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The flatness target curve (FTC) is a fundamental process model in cold rolling flatness control, which directly affects the quality control effect of the strip. The accurate and ...efficient setting of the flatness target curve is the key to ensuring continuous rolling and is a common problem faced by various production companies. This paper establishes a discrete dynamic planning (DDP) setting method for FTC with two-dimensional decision-making. To quantitatively analyze the roles of the coefficients in the FTC, the preprocessing process is established using standardized processing methods and statistical analysis methods. The flatness target curve discrete dynamic programming (FTC-DDP) is based on Bellman optimization theory with a dual structure of local and system decision-making. The decision-making functions are established based on the effect of each coefficient on FTC geometric characteristics. The concepts of “curvature factor” and “wedge factor” are innovatively proposed to obtain the decision-making value functions. The regression analysis establishes the solution equations of even number coefficients, odd number coefficients, and gain coefficients, respectively. Roll bending and tilting roll analyze the FTC’s ability to correct flatness defects. Meanwhile, utilizing a 1450 mm five-stand six-roll cold rolling mill, it is verified that FTC-DDP can quickly and accurately set the FTC, which provides an effective solution for obtaining high-precision and high-quality cold-rolled strips. Application results show that FTC-DDP can reduce the difficulty of setting up FTC by more than 70 %, reduce the setup time to milliseconds, and improve the setup accuracy by more than 50 %.
Predictive energy management has become a new focus of the automobile industry for its high potential of further reducing energy consumption. Based on previous works on predictive speed optimization ...using discrete dynamic programming (DDP), this paper introduces a novel approach of applying DDP with variable step size in stage variable discretization, which can realize a better tradeoff between precision and computational cost. In this approach, a "meshing" algorithm searches the points of interest (POI), such as speed limit change, traffic lights, and road curvatures, where changes in vehicle speed are expected. The algorithm increases the step-size resolution close to these points and reduces the resolutions in positions further away from POI, where the optimized vehicle speed is insensitive to the step size. With this approach, the position of POI can be precisely located to solve the DDP problem. In a test case with a relatively high density of POI, the computational cost is reduced by more than 53% by only sacrificing less than 1% of precision compared to a fixed step-size discretization with high resolutions. It can be expected that, with a lower density of POI, the computational cost will be reduced even further.
Optimization studies for the energy management systems of hybrid electric powertrains have critical importance as an effective measure for vehicle manufacturers to reduce greenhouse gas emissions and ...fuel consumption due to increasingly stringent emission regulations in the automotive industry, strict fuel economy legislation, continuously rising oil prices, and increasing consumer awareness of global warming and environmental pollution. In this study, firstly, the mathematical model of the powertrain and the rule-based energy management system of the vehicle with a power-split hybrid electric vehicle configuration are developed in the Matlab/Simulink environment and verified with real test data from the vehicle dynamometer for the UDDS drive cycle. In this way, a realistic virtual test platform has been developed where the simulation results of the energy management systems based on discrete dynamic programming and Pontryagin’s minimum principle optimization can be used to train the artificial neural network-based energy management algorithms for hybrid electric vehicles. The average fuel consumption in relation to the break specific fuel consumption of the internal combustion engine and the total electrical energy consumption of the battery in relation to the operating efficiency of the electrical machines, obtained by comparing the simulation results at the initial battery charging conditions of the vehicle using different driving cycles, will be analyzed and the advantages of the different energy management techniques used will be evaluated.
Our goal is to solve certain dynamic programming equations associated to a given Markov Chain X, using a regression-based Monte Carlo algorithm. More specifically, we assume that the model for X is ...not known in full detail and only a root sample X¹,..., XM of such process is available. By a stratification of the space and a suitable choice of a probability measure ν, we design a new resampling scheme that allows us to compute local regressions (on basis functions) in each stratum. The combination of the stratification and the resampling allows us to compute the solution to the dynamic programming equation (possibly in large dimenstions) using only a relatively small set of root paths. To assess the accuracy of the algorithm, we establish nonasymptotic error estimates in L²(ν). Our numerical experiments illustrate the good performance, even with M = 20 – 40 root paths.
