Methods of optimisation in machine design

The paper is devoted to the problem of optimal machine design selection by developing and solving the problem of multi-criteria optimisation, using the method suggesting a unified criterion with the use of weighting factors based on expert estimates. Based on the example of the design of a multi-purpose machine for service electric transport, a mathematical model of parametric optimisation of the design of electric and combined propulsion plants is developed. The most efficient system components are selected to meet the customer's requirements.

An Efficient Bi-Objective Optimization Workflow Using the Distributed Quasi-Newton Method and Its Application to Well-Location Optimization

Summary Although it is possible to apply traditional optimization algorithms to determine the Pareto front of a multiobjective optimization problem, the computational cost is extremely high when the objective function evaluation requires solving a complex reservoir simulation problem and optimization cannot benefit from adjoint-based gradients. This paper proposes a novel workflow to solve bi-objective optimization problems using the distributed quasi-Newton (DQN) method, which is a well-parallelized and derivative-free optimization (DFO) method. Numerical tests confirm that the DQN method performs efficiently and robustly. The efficiency of the DQN optimizer stems from a distributed computing mechanism that effectively shares the available information discovered in prior iterations. Rather than performing multiple quasi-Newton optimization tasks in isolation, simulation results are shared among distinct DQN optimization tasks or threads. In this paper, the DQN method is applied to the optimization of a weighted average of two objectives, using different weighting factors for different optimization threads. In each iteration, the DQN optimizer generates an ensemble of search points (or simulation cases) in parallel, and a set of nondominated points is updated accordingly. Different DQN optimization threads, which use the same set of simulation results but different weighting factors in their objective functions, converge to different optima of the weighted average objective function. The nondominated points found in the last iteration form a set of Pareto-optimal solutions. Robustness as well as efficiency of the DQN optimizer originates from reliance on a large, shared set of intermediate search points. On the one hand, this set of searching points is (much) smaller than the combined sets needed if all optimizations with different weighting factors would be executed separately; on the other hand, the size of this set produces a high fault tolerance, which means even if some simulations fail at a given iteration, the DQN method’s distributed-parallelinformation-sharing protocol is designed and implemented such that the optimization process can still proceed to the next iteration. The proposed DQN optimization method is first validated on synthetic examples with analytical objective functions. Then, it is tested on well-location optimization (WLO) problems by maximizing the oil production and minimizing the water production. Furthermore, the proposed method is benchmarked against a bi-objective implementation of the mesh adaptive direct search (MADS) method, and the numerical results reinforce the auspicious computational attributes of DQN observed for the test problems. To the best of our knowledge, this is the first time that a well-parallelized and derivative-free DQN optimization method has been developed and tested on bi-objective optimization problems. The methodology proposed can help improve efficiency and robustness in solving complicated bi-objective optimization problems by taking advantage of model-based search algorithms with an effective information-sharing mechanism. NOTE: This paper is published as part of the 2021 SPE Reservoir Simulation Conference Special Issue.

The effect of weighting factors on income-related energy inequalities: The case of Sweden’s new building code

To ensure building construction with low heating demand, efficient use of sustainable energy carriers, and neutrality between heating technologies, Sweden recently introduced weighting factors (WFs) for different energy carriers which are now used in Energy Performance Certificates (EPCs). As EPC ratings are gaining increased influence in Swedish energy policy and regulation, with recent examples of buildings’ EPC rating acting as base for imperative regulatory requirements, the introduction of WFs is likely to have significant effects on how policy and regulations are distributed in the multifamily building stock. As residents often are directly or indirectly affected by policy that either impose or trigger measures to be undertaken in their building, the aim of this paper is to analyse how WFs affect the assessed energy performance of buildings in different resident income groups. The results show that overall, reduced energy performance from WFs was more common in high-income areas than in low-income areas. However, although the total number of buildings in the lowest EPC ratings was reduced after introducing WFs, the resulting income distribution among worst-performing buildings was more skewed towards low-income households than before introducing WFs. As imperative regulatory requirements previously have targeted worst-performing buildings, these results indicate that energy-related inequalities in the housing stock have become more prominent and should be considered as to not disproportionately burden low-income residents in the energy transition of the housing stock.

An Efficient Bi-Objective Optimization Workflow Using the Distributed Quasi-Newton Method and Its Application to Field Development Optimization

