Influence Coefficient Matrix Research Articles

Aeroelastic Structural Analysis to Calculate Symmetrical Divergence Modes of an Aircraft Wing Using Aerodynamic Lifting Line Theory

This work explores the use of numerical matrix iteration to determine an aircraft wing's divergence speed using the aerodynamic span effects approach. The present work begins with the construction of equilibrium equations in differential and integral forms. In this paper, integral formulas are used because it serves as a convenient basis for numerical solutions of complex practical problems. Second, the straight-tapered wing is divided into a number of Multhopp stations. Subsequently, the stations' torsional influence coefficient matrix has been calculated. Third, lifting line theory was used as a suitable choice of aerodynamic theory, and the governing equations were represented in matrix form. Finally, aerodynamic span effects are taken into consideration with induction effects according to Prandtl’s lifting line theory to calculate the symmetrical divergence speed from the lowest eigenvalue of the homogenous governing integral equation. To get the solution to converge, a matrix has been iterated using the MATLAB environment. The obtained results will aid modern aircraft designers in their understanding of wing instability in steady motion.

Extended influence coefficient method for meshing stiffness evaluation of spur gears considering rotor flexibility

Rotor-supported gears are applied in transmission systems, and the rotor flexiblility leads to the misalignment of the gear pair with multiple degrees of freedom, which ultimately leads to the decrease of meshing stiffness. To evaluate the meshing stiffness of rotor-supported gears, the extended influence coefficient method (EICM) is proposed in this paper. Firstly, the gear contact position adjustment under misalignment condition is carried out. Then, the extended influence coefficients of bending, shearing, axial compression, Hertzian contact and fillet foundation deformation of gears are derived to obtain the extended influence coefficient matrix. Afterward, the load-deformation equations under different contact states are obtained, and the meshing stiffness is calculated. Subsequently, a cantilever rotor-gear coupling dynamic model is established by the rigid body element-extended influence coefficient method (RBE-EICM), and the dynamic meshing stiffness considering rotor flexibility is obtained. The accuracy of EICM and RBE-EICM is verified by comparison with finite element method, literature methods and experimental data, respectively. Finally, the effects of supporting layout, input torque and rotor diameter on the dynamic characteristics of cantilever rotor-supported gears are discussed.

Optimal design of strain sensor placement for distributed static load determination

Abstract In many applications it is desirable to inverse-calculate the distributed loading on a structure using a limited number of sensors. Yet, the calculated loads can be extremely sensitive to the placement of these sensors. In the case of predicting point loading applied at a known location, best results are typically achieved when one sensor is collocated with the force. However, the extension of this rule to distributed loading remains uncertain, and even simple sensor system design scenarios often require the designer to directly optimize the sensor placements using a numerical model. In an effort to provide designers with guidance, we identify optimal sensor configurations for predicting static distributed loads on beams with classical boundary conditions. An influence coefficient method, wherein the strain is related linearly to the static load, is used to estimate the applied forces. The loading distribution on the structure is assumed to be either a piece-wise linearly-distributed load or a uniformly-distributed load, allowing for distributed loads to be estimated using the magnitudes of a small number of control points. Given the simplicity of the beam structure, the equations of the influence coefficient method are derived analytically, which allows for the sensor placement to be specified using continuous optimization methods. The condition number of the influence coefficient matrix is used as a surrogate for error during optimization. ‘Rules of thumb’ for sensor placement are presented based on the optimization results. Results show that the optimal and rule-of-thumb sensor configurations are more resistant to input noise than naïve configurations, with the rule-of-thumb configurations yielding similar force predictions relative to the optimal configurations. We expect the rules of thumb to be useful guidelines for engineers designing tests on beam-like structures such as aircraft wings or marine propellers where the inverse calculation of distributed loads is of interest.

