Equation Method Research Articles

Optimization and Comparative Analysis of micro-perforated panel sound absorbers: A study on structures and performance enhancement

In this study, three MPP (micro-perforated panels) absorber configurations (simple, series, parallel) were investigated via the response surface method (RSM) to broaden the absorption bandwidth. The study focused on the average normal sound absorption coefficient (SAC) in the range of 125–3000 Hz via an impedance tube. The impedance tube results were finally compared with the Finite Element Method (FEM) and Equivalent Circuit Method (ECM) simulations. Samples Fabrication involves 3D printing, with optimized configurations exhibiting expanded absorption bandwidths. The average absorption coefficient was 1.5 times higher in series MPPs and 1.2 times higher in single and parallel MPPs compared to the non-optimal state. In the optimal state, the series and parallel structures outperform the single design, and among the studied factors the hole diameter significantly influenced sound absorption more than others. The alignment of coefficients from various methods with RSM predictions was noteworthy. The results obtained from the FEM and ECM methods align perfectly, This study underscores RSM’s effectiveness, demonstrating optimization benefits and coherence between numerical, theoretical, and experimental models in evaluating MPP absorbers.

Equivalence and Similarity Refutation for Probabilistic Programs

We consider the problems of statically refuting equivalence and similarity of output distributions defined by a pair of probabilistic programs. Equivalence and similarity are two fundamental relational properties of probabilistic programs that are essential for their correctness both in implementation and in compilation. In this work, we present a new method for static equivalence and similarity refutation. Our method refutes equivalence and similarity by computing a function over program outputs whose expected value with respect to the output distributions of two programs is different. The function is computed simultaneously with an upper expectation supermartingale and a lower expectation submartingale for the two programs, which we show to together provide a formal certificate for refuting equivalence and similarity. To the best of our knowledge, our method is the first approach to relational program analysis to offer the combination of the following desirable features: (1) it is fully automated, (2) it is applicable to infinite-state probabilistic programs, and (3) it provides formal guarantees on the correctness of its results. We implement a prototype of our method and our experiments demonstrate the effectiveness of our method to refute equivalence and similarity for a number of examples collected from the literature.

Kinetostatics Modeling and Analysis of a Spherical Parallel Continuum Manipulator

Abstract In this paper, a spherical parallel continuum manipulator (SPCM) which is the flexible version of the 3-RRR“Agile Eye” mechanism is proposed and analyzed. The SPCM consists of three parallel flexible limbs, each limb is formed by compliant truncated cone elements, and the moving platform connects each limb with a passive revolute joint. Three servo motors are used to control the manipulator actively, and the spherical motion is realized by the coupled large deflections of the flexible links. An equivalent compliance analysis method of the element is developed based on finite element analysis and principal axis decomposition. By combining all three limbs, the kinetostatics model of the whole manipulator is derived, and a gradient iteration algorithm is developed to solve the forward and inverse kinetostatics. Finally, a prototype of the manipulator is constructed using 3D-printing technology, and the accuracy for element equivalence and end-effector characteristics is validated by experiments. The results show that the derived kinetostatics model can accurately describe the force–deflection behavior of the SPCM.

An equivalent target plate damage probability calculation mathematics model and damage evaluation method

Aiming at the requirement of damage testing and evaluation of equivalent target plate based on the explosion of intelligent ammunition, this paper proposes a novel method for damage testing and evaluation method of circumferential equivalent target plate. Leveraging the dispersion characteristics parameters of fragment, we establish a calculation model of the fragment power situation and the damage calculation model under the condition of fragment ultimate penetration equivalent target plate. The damage model of equivalent target plate involves the fragment dispersion density, the local perforation damage criterion, the tearing damage model, and the damage probability. We use the camera to obtain the image of the equivalent target plate with fragment perforation, and research the algorithm of fragment distribution position recognition and fragment perforation area calculation method on the equivalent target plate by image processing technology. Based on the obtained parameters of the breakdown position and perforation area of fragments on equivalent target plate, we apply to damage calculation model of equivalent target plate, and calculate the damage probability of each equivalent target plate, and use the combined probabilistic damage calculation method to obtain the damage evaluation results of the circumferential equivalent target plate in an intelligent ammunition explosion experiment. Through an experimental testing, we verify the feasibility and rationality of the proposed damage evaluation method by comparison, the calculation results can reflect the actual damage effect of the equivalent target plate.

