalies. In order to incorporate RTIM, the process control strategy for the overall process, as well as each unit operation, was reviewed and revisions to the strategies proposed. The following items were identified for incorporation of RTIM: - Real-time material balance calculations linked to the process control system; - Use of RTIM instruments to validate the material balance for selected analytes; - Anion analysis for determination of selected semi-volatile species (e.g., chlorine, sulfur, and fluorine) in the recycle stream. Based on the proposed process control strategy, a preliminary list of potential analytical equipment was developed. This was followed by a preliminary survey of instrument technologies currently on the market building on surveys performed for ORP, literature reviews, vendor web sites, and subject matter experts from the Savannah River National Laboratory and other U.S. Department of Energy national laboratories. Each technology was evaluated for measurement capability, operations and maintenance requirements, space requirements, and potential for application as process control instrumentation. The instrument technologies were chosen based on the following criteria: - Ability to perform analyses needed; - Potential to be used or adapted for use as process control instruments; - Potential to be adapted to size and operational constraints of standard WTP sample cabinets; - Operational and maintenance requirements. (authors)

12 MANAGEMENT OF RADIOACTIVE AND NON-RADIOACTIVE W↗
DOE OSTI2020

Exponential Decay in the Sensitivity Analysis of Nonlinear Dynamic Programming

In this report, we study the sensitivity of discrete-time dynamic programs with nonlinear dynamics and objective to perturbations in the initial conditions and reference parameters. Under uniform controllability and boundedness assumptions for the problem data, we prove that the directional derivative of the optimal state and control at time $k$, $x^*_k$, and $u^*_k$, with respect to the reference signal at time $i$, $d_i$, will have exponential decay in terms of $|k-i|$ with a decay rate $\rho$ independent of the temporal horizon length. The key technical step is to prove that a version of the convexification approach proposed by Verschueren et al. can be applied to the KKT conditions and results in a convex quadratic program with uniformly bounded data. In turn, Riccati techniques can be further employed to obtain the sensitivity result, borne from the observation that the directional derivatives are solutions of quadratic programs with structure similar to the KKT conditions themselves. We validate our findings with numerical experiments on a small nonlinear, nonconvex, dynamic program.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2025

Planning Amidst Uncertainty: Identifying Core CCS Infrastructure Robust to Storage Uncertainty

Carbon Capture and Storage (CCS) is a critical technology for reducing anthropogenic CO2 emissions, but its large-scale deployment is complicated by uncertainties in geological storage performance. These uncertainties pose significant financial and operational risks, as underperforming storage sites can lead to costly infrastructure modifications, inefficient pipeline routing, and economic shortfalls. To address this challenge, we propose a novel optimization workflow that is based on mixed-integer linear programming and explicitly integrates probabilistic modeling of storage uncertainty into CCS infrastructure design. This workflow generates multiple infrastructure scenarios by sampling storage capacity distributions, optimally solving each scenario using a mixed-integer linear programming model, and aggregating results into a heatmap to identify core infrastructure components that have a low likelihood of underperforming. A risk index parameter is introduced to balance trade-offs between cost, CO2 processing capacity, and risk of underperformance, allowing stakeholders to quantify and mitigate uncertainty in CCS planning. Applying this workflow to a CCS dataset from the US Department of Energy’s Carbon Utilization and Storage Partnership project reveals key insights into infrastructure resilience. Reducing the risk index from 15% to 0% is observed to lead to an 83.7% reduction in CO2 processing capacity and a 77.1% decrease in project profit, quantifying the trade-off between risk tolerance and project performance. Furthermore, our results highlight critical breakpoints, where small adjustments in the risk index produce disproportionate shifts in infrastructure performance, providing actionable guidance for decision-makers. Unlike prior approaches that aimed to cheaply repair underperforming infrastructure, our workflow constructs robust CCS networks from the ground up, ensuring cost-effective infrastructure under storage uncertainty. These findings demonstrate the practical relevance of incorporating uncertainty-aware optimization into CCS planning, equipping decision-makers with a tool to make informed project planning decisions.