Огляд методів параметричного діагностування агрегатів гідравлічних і паливних систем літальних апаратів

The subject of study in this article is the methods of parametric diagnostics of the technical condition of the units of an air vehicle's hydraulic and fuel systems, which make it possible to ensure the established reliability indicators of these systems throughout their entire life cycle. This work aims to analyze the existing literature on the methods of parametric diagnostics of hydraulic units, determine the basic requirements for the development of diagnostic methods for units of hydraulic, and fuel systems. The objective of the study is to classify the existing methods of parametric diagnostics, applied primarily to hydraulic systems, to analyze the advantages and disadvantages of the algorithms under consideration based on the requirements for diagnostic algorithms established by the authors, and to assess the possibility of effectively using these methodologies to diagnose the technical condition of a complex hydraulic distribution unit. The authors of this work formed the main requirements for the methods of diagnosing a hydraulic and fuel system's units based on the nature of the detected defects, the experience of using diagnostic algorithms, as well as the requirements of existing standards and scientific publications analysis. The authors developed a classification of parametric diagnostic algorithms to systematize existing works. This paper describes the main features and differences between diagnostic algorithms based on methods for identifying a mathematical model of an object and diagnostic algorithms in the space of measured parameters. Methods for forming diagnostic models of hydraulic units have been analyzed, such as the state-space model, the Hammerstein model, the Volterra model, the ARX model, and the matrix of influence coefficients. Established analysis of the application of defect identification algorithms such as a divided difference filter (DDF), a radial basis functions neural network RBF, and a cosine distance method. As a result, the advantages and disadvantages of the monitored diagnostic algorithms were identified and the main tasks for developing an algorithm for parametric diagnostics of the technical condition of a complex hydraulic distribution unit were formulated.

Far-field identification of ice loads on ship structures by radial basis function neural network

The ice load is an environmental load that dominates the ice-resistant design of polar ship structures, and field measurement of ice-induced strains is an important approach to obtain ice loads. Constrained by narrow spaces and watertight structures in the ship-ice interaction area, the monitoring area where strain sensors are mounted sometimes has to be arranged separately from the loading area, which makes the classical influence coefficient matrix method no longer applicable. The far-field identification method for ice loads, based on the radial basis function neural network (RBFNN) with a simple structure and fast convergence, provides an alternative way to solve this problem. The potential mapping relationship between ice loads and far-field ice-induced strains is effectively established based on a generalised RBFNN. The influence of noise on the identification results of the ice loads on the bow shoulder of RV Xue Long 2 is thoroughly studied with finite element numerical analysis and effectively eliminated by noise injection learning algorithm. Under weak strain response and low signal-to-noise ratio, the accurate results of the subsequent scale model test indicate the possibility of engineering application. According to the rationality analysis of the identification results based on full-scale data, the applicability of the RBFNN method to field measurements is verified.

Uncertainty quantification in free vibration and aeroelastic response of variable angle tow laminated composite plate

The influence of uncertainty in material properties on free vibration and aeroelastic response of variable angle tow (VAT) laminated plates is presented in this work. Free vibration analysis is conducted by a finite element model based on third-order shear deformation theory. The FE model is further coupled with MSC. Nastran to carry out aeroelastic analysis of VAT laminates in the subsonic regime. MSC. Nastran helps to extract the aerodynamic influence coefficient matrix at discrete values of reduced frequencies using Doublet Lattice Method. The accuracy and adaptability of the highly efficient radial basis neural network (RBFN) based surrogate model developed for uncertainty analysis are checked by comparing the result with that of the Monte Carlo simulation. Stochastic analysis of natural frequencies and flutter characteristics of VAT laminates are conducted through various parametric studies. Variance-based sensitivity analysis is used to calculate the contribution of individual material properties to the free vibration and aeroelastic response of VAT laminates. Further, the influence of the highly sensitive properties on the structural failure probability is estimated. This research can be leveraged to predict the probability of failure of the structure at different levels of material uncertainty present in it.

Assessing the Contributions of Urban Green Space Indices and Spatial Structure in Mitigating Urban Thermal Environment

