A Planar Mechanism Synthesis Approach Based on Flexible Joint Model

This paper discusses a kind of optimization problem with linear complementarity constraints, and presents a sequential quadratic programming (SQP) algorithm for solving a stationary point of the problem. The algorithm is a modification of the SQP algorithm proposed by Fukushima et al. [Computational Optimization and Applications, 10 (1998), 5-34], and is based on a reformulation of complementarity condition as a system of linear equations. At each iteration, one quadratic programming and one system of equations needs to be solved, and a curve search is used to yield the step size. Under some appropriate assumptions, including the lower-level strict complementarity, but without the upper-level strict complementarity for the inequality constraints, the algorithm is proved to possess strong convergence and superlinear convergence. Some preliminary numerical results are reported.

Multidisciplinary design optimization (MDO) was performed on a helicopter rotor blade. The blade was modeled as a rigid flapping blade for dynamics; Blade Element Theory (BET) was the analysis approach to model the aerodynamic loading, and a simple linearly elastic hollowed rectangular section was the main structural component. MATLAB was used to solve the flapping differential equations and its Sequential Quadratic Programming (SQP) and Genetic Algorithm (GA) were used for the optimization. A Particle Swarm Optimization (PSO) routine was also tested. The optimization process consisted of three cases. The first case was a simple cantilever beam under centrifugal and an assumed bending loads. The optimization was performed using the SQP, GA, and PSO algorithms. The SQP resulted in the superior design with 75.45 compared to the GA's 87.1 and the PSO's 79.2, but a local minimum was present. The second case was an expansion of the first case by turning it into multidisciplinary problem. Aerodynamics was included in the design variables and objective function. Only the SQP algorithm was used and there was a reduction in hub vertical shear by 33.6%. The blade mass increased by 36.84%. The last case was an improvement to the second by creating a multiobjective problem by including the hub radial shear and the results were improved significantly by reducing the hub vertical shear by 34.06% and radial shear by 17.87% with a reduction of blade mass by 23.86%.

Size and configuration syntheses of rigid-link mechanisms with multiple rotary actuators using the constraint force design method

Comparison of SQP and AL algorithms for deterministic constrained production optimization of hydrocarbon reservoirs

Optimal Design of Heat Exchanger Networks by Using SQP Algorithm Based on GPU Acceleration

Recently, with the wide adoption of electric vehicles, transportation network has shown different characteristics and been further developed. In this paper, we present a new time-flow impedance function, which may be more realistic than the existing time-flow impedance functions. Based on this new impedance function, we present an optimization model for a mixed-mode traffic network in which battery electric vehicles (BEVs) and gasoline vehicles (GVs) are chosen. We suggest two approaches to handle the model: One is to use the interior point (IP) algorithm and the other is to employ the sequential quadratic programming (SQP) algorithm. Three numerical examples are presented to illustrate the efficiency of these approaches. In particular, our numerical results show that more travelers prefer to choosing BEVs when the distance limit of BEVs is long enough and the unit operating cost of GVs is higher than that of BEVs, and the SQP algorithm is faster than the IP algorithm.

Performance analysis of support vector machine, Gaussian Process Regression, sequential quadratic programming algorithms in modeling hydrogen-rich syngas production from catalyzed co-gasification of biomass wastes from oil palm

With the widespread application of high-dynamic quadruped robots, the influence of flexible joint structures on their motion control performance has become increasingly significant. Conventional model predictive control (MPC) methods often neglect the stiffness changes of joint drives during motion, leading to unstable foot force distribution and exacerbated center of mass attitude fluctuations. To address this issue, this paper proposes a flexible joint model predictive control method (FJ-MPC) that integrates joint drive parameter identification and real-time optimization. This method constructs a joint flexibility model based on the load-angle-stiffness nonlinear characteristics of harmonic drives, and introduces a stiffness variation penalty term into the cost function to achieve smooth stiffness transitions. Simulation results show that the proposed method significantly reduces stiffness fluctuations and improves center of mass stability under diagonal gaits. This study provides new insights into high-precision flexible modeling and control for quadruped robots, offering significant theoretical value and engineering application potential.