Olson, Daniel↗
DOE OSTI2017

Optimal design and dispatch of a system of diesel generators, photovoltaics and batteries for remote locations

Renewable energy technologies, specifically, solar photovoltaic cells, combined with battery storage and diesel generators, form a hybrid system capable of independently powering remote locations, i.e., those isolated from larger grids. If sized correctly, hybrid systems reduce fuel consumption compared to diesel generator-only alternatives. We present an optimization model for establishing a hybrid power design and dispatch strategy for remote locations, such as a military forward operating base, that models the acquisition of different power technologies as integer variables and their operation using nonlinear expressions. Our cost-minimizing, nonconvex, mixed-integer, nonlinear program contains a detailed battery model. Due to its complexities, we present linearizations, which include exact and convex under-estimation techniques, and a heuristic, which determines an initial feasible solution to serve as a “warm start” for the solver. We determine, in a few hours at most, solutions within 5% of optimality for a candidate set of technologies; these solutions closely resemble those from the nonlinear model. Lastly, our instances contain real data spanning a yearly horizon at hour fidelity and demonstrate that a hybrid system could reduce fuel consumption by as much as 50% compared to a generator-only solution.

14 SOLAR ENERGY↗
DOE OSTI2015

A program-level management system for the life cycle environmental and economic assessment of complex building projects

Climate change has become one of the most significant environmental issues, of which about 40% come from the building sector. In particular, complex building projects with various functions have increased, which should be managed from a program-level perspective. Therefore, this study aimed to develop a program-level management system for the life-cycle environmental and economic assessment of complex building projects. The developed system consists of three parts: (i) input part: database server and input data; (ii) analysis part: life cycle assessment and life cycle cost; and (iii) result part: microscopic analysis and macroscopic analysis. To analyze the applicability of the developed system, this study selected ‘U’ University, a complex building project consisting of research facility and residential facility. Through value engineering with experts, a total of 137 design alternatives were established. Based on these alternatives, the macroscopic analysis results were as follows: (i) at the program-level, the life-cycle environmental and economic cost in ‘U’ University were reduced by 6.22% and 2.11%, respectively; (ii) at the project-level, the life-cycle environmental and economic cost in research facility were reduced 6.01% and 1.87%, respectively; and those in residential facility, 12.01% and 3.83%, respective; and (iii) for the mechanical work at the work-type-level, the initial cost was increased 2.9%; but the operation and maintenance phase was reduced by 20.0%. As a result, the developed system can allow the facility managers to establish the operation and maintenance strategies for the environmental and economic aspects from a program-level perspective. - Highlights: • A program-level management system for complex building projects was developed. • Life-cycle environmental and economic assessment can be conducted using the system. • The design alternatives can be analyzed from the microscopic perspective. • The system can be used to establish the optimal O&M strategy at the program-level. • It can be applied to any other country or sector in the global environment.

54 ENVIRONMENTAL SCIENCES↗
DOE OSTI2021

Parametric study and speciation analysis of rare earth precipitation using oxalic acid in a chloride solution system

Oxalic acid precipitation is a common step in the purification of rare earth elements (REE) from a concentrated pregnant leach solution (PLS). However, the presence of contaminants such as Al, Fe, and Ca in given amounts decreases the REE precipitation efficiency and product purity while also increasing the amount of oxalic acid needed to maximize recovery. As such, a statistically designed test program was performed to identify the optimal conditions necessary for a relatively low REE content PLS containing elevated concentrations of contaminant ions. The performance objective was maximization of REE precipitation efficiency while minimizing the oxalic acid dosage. A central composite design was utilized to quantify performance impacts and identify the ultimate set of parameter values for oxalic acid dosage, Fe(III) contamination concentration, solution pH, and reaction temperature. The resultant model suggested that oxalic acid dosage and reaction pH are the most significant factors for the REE precipitation efficiency, followed by the interaction of oxalic dosage and Fe concentration. Test results indicate that increasing the oxalic acid concentration from 0 g/L to 80 g/L improved the REE precipitation efficiency from approximately 4.2% to 95.0%. Furthermore, raising the solution pH from 0.5 to 2.5 considerably enhanced the precipitation efficiency from 0.0% to 98.9%. A solution temperature elevation decreased REE recovery, which indicated an exothermic reaction between REEs and oxalate anions. Finally, a high level of Fe contamination adversely impacted REE precipitation efficiency. Here, to further the understanding of the REE-oxalate system, a fundamental solution chemistry study was performed using the equilibrium constants of the reactions. The study resulted in the development of oxalate speciation diagrams and provided an analysis of the REE precipitation characteristics at various oxalate anion concentrations and Fe(III) contamination levels using MINTEQ software. The dominant Fe(III) species in the solution system were found to be Fe-(C 2 O 4 ) 3 3- , Fe-(C 2 O 4 ) 2- , and Fe-(C 2 O 4 ) + , which consume the majority of the oxalate anions. The simulated model was found to be in agreement with the experimental findings and helped to explain the adverse impact of increased iron concentrations on REE precipitation efficiency.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2020

