Skip to main content

A modified NARX approach for evaluating the time history effect of climate change on load combination in designing façade structures


In recent years, researchers, designers, and project owners have deemed the dry facade system to be a suitable option. Consequently, much research has been conducted on the structural behavior of the dry facade system when subjected to seismic loads, climate change, thermal loads, etc. Of particular concern is the destructive phenomenon of corrosion due to climate change in coastal areas which can damage the infrastructure of the dry façade. To address this issue, a modified NARX method was employed in this study to predict climate change variables for use in dry facade analysis. The author of this paper developed a flowchart and subroutines in MATLAB as a new toolbox for this purpose. Temperature was identified as the most influential parameter in consequent configurations and was thus considered in load combination for the design of a dry facade structure. The statistical results obtained from NARX showed good agreement with measured data; specifically, there was a low mean absolute error (MAE) of 0.345 °C, a low root-mean-square error (RMSE) of 0.442 °C, and a high coefficient of determination (R2) of 0.998 (P-value = 0.918 > 0.05). Finally, this study proposed a modified formula for load combination to ensure durability and constructability of dry facades in coastal cities.


The global success of dry facade systems in the last decade has been attributed to several advantages, such as their lightweight, durability, and fast construction [1]. This system consists of a cold-formed structure (CFS) that is covered with suitable elements as a building façade [2]. However, climate change poses a significant risk to the safety and performance of dry facade systems. Recent assessments have reported that climate change is having a major impact on light and dry facade systems [3-5]. Unfortunately, there is limited information and fundamental research on adapting to climate change in the construction industry [6]. In buildings designed to meet current standards, future maintenance costs will likely increase significantly due to the effects of climate change. To ensure current and future structures are able to withstand changes in wind speed, severe weather events, temperature fluctuations, rainfall patterns, and relative humidity levels, it is necessary to amend building codes accordingly. The building sector appears to be particularly vulnerable to the challenges posed by climate change, particularly global warming [7]. At the international level, however, due to a lack of effective work codes, limited progress has been made in assessing the preparedness of construction companies for this issue [6]. Moreover, in the dry façade design process, proper attention must be paid to corrosion as an important parameter in climate change [8]. Corrosion of offshore structures is inevitable due to the corrosiveness of seawater which has a significant impact on their strength and reliability [9]. Environmental effects can reduce material properties due to wave climate change and marine corrosion, pitting corrosion is particularly dangerous as it is a time-dependent mechanism [10]. The dry façade as a structural system is prone to corrosion and temperature changes, thus, changes in humidity can lead to its deterioration, especially in dry climates in tropical and coastal areas [11]. Design codes that take into account both local weather conditions and future change scenarios should be considered. These guidelines can be an important step towards a more proactive and dynamic approach towards ensuring high-quality production processes and creating a sustainable environment [12]. The consideration of a local climate that makes the dry facade resistant to future climate change is an important factor in building code [13]. In this regard, the load combination for the allowable stress design and strength design method [14] for the dry façade system was modified in this study to account for the impact of climate change. Specifically, the NARX method was employed to predict temperature using Ws, Td, RH, Tmin, and Tmax. Temperature, relative humidity, and dew point were identified as primary causes of barley corrosion [11]. Thus, in order to prevent future construction failure due to tangible climate change, it is suggested that activists and researchers in the construction industry consider this method when designing all aspects of construction in coastal areas. Consequently, a modified load combination with respect to the dry facade was proposed taking into account climate change variables.


Applying NARX results to the design process

Recently, artificial neural network (ANN)-based models have attracted researchers in various fields of construction due to their ability to obtain nonlinear relationships between inputs and outputs. Different ANN-based methods have been successfully applied to a variety of problems, such as flood [15], rainfall [16], water quality [17], and air temperature [18]. To address some of the issues associated with common ANN approaches, nonlinear autoregressive neural network with exogenous input (NARX was evaluated. NARX with recurrent dynamic networks has feedback connections with multiple different layers. The NARX model is a modification of the ARX model commonly used in time-series modeling [19]. The forward and backward processes between layers were designed for the NARX approach to make a multifaceted effort in simulating data [20]. The general structure of the NARX network is given by Eq. (1) [21]:

$$\mathrm{y}(\mathrm{t}) =\mathrm{ f}(\mathrm{y}(\mathrm{t}-1),\mathrm{ y}(\mathrm{t}-2), \dots ,\mathrm{ y}(\mathrm{t}-\mathrm{ny}),\mathrm{ u}(\mathrm{t}-1),\mathrm{ u}(\mathrm{t}-2), \dots ,\mathrm{ u}(\mathrm{t}-\mathrm{nu}))$$

where y(t) is the predicted output trained based on the existing target value as the final network result [19, 22]. The specifications of the NARX model used in this study are summarized in Table 1. Figure 1 illustrates the flowchart steps of the study.