Based on the traditional automatic transmission, Dedicated Hybrid Transmission (DHT) with P2 configuration is developed by replacing hydraulic torque converter with a wet electronically controlled ...clutch and a driving motor. The paper proposed a coordinated control strategy of the upshift process for the P2 configuration parallel hybrid vehicle equipped with DHT to ensure the shift quality. Firstly, considering the meshing transmission loss, the dynamics modelling of DHT shifting process was built by Lagrange method, and the model parameters were identified by bench test; Secondly, taking no jerk as the constraint and minimum slipping work as the optimisation goal, the forward discrete dynamic programming was used to solve the optimal control law of the transmission torque of the shifting clutch and the input shaft torque of transmission. Besides, for the hybrid operation mode, further considering the influence of the motor, engine and main clutch, two coordinated control strategies of the main clutch engagement and slipping were proposed. The simulation results show that the two coordinated control strategies can achieve small jerk and slipping work, ensure smoothness in the course of gear shift. And by the method of slipping control of the main clutch, the shifting time can be shortened.
We combine nonparametric price response modeling and dynamic pricing. In particular, we model sales response for fast-moving consumer goods sold by a physical retailer using a Bayesian semiparametric ...approach and incorporate the price of the previous period as well as further time-dependent covariates. All nonlinear effects including the one-period lagged price dynamics are modeled via P-splines, and embedding the semiparametric model into a Hierarchical Bayesian framework enables the estimation of nonlinear heterogeneous (i.e., store-specific) immediate and lagged price effects. The nonlinear heterogeneous model specification is used for price optimization and allows the derivation of optimal price paths of brands for individual stores of retailers. In an empirical study, we demonstrate that our proposed model can provide higher expected profits compared to competing benchmark models, while at the same time not seriously suffering from boundary problems for optimized prices and sales quantities. Optimal price policies for brands are determined by a discrete dynamic programming algorithm.
Motorists often have to choose routes helping them to realize faster journey times. Route choices between an origin and a destination might involve direct main roads, shorter routes through narrow ...side streets, or longer but (potentially) faster journeys using motorways or ring-roads. In the absence of effective traffic control measures, an approximate equilibrium travel time may result between the routes available, which is generally expected to be far from optimal. In this paper, we investigate discrete and continuous optimization and equilibrium-type problems, for a simplified traffic assignment problem on a simple network with parallel links and fixed demand. We explore the interplay between solutions of certain optimization and equilibrium problems which can be solved by dynamic programming. The results are supported by numerical simulations, in which the price of anarchy is calculated to highlight the demand levels where there is a change in road choice and usage.
In this paper, an optimal link selection and data rate assignment algorithm for spatial time division multiple access (STDMA) medium access control (MAC) protocols is exploited. The motivation for ...this study is jointly searching for optimal links and corresponding rates in simultaneous transmission environments in order to maximize the throughput capacity in each time slot. A mathematical formulation for exploring such links and rates combination under power and delay constrains is developed. Then, we transform this formulation into a standard knapsack problem (KP). Finally, we solve this KP using discrete dynamic programming (DDP) and propose a joint optimal link and rate search (JOLRS) algorithm which can be generically embedded with any existing STDMA MAC protocol. Through theoretical and experimental studies, we show that our JOLRS algorithm significantly outperforms baseline alternatives and similar existing algorithms in throughput, power consumption, and PER performance.
This paper explores the possibility of using recorded road slope data in order to reduce fuel consumption for off-road construction vehicles such as articulated haulers. An optimal control algorithm ...based on model predictive control and dynamic programming is formulated to find an optimal gear shift sequence. Computer simulation shows that both fuel consumption and travel time can be reduced simultaneously. In addition, the optimal gear shift sequence resembles the behavior of an experienced driver.
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