Miura-ori based reconfigurable multilayer absorber for high-efficiency wide-angle absorption.

Radar stealth structures that can achieve high-efficiency wide-angle absorption are key components of future military equipment. However, it is difficult for both planar and three-dimensional (3D) absorbers to achieve efficient absorption in a large incidence angle range. The multilayer reconfigurable absorber component based on Miura origami provides a unique solution. First, the multilayer origami absorber is parameterized in the simulation software. Each origami structure is covered with resistive films that fit the panels. Geometric constraints are satisfied among the multilayer structures. They support reconfigurability in the range of continuous states (as opposed to discrete states), which is conducive to finding the folded state with a more efficient absorption rate within the frequency band. Secondly, the designed structure does not require a specialized mechanically supported multilayer origami absorber. In addition, the equivalent analogue circuit method is used to analyze the efficient absorption of multilayer origami under oblique incidence. Finally, our proposed absorber satisfies the requirements of multiple absorption metrics: broadband, high efficiency, wide incidence angle, and polarization insensitivity. As the validation, we simulated and fabricated a double-layer origami absorber. Our proposed origami absorber can maintain an absorption rate of more than 90% for both transverse electric (TE) and transverse magnetic (TM) polarizations in the operating frequency band (5-20 GHz) over a wide range of incidence angles (0°-70°). When the incidence angle qinc = 40°, the double-layer origami absorber (q1 = 90°, α1 = 60°, and a2 = 75°) can achieve at least 10 dB reflection reduction of -18 dB and -20 dB in TE and TM modes, respectively. The proposed origami absorber provides a reference for the design of other absorbers.

A method for calculating the time‐varying equivalent circuit parameters of large‐capacity synchronous condenser considering field mutual leakage reactance

AbstractAccurate calculation of equivalent circuit parameters is a prerequisite for accurately calculating the large‐capacity synchronous condenser parameter model. Due to its special transient operating conditions, the high transient magnetic saturation effect during operation causes the non‐linearity and time‐varying of the equivalent circuit parameters. The field mutual leakage reactance is the critical factor affecting the field current, and the time‐varying of the equivalent circuit parameters is closely related to the field current. However, the existing equivalent circuit parameter calculation methods considering field leakage reactance cannot achieve time‐varying parameters. A calculation method of time‐varying equivalent circuit parameters based on a back propagation neural network algorithm is proposed, which solves the calculation problem of time‐varying equivalent circuit parameters considering field mutual leakage reactance. Then, a 300MVar condenser is taken as the research object, and the proposed method is used to simulate the different operating conditions of the condenser and verified by the finite element method and experiment. The results show that the method improves the calculation accuracy of the equivalent circuit parameter model, reduces the calculation time, and applies to different operating conditions.

Potential of conservation tillage, cover crops, and digestate application as integrated C farming practices for processing tomato

Conventional soil management — based on intensive tillage and low input of organic material – negatively impacts soil quality via carbon (C) losses as carbon dioxide emissions (CO2), exacerbating the effect of climate change on agriculture. Carbon farming practices (CFPs), such as minimum tillage (MT) and strip tillage (ST), offer promising solutions to maintain soil fertility, sustain crop yields, and mitigate environmental impacts. However, applying CFPs in processing tomato (Solanum lycopersicum L.) cropping presents unique challenges due to specific crop and tillage characteristics. Our two-year field study investigated the effects of conservation tillage practices (i.e., MT and ST), both combined with cover crops and digestate application, on soil quality parameters and processing tomato yield. The field studies were conducted in fields with varying soil textures (i.e., clay and silty clay loam), and aimed to evaluate responses in terms of soil C sequestration, nutrient concentrations, soil structure, and abundance of earthworms. We hypothesized that both MT and ST would enhance soil quality parameters also in tomato cropping systems, with ST potentially outperforming MT in C sequestration. Results revealed that CFPs significantly increased soil organic matter, total nitrogen, and available phosphorous compared with conventional tillage. Both MT and ST increased soil C sequestration (up to 1.06 Mg C ha−1 y−1 and 1.21 Mg C ha−1 y−1, respectively) compared with conventional tillage (CT), which lost around 0.88 Mg C ha−1 y−1 under silty-clay loam soil, and had negligible C sequestration (+0.02 Mg C ha−1 y−1) under clay soil. We found no significant difference between MT and ST when using the equivalent soil mass method for calculating C sequestration. Noteworthy, CFPs enhanced fertility parameters without a negative impact on yields, underscoring their potential for enhancing soil C sequestration, improving nutrient availability, and supporting processing tomato yield under adaptation scenarios to climate change.

