Corrective Forces Research Articles

Effect of different corrective force directions applied by spinal orthoses on the patients with adolescent idiopathic scoliosis.

Spinal orthoses are commonly prescribed for adolescent idiopathic scoliosis (AIS), yet their three-dimensional correction was not fully understood. The amount of deformity control largely depends on the corrective forces applied, which remain empirically based due to a lack of consensus on optimal force application. This study investigated the effects of different corrective force directions exerted by spinal orthoses on patients with AIS. A retrospective analysis was conducted on 78 subjects. The trunk was segmented into four quadrants using coronal and sagittal planes from a top-down perspective. Each left or right posterolateral quadrant (with 90°) was further subdivided into zones 1-4, from the sagittal to coronal planes. Based on the zone where the resultant corrective force direction fell, the subjects were categorized into Group 1 (zone 1), Group 2 (zone 2), Group 3 (zone 3), or Group 4 (zone 4). The direction of the corrective force was estimated using modified models of the subjects' bodies, designed through a computer-aided design and manufacturing system integral to the orthosis fabrication process. The effects of corrective forces in different zones on scoliotic spine were assessed. Among the subjects, 3 were in Group 1, 17 in Group 2, 52 in Group 3, and 6 in Group 4. Due to the limited number of subjects, data from Groups 1 and 4 were not analysed. Groups 2 and 3 showed significant reductions in Cobb angle in the coronal plane and plane of maximum curvature (PMC) following orthosis fitting (p < 0.05). Group 2 displayed a significant decrease > 5º in thoracic kyphosis (p < 0.05). Both Groups 2 and 3 exhibited significant reductions in lumbar lordosis. PMC orientation remained unchanged over time (p > 0.05) but was notably higher in Group 2 after orthosis fitting (p < 0.05). Corrective forces applied by spinal orthoses in zones 2 and 3 effectively controlled lateral curve progression. Notably, only forces in zone 3 neither significantly reduced thoracic kyphosis nor exacerbated the deviation of scoliotic spine from the sagittal plane. Further research is needed to validate and expand upon these results.

Reducing the Brace Correction Stress on the Secondary Lumbar Curve Results in Excellent Muscle, Bone, and Disc Mechanical Performance: A Musculoskeletal Finite Element Simulation of AIS Patient With Rigo A3.

The biomechanical mechanism of brace intervention on bone, muscle, and disc should be comprehensively considered for AIS patients. We aimed to developmentally construct a musculoskeletal finite element model of adolescent idiopathic scoliosis to simulate the coupling of corrective forces and analyze the mechanical properties of bone, muscle, and disc. Investigateing, more effective clinical interventions to break the vicious cycle of patients during growth. A finite element model, including muscle, bone, and disc, was established using computed tomography data of a patient with RigoA3 adolescent idiopathic scoliosis. The three-point force coupling, antigravity, and bending effects of the Chêneau brace were simulated, and the correction force of the secondary lumbar bend was gradually reduced while observing the mechanical characteristics of bone, muscle, and disc. The correction force in line with symmetrical spine growth was comprehensively evaluated. The correction rate of the main thoracic (MT) curve, the intervertebral space height on the concave side of the vertebrae at the apex, and the stress ratio of the intervertebral discs were optimal when the maximum corrective pressure threshold was reached. However, the proximal thoracic (PT) curve was aggravated and the axial forces on the concave side were unbalanced. At this time, the biomechanical performance of the model is also not optimal. The correction rate of the Cobb Angle of the MT curve decreased with the decrease of the correction pressure in the lumbar region. When reduced to 25% of the maximum threshold, the convex side of disc stress, intervertebral space, and muscle axial force is more in line with the biomechanical mechanism of correction and can avoid sacrificing the PT curve. Downward adjustment of the corrective force to the secondary lumbar curve, using the Chêneau brace, results in better primary thoracic curvature mechanics in the musculoskeletal finite element model, suggesting that breaking the vicious cycle of scoliosis progression to guide benign spinal growth is beneficial.

