ks function
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Abstract The center of gravity (CG) has a significant influence on the controllability, stability, and fuel efficiency of the aircraft. For the aircraft with multiple fuel tanks, the CG position can be controlled by the fuel quality of different fuel tanks during flight. In this paper, an optimization method based on discrete cosine transform (DCT) compression is proposed to solve the optimization strategy of aircraft multi-tank fuel supply according to the current aircraft mission and engine working requirements. The transform coefficients of the low frequency components are used as design variables to represent the fuel supply curves. The improved KS function is proposed to deal with constraints. The numerical example is demonstrated to verify the effectiveness of the proposed method.

In this paper, we propose a novel solution strategy to explicitly describe the design space in which no recourse is considered for the realization of the parameters. First, to smooth the boundary of the design space, the Kreisselmeier-Steinhauser (KS) function is applied to aggregate all inequality constraints, and project them into the design space. Next, for creating a surrogate polynomial model of the KS function, we focus on finding the sampling points on the boundary of KS space. After testing the feasibility of Latin hypercube sampling points, two methods are presented to efficiently extend the set of boundary points. Finally, a symbolic computation method, cylindrical algebraic decomposition, is applied to transform the surrogate model into a series of explicit and triangular subsystems that can be further converted to describe the KS space. Two case studies are considered to show the efficiency of the proposed algorithm.

AbstractThe purpose of this study is to compare perception of leg length discrepancy (LLD) and clinical results of total knee arthroplasties (TKA) in patients with or without previous ipsilateral hip arthroplasty. Between 2008 and 2015, navigation-assisted TKA was performed in 43 patients with previous hip arthroplasty after hip fracture. After 1:3 propensity score matching was performed, 108 patients of primary navigation-assisted TKA (group 1) and 36 patients with hip arthroplasty (group 2) were included. Knee Society (KS) scores, Western Ontario and McMaster Universities Index (WOMAC) scores, and patients' satisfaction including perception of LLD were evaluated. Radiographic evaluation included mechanical axis, component position, and LLD. Logistic regression analysis was performed to find the factors that affect the clinical outcomes. No significant differences in radiologic and clinical evaluations, except for KS function score, patient's satisfaction and LLD (p< 0.001), were detected between the groups. LLD and its perception were significantly higher in group 2 (1.8 ± 3.4 mm in group 1 and 9.7 ± 4.1 mm in group 2, p = 0.000). Risk factors for the low KS function score were found as LLD (odds ratio [OR]: 1.403, p = 0.008) and previous hip arthroplasty itself (OR: 15.755, p = 0.002), but much higher OR was found in previous hip arthroplasty. Although the outcomes of TKA in patients with ipsilateral hip arthroplasty are comparable to those of primary TKA, LLD was high and patient's satisfaction and functional outcomes were low in patients with previous ipsilateral hip arthroplasty. Care should be taken when considering TKA in patients with previous hip arthroplasty. This is a Level III, case control study.

Topology optimization with moving morphable voids (MMVs) is studied in this paper. B-spline curves are used to represent the boundaries of MMVs in the structure. Kreisselmeier–Steinhauser (KS)-function is also implemented to preserve the smoothness of the structural boundary in case the intersection of the curves happen. In order to study the influence of continuity, we propose pseudo-periodic closed B-splines (PCBSs) to construct curves with an arbitrary degree. The selection of PCBS parameters, especially the degree of B-spline, is studied and discussed. The classic Messerschmitt–Bolkow–Blohm (MBB) case is taken as an example in the numerical experiment. Results show that with the proper choice of B-spline degrees and number of control points, PCBSs have enough flexibility and stability to represent the optimized material distribution. We further reveal the mechanism of the merging process of holes and find that high-order degree PCBS could preserve more separated voids. A support beam design problem of microsatellite is also studied as an example to demonstrate the capability of the proposed method.

Aims It has been suggested that mobile-bearing total knee arthroplasty (TKA) might lead to better outcomes by accommodating some femorotibial rotational mismatch, thereby reducing contact stresses and polyethylene wear. The aim of this study was to determine whether there is a difference between fixed- and mobile-bearing versions of a contemporary TKA with respect to durability, range of movement (ROM) and function, ten years postoperatively. Patients and Methods A total of 240 patients who were enrolled in this randomized controlled trial (RCT) underwent a primary cemented TKA with one of three tibial components (all-polyethylene fixed-bearing, modular metal-backed fixed-bearing and mobile-bearing). Patients were reviewed at a median follow-up of ten years (IQR 9.2 to 10.4). Results There was no difference in durability, as measured by survivorship free of revision for any reason, nor in mean maximal ROM at ten years (p = 0.8). There was also no difference in function, as measured by Knee Society (KS) function scores (p = 0.63) or the prevalence of patellar tilt (p = 0.12). Conclusion In this clinical RCT, the mobile-bearing design of TKA was found to be reliable and durable, but did not provide better maximum knee flexion, function or durability ten years postoperatively compared with a posterior-stabilized, fixed-bearing design incorporating either an all-polyethylene or a modular-metal-backed tibial component. Cite this article: Bone Joint J 2018;100-B:925–9.

