Adjustment Coefficient Research Articles

Predicting asphalt mixture fatigue life via four-point bending tests based on viscoelastic continuum damage mechanics

A more technically accurate approach to predict fatigue life of asphalt mixtures can enhance the precision of performance evaluation for asphalt pavements. This study applied the viscoelastic continuum damage mechanics (VECD) to investigate the fatigue behavior of asphalt mixtures. The fatigue life of typical asphalt mixtures was evaluated through four-point bending tests under various conditions. The strain-modulus empirical equation was firstly employed to fit the experimental data. However, it was noted that this equation was not entirely suitable for all conditions, as factors like temperature and loading frequency can influence fatigue life not only through the dynamic modulus but also via the damage properties of asphalt mixtures. To address this limitation and achieve a comprehensive fatigue life prediction equation, the Time-Strain Superstition Principle (TSSP) and Frequency-Strain Superstition Principle (FSSP) were introduced to characterize the impact of temperature and loading frequency on fatigue life, which can reduce fitting errors. Additionally, a mechanical prediction equation was also derived by the VECD approach, and its applicability under different conditions was explored. The results revealed that the damage characteristic curve (C-S curve) remained unaffected by loading frequency and strain level but was highly dependent on temperature. Significant fitting errors were observed in different temperatures when employing the VECD method for fatigue life prediction, as the VECD method did not account for the influence of temperature on the viscoelastic properties of asphalt mixtures, which in fact plays a critical role in fatigue life. In response, temperature adjustment coefficients were introduced into the derived equation. The predicted results demonstrated that the newly modified method significantly improved prediction precision, yielding an error of less than 20%.

Business cycles, sectoral price stabilization, and climate change mitigation: A model of multi-sector growth in the tradition of the Bielefeld disequilibrium approach

Sectoral price stabilization is critical in the pressing context of de-globalization and the climate crisis. Strategic price controls may be effective in reducing economic volatility, but fail to curb emissions, unlike quantity controls such as rationing consumption. In contrast, carbon pricing may accelerate decarbonization, but generate inflationary pressures. In order to evaluate the effectiveness of sector-oriented policies in stabilizing sectoral prices and accelerating the low-carbon transition at the same time, this paper employs a novel environmentally-extended, data-driven dynamic model of multi-sector growth based on the Bielefeld disequilibrium approach to the microeconomic stability of competitive economies. The general composite model allows to empirically characterize the network structure and intensity of dynamic price-quantity interactions at the sector level, which capture heterogeneous firm behavior by integrating long-run Walrasian price and classical quantity dynamics coupled with short-run Keynesian features in the form of target rate of return pricing and demand-led investment. A Bayesian hierarchical model on US BEA data empirically estimates the linear adjustment coefficients and stable combinations are computed. The US economy is shown to feature a highly hierarchical network structure of intermediate production that is particularly vulnerable to micro-economic shocks driven by wars and climate change. Tax-subsidy schemes are shown to be the most effective in stabilizing sectoral prices and economy-environment interactions.

The Development of the Solution Search Method Based on the Improved Bee Colony Algorithm

Active digitization of people's daily life leads to the use of the decision making support systems (DMSS). DMSS is actively used in data processing, forecasting the course of various processes, providing informational support for the decision making process by decision makers. However, a number of problems arise while evaluating monitoring objects, namely: a large number of destabilizing factors affecting the efficiency of the processes of information collection, processing and transmission; high dynamism of changes in the state and composition of heterogeneous monitoring objects during the conduct of hostilities (operations); high dynamism of conducting hostilities (operations); the uncertainty of the initial situation and the noise of the initial data. In this article, a method of finding solutions based on an improved bee colony algorithm was developed. The efficiency of information processing is achieved by learning the architecture of artificial neural networks; taking into account the type of uncertainty of the information to be evaluated; the use of an improved algorithm of the bee colony, the use of an unordered linguistic scale of measurements with adjustment coefficients for the degree of awareness and the degree of noise of the initial data. An approbation of the use of the proposed method was carried out on the example of assessing the state of the operational grouping of troops (forces). The method is proposed to be used in the development of software for automated systems of control of troops and weapons, namely, in the modernization of existing and development of new automated systems of control of troops and weapons. The evaluation of the effectiveness of the proposed method showed an increase in the efficiency of the evaluation at the level of 21–28% in terms of the efficiency of information processing.