Computational Methods for Verifying the Normative Requirements Regarding the Lateral Correction Force of a Powered Roof Support

The article discusses laboratory methods and the corresponding computational methods verifying compliance with the normative requirements regarding the lateral correction force of the powered roof support. The currently used flat model only allows for checking the normative requirement in relation to the sum of active forces of the correction cylinders installed in the roof support. Determining the required value of the active force of each cylinder is possible due to the simplified FEM model of a powered roof support, described in the research work, treated as a uniform weightless elastic body loaded with a concentrated force recreating the weight of the roof support located on an inclined longwall panel. The third analysed computational method involves determining the reaction in the four correction cylinders of the roof support, creating a spatial, statically indeterminate system of forces. It enables determining the range of variability of the response in the correction cylinders as a function of the distribution of floor pressure on the roof support base. The discussed computational methods were used to determine, for example, the lateral correction force of one of the types of powered supports used in a longwall panel inclined at an angle of 35°. The usefulness of the discussed calculation methods at various stages of the designing process of the powered support and its certification has been confirmed.

The Enhancement of Machine Learning-Based Engine Models Through the Integration of Analytical Functions

The integration of analytical functions into machine learning-based engine models represents a significant advancement in predictive performance and operational efficiency. This paper focuses on the development of hybrid approaches to model engine combustion and temperature indices and on the synergistic effects of combining traditional analytical methods with modern machine learning techniques (such as artificial neural networks) to enhance the accuracy and robustness of such models. The main innovative contribution of this paper is the integration of analytical functions to improve the extrapolation capabilities of the data-driven models. In this work, it is demonstrated that the integrated models achieve superior predictive accuracy and generalization performance across dynamic engine operating conditions, with respect to purely neural network-based models. Furthermore, the analytical corrective functions force the output of the complete model to follow a physical trend and to assume consistent values also outside the domain of values assumed by the input features during the training procedure of the neural networks. This study highlights the potential of this integrative approach based on the implementation of the effects superposition principle. Such an approach also allows us to solve one of the intrinsic issues of data-driven modeling, without increasing the complexity of the training data’s collection and pre-processing.

Design and Stability Analysis of Six-Degree-of-Freedom Hydro-Pneumatic Spring Wheel-Leg

Traditional hydro-pneumatic spring suspensions are limited to a single vertical degree of freedom, which cannot accommodate the significant technological changes introduced by the new in-wheel motor drive mode. Integrating the motor into the vehicle’s hub creates a direct motor drive mode, replacing the traditional engine–transmission–drive shaft configuration. Together with the dual in-wheel motor wheelset structure, this setup can achieve both drive and differential steering functions. In this study, we designed a six-arm suspension wheel-leg device based on hydro-pneumatic springs, and its structural composition and functional characteristics are presented herein. The external single-chamber hydro-pneumatic springs used in the six-arm structure suspension were analyzed and mathematically modeled, and the nonlinear characteristic curves of the springs were derived. To overcome the instability caused by inconsistent extension lengths of the hydro-pneumatic springs during horizontal steering, the spring correction force, horizontal rotational torque, consistency, and stiffness of the six-degree-of-freedom hydro-pneumatic spring wheel-leg device were analyzed. Finally, with the auxiliary action of tension springs, the rotational torque of the hydro-pneumatic springs and the tension resistance torque of the tension spring counterbalanced each other, keeping the resultant torque on the wheelset at approximately 0 N∙m. The results suggest that the proposed device has excellent self-stabilizing performance and meets the requirements for straight-line driving and differential steering applications. This device provides a new approach for the drive mode and suspension design of the dual in-wheel motor wheelset.

‘No es la democracia que míster superman quiere imponernos desde Washington’: An analysis of populist attitudes on democracy from Latin American legislators

AbstractIn studies on Populism, extensive discussion has mounted around whether the phenomenon represents a threat to democracy or a corrective force. In line with this concern, we examine whether the populist attitudes held by legislators are related to their opinions on the functioning of and satisfaction with three central aspects of governance: (I) democracy itself; (II) its institutions; and (III) the separation of powers. Using the ideational approach and survey information collected for the PELA‐USAL database, we first measure the populist attitudes of legislators in 12 Latin American countries. We then test through multivariate analysis two theoretical arguments: (1) that populism is relatively hostile to democracy and its institutions; and (2) that ideological extremism and the situation of the legislator in the government/opposition dynamic serve as moderators (enhancers) of that hostility. The results suggest that the populist attitudes of these legislators are indeed significantly connected to lower levels of trust and satisfaction with democracy and its institutions and that populism in combination with ideological extremism sharpens that critical perspective, while a legislator's affiliation with the ruling party or coalition in government tends to temper it.