A numerical computation approach based on constraint aggregation and pseudospectral method is proposed to solve the optimal control of alkali/surfactant/polymer (ASP) flooding. At first, all path constraints are aggregated into one terminal condition by applying a Kreisselmeier-Steinhauser (KS) function. After being transformed into a multistage problem by control vector parameter, a normalized time variable is introduced to convert the original problem into a fixed final time optimal control problem. Then the problem is discretized to nonlinear programming by using Legendre-Gauss pseudospectral method, whose numerical solutions can be obtained by sequential quadratic programming (SQP) method through solving the KKT optimality conditions. Additionally, two adaptive strategies are applied to improve the procedure: (1) the adaptive constraint aggregation is used to regulate the parameter ρ in KS function and (2) the adaptive Legendre-Gauss (LG) method is used to adjust the number of subinterval divisions and LG points. Finally, the optimal control of ASP flooding is solved by the proposed method. Simulation results show the feasibility and effectiveness of the proposed method.

AbstractProper femoral component alignment in the axial plane during total knee arthroplasty (TKA) depends on accurate bone cuts and soft tissue balancing. Two methods that are used to achieve this are “measured resection” and “gap balancing.” However, a controversy exists as to which method is more accurate and leads to better outcomes. Therefore, the purpose of this study was to evaluate: (1) implant survivorship, (2) patient outcomes, (3) complications, and (4) radiographic analysis comparing patients who underwent TKA with either gap-balancing or measured resection techniques. A total of 214 consecutive patients (221 knees) underwent primary TKA by a single surgeon between 2011 and 2012. Component alignment was achieved by using measured resection in 116 knees and gap balancing was used in 105 knees. The patients had a mean age of 66 years (range, 44–86 years) and a mean body mass index of 32 kg/m2 (range, 22–52 kg/m2). Patient range-of-motion (ROM) and Knee Society (KS) function and pain scores, and radiographic assessment, were assessed preoperatively and postoperatively at ∼6 weeks, 3 months, 1 year, and then annually. The mean follow-up time was 3 years. A Kaplan–Meier's analysis was performed to calculate the survivorship. The aseptic survivorship was 98% in both the measured resection and gap-balancing groups. The mean ROM was not significantly different between the measured resection and gap-balancing groups (123 vs. 123 degrees, p = 0.990). There were no significant differences between the two groups in terms of the KS function scores (86 vs. 85 points, p = 0.829) or the KS pain scores (93 vs. 92 points, p = 0.425). Otherwise, the radiographic evaluation at latest follow-up did not demonstrate any evidence of progressive radiolucencies or loosening, of any prosthesis. The results of this study found that at a mean follow-up of 3 years, both the measured resection and gap-balancing techniques achieved excellent survivorship and postoperative outcomes. This demonstrates that both methods can be used to achieve accurate femoral component alignment with similar short-term outcomes.

Introduction: The purpose of this study was to evaluate the results of total knee arthroplasty for patients with ankylosed knees. Methods: We evaluated seven patients (10 knees) who underwent total knee arthroplasties for ankylosed knees from 1995 to 2008. There were two men and five women, with a mean age of 44.1 years (42–48 years). The mean follow-up period was 10.2 years (1–19.5 years). A rectus snip was performed in all cases, and V-Y quadricepsplasty was used in one case of severe quadriceps contracture. In all cases, we used the PFC Sigma PS fixed model (DePuy Orthopaedics Inc., Warsaw, Indiana, USA). The goal was more than 90° of flexion. Clinical evaluation was performed using range of motion (ROM), Knee Society (KS) Knee Score, KS Function Score, and complications. Radiographs were used to evaluate loosening or osteolysis. Results: The ROF was improved from 9.5° (0–30°) to 78.5° (15–115°), The Knee Score improved from 42.6 (25–70) to 68.6 (41–97), and the Function Score improved from 39 (0–60) to 66 (40–90). A radiolucent line was detected in two cases (one patient) around the tibial component, and one case had a necrosis of skin edge. Only one case had no improvement of motion. Conclusion: Total knee arthroplasty conversion for patients with ankylosed knees can achieve good results for motion and function without osteotomy of the tibial tuberosity when there is good quality soft tissue of the thigh.

Load-normalized strain energy increments between consecutive load steps are aggregated through the Kreisselmeier-Steinhauser (KS) function, and the KS function is proposed as a stiffness criterion of geometrically nonlinear structures. A topology optimization problem is defined to minimize the KS function together with the perimeter of structure and a volume constraint. The finite element analysis is done by remeshing, and artificial weak material is not used. The topology optimization problem is solved by using the level set method. Several numerical examples in two dimensions are provided. Other criteria of stiffness, i.e., the end compliance and the complementary work, are compared.