Table 1 NARX model specifications
Fig. 1
figure 1

Main flowchart of this study

First, in order to assess the impact of climate change, it is necessary to determine the project plan according to climate change policies. Subsequently, data on climate change variables must be collected from reliable sources for 365 days for the considered cities. The input and output data were then categorized into three scenarios and analyzed using the NARX method to predict the ideal temperature based on the history of temperature. To account for temperature in load combination evaluation, the predicted temperature was replaced with a “T” term in the equation. This resulted in an improved load combination equation. Finally, after producing materials based on this equation, it must be determined whether they meet the criteria of climate change, and if not, reforms and problem-solving measures must be taken.

Common load combinations for the design process are outlined in Table 2.

Table 2 Load combination formula based on ASCE

By substituting the temperature predicted from this step into the load combination equation, an improvement in the load combination equation can be achieved. Finally, after producing materials based on this step, it is necessary to ascertain whether they meet the criteria of climate change. When interpreting future weather forecasts, numerous uncertainties must be taken into account.

Climate change scenarios

Climate change scenarios are utilized to explore how the future will develop under a variety of alternative conditions or how to attain optimal results and avert unfavorable outcomes [23, 24]. Narrative descriptions of future events or weather patterns can be incorporated into the scenarios to enhance the consideration of extreme events [25]. Numerous uncertainties must be taken into account when interpreting future weather forecasts. On the other hand, to mitigate the effects of climate change on buildings, regional climate change must be taken into consideration [7]. Therefore, in this study, three scenarios were proposed with nine configurations. Scenario 1 included Ws, RH, Td, Tmin, and Tmax as input data and T as output data. Relative humidity was chosen as the target, and Ws, T, Td, Tmin, and Tmax were selected as inputs in scenario 2. In scenario 3, Ws, T, RH, Tmin, Tmax, and Td were chosen as inputs and output data, respectively.

Four statistical metrics were utilized in this study to evaluate the performance of the NARX model in predicting targets. These metrics include the mean absolute error (MAE), root-mean-square error (RMSE), correlation coefficient (R2), and P-value. These criteria are commonly used statistical measurements to assess the accuracy of predictive models, as noted by Bateni, Vosoughifar, and Ek et al. [26].

$$MAE=\frac{1}{N}\sum\nolimits_{i=1}^{N}\left|{O}_{i }- {P}_{i}\right|$$
$$RMSE=\sqrt{\frac{\sum_{i=1}^{N}{({O}_{i }- {P}_{i})}^{2}}{N}}$$
$${R}^{2}=\frac{\sum_{i=1}^{N}{({O}_{i }- \overline{O })({P}_{i}- \overline{P })}}{\sqrt{\sum_{i=1}^{N}{({O}_{i}- \overline{O })}^{2} \sum_{i=1}^{N}{({P}_{i}- \overline{P })}^{2}}}$$

The P-value is a probability measure that ranges from 0 to 1. When this value falls below 0.05, it indicates a significant difference between two data sets [27, 28].

Case study

This study focuses on several case studies in coastal cities to evaluate the impact of climate change on dry facades. Figure 2 a, b, and c depicts the selected coastal cities for analysis purposes. The number of meteorological stations in Western Australia, California, and Iran is two, eighteen, and nine, respectively. Daily weather data from these stations were obtained from sources such as evapotranspiration for Western Australia [29], CIMIS for California [30], and I.R. of Iran Meteorological Organization (IRIMO) | E-Library [31] for Iran to obtain the best climate change scenarios.

Fig. 2
figure 2

The location of case studies. a Australia. b California. c Iran

Table 3 summarizes the mean value and standard deviation of each selected station’s climatic data for analysis purposes.

Table 3 The mean (μ) and standard deviation (σ) values were calculated for each selected coastal station

Table 4 summarizes the geographical locations of the selected weather stations [32].