Identification of physically consistent dynamics parameter of the ABB IRB 360-6/1600 delta robot and its use for time-optimal motion planning under consideration of constraint forces

Model-based control schemes, forward dynamics simulations, constraint force computation and time-optimal motion planning have one major thing in common, they all depend on the dynamics parameters of the system. Physical consistency of the dynamics parameters ensures a positive definite mass matrix and correct constraint forces. The most common inverse dynamics identification method – the base-parameters – lack physical consistency. This paper proposes an identification method to identify physically consistent dynamics parameters for Delta-like robots while further showing the effects of friction in passive joints. A tailored model to compute the crucial constraint forces appearing in the mechanism based on the identified dynamics parameters is derived. This model is used to additionally consider constraint forces besides actuation torques for time-optimal motion planning of a typical pick and place task. This is done without any prior CAD data of the robot from the manufacturer.

A practical multiscale analysis for nonlinear RC structures using a smart substructure replacement strategy

This paper presents a novel practical multiscale analysis (MSA) method for simulating local damages in large reinforced concrete (RC) structures during seismic events. Traditional techniques like the finite element (FE) method often struggle to balance computational costs with detailed simulation. The proposed method facilitates sequential local refinement from macroscopic to mesoscopic scales of RC structures, focusing strategically on critical areas prone to damage and cracking. Key features include: (1) 'Correction forces' enable integration and collaboration among models of different refinement levels, keeping models unchanged (i.e., without additions, deletions, or further refinement of elements), streamlining analysis and independent implementation across methods, scales, and platforms. (2) A smart replacement strategy ensures smooth transitions and prevents abrupt force changes between models at different refinement levels. (3) A ‘training process’ before performing the replacement and a semi-explicit method guarantee the accuracy and efficiency of the MSA method. (4) Parallel and distributed computing is seamlessly applied, significantly accelerating the analysis at each level. Implemented in the open-source software OpenSees, this method is illustrated through three examples that efficiently capture both the macroscopic mechanical responses and detailed local damage behaviors. This approach provides a valuable tool for the refined analysis of large-scale RC structures.

Nonlinear NMM analysis for large deformation and contact problems: Using full strain-rotation decomposition algorithm and augmented Lagrangian method enhanced open-closed iteration

Nonlinear analysis deals with problems that involve large displacements, strains, rotations, and contact problems. Accurate results can be obtained by choosing a reasonable method for decomposing strain and rotation to avoid errors and ensure the correct contact force. A novel full strain-rotation (S-R) decomposition and an augmented Lagrangian enhanced contact model are established within the numerical manifold method (NMM) framework. Limitations in simplified S-R NMM are overcome using our redesigned resolution procedure. A new method has been applied to analyse beams with large deflections, block columns under compression, block sliding, rock falling, and semi-ring contact with block problems. Promising results from the analysis indicate that proposed method is more accurate and effective in theory and numerically than prior approaches when resolving contact problems and large deformations.

Low-Cost Dynamometer for Measuring and Regulating Wrist Extension and Flexion Motor Tasks in Electroencephalography Experiments.

A brain-computer interface could control a bionic hand by interpreting electroencephalographic (EEG) signals associated with wrist extension (WE) and wrist flexion (WF) movements. Misinterpretations of the EEG may stem from variations in the force, speed and range of these movements. To address this, we designed, constructed and tested a novel dynamometer, the IsoReg, which regulates WE and WF movements during EEG recording experiments. The IsoReg restricts hand movements to isometric WE and WF, controlling their speed and range of motion. It measures movement force using a dual-load cell system that calculates the percentage of maximum voluntary contraction and displays it to help users control movement force. Linearity and measurement accuracy were tested, and the IsoReg's performance was evaluated under typical EEG experimental conditions with 14 participants. The IsoReg demonstrated consistent linearity between applied and measured forces across the required force range, with a mean accuracy of 97% across all participants. The visual force gauge provided normalised force measurements with a mean accuracy exceeding 98.66% across all participants. All participants successfully controlled the motor tasks at the correct relative forces (with a mean accuracy of 89.90%) using the IsoReg, eliminating the impact of inherent force differences between typical WE and WF movements on the EEG analysis. The IsoReg offers a low-cost method for measuring and regulating movements in future neuromuscular studies, potentially leading to improved neural signal interpretation.