The use of global versus region-specific data for the prediction of co-seismic landslides

This study compares the impact of global and region-specific variables on the prediction of co-seismic landslides, investigating whether the incorporation of higher-resolution data into a global framework can improve the prediction outcome for regional landslide assessments. Based on a statistical landslide model, which was developed through logistic regression involving various global landslide inventories, the likelihood of a landslide occurring during an earthquake is estimated for a regional event. Using the recently updated landslide inventory of the 2016 MW7.8 Kaikōura earthquake (centroid of landslide source area), the prediction performance of the model is evaluated by individually replacing the global variables for slope, compound topographic index, lithology and land cover with New Zealand specific datasets that offer higher resolution and/or more accurate information. Statistical metrics are used to compare the changes in the prediction performance of each modification, while probability maps and binary prediction maps are evaluated to identify spatial differences. The results suggest that calculating the slope variable from a higher-resolution DEM (e.g., 25 m) improves the model's prediction performance without changing the model equation or replacing the other global variables. Other region-specific variables such as land cover show stronger correlation but require an adjustment of the model coefficients (e.g., regression analysis). As the region-specific datasets increase the landslide estimates, a sensible interpretation of the model results is important, including the identification of a probability threshold which allows for a binary prediction (landslide occurs versus landslide does not occur). Future research should investigate the role of global and region-specific datasets for other earthquake events and consider incorporating other variables (e.g., local slope relief). The findings demonstrate the limitations of global variables for regional landslide predictions and illustrate the impact as well as implications of region-specific datasets on the model outcome, providing a better understanding on how incorporating region-specific datasets into a global approach can improve the landslide prediction in areas where regional models are not available or where inventory data is not sufficient to develop a robust model.

Beyond visual range maneuver intention recognition based on attention enhanced tuna swarm optimization parallel BiGRU

This paper researches the problem of Beyond Visual Range (BVR) air combat maneuver intention recognition. To achieve efficient and accurate intention recognition, an Attention enhanced Tuna Swarm Optimization-Parallel Bidirectional Gated Recurrent Unit network (A-TSO-PBiGRU) is proposed, which constructs a novel Parallel BiGRU (PBiGRU). Firstly, PBiGRU has a parallel network structure, whose proportion of forward and backward network can be adjusted by forward coefficient and backward coefficient. Secondly, to achieve object-oriented adjustment of forward and backward coefficients, the tuna swarm optimization algorithm is introduced and the negative log-likelihood estimation loss function is used as the objective function, it realizes the dynamic combination of sequence guidance and reverse correction. Finally, the attention mechanism is used to obtain more useful information to improve the recognition accuracy. Through offline recognition experiment, it is proved that A-TSO-PBiGRU can effectively improve the convergence speed and recognition accuracy compared with GRU-related networks. Compared with the other six comparison algorithms, maneuver intention recognition accuracy also has significant advantages. In the online recognition experiment, maneuver intention recognition accuracy of A-TSO-PBiGRU is 93.7%, it shows excellent maneuver intention recognition ability.

Optimal Predictive Torque Distribution Control System to Enhance Stability and Energy Efficiency in Electric Vehicles

This article presents a novel approach to address the critical issues of stable rotation and energy efficiency in electric vehicles (EVs). To achieve these objectives, we propose a comprehensive control system that leverages the power of optimization through optimal predictive control methods. The central idea revolves around minimizing the predicted tracking error for future time steps by intelligently determining control inputs. In this innovative approach, we emphasize the dynamic adjustment of weight coefficients and optimization of wheel torque to strike a delicate balance between energy consumption and enhanced vehicle stability. The result is an adept controller that not only ensures vehicle stability but also significantly reduces energy consumption. Given the inherent limitations of electric motors, especially in terms of torque during vehicle operation, and the growing importance of energy conservation, our method tailors weight coefficients to generate optimal wheel torque. This ensures that the electric motors operate within their power range, thereby minimizing energy consumption and extending the overall efficiency of EVs. The combination of stable rotation and energy efficiency offered by this control system represents a promising step forward in the realm of electric vehicles, making them more sustainable and environmentally friendly while maintaining the high standards of performance and safety that consumers expect.