Refueling infrastructure planning in intercity networks considering route choice and travel time delay for mixed fleet of electric and conventional vehicles

The range anxiety has been a major factor that affects the market acceptance of electric vehicles. Even with the recent development of battery technologies, a lack of charging stations and range anxiety are still significant concerns, specifically for intercity trips. This calls for more investments in building charging stations and advancing battery technologies to increase the market share of electric vehicles and improve sustainability. This study suggests a configuration for plug-in electric vehicle charging infrastructure to support long-distance intercity trips of electric vehicles at the network level. A model is proposed to minimize the total system cost including infrastructure investment (building charging stations/spots) and travel time delays (charging time, waiting time in the queue, and detour time to access charging stations). This study fills existing gaps in the literature by capturing realistic patterns of travel demand and considering flow-dependent charging delays at charging stations. Furthermore, the proposed model, which is formulated as a mixed-integer program with nonlinear constraints, solves the optimization problem at the network level. At the network level, impacts of charging station locations on the traffic assignment problem with a mixed fleet of electric and conventional vehicles need to be considered. To this end, a traffic assignment module is integrated with a simulated annealing algorithm. The numerical experiments show a satisfactory application of the model for a full-scale case study (intercity network in Michigan). The solution quality and efficiency of the proposed solution algorithm are evaluated against those of an enumeration approach for a small case study. The results suggest that even for the current market share and charging stations’ setting, a significant investment is needed to support intercity trips without range anxiety issues and with acceptable delays. Additionally, through sensitivity analyses, the required infrastructure and battery investments to support intercity trips with acceptable delays are established for hypothetical increased market shares and battery size in the future.

42 ENGINEERING↗
DOE OSTI2025

Machine-Learned Force Field for Molecular Dynamics Simulations of Nonequilibrium Ammonia Synthesis on Iron Catalysts

Ammonia (NH 3 ) is one of the most important industrial chemicals. The conventional NH 3 synthesis method-the Haber–Bosch process-converts atmospheric nitrogen (N 2 ) into NH 3 using H 2 with an iron (Fe) catalyst. However, this process requires high pressures (100–200 atm) and temperatures (700–800 K) near thermal equilibrium. Recently, Fe-based nanocatalysts have been reported to produce promising NH 3 yields under atmospheric pressures and temperature-modulated nonequilibrium conditions. Understanding the mechanism of nonequilibrium catalysis with programmed temperature variation could help to optimize this fully electrified and less energy-intensive process. Although reactive molecular dynamics (RMD) simulations can be a useful tool to model nonequilibrium catalytic processes, they require the development of accurate force fields (i.e., interatomic potentials). Here, we present a machine-learned (ML) force field within the Deep Potential MD (DPMD) framework, trained using periodic density functional theory (DFT) calculations, to model NH 3 synthesis on Fe catalysts with various surface adsorbates such as *N, *H, *N 2 , *H 2 , *NH, *NH 2 , and *NH 3 . Here, we generated the DFT data from static models of elementary reactions on the most stable (110) surface of body-centered cubic Fe, which then were augmented by data from constant number of particles–volume–temperature (NVT) DFT-MD trajectories at various temperatures. Finally, we utilized the fully optimized ML force field to investigate reaction dynamics at an Fe(110) surface at linearly increasing temperatures using NVT-DPMD simulations. Our simulations indicate that pulsed temperature ramping could prove favorable for NH3 synthesis. For example, we conducted ramping under multiple sets of conditions: (i) from 900 to 1200 K over periods of 0.1–0.3 ns for Fe surfaces precovered with N or NH along with H; and (ii) from 300 to 600 K over 0.1–0.3 ns for Fe surfaces precovered with NH 3 . While our simulations so far are limited to short time scales (very rapid heating), these observations shed light on the mechanism of the high NH 3 synthesis rate achieved in a novel temperature-modulated nonequilibrium catalytic reactor using pulsed heating and cooling.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2024

