The optimal operation of railway systems minimizing total energy consumption is discussed in this paper. Firstly, some measures of finding energy-saving train speed profiles are outlined. After the characteristics that should be considered in optimizing train operation are clarified, complete optimization based on optimal control theory is reviewed. Their basic formulations are summarized taking into account most of the difficult characteristics peculiar to railway systems. Three methods of solving the formulation, dynamic programming (DP), gradient method, and sequential quadratic programming (SQP), are introduced. The last two methods can also control the state of charge (SOC) of the energy storage devices. By showing some numerical results of simulations, the significance of solving not only optimal speed profiles but also optimal SOC profiles of energy storage are emphasized, because the numerical results are beyond the conventional qualitative studies. Future scope for applying the methods to real-time optimal control is also mentioned. 

An algorithm optimizing train running profile with Bellman's Dynamic Programming (DP) is investigated in this paper. Optimal running trajectory of a train which minimizes amount of total energy consumption has been produced under fixed origin and destination, stipulated running time and various track profile. Many previous works on this area adopt the numerical techniques of calculus of variations, Pontryagin's maximum principle, and so on. But these methods often meet some difficulties accounting for complicated actual train running preconditions, e.g. complicated functions which describe electrical motive/brake torque, local constraints of the state variable as speed limitations, nonlinear running resistance and variable grade profiles. Basic numerical DP algorithm can cope with such comlicated conditions and give the globally optimal solution. But this method consumes too large computation time for practical uses. We have made the improvements for shorter calculation time of whole optimization process and reducing the numerical error. The confined state space and irregular lattice play most important role for them. Dynamic meshing and effective utilization of system memory also realize shorter computation time. The effectiveness of the proposed method is demonstrated using various complicated running conditions.

In this paper, we formulate a train run-curve optimization problem as an optimal control problem with equality constraints and inequality constraints in a DC feeding system. The objective function to be minimized is given as the total energy consumption at the substation. The train position and speed are the state variables and the kinetic equation of the train is the state equation of the objective system. The boundary conditions on state variables can promise the train transfers from departure station to arrival station in the given transfer time. The maximum amount of the motive and braking torque is described as inequality constraint on control input in mathematical formulation. The speed limits of the train give inequality constraint on the state variable. The circuit equation of DC feeding system which determines the catenary voltage is described as equality constraint in the optimal control problem.We also design a numerical algorithm to solve this optimization problem with several constraints based on the conventional conjugate gradient method, which could be useful for large scale problems of future works for its light computer load. Several numerical examples are demonstrated to verify the reliability and validity of the proposed method. For example, Fig. 1 The optimal run-curve shows the impact of feeding loss in acceleration and that of squeezing control of regenerative current. Acceleration with small motive force at middle and high speed area is caused by feeding loss. Deceleration with small electrical brake force at middle and high speed area is caused by sqeezing control. These characteristics are not considered in previous works of train energy-saving optimal operation. Only our proposed method makes it possible and can give some numerical examples. The other numerical examples-in complicated track profile case, run-curve and substation voltage optimization problem, run-curve optimization problem about two train, and so on-also show some aspects of proposed mathematical formulation, numerical method and its application useful for detailed consideration for energy-saving train operation.

The optimal train operation which minimizes sum of supplied energy from substations is presented in this paper. In recent years, the energy storage devices have enough energy and power density to use in trains as on-board energy storage. The electric double layer capacitor (EDLC) is assumed as an energy storage device in our study, because of its high power density. The on-board storage can assist the acceleration/deceleration of the train and may decrease energy consumption. Many works on the application of the energy storage devices to trains were reported, however, they did not deal enough with the optimality of the control of the devices. On the other hand, our previous works were to optimize acceleration/deceleration commands of the train for minimizing energy consumption without the energy storage device. Therefore, we intend to optimize acceleration/deceleration commands together with current commands through energy storage devices as our next research target. The proposed method can determine the optimal acceleration/deceleration and current commands at every sampling point. For this purpose, the optimal control problem of the train operation is formulated mathematically. It is generally difficult to solve the problem because the problem is composed of a large-scale non-linear system. However, the Sequential Quadratic Programming (SQP) can be applied to solve the problem. Two results with and without on-board energy storage device are compared. These optimized results indicate that the total energy consumption is reduced by at least 0.35% by using the EDLC. The relation between internal resistance and energy consumption is also revealed.