Mechanical Properties of Glass Plate During Anticlastic Cold Bending

Anticlastic glass surfaces play a significant role in free-form glass facades. For realizing anticlastic surface, cold bending by loading at the corner of the plate is more adaptive and more economic than traditional hot bending method. Previous research on anticlastic cold bending mainly focuses on the description of instability phenomenon and qualitative analysis of parameters. However, the failure mechanisms of glass plates during cold bending and the influence of lamination remains unclear. In this paper, the anticlastic cold bending test was conducted to explore the influence of various factors, including aspect ratio, scale and composition of the plates. Subsequently, an effective finite element model was established and validated by test results, which is used for further explore the cold bending controlling condition for better engineering practice. The failure modes are considered as instability and strength failure. For laminated glass, maximum stresses can be derived from monolithic glass based on equivalent thickness method. The instability is induced by the compression area in the middle surface of glass plate which is significantly influenced by the composition of the laminates. Consequently, thin glass laminates exhibit enhanced stability because a reduced glass to PVB thickness ratio changes the compression area from bi-directional to uni-directional.

A stochastic modeling method for three-dimensional corrosion pits of bridge cable wires and its application

ABSTRACT Cables have usually served as critical and vulnerable structural components in long span cable-supported bridges. Cable inspections revealed that corrosion, fatigue or coupled corrosion-fatigue were the ones of the main failure mechanisms. This paper proposed a stochastic modelling method for three-dimensional (3-D) corrosion pits of high-strength bridge wires, which can be applied to rapid fatigue life evaluation according to mass loss caused by surface corrosion pits of bridge wires nondestructively. High-strength steel wire specimens dismantled from the cable-stayed bridge served for 15 years were scanned to obtain the original surface corrosion data. The spatial position coordinate of corrosion pits were considered as random variable and can be well fitted by uniform distribution. While the number of corrosion pits can be fitted with generalized extreme value (GEV) distribution. The uniform corrosion depth du, which can be equivalent to mass loss rate, was calculated as the input corrosion parameter for 3-D corrosion pit modelling. The maximum pitting depth dmax for the steel wire was found to be associated with du. The geometric parameters for individual corrosion pits were recognized as pit depth d, depth-to-width ratio d/b, and aspect ratio b/a, which were fitted with different probability distributions. What follows is 3-D spatial corrosion pits simulation based on the individual corrosion parameter that were sampled and combined from the corresponding probabilistic distributions. Hereafter, fatigue life evaluation of corroded wires was conducted based on equivalent surface defect method and compared with the experimental results, verifying the effectiveness of the proposed modelling approaches.

Few-shot learning for COVID-19 chest X-ray classification with imbalanced data: an inter vs. intra domain study

Medical image datasets are essential for training models used in computer-aided diagnosis, treatment planning, and medical research. However, some challenges are associated with these datasets, including variability in data distribution, data scarcity, and transfer learning issues when using models pre-trained from generic images. This work studies the effect of these challenges at the intra- and inter-domain level in few-shot learning scenarios with severe data imbalance. For this, we propose a methodology based on Siamese neural networks in which a series of techniques are integrated to mitigate the effects of data scarcity and distribution imbalance. Specifically, different initialization and data augmentation methods are analyzed, and four adaptations to Siamese networks of solutions to deal with imbalanced data are introduced, including data balancing and weighted loss, both separately and combined, and with a different balance of pairing ratios. Moreover, we also assess the inference process considering four classifiers, namely Histogram, kNN, SVM, and Random Forest. Evaluation is performed on three chest X-ray datasets with annotated cases of both positive and negative COVID-19 diagnoses. The accuracy of each technique proposed for the Siamese architecture is analyzed separately. The results are compared to those obtained using equivalent methods on a state-of-the-art CNN, achieving an average F1 improvement of up to 3.6%, and up to 5.6% of F1 for intra-domain cases. We conclude that the introduced techniques offer promising improvements over the baseline in almost all cases and that the technique selection may vary depending on the amount of data available and the level of imbalance.