This paper deals with the synthesis of planar and spherical adjustable fourlink mechanisms whose coupler point can approximately trace two or more paths prescribed by a large number of points. A single adjustment in one of the mechanism parameters is used to approximately obtain the prescribed paths. A two stage approach is used to first determine the parameters of the driving dyad and then the parameters of the driven dyad. The use of novel and appropriate objective functions with minimum number of variables and a sequential quadratic programming (SQP) algorithm to search for the optimal mechanism parameters leads to quick and accurate synthesis of the four-link mechanisms.

Many statistical models have been proposed in the literature for the analysis of longitudinal data. One may propose to model two or more correlated longitudinal processes simultaneously, with a goal of understanding their association over time. Joint modeling is then required to carefully study the association structure among the outcomes as well as drawing joint inferences about the different outcomes. In this study, we sought to model the associations among six nutrition outcomes while circumventing the computational challenge posed by their clustered and high-dimensional nature. We analyzed data from a 2 2 randomized crossover trial conducted in Kenya, to compare the effect of high-dose and low-dose iodine in household salt on systolic blood pressure (SBP) and diastolic blood pressure (DBP) in women of reproductive age and their household matching pair of school-aged children. Two additional outcomes, namely, urinary iodine concentration (UIC) in women and children were measured repeatedly to monitor the amount of iodine excreted through urine. We extended the model proposed by Mwangi etal. (2021, Communications in Statistics: Case Studies, Data Analysis and Applications, 7(3), 413-431) allowing flexible piecewise joint models for six outcomes to depend on separate random effects, which are themselves correlated. This entailed fitting 15 bivariate general linear mixed models and deriving inference for the joint model using pseudo-likelihood theory. We analyzed the outcomes separately and jointly using piecewise linear mixed-effects (PLME) model and further validated the results using current state-of-the-art Jones and Kenward methodology (JKME model) used for analyzing randomized crossover trials. The results indicate that high-dose iodine in salt significantly reduced blood pressure (BP) compared to low-dose iodine in salt. Estimates for the random effects and residual error components showed that SBP and DBP had strong positive correlation, with effect of the random slope indicating that significantly related outcomes are strongly associated in their evolution. There was a moderately strong inverse relationship between evolutions of UIC and BP both in women and children. These findings confirmed the original hypothesis that high-dose iodine salt has significant lowering effect on BP. We further sought to evaluate the performance of our proposed PLME model against the widely used JKME model, within the multivariate joint modeling framework through a simulation study mimicking a crossover design. From our findings, the multivariate joint PLME model performed exceptionally well both in estimation of random-effects matrix (G) and Hessian matrix (H), allowing satisfactory model convergence during estimation. It allowed a more complex fit to the data with both random intercepts and slopes effects compared to the multivariate joint JKME model that allowed for random intercepts only. When a hierarchical viewpoint is adopted, in the sense that outcomes are specified conditionally upon random effects, the variance-covariance matrix of the random effects must be positive definite. In some cases, additional random effects could explain much variability in the data, thus improving precision in estimation of the estimands (effect size) parameters. The key highlight in this evaluation shows that multivariate joint JKME model is a powerful tool especially while fitting mixed models with random intercepts only, in crossover design settings. Addition of random slopes may lead to model complexities in most cases, resulting in unsatisfactory model convergence during estimation. To circumvent convergence pitfalls, extention of JKME model to PLME model allows a more flexible fit to the data (generated from crossover design settings), especially in the multivariate joint modelingframework.