Table 4 The geographical locations of the selected weather stations

Temperature consideration is a crucial parameter in the dry façade design process. To establish a suitable load combination relation in the design of the dry façade structure, nine configurations were considered. Table 5 presents the selected configurations as scenarios of climate change.

Table 5 Configurations of climate change

To illustrate the input and output data distribution based on time history, Figs. 3, 4, 5, 6, 7, and 8 depict wind speed (Ws), relative humidity (RH), minimum temperature (Min T), maximum temperature (Max T), dew point temperature (Td), and temperature (T), respectively.

Fig. 3
figure 3

Wind speed based on 365 days from various stations

Fig. 4
figure 4

Mean of relative humidity based on 365 days from various stations

Fig. 5
figure 5

Minimum of temperature based on 365 days from various stations

Fig. 6
figure 6

Maximum of temperature based on 365 days from various stations

Fig. 7
figure 7

Temperature of dew point based on 365 days from various stations

Fig. 8
figure 8

Mean of temperature based on 365 days from various stations

Results and discussions

NARX relation

Temperature, relative humidity, and dew point temperature were trained using the NARX approach. Figure 9 displays the scatter plot between observed and predicted data for training, testing, and validation processes in scenario 1. Figures 10 and 11 show these processes for scenarios 2 and 3, respectively.

Fig. 9
figure 9

Scatter plot of training, testing, validation steps, and all data for scenario 1

Fig. 10
figure 10

Scatter plot of training, testing, validation steps, and all data for scenario 2

Fig. 11
figure 11

Scatter plot of training, testing, validation steps, and all data for scenario 3

It is evident from Figs. 9, 10, and 11 that configurations 1 through 3 and configurations 7 through 9 provide the closest predictions to the target. These configurations exhibit the highest level of agreement in the vicinity of the 45° line. Conversely, scenario 2, which encompasses configurations 4 to 6, demonstrates the poorest agreement within this region. Figure 12 illustrates the number of epochs versus fitness values (RMSE) for configurations 1 through 9.

Fig. 12
figure 12

Number of epoch versus fitness value (RMSE) for all configurations

The findings presented in Fig. 10 indicate that the endeavor to attain optimal data with minimum RMSE in configurations 1, 2, 3, 7, 8, and 9 is superior to that of other configurations. Configuration 2 specifically displays a low RMSE value of only 0.442 °C and boasts superior accuracy when compared to other configurations. Statistical metric values for all configurations are provided in Table 6.

Table 6 Statistical analysis of training, testing, and validation across all configurations

In configuration 2, the mean absolute error (MAE) and root-mean-squared error (RMSE) are both low, at 0.345 °C and 0.442 °C, respectively, while the coefficient of determination (R^2) is high at 0.998. The comparison based on P-value indicates that there are no significant differences between data, with a P-value of 0.894 which is greater than the significance level of 0.05. In scenario 2, configuration 5 stands out as the best option with a low MAE of 3.333% and RMSE of 3.907%, high R^2 of 0.977, and a P-value of 0.95 which is also greater than the significance level of 0.05. In scenario 3, configurations 7 to 9 exhibit accuracy levels similar to those in scenario 1. However, configuration 8 stands out with a low MAE of 0.734 °C and RMSE of 0.976 °C, high R^2 of 0.986, and a P-value of 0.344.

Sensitivity analysis

This study employed sensitivity analysis to evaluate the impact of each input variable on temperature (T), relative humidity (RH), and dew point temperature (Td). The aim was to determine the relative importance of each input variable including wind speed (Ws), RH, minimum temperature (Tmin), maximum temperature (Tmax), Td, and T on three different configuration scenarios with three targets. Each sensitivity test involved varying only one input variable at a constant rate while observing its influence on T, RH, and Td at constant rates ranging from 5 to 20%. Equation 5 was used to obtain target sensitivity values by changing input variables’ values at different rates. Overall, this study provides valuable insights into the impact of input variables on T, RH, and Td, which can inform the development of more accurate weather forecasting models.

$${\mathrm{Sensitivity\ of}\ Target}_{conf.}=\frac{1}{\mathrm{N}}\sum\nolimits_{\mathrm{i}=1}^{\mathrm{Nt}}\left(\frac{\mathrm{\%Change\ in }\ {Target}_{conf.}}{\mathrm{\%\ Change\ in\ the\ input\ variable}}\right)\times 100$$