Online ultrasonic monitoring of FDM nozzle temperature based on metamaterial buffer rod

Abstract Fused deposition modeling (FDM) has been widely used for fabricating parts with complex geometries. However, during the printing process the nozzle temperature fluctuates which may cause nozzle blockage, inter-filament delamination, over-melting, etc. Therefore, it is of significance to develop an online and in-situ nozzle monitoring system which could overcome such drawbacks for quality assurance. In this work, a multifunctional system is designed by incorporating a traditional ultrasonic probe and a metamaterial buffer rod to online monitor the nozzle temperature and ensure a correct extrusion force and speed. A parametric simulation model is first constructed implicitly based on thermal-acoustic metamaterial structures for the buffer rod. Secondly, since the high-fidelity calculation is computationally expensive, an efficient surrogate model with kriging approach is constructed based on the dataset drawn from limited trials for rapid prediction. Thirdly, multidisciplinary optimization is performed by the NSGA-III algorithm considering the thermal insulation performance, ultrasonic attenuation and structure integrity. The rod is fabricated according to the best parameters decided. A cross-correlation algorithm is calibrated with thermocouple measurement after waveform recording at different temperatures. The online and in-situ temperature measurement can be realized during 3D printing successfully eventually. This will help to improve the printing quality with potential feedback strategies.

Automated External Bone Fixation Robot Design and Orthopedic Analysis

Background: Bone external fixation technology is an important therapeutic approach for limb correction, primarily involving a class of external fixation correction mechanisms. It has achieved good results in limb lengthening and correcting deformities to restore limb function. In clinical practice, existing correction mechanisms face challenges such as high resistance between components, complex installation procedures, and high precision requirements for installation, requiring manual adjustment by physicians, which limits precise control and quantification of correction parameters. Objective: To address these issues, an automated correction bone external fixation robot was designed based on traditional Ilizarov external fixation devices(TIEFD). Methods: By increasing the number of unidirectional hinge connections, the robot can effectively reduce motion resistance. Subsequently, the robot was combined with the tibia for correction motion simulation, obtaining the motion parameters θ of the deformed bones during the correction process based on the trajectory of the tibia's point mass. Finally, correction motion experiments and finite element analysis(FEA) were conducted on the robot combined with a control system. Results: The results showed that the robot could precisely control correction parameters, with the error range for rotational correction not exceeding 0.5 radians and the error range for traction correction not exceeding 0.2 mm. FAE, based on corrective force data, concluded that compared to (TIEFD), the robot could reduce bone stress by 16 MPa during the correction process. Conclusion: The robot effectively reduces patient discomfort, this provides a reliable theoretical basis for bone external fixation technology and holds positive significance for the treatment of skeletal deformities.

Getting the intermolecular forces correct: introducing the ASTA strategy for a water model.

Having a force field for water providing good bulk properties is paramount for modern studies of most biological systems. Some of the most common three-site force fields are TIP3, SPC/ε or OPC3, providing a decent range of bulk properties. That does not mean though, that they have realistic inter-atomic forces. These force fields have been parameterized with a top-down approach, meaning, by fitting the force field parameters to the experimental bulk properties. This approach has been the governing strategy also for many variants of four- and more-site models. We test a bottom-up approach, in which the force field is parameterized by optimizing the non-bonded inter-atomic forces. Our philosophy is that correct inter-atomic forces lead to correct geometrical and dynamical properties. The first system we try to optimize with the accurately system tailored atomic (ASTA) approach is water, but we aim to eventually probe other systems in the future as well. We applied our ASTA strategy to find a good set of parameters providing accurate bulk properties for the simple three-site force field forms, and also for AMOEBA, a more detailed and polarizable force field. Even though our bottom-up approach did not provide satisfactory results for the simple three-site force fields (with fixed charges), for the case of the AMOEBA force field it led to a modification of the original strategy, giving very good intra- and inter-molecular forces, as compared to accurate quantum chemically calculated reference forces. At the same time, important bulk properties, in this study restricted to the density and diffusion, were accurately reproduced with respect to the experimental values.