The dynamics and near‐optimal controls of a dengue model with threshold policy

In this paper, a piecewise smooth dengue model with threshold policy is developed, and the impacts of different control measures on the spread of dengue fever are also investigated. The number of dengue infections is used as a threshold level to determine whether to implement control, and control measures are triggered only if the number of infected individuals exceeds . Using the Routh–Hurwitz criterion, the dynamic behaviors of the free system and control system are studied. Then, the existence of the sliding mode is verified, and the sliding dynamics are analyzed by using the Utkin equivalent control method. It is shown that model solutions eventually converge to one of two endemic equilibria or the sliding equilibrium depending on . In addition, by using Ekeland's principle and maximum principle, the sufficient and necessary conditions for near‐optimal controls of this model are obtained. Finally, numerical simulations are carried out to explain and supplement the theoretical results.

Politeness in Language in Student Discussions at Akprind University Indonesia

Language politeness is a very important aspect in shaping students' language and character. Therefore, it is necessary to pay attention to aspects of politeness in language, so it is necessary to analyze any deviations and comply with the principles of politeness in language in discussions in the classroom. The method used in this research is a qualitative descriptive method. Data collection techniques use proficient free-involved listening techniques and note-taking techniques. Data analysis uses the practical equivalent method. Determining deviations and compliance with the principles of language politeness is based on indicators of language politeness with Leech's theory. The research results show that: 1) The maxims that are often violated in learning using the discussion method are: the maxim of generosity, the maxim of humility, and the maxim of agreement. 2) The maxim of that do not appear in learning using the discussion method are: the maxim of wisdom, the maxim of acceptance, and the maxim of sympathy. 3) The use of language in learning using the discussion method often uses inappropriate diction/word choices. 4) Language politeness in learning using the discussion method has not been fulfilled properly

Spatiotemporal Response of Ecosystem Service Value to Land Use Change in the Lanzhou-Xining Urban Agglomeration over the Past 20 Years

With rapid urbanization and human activities exacerbating threats to the degradation of various ecosystem services in modern urban agglomerations, the exploration of the state of ecological security at the scale of urban agglomerations is of great significance. This study considered the Lanzhou-Xining Urban Agglomeration as the research area, based on the land use data in 2000, 2005, 2010, 2015, and 2020. At the same time, the landscape ecological risk index was introduced. The land use change characteristics of the Lanzhou-Xining Urban Agglomeration were analyzed by using the land use transfer matrix, the value per unit area equivalent factor method, and the bivariate spatial autocorrelation analysis method to elucidate the impacts of the changes in the ecological risk index induced by the land use transition on the value of ecosystem services. This study analyzed the land use change characteristics of the Lanzhou-Xining Urban Agglomeration and elucidated the impacts of changes in the ecological risk index on the value of ecosystem services caused by land use transformation. The results showed that:① During the period from 2000 to 2020, the land use types of the Lanzhou-Xining Urban Agglomeration were mainly dominated by grassland, cropland, and forest land. The construction land area had expanded significantly mainly from cropland and grassland, and the six land use types had strong cross-transformation. The total area of land use change was 6 646.05 km2. ② In terms of spatial changes, the spatial pattern of ecosystem service value in the Lanzhou-Xining Urban Agglomeration had not undergone obvious transformation. However, the regional variability was significant, generally showing the distribution characteristics of high in the northwest and low in the southeast. ③From the perspective of temporal change, the value of ecosystem services in the Lanzhou-Xining Urban Agglomeration showed an upward trend, with the total flow of value increasing from 186.459 billion yuan to 192.156 billion yuan, with a total value-added of 5.697 billion yuan. ④ There was a rising trend in the overall ecological risk index of the Lanzhou-Xining Urban Agglomeration over the past 20 years. Low ecological risk areas and lower ecological risk areas dominated the ecological risk areas. There was a significant positive correlation between the value of ecosystem services and the ecological risk index. This study aimed to reveal the understanding of the impacts of land-use practices on ecosystem service values and ecological risks, to provide important references for regional ecological risk management and land-use policy formulation, and thus to promote the high-quality development of the ecological environment in the Yellow River Basin.