A sensitivity analysis was conducted to evaluate the relative importance of each input variable on the issue of climate change, as reported by Bateni, Vosoughifar, and Truce et al. [33]. Figure 13 presents the sensitivity analysis when T is the target variable, and Ws, RH, Tmin, Tmax, and Td are considered as inputs. Similarly, Fig. 14 illustrates the sensitivity analysis when RH is the target variable and Ws, T, Tmin, Tmax, and Td are considered as inputs. The results of sensitivity analysis when Td was selected as the target variable are presented in Fig. 15. Sections a, b, c, and d in Figs. 13, 14, and 15 depict an increase of 5%, 10%, 15%, and 20% in each input variable.

Fig. 13
figure 13

Sensitivity analysis chart for configuration scenario 1

Fig. 14
figure 14

Sensitivity analysis chart for configuration scenario 2

Fig. 15
figure 15

Sensitivity analysis chart for configuration scenario 3

The findings from Fig. 13 indicate that RH and Td have the most significant impact on temperature. Specifically, RH decreases with increasing T while being inversely related to it. This relationship is evident in scenario 2 of Fig. 14 where T decreases with increasing RH due to their inverse relationship. Conversely, Td increases with increasing RH while being directly related to it. In contrast, Fig. 15 reveals that Rh and Tmax have the most significant impact on dew point temperature. Specifically, Rh and Tmax increase with increasing Td while being directly related to it.

The issue of climate change has been recognized as a crucial factor in the creation of construction quality, particularly in coastal areas, with a significant impact on occupational health and safety. Neglecting the effects of climate change can result in destructive consequences on the building’s facade. Despite this, limited international efforts have been made to evaluate the preparedness of consulting and construction companies to adapt to climate change risks. One potential danger that may lead to the destruction of dry facades is the lack of consideration for climate change variables during the design process. The corrosion of steel elements due to relative humidity and temperature changes within a facade system can cause damage that negatively affects structural performance. To address this issue, this study selected corrosion as an important factor and utilized it as input data to consider this phenomenon within the appropriate network target. The NARX method was employed to establish a relationship between climate change data variables and their application in dry facade design. The proposed network presents a novel method for predicting temperature data in conjunction with other important variables, which can be applied to dry façade loads. One of the most critical aspects of designing a dry facade structure is determining load combinations. In traditional research and design, temperature is typically considered as the average of historical data in load combinations. However, this study recommends a modified temperature term to be included in the load combinations. This modified NARX approach offers an innovative solution for evaluating the impact of climate change on load combination in designing façade structures. By incorporating historical temperature data and other relevant variables, designers can more accurately predict future load combinations and ensure that their structures are resilient to changing environmental conditions. This paper presents a detailed analysis of the proposed approach and its potential applications in the field of architecture and engineering.


  • This study employs a comprehensive approach that takes into account various meteorological parameters, including wind speed (Ws), relative humidity (RH), minimum temperature (Tmin), maximum temperature (Tmax), and dew point temperature (Td) over a specified time period to investigate the phenomenon of climate change. The participants were categorized into nine groups.

  • The results indicate that configuration 2 outperforms the other categories. This configuration exhibits a low mean absolute error (MAE) of 0.345 °C, low root-mean-square error (RMSE) of 0.442 °C, and high coefficient of determination (\({R}^{2}\)) of 0.998. Furthermore, the P-value suggests that there are no significant differences between the data (P-value = 0.918 > 0.05).

  • The findings reveal that configurations 2, 5, and 8 are the most effective configurations for scenarios 1, 2, and 3, respectively. Therefore, configurations 2, 5, and 8 can be utilized to simulate temperature, corrosion, and temperature-corrosion concurrently in load combination.

  • The present research offers a significant advantage in proposing a network that can effectively respond to climate change by modifying the structure and type of system through load combination.

  • This approach is particularly relevant given the current global conditions of climate change. In structural design, temperature calculations are typically based on historical data [34], with traditional analysis being recommended as a source for designing and calculating structure requirements by ASCE [14]. However, the findings of this study suggest that predicted temperature should be used in load combination instead of relying solely on average historical temperature.

  • It is important to note that the proposed approach is not limited to dry facades but can be applied to many other systems where changes indicated by damage-sensitive properties are affected by climate change, such as corrosion or erosion.