Hybrid Sensor Fusion Mixed with Reinforcement Learning in Autonomous Dual-Arm Lifting Tasks Performed by Humanoid Robots

Humanoid robots often struggle with tasks such as lifting objects due to the complexity involved in identifying contact points, applying the correct force, and tracking task progress. We propose an integrated solution that leverages the dual-arm capability of humanoids and utilizes sensor fusion from vision and force sensors. Our system employs a computer vision algorithm to detect and characterize object properties (shape, size, position, orientation) and differentiate between parallel and non-parallel bi-manipulation tasks. The controller then identifies optimal contact points for the end effectors, generating trajectories fed into a closed-loop controller using force feedback. For parallel bi-manipulation, momentum cancellation is achieved through sensor fusion. For non-parallel surfaces, a reinforcement learning algorithm determines the appropriate lifting force to prevent slippage using only two contact points. Experimental validation on a real humanoid platform demonstrates the effectiveness of our approach in autonomously lifting objects, regardless of contact surface configuration. This advancement significantly enhances the reliability and versatility of humanoid robots in performing complex manipulation tasks, contributing to their practical deployment in human-oriented environments.

An All-in-One Array of Pressure Sensors and sEMG Electrodes for Scoliosis Monitoring.

Scoliosis often occurs in adolescents and seriously affects physical development and health. Traditionally, medical imaging is the most common means of evaluating the corrective effect of bracing during treatment. However, the imaging approach falls short in providing real-time feedback, and the optimal corrective force remains unclear, potentially slowing the patient's recovery progress. To tackle these challenges, an all-in-one integrated array of pressure sensors and sEMG electrodes based on hierarchical MXene/chitosan/polydimethylsiloxane (PDMS)/polyurethane sponge and MXene/polyimide (PI) is developed. Benefiting from the microstructured electrodes and the modulus enhancement of PDMS, the sensor demonstrates a high sensitivity of 444.3 kPa-1 and a broad linear detection range (up to 81.6kPa). With the help of electrostatic attraction of chitosan and interface locking of PDMS, the pressure sensor achieves remarkable stability of over 100000 cycles. Simultaneously, the sEMG electrodes offer exceptional stretchability and flexibility, functioning effectively at 60% strain, which ensures precise signal capture for various human motions. After integrating the developed all-in-one arrays into a commercial scoliosis brace, the system can accurately categorize human motion and predict Cobb angles aided by deep learning. This study provides real-time insights into brace effectiveness and patient progress, offering new ideas for improving the efficiency of scoliosis treatment.

A New Approach to Prevent Injuries Related to Manual Handling of Carts: Correcting Resistive Forces between Floors and Wheels to Evaluate the Maximal Load Capacity

Test methods that use pushing forces to evaluate the maximal load capacities of carts in design standards require a flat, smooth and horizontal steel plate and thus do not take into account the real conditions of work. Resistive forces of a single wheel of a cart in a uniform rectilinear motion were measured using a unique test bench with five loads. Forty-four wheels were tested (varying diameters, treads and bearings) with one steel plate and four resilient floor coverings. Based on a linear mixed model, all the following results were significant (p &lt; 0.05). Resistive forces were increased linearly with the load and depended on the characteristics of both the wheel and floor. These forces decreased as the diameter increased. They were important for wheels with sleeve bearings but decreased for cone ball bearings and precision ball bearings. Resistive forces depended on the material of the tread and were higher for solid rubber treads. In contrast, the hardness of the tread had little effect. Resistive forces strongly depended on the hardness of the base foam of resilient floor coverings: the softer the base foam, the higher the resistive forces. Test methods in design standards should be reviewed, using corrective forces based on these present results, to prevent musculoskeletal disorders.

IMMEDIATE EFFECT OF CUSTOM-MADE BOSTON-TYPE THORACO-LUMBO-SACRAL ORTHOSIS ON BALANCE AND POSTURAL STABILITY IN ADOLESCENT IDIOPATHIC SCOLIOSIS