Gravity-driven close contact melting heat transfer in gradient latent heat storage units

Numerical modeling of efficient close contact melting (CCM) has been a significant challenge in phase-change heat transfer research. This work addresses this issue by developing a modified equivalent heat capacity method to construct a universal CCM model, considering physicals such as conduction, heat convection, and solid sinking. The enhanced heat transfer mechanism of CCM compared to conventional constrained melting (CM) in finned latent heat storage (LHS) units is investigated. The results reveal that the early stages of CM and CCM are dominated by heat conduction, while natural convection and mixed convection are induced in the late stage of CM and CCM, respectively. The CM and CCM performance is optimized under upward and downward flows, respectively. The complete melting time of CCM is reduced by a substantial 36.7% and 29.7% compared to CM for both downward and upward flow cases. The inlet temperature and volume flow rate are positively correlated with CM and CCM performance, but the effect of volume flow rates is smaller. The gradient fin maximizes melting performance at a height gradient of 1. Compared to the uniform layout, the complete melting time of CM and CCM in the optimized gradient LHS unit is reduced by 5.6% and 8.5%.

Fatigue Analysis of Composite Bolted Joints under Random and Constant Amplitude Fatigue Loadings.

This paper attempts to analyze the random fatigue life and failure modes of joints using two calculation methods. Three kinds of tests were carried out, which were the static test, constant amplitude fatigue test and the random fatigue test, and four kinds of joints were designed. After the static test, the joint was subjected to a constant amplitude fatigue test by selecting different percentages of load according to the static strength. In order to predict the random fatigue life more precisely, two calculation methods were carried out, which were the linear cumulative damage method and the equivalent loading finite element method. Based on the linear cumulative damage hypothesis, the fatigue life of the joint was established as a function of the load amplitude, and then, the random life prediction was calculated by the amplitude distribution of the random loading. Another method was the equivalent loading method, which was to obtain the equivalent constant amplitude fatigue loading of the random loading spectrum. The finite element model was established based on the stiffness and strength degradation rule. The equivalent random life and fatigue failure modes of the joint were modeled. The two life prediction methods show good agreement with the fatigue experimental result, and all prediction results were included in a scatter band of the factor of 2.

Research on size effects in the low‐velocity impact (LVI) and compression after impact (CAI) characteristics of composite laminates

AbstractThe load‐bearing capacity and failure characteristics of composite structures are closely related to their dimensions. In this study, low‐velocity impact, ultrasonic non‐destructive testing, and compression after impact tests were conducted on composite laminates of varying widths to investigate the influence of size effects. Distinct impact response profiles and compression failure modes were characterized. The results indicate that under impact loading, the delamination threshold load (6700 N ~ 7200 N) and the knee‐point energy (40 J) are not affected by width. However, variations in width lead to differences in indentation depth, impact duration, peak load, delamination characteristics, and energy absorption. Furthermore, increasing impact energy further magnifies these differences. Under compression loading, wider laminates exhibit lower residual strength, with the influence of impact energy on residual strength decreasing as width increases. Importantly, the observed compression failure deformation mode transitions from localized buckling to widespread sub‐layer delamination‐induced compression failure. This suggests that changes in width alter the governing mechanical mechanisms of CAI failure. Consequently, the use of a single‐size laminate to represent both LVI and CAI processes is not recommended. Based on experimental results, the reliability of the equivalent damage method in predicting the residual compression strength of laminates of different widths was confirmed, providing valuable insights for practical engineering applications.Highlights Assess the variations in the low‐velocity impact process of laminates with different widths. Evaluate the delamination damage of laminates after impacts by ultrasonic C‐scan techniques. Investigate the effect of variation in widths on the compression behavior of laminates after impact. Validate the feasibility of equivalent damage modeling for calculating residual strength.