Urban green space takes a dominant role in alleviating the urban heat island (UHI) effect. Most investigations into the effects of cooling factors from urban green spaces on the UHI have evaluated the correlation between each factor and land surface temperature (LST) separately, and the contribution weights of various typical cooling factors in mitigating the thermal environment have rarely been analyzed. For this research, three periods of Landsat 8 data captured between 2014 and 2018 of Xuzhou during the summer and autumn seasons were selected along with corresponding meteorological and flux measurements. The mono-window method was employed to retrieve LST. Based on the characteristics of the vegetation and spatial features of the green space, eight factors related to green space were selected and computed, consisting of three indices that measure vegetation and five metrics that evaluate landscape patterns: vegetation density (VD), evapotranspiration (ET), green space shading degree (GSSD), patch area ratio (PLAND), largest patch index (LPI), patch natural connectivity (COHESION), patch aggregation (AI), and patch mean shape index distribution (SHPAE_MN). Linear regression and bivariate spatial autocorrelation analyses between each green space factor and LST showed that there were significant negative linear and spatial correlations between all factors and LST, which proved that the eight factors were all cooling factors. In addition, LST was strongly correlated with all factors (|r| > 0.5) except for SHPAE_MN, which was moderately correlated (0.3 < |r| < 0.5). Based on this, two principal components were extracted by applying principal component analysis with all standardized green space factors as the original variables. To determine the contribution weight of each green space factor in mitigating the urban heat island (UHI) effect, we multiplied the influence coefficient matrix of the initial variables with the standardized multiple linear regression coefficients between the two principal component variables and LST. The final results indicated that the vegetation indices of green space contribute more to the alleviation of the UHI than its landscape pattern metrics, and the contribution weights are ranked as VD ≥ ET > GSSD > PLAND ≈ LPI > COHESION > AI > SHAPE_MN. Our study suggests that increasing vegetation density is preferred in urban planning to mitigate urban thermal environment, and increasing broadleaf forests with high evapotranspiration and shade levels in urban greening is also an effective way to reduce ambient temperature. For urban green space planning, a priority is to multiply the regional green space proportion or the area of largest patches. Second, improving the connectivity or aggregation among patches of green space can enhance their ability to cool the surrounding environment. Altering the green space spatial shape is likely the least significant factor to consider.

Active Shape Control of Satellite Antenna Reflectors with Limited Power Supplies

This paper proposes an active shape control method for an antenna control system under a limited number of power supplies with a reduction in weight and cost. An analytical model of a grid reflector with embedded piezoelectric actuators was first established, from which an influence coefficient matrix was derived for controller design. A shape controller was designed by synergistically optimizing the actuator group and power supply voltage. The optimization objectives include the root-mean-square (RMS) error, control energy consumption, and a multiobjective combination of both. The design variables include the actuator group and power supply voltage. A dynamic actuator group design with a detached power supply is proposed to improve the control performance, which also significantly increases the design domain of this optimization problem. A hybrid optimization method is proposed based on the general genetic algorithm and least-squares method to reduce the difficulty and complexity of this optimization problem with a large-dimensional design domain. Numerical simulations were carried out to illustrate the effect of the proposed hybrid optimization control method. The results indicate that the RMS error can be reduced by more than 90%, even if only two power supplies are used. The introduction of a group design with a detached power supply can clearly improve the control performance, especially by reducing the energy consumption. By employing multiobjective optimization with a uniform consideration of the RMS error and control energy consumption, a series of Pareto-optimal results can be obtained, and these results can provide meaningful references for engineering designers.

The influence and application of nonlinear aerodynamics on static derivatives in transonic regime

This paper details two static aeroelastic analysis methods applied to a passenger aircraft model with high aspect ratio wing. The influence of nonlinear aerodynamic force on static aeroelastic derivatives in the transonic regime is analysed. The traditional aerodynamic influence coefficient (AIC) matrix method can produce fast and reliable aerodynamic force and is widely used in aeroelastic analysis. However, the AIC matrix computed by linear aerodynamics will lead to some errors in transonic regime because of the nonlinear effect of aerodynamics. By generating the correction matrices, the AIC matrix is modified, and the accuracy of transonic static aeroelastic correction of aerodynamic data can be improved. The static derivatives are compared to the results of the computational fluid dynamics (CFD) / computational structural (CSD) interaction method.

Machine learning performance comparison for main propulsive shafting systems alignment

The ship shaft alignment is crucial to achieve a high-performance propulsion system. This alignment is carried out, still in drydock, by adjusting the bearings' offsets. However, there are numerous available combinations sets of vertical offsets which results in good alignment final condition. Defining an optimum set of vertical displacements is costing shipyards a valuable time. Therefore, this work proposes the use of machine learning algorithms to predict if a given set of offsets, following the mandatory rules in force, should be implemented or not. In this manner, this paper presents a case study where a finite element model of an Anchor Handling Tug Supply (AHTS) vessel’ shaft line was assembled in order to obtain the bearings reactions, shaft line deflections, shear forces, bending moments and, finally, the influence coefficients matrix (ICM). Those data were used to feed machine learning (ML) models based on four different algorithms, namely, K-Nearest-Neighbors, Extremely Randomized Trees, Random Forest and Gradient Boosting in order to solve multiclass classification problems concerning the offset's set to be applied in the alignment of the shaft line. Results showed that the Gradient Boosting and Random Forest algorithms presented the best results, achieving up to 98.1% of precision in one of the 36 scenarios tested, and an average precision above 96.0%. Such results corroborated with the authors' proposal to implement ML techniques as a way to speed up the currently very time-consuming shaft alignment process.