Flooding in the urban fringes: Analysis of flood inundation and hazard levels within the informal settlement of Kibera in Nairobi, Kenya

Overlapping conditions of rapid urbanisation and climate change across developing countries are threatening the capacity of cities to manage climate risks, especially in the flood-exposed low-income peripheral areas. Limited studies have applied hydrodynamic flood models in ascertaining flooding conditions, supportive of risk-informed decisions in such urban fringes. Against this backdrop, we assessed plausible flooding and hazard conditions in the low-lying villages of Lindi and Silanga in Kibera informal settlement. The coupled one-dimensional and two-dimensional hydrodynamic model, customised from the Hydrological Engineering Centre's River Analysis System (HEC-RAS) was parameterised for flood simulation under different hydrological regimes and scenarios associated with flooding in Kibera. Volumetric flow estimates and a computed energy slope were used to define the upstream and downstream modelling boundary conditions respectively. Trial-and-error adjustment of the flow resistance coefficients from land-use features was applied in model calibration, and the results compared to the surveyed flood of 23rd April 2019. Results show that proximal areas to the Ngong River and Nairobi dam face high flood risks. A flood volume of 11.7×105m3 from a 2.5h, 50 mm rainfall could potentially inundate about 2.0% and 8.3% of areas in Lindi and Silanga respectively, while a volume of 48.9×105m3 from a 100-year storm of 172 mm could inundate about 10.6% of Lindi and 29.1% of Silanga. Upstream steeply sloping topographies of the villages increase flood velocities and risk of drowning, while the lower reaches at relatively flatter topographies, experience attenuated flow and rapid accumulation of flood waters, hence, higher flood depths. These results can support policy interventions for integrated flood risk management in Kibera, as a way of mainstreaming the underserved urban communities in climate risk management.

Damage detection in variable temperature conditions using artificial intelligence

When considering damage detection using the natural frequencies of structures, small frequency drops can indicate either the presence of cracks or a temperature change. This change can lead to additional stress affecting the modal parameters for specific structures, making it much harder to detect, locate, and evaluate damage accurately. The current research aims to describe a method for detecting transverse cracks in beams, considering temperature variations. The considered beam is fixed at both ends, thus inducing axial forces when the temperature is increased. The influence of temperature is considered using adjustment coefficients developed for each vibration mode. This coefficient can be used to accurately calculate the natural frequency for an intact or damaged beam. An analytical method for determining the natural frequencies caused by the changing temperature and the presence of a transverse crack is described and used to generate data for training a feedforward artificial neural network (ANN). The ANN’s capability of determining the position of transverse cracks in double-clamped beams subjected to small temperature changes is proven by creating numerical simulations with known crack positions and thermal conditions for testing the developed method.

Adaptive droop control strategy of parallel LLC converters

AbstractWhen the resonant converters are connected in parallel, the output current is unbalanced without additional current‐sharing measures due to differences in resonant component. In the input‐parallel output‐parallel resonant converter system, the output voltage accuracy of the converter under the traditional droop control is analyzed when the load changes. In this paper, an adaptive droop control is proposed, in which the droop coefficient is adaptively adjusted as the load changes. The control method proposed in this paper realizes the current sharing between the converters and solves the shortcomings of the output voltage changing under different loads in the conventional droop control. Taking two parallel LLC converters as an example, the control block diagram of the parallel control method for adaptive adjustment of the droop coefficient proposed in this paper is given, and the stability of the control loop is analyzed. Finally, two parallel prototypes of LLC converters with input 200 V/output 24 V input are built by digital control, and the experiment shows that the proposed control method improves the shortcomings of excessive output voltage droop caused by traditional droop control during dynamic load switching, which verifies the effectiveness of the method.

AlSb/ZrS2 heterojunction: A direct Z-scheme photocatalyst with high solar to hydrogen conversion efficiency and catalytic activity across entire PH range

Using the First principles method, the electrical, optical, and photocatalytic characteristics of AlSb/ZrS2 van der Waals heterojunctions (vdwH) with direct Z-scheme photogenerated electron transfer mechanism were calculated in this study. The inherent type-II band structure, the built-in electric field that facilitates photogenerated carrier separation, and the high mobility of electrons and holes along the x and y axes all contribute to the strong photocatalytic activity. Furthermore, the AlSb/ZrS2 van der Waals heterojunction has better light absorption performance than monolayers, with a light absorption coefficient of 4.7 × 105 cm−1 at 500 nm and a solar to hydrogen efficiency of 25.81%. Meanwhile, the breakdown reaction of heterojunctions for water can be spontaneously reacted under the light, according to the free energy calculations of the Hydrogen Evolution Reaction (HER) and Oxygen Evolution Reaction (OER) processes. Unexpectedly, adding biaxial strain to the heterojunction allows for effective band gap and light absorption coefficient adjustments. and the photolysis reaction of water can be realized in the whole PH range within a suitable strain range. The AlSb/ZrS2 van der Waals heterojunction is expected to be a promising candidate for Z-scheme heterojunction photocatalysts for the whole hydrolysis in the future.