An equivalent modeling method for coupling stiffness of metal braided sleeve based on hyper-elastic material function

Abstract Metal hoses are important connecting components in pipelines, used for compensation in length and vibration reduction in system. Due to the complex structure of the metal braided sleeve on the outer layer of the metal hose and the nonlinear stiffness caused by coupling with the metal corrugated pipe during the combination process, modeling and calculation are difficult. In this paper, an equivalent modeling method for the coupling stiffness of metal braided sleeve based on Hyper-elastic material function is proposed. The parameters of Hyper-elastic material function are obtained through experiments. Experiments and simulations show that this method has a high accuracy, which propose an efficient way to solve the problems in theoretical analysis and simulation modeling of metal hose.

Comparison of analytical and numerical methods for estimating notch strains**

AbstractIn fatigue assessments, local strains and stresses can be easily evaluated using accurate finite element analysis in a case of an individual fatigue‐critical notch or structural detail. In practical design and analysis of global models, the consideration of local notch effects using suitable estimation rules in the combination with linear elastic analysis is reasonable. Various notch rules exist but the current knowledge lacks understanding how applicable different notch rules are for estimating notch strains from elastic stresses. This work studies the Neuber′s rules for sharp and mild notches, Glinka′s equivalent strain energy density method, the correction of Neuber′s rule proposed by Sonsino for mild notches, as well as the Seeger‐Beste method. The application of different estimation rules for notch strains, applied to the elastic‐perfectly plastic steel material and to Ramberg‐Osgood material model for the aluminum material, including work hardening effect, was studied in this work by comparing the estimations with the corresponding experimental data and finite element analysis results. The Neuber′s rule for mild notches and Sonsino′s averaging method gave best correlations with the experimental data and numerical (finite element analysis) results and can be thus recommended for such analyses in compatible cases studied in this work.

Energy-based seismic design method for seismically isolated structures with friction pendulum systems

Friction pendulum systems (FPSs) serve as effective isolators that can help ensure adequate seismic performance of structures against significant aftershocks. A commonly used method for FPS design is the equivalent static analysis method outlined in ASCE 7-22. However, this method risks underestimating the seismic performance of FPSs due to its inability to account for energy dissipation from multiple hysteresis loops exceeding two cycles. Moreover, it is not well-suited for designing FPSs with conical friction surfaces, which exhibit nonlinear elastic behavior and hysteresis. A straightforward solution to address these issues is to apply an energy-based seismic design method. In this study, we propose and analytically validate one such method tailored for seismically isolated structures employing FPSs. Our analysis considers FPSs with both spherical (ISF) and conical (ICF) friction surfaces. For ISFs, the design follows the energy-based seismic design method proposed by Akiyama, whereas, for ICFs, it is based on the energy input to the device and its geometric approximation to an ISF. The conclusions of this study are summarized as follows: (1) the proposed energy-based design method effectively predicts the maximum FPS deformation, facilitating a rough estimation of FPS size; (2) because the design assumes symmetrical seismic response of the isolation layer in both the positive and negative directions and the friction surfaces of the ISF and ICF are geometrically similar, in the proposed method, the maximum deformation of an isolation layer with a natural period greater than 2 s depends solely on the friction coefficient, regardless of the friction surface type; (3) to satisfy the relevant conditions, the appropriate FPS design range is determined through nonlinear analysis. The results of this study demonstrate that the proposed energy-based seismic design method provides a reliable and effective means of designing FPSs for enhanced seismic performance.

Novel method for measuring surface residual stress using flat-ended cylindrical indentation

Instrumented indentation is a promising technique for estimating surface residual stresses and mechanical properties in engineering components. The relative difference between the indentation loads for unstressed and stressed specimens was selected as the key parameter for measuring surface residual stresses in flat-ended cylindrical indentations. Based on the equivalent material method and finite element simulations, a dimensionless mapping model with six constants was established between the relative load difference, constitutive model parameters, and normalized residual stress. A novel method for measuring the surface residual stress and constitutive model parameters of metallic material through flat-ended cylindrical indentations was proposed using this model and a mechanical properties determination method. Numerical simulations were conducted using numerous elastoplastic materials with different residual stresses to verify the proposed model; good agreements were observed between the predicted residual stresses and those previously applied in finite element analysis. Flat-ended cylindrical indentation tests were performed on four metallic materials using cruciform specimens subjected to various equibiaxial stresses. The results exhibited good conformance between the stress–strain curves obtained using the proposed method and those from traditional tensile tests, and the absolute differences between the predicted residual stresses and applied stresses were within 40 MPa in most cases.