A Modification to the Enhanced Correction Factor Technique for the Subsonic Wing–Body Interference Model

In this work, the enhanced correction factor technique (ECFT) is modified for a subsonic wing–body interference model, which can consider the forces on both the lifting boxes and the body elements of an idealized airplane, termed the advanced ECFT method. A passenger aircraft model is chosen as the simulation model, and the longitudinal static aeroelasticity at the transonic situation for two-degree freedom, including the α (angle of attack) degree and ϕ (angle of horizontal tail) degree, is simulated in this paper. The corresponding CFD results are used to correct the aerodynamic influence coefficients (AIC) matrix, which is then simulated by MSC.NASTRAN. The pressure distribution results of different aircraft components received by the advanced ECFT method indicate that it is suitable for the subsonic wing–body interference model. Compared with the uncorrected linear method and the diagonal corrected method, it is generally more consistent with the CFD/CSD coupling method, not only for the lifting boxes, but also for the body elements. In addition, the aerodynamic derivative results also show good agreement with the flight test data, which solidly verifies the advance ECFT method.

Eliminating the influence of measuring point failure in ice load identification of polar ship structures

Ice loads are extreme environmental loads for polar ships sailing in ice regions. Field measurement of polar ship structures is the most direct approach for obtaining ice loads. This study investigates the influence of measuring point failure in ice load identification of polar ship structures and consequently proposes effective practices to eliminate this influence considerably. Based on the simulated strain of a typical polar ship's side grillage, the influence is studied in detail, and the spatial distribution characteristics of the identification error in the monitoring area are subsequently determined. According to the systematic analysis of the strain data at measuring points along frames, the spatial distribution characteristics of the strains are determined and further verified considering typical load scenarios. Consequently, the least squares fitting (LSF) method for the estimation of the strains at failed points is proposed. Practical schemes for ice load identification using the influence coefficient matrix (ICM) method under the influence of measuring point failure are presented and discussed as well. It is found that the LSF method decreases the identification error in the loading area, thereby significantly eliminating the influence. Thus, the scheme associating subarea combination with strain fitting results in higher fineness and better accuracy of ice load identification, which is recommended for adoption and has broad application prospects in the future.

A wheel–rail normal contact model using the combination of virtual penetration method and strip-like Boussinesq’s integral

This paper reports a new non-Hertz normal contact model for the engineering computations such as vehicle-track dynamics and wheel-rail damage prediction. The model is developed as a combination of virtual penetration method and Boussinesq’s integral. A first novel aspect is the proposed virtual penetration method to compensate the inconsistence introduced by this combination, (i) a ‘stepwise penetration scaling coefficient’ approach that adapts to the lateral contact boundary is presented; (ii) we propose a new formula for the longitudinal contact boundary to compensate the error introduced by the step-by-step increase of interpolated penetration. A second novelty is the use of strip-like Boussinesq’s integral for strip discretized contact patch to achieve the fast computation. On the one hand, it makes this model easier to convergence since it only considers the result in the center of each strip. On the other hand, we propose a fast method of generating influence coefficient matrix. Some numerical tests are evaluated by the CONTACT software and compared with KP method and STRIPES. In addition, the comparison of modeling approach and computational cost are discussed in detail.