Although it is possible to apply traditional optimization algorithms to determine the Pareto front of a multi-objective optimization problem, the computational cost is extremely high, when the objective function evaluation requires solving a complex reservoir simulation problem and optimization cannot benefit from adjoint-based gradients. This paper proposes a novel workflow to solve bi-objective optimization problems using the distributed quasi-Newton (DQN) method, which is a well-parallelized and derivative-free optimization (DFO) method. Numerical tests confirm that the DQN method performs efficiently and robustly. The efficiency of the DQN optimizer stems from a distributed computing mechanism which effectively shares the available information discovered in prior iterations. Rather than performing multiple quasi-Newton optimization tasks in isolation, simulation results are shared among distinct DQN optimization tasks or threads. In this paper, the DQN method is applied to the optimization of a weighted average of two objectives, using different weighting factors for different optimization threads. In each iteration, the DQN optimizer generates an ensemble of search points (or simulation cases) in parallel and a set of non-dominated points is updated accordingly. Different DQN optimization threads, which use the same set of simulation results but different weighting factors in their objective functions, converge to different optima of the weighted average objective function. The non-dominated points found in the last iteration form a set of Pareto optimal solutions. Robustness as well as efficiency of the DQN optimizer originates from reliance on a large, shared set of intermediate search points. On the one hand, this set of searching points is (much) smaller than the combined sets needed if all optimizations with different weighting factors would be executed separately; on the other hand, the size of this set produces a high fault tolerance. Even if some simulations fail at a given iteration, DQN’s distributed-parallel information-sharing protocol is designed and implemented such that the optimization process can still proceed to the next iteration. The proposed DQN optimization method is first validated on synthetic examples with analytical objective functions. Then, it is tested on well location optimization problems, by maximizing the oil production and minimizing the water production. Furthermore, the proposed method is benchmarked against a bi-objective implementation of the MADS (Mesh Adaptive Direct Search) method, and the numerical results reinforce the auspicious computational attributes of DQN observed for the test problems. To the best of our knowledge, this is the first time that a well-parallelized and derivative-free DQN optimization method has been developed and tested on bi-objective optimization problems. The methodology proposed can help improve efficiency and robustness in solving complicated bi-objective optimization problems by taking advantage of model-based search optimization algorithms with an effective information-sharing mechanism.

Improving reproducibility of proton MRST by optimally averaging temperatures measured from multiple references: theoretical and empirical approaches

Purpose: In 1H MRS-based thermometry of brain, averaging temperatures measured from more than one reference peak offers several advantages including improving the reproducibility, i.e. precision, of the measurement. This paper proposes theoretically and empirically optimal weighting factors to improve the weighted average of temperatures measured from three references. Methods: We first proposed concepts of equivalent noise and equivalent signal-to-noise ratio in terms of frequency measurement and a concept of relative frequency that allows the combination of different peaks in a spectrum for improving the accuracy of frequency measurement. Based on these, we then developed a theoretically optimal weighting factor and suggested an empirical weighting factor for weighted average of temperatures measured from three references in 1H MRS-based thermometry. We assessed the two new weighting factors, together with other two previously proposed weighting factors, by comparing the errors of temperatures measured from individual references and the errors of averaged temperatures using these differing weighting factors. These errors were defined as the standard deviations in repeated measurements and in Monte Carlo studies. We also performed computer simulations to aid error analyses in temperature averaging. Results: Both the proposed theoretical and empirical weighting factors outperformed the other two previously proposed weighting factors as well as the three individual references in all phantom and in vivo experiments. In phantom experiments with 4 Hz or 10 Hz line broadening, the theoretical weighting outperformed the empirical one, but the latter was superior in all other repeated and Monte Carlo tests performed on phantom and in vivo data. Computer simulations offered explanations for the performances of the two new proposed weightings. Conclusion: The proposed two new weighting factors are superior to the two previously proposed weighting factors and can improve the measurement of temperature using 1H MRS-based thermometry.

An experimental comparison of different hierarchical self-tuning regulatory control procedures for under-actuated mechatronic systems

This paper presents an experimental comparison of four different hierarchical self-tuning regulatory control procedures in enhancing the robustness of the under-actuated systems against bounded exogenous disturbances. The proposed hierarchical control procedure augments the ubiquitous Linear-Quadratic-Regulator (LQR) with an online reconfiguration block that acts as a superior regulator to dynamically adjust the critical weighting-factors of LQR’s quadratic-performance-index (QPI). The Algebraic-Riccati-Equation (ARE) uses these updated weighting-factors to re-compute the optimal control problem, after every sampling interval, to deliver time-varying state-feedback gains. This article experimentally compares four state-of-the-art rule-based online adaptation mechanisms that dynamically restructure the constituent blocks of the ARE. The proposed hierarchical control procedures are synthesized by self-adjusting the (i) controller’s degree-of-stability, (ii) the control-weighting-factor of QPI, (iii) the state-weighting-factors of QPI as a function of “state-error-phases”, and (iv) the state-weighting-factors of QPI as a function of “state-error-magnitudes”. Each adaptation mechanism is formulated via pre-calibrated hyperbolic scaling functions that are driven by state-error-variations. The implications of each mechanism on the controller’s behaviour are analyzed in real-time by conducting credible hardware-in-the-loop experiments on the QNET Rotary-Pendulum setup. The rotary pendulum is chosen as the benchmark platform owing to its under-actuated configuration and kinematic instability. The experimental outcomes indicate that the latter self-adaptive controller demonstrates superior adaptability and disturbances-rejection capability throughout the operating regime.