Discovery of a Peptoid-Based Nanoparticle Platform for Therapeutic mRNA Delivery via Diverse Library Clustering and Structural Parametrization

Nanoparticle-mediated mRNA delivery has emerged as a promising therapeutic modality, but its growth is still limited by the discovery and optimization of effective and well-tolerated delivery strategies. Lipid nanoparticles containing charged or ionizable lipids are an emerging standard for in vivo mRNA delivery, so creating facile, tunable strategies to synthesize these key lipid-like molecules is essential to advance the field. Here, we generate a library of N-substituted glycine oligomers, peptoids, and undertake a multistage down-selection process to identify lead candidate peptoids as the ionizable component in our Nutshell nanoparticle platform. First, we identify a promising peptoid structural motif by clustering a library of >200 molecules based on predicted physical properties and evaluate members of each cluster for reporter gene expression in vivo. Then, the lead peptoid motif is optimized using design of experiments methodology to explore variations on the charged and lipophilic portions of the peptoid, facilitating the discovery of trends between structural elements and nanoparticle properties. We further demonstrate that peptoid-based Nutshells leads to expression of therapeutically relevant levels of an anti-respiratory syncytial virus antibody in mice with minimal tolerability concerns or induced immune responses compared to benchmark ionizable lipid, DLin-MC3-DMA. Through this work, we present peptoid-based nanoparticles as a tunable delivery platform that can be optimized toward a range of therapeutic programs.

59 BASIC BIOLOGICAL SCIENCES↗
DOE OSTI2019

Utilising demand response for distribution service restoration to achieve grid resiliency against natural disasters

The increased frequency of power outages due to natural disasters in recent years has highlighted the urgency of enhancing distribution grid resilience. The effective distribution service restoration (DSR) is an important measure for a resilient distribution grid. In this work, the authors demonstrate that DSR can be significantly improved by leveraging the flexibility provided by the inclusion of demand response (DR). The authors propose a framework for this by considering integrated control of household-level flexible appliances to vary the load demand at the distribution-grid level to improve DSR. The overall framework of the proposed system is modelled as a three-step method considering three optimization problems to (i) calculate feasible controllable aggregated load range for each bus, (ii) determine candidate buses to perform DR and their target load demand, and (iii) maintain the load level in each house through home energy management during the DSR, considering uncertainties in load and solar generation sequentially. The optimization problems are formulated as linear programming, mixed-integer linear programming, and multistage stochastic programming (solved using the stochastic dual dynamic programming) models. Finally, case studies performed in the IEEE 123-node test feeder show improvements in resilience in terms of energy restored compared to the restoration process without DR.