Estimation of ice loads on offshore structures using simulations of level ice-structure collisions with an influence coefficient method

During their service, ice-class vessels are exposed to ice collision loads. Precise estimation of such ice loads is essential to the design of ice-class vessels. Due to difficulties encountered in real measurement of ice loads, a simple yet logically straightforward method, namely the influence coefficient method (ICM), has been widely employed to convert strain data to ice pressures. However, the method's accuracy and reliability depend on how strain gauges are arranged and load cells are divided accordingly. This study investigated those aspects in order to enhance the accuracy and reliability of the ICM in estimating ice loads incurred in collisions of ice with offshore structures. It began by developing a numerical model of level ice-structure interactions. For this, an ice-material model applying the Drucker-Prager (DP) plasticity model combined with an element erosion technique's simplified damage mechanics was developed. The developed numerical model was verified by comparing its results with the relevant model test data and corresponding numerical results available in the open literature, and good agreement was achieved. Next, the present study performed, based on the numerical simulation strategy thus validated, simulations of level ice collisions with actual offshore structures showing inflexible and deformable behaviors. Subsequently, a finite element (FE) model of the structures’ instrumented area, which is the same as the scantling used in the ice collision simulation, was developed to construct an influence coefficient matrix for the ICM. The structural responses, including stress/strain data and ice-contact pressure observed numerically, were then applied to an investigation of the ICM capability. The effects of the strain gage arrangements and corresponding load cells on the estimation of the local ice pressures acting on actual offshore structures were demonstrated. The proposed procedure is expected to provide insights into how the ICM can be improved in reliably and cost-effectively estimating ice loads on ice-class offshore structures.

쇄빙연구선 ARAON호의 국부 빙하중 추정을 위한 영향계수행렬의 보완

This paper focuses on the improvement of the influence coefficient matrix method for estimation of local ice load on the icebreaking research vessel ARAON. The influence coefficient matrix relates ice pressure on the hull plate to the measured/calculated hull strain/stress. Conventionally von Mises equivalent stresses representing hull stresses and ice pressure acting on the hull plate are utilized to assemble the influence coefficient matrix. Because of the three dimensional features of the ship-ice collision process, an enhanced method to assemble the influence coefficient matrix is derived considering ice loads in the X, Y, and Z direction simultaneously. Furthermore the location of ice loads acting on hull-plate may fall outside the measuring sensor area, and the enhanced influence coefficient matrix is modified to reduce the difference between the actual and the estimated ice loads by expanding the domain outward from the sensor area. The developed method for enhanced influence coefficient matrix is applied to IBRV ARAON during the 2019 Antarctic ice field test and the local ice loads in three directions are efficiently calculated compared to those by a conventional method.

Алгоритм классификации технического состояния топливного регулятора в пространстве параметров рабочего процесса

This article solves the problem of constructing an algorithm for classifying the technical state of the fuel regulator of a turboshaft engine of a helicopter in the parameter space of the regulator's working process and obtaining estimates of the state of the investigated product. In the introduction to this work, the main methods of classifying the technical state are considered, and a brief justification for the choice of the method for classifying the state of the product in the space of measured parameters used to construct the algorithm is considered in this article, is given. The criteria for the presence of a malfunction in the investigated controller are determined and the basic requirements for the classification algorithm are formed. To simplify the problem being solved, many assumptions about the diagnosed defects were made. The article provides descriptions of all components of the classification algorithm. A brief description of the mathematical model of the fuel regulator is given. The operating mode of the regulator for analysis is selected, and the list of state parameters required for diagnostics and the list of diagnostic parameters of the working process is given. The technique of linearization of the mathematical model of the controller and the technique of constructing the matrix of influence coefficients, which is the basic element of the entire algorithm, is described. The probabilistic characteristic of the credibility of the classification algorithm is determined, and the derivation of the formula for its calculation, based on the Bayes theorem, is also given. To assess the quality of the classification by the diagnostic algorithm, a test sample of workflow parameters was formed. The methodology for constructing a test sample is described and its size is determined. After the product condition estimates are obtained according to the test sample data by the classification algorithm, such a quality criterion as the recall is calculated. As a result of assessing the recall, a table was formed with the values of this criterion for each class. The recall of the algorithm on average for all defects was 89 %. The conclusions indicate possible methods for improving the quality of diagnosis by the algorithm.