Estimating Healthcare Demand for an Aging Population: A Flexible and Robust Bayesian Joint Model

Missing data and noisy observations pose significant challenges for reliably predicting events from irregularly sampled multivariate time series (longitudinal) data. Imputation methods, which are typically used for completing the data prior to event prediction, lack a principled mechanism to account for the uncertainty due to missingness. Alternatively, state-of-the-art joint modeling techniques can be used for jointly modeling the longitudinal and event data and compute event probabilities conditioned on the longitudinal observations. These approaches, however, make strong parametric assumptions and do not easily scale to multivariate signals with many observations. Our proposed approach consists of several key innovations. First, we develop a flexible and scalable joint model based upon sparse multiple-output Gaussian processes. Unlike state-of-the-art joint models, the proposed model can explain highly challenging structure including non-Gaussian noise while scaling to large data. Second, we derive an optimal policy for predicting events using the distribution of the event occurrence estimated by the joint model. The derived policy trades-off the cost of a delayed detection versus incorrect assessments and abstains from making decisions when the estimated event probability does not satisfy the derived confidence criteria. Experiments on a large dataset show that the proposed framework significantly outperforms state-of-the-art techniques in event prediction.

Paired pectoral fins that are capable of rowing motions are an important actuation mechanism for robotic fish. Existing work in this area typically adopts a rigid connection between the actuator and the pectoral fins, which requires a faster actuation speed in the power stroke than in the recovery stroke to produce a net thrust or moment. In addition to increasing the control complexity, the latter requirement leads to slow robot speeds due to prolonged deceleration during the recovery stroke. In this paper, we propose the design of a novel flexible passive joint that connects the servomotor arm to the pectoral fin, to overcome the aforementioned problem. A dynamic model is developed for the joint and for a robotic fish equipped with such joints. The design and the model are evaluated with extensive experimental results. With symmetric actuation patterns during the power and recovery strokes, the robotic fish with the proposed joints shows clear speed advantage over the case involving rigid joints and asymmetric actuation. Motivated by the need for design optimization, the model is further utilized to investigate the influence of the joint length and stiffness on the robot locomotion performance and efficiency. It is found that, for low fin-beat frequencies, longer or more flexible joints lead to higher speeds, and the trend is reversed at high fin-beat frequencies. On the other hand, while the mechanical efficiency shows a decreasing trend when the frequency increases, it is higher with shorter joints. These findings suggest the utility of the proposed model for multiobjective design of the joint and its operating frequency.

This research extends the generalized recursive formulas for the rigid body dynamics to the flexible body dynamics using the backward difference formula (BDF) and the relative generalized coordinate. When a new force or joint module is added to a general purpose program in the relative coordinate formulations, the modules for the rigid bodies are not reusable for the flexible bodies. Since the flexible body dynamics handles more degrees of freedom than the rigid body dynamics does, implementation of the flexible dynamics module is generally complicated and prone to coding mistakes. In order to overcome the implementation difficulties, a virtual rigid body is introduced at every joint and force reference frames. A virtual flexible body joint is introduced between two body reference frames of the virtual and original bodies. Since the multibody system dynamics are formulated by highly nonlinear algebraic and differential equations and there are many different types of joints, a tremendous amount of computer implementation is required to develop a general purpose dynamic analysis program using the relative coordinate formulation. The implementation burden is relieved by the generalized recursive formulas. The notationally compact velocity transformation method is used to derive the equations of motion in the joint space. The terms in the equations of motion which are related to the transformation matrix are classified into several categories each of which recursive formula is developed. Whenever one category of the terms is encountered, the corresponding recursive formula is invoked. Since computation time in a relative coordinate formulation is approximately proportional to the number of the relative coordinates, computational overhead due to the additional virtual bodies and joints is minor. Meanwhile, implementation convenience is dramatically improved.

The sequential quadratic programming and genetic algorithms are finely tuned on the optimal design of a brushless DC wheel motor. Combining both methods, a hybrid approach is tested. Multiobjective optimizations are performed using Nondominated Sorting Genetic Algorithm, Strength Pareto Evolutionary Algorithm, and a variable weighted sum of objectives with the sequential quadratic programming. The Pareto fronts are compared in term of accuracy, uniformity, and coverage criteria using some quality indicators.