24 POWER TRANSMISSION AND DISTRIBUTION↗
DOE OSTI2022

Qubit Assignment Using Time Reversal

As quantum computers with large numbers of qubits become increasingly available, experiments executed on a given device may not utilize all available qubits. In this case, the outcome of executing a quantum program will depend on the ability to efficiently select a subset of high-performing physical qubits. For any given quantum program and device there are many ways to assign physical qubits for execution of the program, and assignments will differ in performance due to the variability in quality across qubits and entangling operations on a single device. Evaluating the performance of each assignment using fidelity estimation introduces significant experimental overhead and will be infeasible for many applications, while relying on standard device benchmarks provides incomplete information about the performance of any specific program. Furthermore, the number of possible assignments grows combinatorially in the number of qubits on the device and in the program, motivating the use of heuristic optimization techniques. We demonstrate a practical solution to the problem of qubit assignment by using simulated annealing with a cost function based on the Loschmidt echo, a diagnostic that measures the reversibility of a quantum process. We provide theoretical justification for this choice of cost function by demonstrating that the optimal qubit assignment coincides with the optimal qubit assignment based on state fidelity in the weak error limit, and we provide experimental justification using diagnostics performed on Google’s superconducting qubit devices. We then establish the performance of simulated annealing for qubit assignment using classical simulations of noisy devices as well as optimization experiments performed on a quantum processor. Our results demonstrate that the use of Loschmidt echoes and simulated annealing provides a scalable and flexible approach to optimizing qubit assignment on near-term hardware.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2025

Adaptive PID Gain Scheduling Control for Hydropower Turbine Using Neural CDE and Stochastic Distribution Shaping

This paper introduces a gain-scheduling PID controller design strategy for hydroturbine frequency control mode. This scheme first uses real data to learn the nonlinear dynamics of the hydroturbine using neural controlled differential equations and then perturbs the obtained nonlinear system at different equilibrium points, based on which a static output feedback adaptive dynamic programming algorithm is then used to optimize the PID gains for each equilibrium point. Moreover, a continuous-time version of stochastic distribution control is proposed to further fine-tune the optimized PID gains. Finally, the controller is obtained by implementing linear interpolation between the optimized PID control gains. The simulation results show that the proposed gain-scheduling PID controller can control a larger range of operation points compared with the given fixed PID controller and the baseline method. Compared with the given fixed PID controller, the proposed gain-scheduling PID controller can regulate hydroturbine frequency against disturbances induced by power-load variation with over 50% less overshoot for some operation points.

13 HYDRO ENERGY↗
DOE OSTI2020

Cooperative Load Scheduling for Multiple Aggregators Using Hierarchical ADMM

Demand response (DR) serves an important role in improving the efficiency and stability of power systems. In recent years, with advances in communication and smart device technologies, many aggregators have emerged to facilitate end customer participation in DR programs. These aggregators, equipped with customized optimal control algorithms, are capable of providing various grid services. Among them is load scheduling during DR events, namely following a load signal provided by the utility company while minimizing overall customer discomfort. However, as the number of aggregators keeps increasing, it becomes challenging for utility companies to conduct load scheduling for multiple aggregators and generate reference signals for each of them. This paper proposes an optimization framework using hierarchical alternating direction method of multipliers (H-ADMM) to optimally generate load following signals for multiple aggregators. Under this framework, utility and multiple aggregators work in a cooperative manner, aiming at minimizing an overall system cost from different levels of the power system hierarchy, while protecting user privacy. A case study has been conducted in a system with multiple aggregators, based on control of HVAC loads. Experimental results validate the effectiveness of the proposed algorithm.

ADMM↗
DOE OSTI2022

Inverse Calculation of Burden Distribution Matrix Using B-spline Model Based PDF control in Blast Furnace Burden Charging Process

The inverse calculation of burden distribution matrix (BDM) is one of the most important challenges in the blast furnace operation in iron-making processes. In general, blast furnace consumes 65% of the total energy for the whole steel-making. Focusing on this practical challenge, this article proposes a new burden distribution spatial model in calculating burden charging process, and develops a B-spline approximation-based probability density function (PDF) control algorithm to assign the expected thickness distribution of burden layer and, thus, develops a new method for the required inverse calculation of BDM. First, a novel method for the thickness distribution of burden layer is given using B-spline model to produce an expected distribution shape subjected to a desired tracking within a specific spatial constraint. Then, according to the coexistence of continuous and bounded discrete variables in BDM, a novel hybrid optimization control method by combining integer programming and PDF tracking is further established for the effective inverse calculation of BDM. Finally, the proposed PDF-based iterative inverse calculation of BDM using B-spline models are tested using various data from industrial examples. Furthermore, the simulation results show that the proposed method is well suited to solve the BDM inverse calculation problem in practice.

42 ENGINEERING↗