Adolescent idiopathic scoliosis (AIS) can impair postural stability and balance functions. Boston brace systems with varying external corrective force strategies are used as one of the common conservative treatments in AIS. Although multiple studies have found that various orthotic therapies enhance curve advancement, the effects of spinal bracing on postural equilibrium and stability remain unknown. The primary objective of this study was to examine the effect of the immediate use of custom-made Boston-type thoraco-lumbo-sacral orthosis (TLSO) on balance and postural stability in AIS. Postural balance using the center of pressure (CoP) measures was measured by the HUMACⓇ Balance &amp; Tilt System (CSMi, Stoughton, MA). The line laser tool (Bosch, GLL 3 X P, Stuttgart, Germany) was used for measuring the decompensation distance for postural evaluation. The balance parameters such as stability score (%), path length (cm), average velocity (cm/s), and compensation–decompensation for posture were evaluated and compared between brace-on and brace-off conditions. Improvement of standing posture indicates spinal symmetry and cosmesis whereas enhancement of static balance was statistically nonsignificant ([Formula: see text] &gt; 0.05). Although the mean stability score, path length and average velocity of CoP in braced condition (91.4 ± 4.57, 115.62 ± 22.34 cm and 1.05 ± 0.12 cm/s) was found to be improved than unbraced condition (90.5 ± 5.09, 121.46 ± 35.52 cm and 1.11 ± 0.24 cm/s), the results were nonsignificant ([Formula: see text] = 0.078, 0.425 and 0.263). The scoliotic compensation was improved in the braced condition (0.64 ± 0.60 cm) compared to brace-off condition (1.74 ± 0.61 cm) showing improved posture ([Formula: see text] = 0.00013). Wearing the custom-made Boston-type TLSO showed positive effects on static posture and mean balance parameters. In future studies, the long-term effectiveness of this brace should be examined in patients with different spinal curve patterns and degrees of scoliosis.

Physically consistent modelling of surface tension forces in the Volume-of-Fluid method for three or more phases

Multiphase numerical simulations have become a widely sought methodology for modelling capillary flows due to their scientific relevance and multiple industrial applications. Much progress has been achieved using different approaches, and the volume of fluid is one of the most popular methods widely used for modelling two or more phases due to its simplicity, accuracy and robustness. However, when prescribing the forces emerging from three or more fluid-fluid interfaces, the force balance is not guaranteed and can lead to spurious self-propulsion. Here, a new approach to account for the surface tension forces for multiphase flows with a correct force balance is proposed. The newly proposed method is successfully validated for a wide range of tests, including contact angles for the fluid-fluid and fluid-solid triple line. Additionally, complete spreading phenomena of fluid on fluid and fluid on solid have been found to emerge naturally from the newly proposed surface tension force model. Finally, simulation results are compared against experiments of lubricant-impregnated surfaces to demonstrate the practical applicability of the newly proposed method.

A super-elastic alloy hallux valgus brace – a novel orthotic device

Objective: Evaluate the efficacy of a new orthotic-made super-elastic alloy brace to correct hallux valgus (HV) deformity.Methods: Five female patients diagnosed with HV deformity wore the newly developed orthotic daily for six weeks. The orthotic wasdeveloped using a super-elastic alloy brace to correct great toe lateral deviation, first metatarsal medial deviation, and fixation belts.The correction was evaluated by measuring the load at which the big toe begins to move and the distance moved by 15 gf force whenpulled from the side. Results: The orthotic was worn by all patients without causing any sleep disruptions. In the initial state, a strong force was required to move the big toe, but after two weeks, it was significantly improved to be mobile in all patients. Conclusion: The developed HV orthotic has a high wearability without causing pain or discomfort. Long-term use can provide a consistent and continuous correction force to the big toe, resulting in the successful release of the big toe metatarsophalangeal joint contracture within two weeks. Level of Evidence: Level 4.

A variational data assimilation approach for sparse velocity reference data in coarse RANS simulations through a corrective forcing term

The Reynolds-averaged Navier–Stokes (RANS) equations provide a computationally efficient method for solving fluid flow problems in engineering applications. However, the use of closure models to represent turbulence effects can reduce their accuracy. To address this issue, recent research has explored data-driven techniques such as data assimilation and machine learning.An efficient variational data assimilation (DA) approach is presented to enhance steady-state eddy viscosity based RANS simulations. To account for model deficiencies, a corrective force term is introduced in the momentum equation. In the case of only velocity reference data, this term can be represented by a potential field and is divergence-free. The DA implementation relies on the discrete adjoint method and approximations for efficient gradient evaluation.The implementation is based on a two-dimensional coupled RANS solver in OpenFOAM, which is extended to allow the computation of the adjoint velocity and pressure as well as the adjoint gradient. A gradient-based optimizer is used to minimize the difference between the simulation results and the reference data. To evaluate this approach, it is compared with alternative data assimilation methods for canonical stationary two-dimensional turbulent flow problems. For the data assimilation, sparsely distributed reference data from averaged high-fidelity simulation results are used.The results suggest that the proposed method achieves the optimization goal more efficiently compared to applying data assimilation for obtaining the eddy viscosity, or a field modifying the eddy viscosity, directly. The method works well for different reference data configurations and runs efficiently by leveraging coarse meshes.