  • The findings of the statistical analysis tests ultimately underscore the significance of integrating climate change considerations into structural design practices. This integration is crucial in ensuring optimal performance and resilience in the face of evolving environmental conditions.

Availability of data and materials

The data that support the findings of this study are available from the authors upon reasonable request.


ANNs :

Artificial neural networks


Allowable stress design


Cold formed structure

D :

Dead loads

f :

Nonlinear function that can be approximated by a multilayer perceptron

L :

Live loads


Load and resistant factor design


Mean absolute error


Number of observations values

Nt :

Number of testing data points used


Nonlinear autoregressive neural network with exogenous input

n u :

Input sequence

n y :

Output sequence


Number of observed values


Number of predicted values


Probability of comparison

\({R}^{2}\) :

Correlation coefficient

Rh :

Relative humidity in percent


Root-mean-square error


Sensitivity analysis

T :

Observed temperature

T 1 :

Temperature, creep, shrinkage loads

T d :

Dew point temperature

u( t) :


W s :

Wind speed

y( t) :


\(\mu\) :

Mean deviation

\(\sigma\) :

Standard deviation


  1. Paech C (2016) Structural membranes used in modern building facades. Procedia Eng 155:61–70.

    Article  Google Scholar 

  2. Badr AR, Elanwar HH, Mourad SA (2019) Numerical and experimental investigation on cold-formed walls sheathed by fiber cement board. J Constr Steel Res 158:366–380.

    Article  Google Scholar 

  3. Eisenberg DA (2016) Transforming building regulatory systems to address climate change. Http://Dx.Doi.Org/10.1080/09613218.2016.1126943 44(5–6):468–473.

  4. Lacasse MA, Gaur A, Moore TV (2020) Durability and Climate Change—Implications for Service Life Prediction and the Maintainability of Buildings. National Research Council Canada, Construction Research Centre, 1200 Montreal Road, Building M24, Ottawa, ON K1A 0R6, Canada. Buildings 10(3):53.

  5. Van Den Bossche N, Janssens A, Moore T, Lacasse M (2020) Development of numerical model for determination of pressure equalization in facades during wet conditions. Build Environ 178:106919.

    Article  Google Scholar 

  6. Hurlimann AC, Warren-Myers G, Browne GR (2019) Is the Australian construction industry prepared for climate change? Build Environ 153:128–137.

    Article  Google Scholar 

  7. Yau YH, Hasbi S (2013) A review of climate change impacts on commercial buildings and their technical services in the tropics. Renew Sustain Energy Rev 18:430–441.

    Article  Google Scholar 

  8. Nguyen MN, Leicester RH, W CH (2008) Climate change: implications for buildings. Key findings... - Google Scholar. Service life models for timber structures protected in building envelope, CSIRO Sustainable ecosystems.…,+2014&hl=en

  9. Du J, Wang H, Wang S, Song X, Wang J, Chang A (2020) Fatigue damage assessment of mooring lines under the effect of wave climate change and marine corrosion. Ocean Eng 206:107303.

    Article  Google Scholar 

  10. Jimenez-Martinez M (2021) Harbor and coastal structures: a review of mechanical fatigue under random wave loading. Heliyon 7(2021):e08241.

    Article  Google Scholar 

  11. Soufeiani L, Foliente G, Nguyen KTQ, San Nicolas R (2020) Corrosion protection of steel elements in façade systems – a review. J Build Eng 32:101759.

    Article  Google Scholar 

  12. Lisø KR (2011) Integrated approach to risk management of future climate change impacts. Http://Dx.Doi.Org/10.1080/09613210500356022 34(1):1–10.

  13. Lisø KR, Aandahl G, Eriksen S, Alfsen KH (2003) Preparing for climate change impacts in Norway’s built environment. Build Res Inf 31(3–4):200–209.

    Article  Google Scholar 

  14. American Society of Civil Engineers Minimum Design Loads for Buildings and Other Structures, ASCE STANDARD (2020) ASCE 7-10 ASD Load Combinations. Chapter 2, Combinations of loads. ISBN 978-0-7844-1085-1 (alk. paper)

  15. Yang T, Sun F, Gentine P, Liu W, Wang H, Yin J, Du M, Liu C (2019) Evaluation and machine learning improvement of global hydrological model-based flood simulations. Environ Res Lett 14(11).

  16. Lee J, Kim CG, Lee JE, Kim NW (2018) Kim H Application of artificial neural networks to rainfall forecasting in the Geum River Basin, Korea. Water 10(10):1448.