Background Patients with pulmonary arterial hypertension (PAH) carrying bone morphogenetic protein receptor type 2 (Bmpr2) mutations present earlier with severe hemodynamic compromise and have poorer survival outcomes than those without mutation. The mechanism underlying the worsening clinical phenotype of PAH with Bmpr2 mutations has been largely unaddressed in rat models of pulmonary hypertension (PH) because of the difficulty in reproducing progressive PH in mice and genetic modification in rats. We tested whether a clinically-relevant Bmpr2 mutation affects the progressive features of monocrotaline (MCT) induced-PH in rats. Methods A monoallelic single nucleotide insertion in exon 1 of Bmpr2 (+/44insG) was generated in rats using clustered regularly interspaced short palindromic repeats (CRISPR)/CRISPR-associated protein 9, then PH, pulmonary vascular disease (PVD) and survival after MCT injection with or without a phosphodiesterase type 5 inhibitor, tadalafil, administration were assessed. Results The +/44insG rats had reduced BMPR2 signalling in the lungs compared with wild-type. PH and PVD assessed at 3-weeks after MCT injection were similar in wild-type and +/44insG rats. However, survival at 4-weeks after MCT injection was significantly reduced in +/44insG rats. Among the rats surviving at 4-weeks after MCT administration, +/44insG rats had increased weight ratio of right ventricle to left ventricle plus septum (RV/[LV + S]) and % medial wall thickness (MWT) in pulmonary arteries (PAs). Immunohistochemical analysis showed increased vessels with Ki67-positive cells in the lungs, decreased mature and increased immature smooth muscle cell phenotype markers in the PAs in +/44insG rats compared with wild-type at 3-weeks after MCT injection. Contraction of PA in response to prostaglandin-F2α and endothelin-1 were significantly reduced in the +/44insG rats. The +/44insG rats that had received tadalafil had a worse survival with a significant increase in RV/(LV + S), %MWT in distal PAs and RV myocardial fibrosis compared with wild-type. Conclusions The present study demonstrates that the Bmpr2 mutation promotes dedifferentiation of PA smooth muscle cells, late PVD and RV myocardial fibrosis and adversely impacts both the natural and post-treatment courses of MCT-PH in rats with significant effects only in the late stages and warrants preclinical studies using this new genetic model to optimize treatment outcomes of heritable PAH.

An algorithm optimizing total energy consumption of multiple train operation considering a DC feeding circuit is investigated in this paper. Our mathematical formulation includes several characteristics of trains which depend on feeding voltage. It makes it possible to give detailed consideration to an energy-saving operation. It is especially important for us to be able to discuss the influence of squeezing control of regenerating current and feeding loss. We constructed the optimizing algorithm based on the gradient method applicable to large-scale problems for future works. Several numerical examples are demonstrated to verify the reliability and validity of the proposed method. Every optimisation result is obtained within a minute.

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The optimal train operation which minimizes sum of supplied energy from substations is presented in this paper. In recent years, the energy storage devices have enough energy and power density to use in trains as on-board energy storage. The electric double layer capacitor (EDLC) is assumed as an energy storage device in our study, because of its high power density. The on-board storage can assist the acceleration/deceleration of the train and may decrease energy consumption. Many works on the application of the energy storage devices to trains were reported, however, they did not deal enough with the optimality of the control of the devices. On the other hand, our previous works were to optimize acceleration/deceleration commands of the train for minimizing energy consumption without the energy storage device. Therefore, we intend to optimize acceleration/deceleration commands together with current commands through energy storage devices as our next research target. The proposed method can determine the optimal acceleration/deceleration and current commands at every sampling point. For this purpose, the optimal control problem of the train operation is formulated mathematically. It is generally difficult to solve the problem because the problem is composed of a large-scale non-linear system. However, the Sequential Quadratic Programming (SQP) can be applied to solve the problem. Two results with and without on-board energy storage device are compared. These optimized results indicate that the total energy consumption is reduced by at least 0.35% by using the EDLC. The relation between internal resistance and energy consumption is also revealed.