Thermal Influence Coefficients-Based Electrothermal Modeling Approach for Power Electronics

An inverter or converter achieves the desired dc-ac or dc-dc conversion as required by electric and hybrid electric vehicles. This conversion is typically performed using semiconductor switches such as Insulated Gate Bipolar Transistors (IGBTs) modules consisting of transistors and diodes. Multiple transistors-diode pairs are integrated under a common copper base plate (also referred to as case). As power density increases, the heat dissipation of each device is influenced by other devices. The heat loss from semiconductor devices needs to be effectively dissipated to the ambient to maintain the temperature of IGBTs and diodes within acceptable limits (mentioned by the component manufacturer or based on the desired thermal margin in design). The over-temperature of the IGBT junction causes reliability issues resulting in solder fatigue and bond wire wear-out. The current work comprises predicting the temperature-dependent heat loss (electrothermal modeling) and thermal management techniques to dissipate these losses effectively to the ambient. An influence coefficient matrix is defined for liquid-cooled IGBT modules and used to estimate the die-to-die thermal influence. The IGBT module's heat distribution and its effect on the die temperature are studied for dc-dc and dc-three phase ac conversion.

Effects of Nonuniform Blade Spacing on Compressor Rotor Flutter Stability

A generalized flat plate cascade model is used in this study to predict the unsteady aerodynamics of a vibrating blade row with nonuniform blade spacing in subsonic compressible flow. The blade row is assumed to vibrate in an isolated family of blade-dominated modes. The effect of nonuniform blade spacing on compressor rotor flutter stability is demonstrated by case studies based on the geometric and flow conditions of a high-speed three-stage axial research compressor. The results show that nonuniform blade spacing can greatly alter the blades’ aerodynamic damping. At certain vibrational nodal diameters, some blades are destabilized so much that their aerodamping becomes negative. However, negative aerodamping of some blades do not necessarily lead to the instability of the whole blade row. A general multibladed system aeroelastic model is derived to study the effects of the nonuniform blade spacing on rotor stability through an eigenvalue approach. The aerodynamic influence coefficients matrix can be calculated using the generalized flat plate cascade model for a blade row with any user-specified blade spacing patterns. The case studies investigated in this paper show that alternating blade spacing and shifting only one blade position can slightly increase the stability of the least-stable eigenmode, whereas sinusoidal blade spacing has a slightly destabilizing effect. On the other hand, the eigenvectors of the least-stable mode for the nonuniformly spaced blade rows can be significantly different from the uniform blade spacing case.

An Improved New Convolutional Neural Network Method for Inverting the Pore Pressure in Oil Reservoir by Surface Vertical Deformation

Abstract Average pore pressure in oil formation is an important parameter to measure energy in the formation and the capacity of injection–production. In past studies, average pore pressure mainly depends on pressure build-up test results, which have a high cost and need a long testing time, so it is not conducive to utilize. In this paper, the vertical deformation of the Earth’s surface was used to calculate changes in reservoir pore pressure. We set up the marker stake for measuring ground displacement and measured the vertical deformation at the in situ position. Furthermore, we provided an improved new convolutional neural network (CNN), which adopted image-to-image mode, removed pooling layers and full connection layers, and used a new loss function considering the boundary influence coefficient matrix. Then, the machine learning method was used to invert surface vertical deformation to change pore pressure in the oil reservoir. The method was tested in the block of the Sazhong X development zone, in the Daqing Oilfield of China. The average pore-pressure change values of 20 grids whose area was 900×900 m each were determined by the inversion of the corresponding surface vertical deformation at 27 marker stakes. The pore pressure change accuracy reached 82.34%. This study provides a new method for calculating average pore pressure in terms of an oil block. At the same time, it also provides a new technical method for inversion calculations.

The measurement accuracy of instrumented ship structures under local ice loads using strain gauges

Strain gauges are commonly used for the instrumentation of ship structures to measure ice loads on the basis of shear strain differences. Finite Element Analysis (FEA) is used to determine the load–strain relation of the instrumented area by calculating an Influence Coefficient Matrix (ICM). However, the accuracy of the measurement method and the influence of the load location and load length on the accuracy of the load determination are rarely assessed. Consequently, this paper identifies the accuracy of the ICM, discusses which structures are suitable for measurements of shear strain differences and presents possible improvements regarding these measurements. As load cases are systematically varied over a finite element model, the external load is recalculated based on the resulting shear strains. The number of strain gauges used for the measurement of shear strains has a significant impact on the ICM. For common instrumentation it was found that the ice load can only be accurately determined, if the ice load acts within the instrumented area. To overcome this limitation, an approach to determine the load location is presented among further recommendations.