Bio sorption of textile dyes from aqueous solution onto three different pine barks: kinetics and isotherm studies

The main objective of the present study is to evaluate the sorption capacities of some natural raw materials of vegetable origin for the treatment of the sewage coming from the textile industry. The selected barks are: maritime pine (MP), pine pinion (PP) and Aleppo pine (AP) bark. The effectiveness of these barks was evaluated in the removal of three dye; rhodamine B (RhB), Green Malachite (GM) and Methyl Orange (MO). Initially, the effects of some parameters such as the nature of the adsorbents, the nature of the dyes and the pH were studied. Obtained results reveals that the speed sorption is strongly influencing by the pH medium and the comparative study shows that the adsorption is favourable in the acidic medium with a sorbed amount of (Q=40mg/g) for rhodamine B. The results of the biosorption kinetics reveal that the GM molecules are better biosorbed (Q=48 mg/g) than those of RhB (Q=46 mg/g) and methyl orange (Q=18mg/g), with an equilibrium time of 6 hours. The results of the biosorption isotherms show clearly that the maritime pine bark is the most effective biosorbents with sorbed amount of (QRhB=200mg/g) and (QMO=88mg/g) followed by pignon pine (PP) with (QRhB=184mg/g) and (QMO=56mg/g) and finally Aleppo pine (AP) bark with (QRhB=131mg/g) and (Qmo=46mg/g). All obtained isotherms are modeled using the Langmuir and Freundlich models. According to the adjustment coefficient values R2, corresponding isotherms are well represented by Freundlich model.

Combined Use of Enhanced Coefficient Adjustment Technique and Module-based Substitution to Hide Secret Message in ECG Signal

Combined Use of Enhanced Coefficient Adjustment Technique and Module-based Substitution to Hide Secret Message in ECG Signal

Ecological and economic assessment of sustainable spatial land management in the context of global climate change: economic and mathematical modeling

This article emphasises that the degree of anthropogenic (ecodestructive) impact on the state of agricultural production is the main criterion for assessing the development of sustainable spatial land management under certain ecological and economic constraints. The aim of the study is to model the ecological and economic assessment of the transformation of the territorial-spatial management of agricultural land at different levels of management, taking into account the impact of anthropogenic (ecodestructive) factors to ensure sustainable land use in the context of global climate change. Thus, the methodology of territorial-spatial analysis of the efficiency of transformation of modern agricultural land use and use of land and resource potential is aimed at determining its holistic assessment as a systemic and complex phenomenon. An economic-mathematical model for calculating the optimal structure of sown areas by placing crops between production structures of different levels of management, taking into account their susceptibility to the action of a particular ecodestructive (anthropogenic) factor, is proposed. The allocation of agricultural production based on the presented model implies redistribution of production of certain types of products, taking into account minimisation of economic losses from anthropogenic (ecodestructive) factors, in particular, industrial air pollution. The paper considers the possibilities of quantifying the economic consequences of climate change in the system of agricultural land use. It is proved that the assessment of economic losses from climate change in the system of sustainable agricultural land use requires the development of a system of cost standards that correspond to the input climate parameters. This article presents natural indicators and regional adjustment coefficients of agricultural production in case of an increase in the average annual air temperature by one degree, with differentiation by regions of Ukraine. An algorithm for economic assessment of the impact of changes in the thermal regime of the atmosphere on the efficiency of the crop production industry is presented. The proposed modelling of the territorialspatial improvement of agricultural land use efficiency is a methodological approach to assessing the environmental consequences of transforming the efficiency of management in agriculture in terms of reducing and preventing economic losses from anthropogenic (ecodestructive) factors in the context of global climate change. So, the practical implementation of the presented methodological approach to the economic assessment of the impact of global climate change on agriculture will allow to substantiate recommendations for the formation of a system of actions that would allow to avoid or at least reduce the negative climate impact.

Stability and sensitivity characteristic analysis for the hydropower unit considering the sloping roof tailrace tunnel and coupling effect of the power grid

This paper focuses on the stability and dynamic characteristics of the coupled system of nonlinear hydraulic turbine regulating system (HTRS) and power grid (PG). By establishing a nonlinear mathematical model considering the downstream surge chamber and sloping roof tailrace tunnel, the coupling effect and influence mechanism between the hydropower station and power grid are revealed. First, with regard to the coupled system, HTRS considering downstream surge chamber and sloping roof tailrace tunnel and PG model is established. Then, dynamic performance of the coupled system is investigated based on the nonlinear mathematical model as well as Hopf bifurcation theory and validated by numerical simulation. Meanwhile, the impact mechanism of HTRS and PG is revealed by investigating dynamic characteristics. In addition, stability is studied by using eigenvalue method according to the Jacobian matrix of the coupled system. Finally, parameter sensitivity is investigated to quantify parameter effects on system performance. The experimental results indicate that bifurcation line divides the whole proportional–integral adjustment coefficient plane into two parts and the region at the bottom of bifurcation line is stability region. HTRS and PG possess a coupling effect on stable domain and dynamic properties of the coupled system. The variation of HTRS parameters is most significant for the coupled system, especially for the inertia time constant of the hydraulic turbine unit and penstock flow inertia time constant.

Mixed Bayesian Network for reliability assessment of RC structures subjected to environmental actions

Under environmental action, reinforced concrete (RC) structures might suffer from reinforcement corrosion caused by the surrounding environment, dramatically reducing structural reliability and threatening social development. However, most of the existing reliability assessment methods for RC structures only focused on the structural performance at the design stage given the original unchanged environment, ignoring the effects of realistic exposure conditions and inspection results on reliability evaluation. Thus, this paper develops a general reliability assessment framework based on a Mixed Bayesian network (MBN), incorporating three modules, i.e., durability assessment, load-bearing capacity analysis, and time-dependent reliability analysis. In MBN, separate sub-BNs are built based on different modules and connected by pinch point variables where probabilistic information is transmitted via soft evidence. Besides, this framework considers time-dependent environmental parameters and two-dimensional chloride transport and their effects on reliability. Meanwhile, adjustment coefficients are applied to improve the results of the analytical mechanical model with respect to different limit states through the finite element model (FEM). The proposed MBN framework is illustrated for a corroded RC beam under a marine atmospheric environment to investigate the effects of environmental modeling, chloride transport patterns, and concrete crack inspection on reliability assessment. The results indicate that under the assumed conditions in the case study, early inspection of large cracks may significantly overestimate the failure probability by about 500%. Besides, failure probability might be underestimated by about 95%, ignoring the time-variant environment and two-dimensional chloride transport.

Kriging-boosted CR modeling for prompt infill drilling optimization

The capacitance-resistance model (CRM) has been a useful physics-based tool for obtaining production forecasts for decades. However, the model's limitations make it difficult to work with real field cases, where a lot of various events happen. Such events often include new well commissioning (NWC). We introduce a workflow that combines CRM concepts and kriging into a single tool to handle these types of events during history matching. Moreover, it can be used for selecting a new well placement during infill drilling. To make the workflow even more versatile, an improved version of CRM was used. It takes into account wells shut-ins and performed workovers by additional adjustment of the model coefficients. By preliminary re-weighing and interpolating these coefficients using kriging, the coefficients for potential wells can be determined. The approach was validated using both synthetic and real datasets, from which the cases of putting new wells into operation were selected. The workflow allows a fast assessment of future well performance with a minimal set of reservoir data. This way, a lot of well placement scenarios can be considered, and the best ones could be chosen for more detailed studies.

Ferroelastic rare‐earth tantalates for multifunctional thermal/environmental barrier coatings: A perspective

AbstractThis perspective outlines the research directions of ferroelastic rare‐earth (RE) tantalates (RETaO4), which have been studied as multifunctional thermal/environmental barrier coatings (T/EBCs) with working temperatures above 1600°C. Ferroelastic RETaO4 ceramics exhibit several distinct features, including the reversible second‐order ferroelastic phase transition, high toughness, low thermal conductivity, low oxygen ion conductivity, and adjustable thermal expansion coefficients. This perspective provides a concise summary of the research progress on tantalate coatings synthesized via air plasma spraying and electron beam physical vapor deposition. The service performance of tantalate coatings is typically evaluated through thermal fatigue and shock measurements. Uncovering the failure mechanisms and understanding influencing factors are key aspects for future studies. In this regard, establishing the synthesis‐structure‐property relationship of RETaO4 coatings is essential. This brief perspective can serve as a guide for future work on RETaO4 coatings and further advancements in their applications across various fields, including aviation engines and gas turbines.

Case study: The Adjusted Valuation of the High-tech Newly-listed Company in Mainland China

Given the enormous contribution of high-tech startups to social development, a systematic approach to accurately evaluate these companies is significant for venture capital firms, equity investors, and other investors in the market. However, the conventional methods, including the cost and income approaches, cannot fulfill the valuation goal without any development due to the insufficient financial information and future uncertainty of these firms. This paper investigates a new valuation method that combines the beta coefficient adjustment and future cash flow scenario discussion. This newly established method is employed to value one of the most influential newly listed semiconductor firms: Semiconductor Manufacturing International Corporation in mainland China. If this new combination works well for firms under such circumstances, analytics could apply similar ideas to handle the lack of historical data and uncertainty of future cash flows.

Service Function Chaining to Support Ultra-Low Latency Communication in NFV

Network function virtualization (NFV) has the potential to fundamentally transform conventional network architecture through the decoupling of software from dedicated hardware. The convergence of virtualization and cloud computing technologies has revolutionized the networking landscape, offering a wide range of advantages, including improved flexibility, manageability, and scalability. The importance of network capability in enabling ultra-low latency applications has been greatly amplified in the current era due to the increased demand for emerging services such as autonomous driving, teleoperated driving, virtual reality, and remote surgery. This paper presents a novel and efficient methodology for service function chaining (SFC) in an NFV-enabled network that aims to minimize latency and optimize the utilization of physical network resources, with a specific focus on ultra-low latency applications. In our proposed methodology, we offer flow prioritization and an adjustable priority coefficient factor (µ) to reserve a portion of physical network resources exclusively for ultra-low latency applications in order to optimize the deployment paths of these applications further. We formulate the SFC deployment problem as an integer linear programming (ILP) optimization model. Furthermore, we propose a set of heuristic algorithms that yield near-optimal solutions with minimal optimality gaps and execution times, making them practical for large-scale network topologies. Performance evaluations demonstrate the effectiveness of our proposed methodology in enabling ultra-low latency applications in an NFV-enabled network. Compared to existing algorithms, our proposed methodology achieves notable enhancements in terms of the end-to-end delay (up to 22 percent), bandwidth utilization (up to 28 percent), and SFC acceptance rate (up to 13 percent).

Effect of Cu Doping on Phase Transition, Thermal Strain, and Thermal Expansion Property in Polycrystalline Ni50Mn23−xCuxGa27 Alloys

The influence of Cu doping on phase transition, thermal strain, and thermal expansion property of polycrystalline Ni50Mn23−xCuxGa27(x = 1, 3, 5, 6 and 7) alloys is investigated. The results show that with increasing Cu concentration, martensitic transformation gradually gets close to Curie transition. A magnetostructural transition (MST) is observed in samples with x = 6 and 7. Such MST can enhance magnitude of transformation strain. Besides, Ni50Mn23−xCuxGa27 alloys possess an isotropic, recoverable, and thermally stable thermal strain. Excitedly, Cu doping can effectively tune the phase transition, thermal strain, and thermal expansion properties of Ni50Mn23−xCuxGa27 alloys. Adjustable coefficients of thermal expansion from positive to negative are obtained by Cu‐doped Ni50Mn23−xCuxGa27 alloys. The average linear expansion coefficient (α) between −140.44 and −207.70 ppm K−1 is observed in samples with x = 6 and 7 for a narrow temperature span of 11–14 K. When the temperature span is about 72 K (x = 6) and 73 K (x = 7), which is the largest temperature span observed in Ni–Mn–Ga‐based alloys recently, the α values decrease to about −36 ppm K−1. These findings are beneficial for manipulating the thermal expansion property of Ni–Mn–Ga–Cu alloys and their multifunctional applications.