    Article  MathSciNet  Google Scholar 

  17. Zou Q, Xiong Q, Li Q, Yi H, Yu Y, Wu C (2020) A water quality prediction method based on the multi-time scale bidirectional long short-term memory network. Environ Sci Pollut Res 27(14):16853–16864.

    Article  Google Scholar 

  18. AltanDombayci Ö, Gölcü M (2009) Daily means ambient temperature prediction using artificial neural network method: a case study of Turkey. Renew Energy 34(4):1158–1161.

    Article  Google Scholar 

  19. Di Nunno F, Granata F (2020) Groundwater level prediction in Apulia region (Southern Italy) using NARX neural network. Environ Res 190:110062.

    Article  Google Scholar 

  20. Shahbaz M, Taqvi SAA, Inayat M, Inayat A, Sulaiman SA, McKay G, Al-Ansari T (2020) Air catalytic biomass (PKS) gasification in a fixed-bed downdraft gasifier using waste bottom ash as catalyst with NARX neural network modelling. Comput Chem Eng 142:107048.

    Article  Google Scholar 

  21. Sum JPF, Kan WK, Young GH (2014) A note on the equivalence of NARX and RNN. Neural Comput Appl 1999 8:1, 8(1), 33–39.

  22. Ezzeldin R, Hatata A (2018) Application of NARX neural network model for discharge prediction through lateral orifices. Alex Eng J 57(4):2991–2998.

    Article  Google Scholar 

  23. O’Neill BC, Carter TR, Ebi K, Harrison PA, Kemp-Benedict E, Kok K, Kriegler E, Preston BL, Riahi K, Sillmann J, van Ruijven BJ, van Vuuren D, Carlisle D, Conde C, Fuglestvedt J, Green C, Hasegawa T, Leininger J, Monteith S, Pichs-Madruga R (2020) Achievements and needs for the climate change scenario framework. Nat Clim Change 10(12):1074–1084.

    Article  Google Scholar 

  24. Van Vuuren DP, Riahi K, Moss R, Edmonds J, Thomson A, Nakicenovic N, Kram T, Berkhout F, Swart R, Janetos A, Rose SK, Arnell N (2012) A proposal for a new scenario framework to support research and assessment in different climate research communities. Glob Environ Chang 22(1):21–35.

    Article  Google Scholar 

  25. Grant N, Hawkes A, Napp T, Gambhir A (2020) The appropriate use of reference scenarios in mitigation analysis. Nat Clim Change 2020 10:7, 10(7), 605–610.

  26. Bateni SM, Vosoughifar H, Ek MB, Xu T, Bateni SM, Vosoughifar H, Ek MB, Xu T (2019) Estimation of daily reference evapotranspiration from limited climatic variables in coastal regions. AGUFM, 2019, H31L-1880.

  27. Adda J, Gonzalo J (1996) P-values for non-standard distributions with an application to the DF test. Econ Lett 50(2):155–160.

    Article  MATH  Google Scholar 

  28. Baduashvili A, Evans AT, Cutler T (2020) How to understand and teach P values: a diagnostic test framework. J Clin Epidemiol 122:49–55.

    Article  Google Scholar 

  29. Evapotranspiration (n.d.) Retrieved September 9, 2021, from

  30. CIMIS (n.d.) Retrieved September 9, 2021, from

  31. I.R. of Iran Meteorological Organization (IRIMO) | E-Library (n.d.) Retrieved September 9, 2021, from

  32. Google Earth (n.d.) Retrieved September 9, 2021, from

  33. Bateni SM, Vosoughifar HR, Truce B, Jeng DS (2019) Estimation of clear-water local scour at pile groups using genetic expression programming and multivariate adaptive regression splines. J Waterw Port Coast Ocean Eng 145(1):04018029.

    Article  Google Scholar 

  34. Reksowardojo AP, Senatore G, Smith IFC (2020) Design of structures that adapt to loads through large shape changes. J Struct Eng 146(5):04020068.

    Article  Google Scholar 

Download references


I would like to express my sincere gratitude to Dr. Vosoughifar for his tremendous support and assistance in completing this article and for providing me with an excellent opportunity to work on a project related to load combination and NARX during global climate change. Without his help and insights, completing this paper would not have been possible.


No funding was received for this study.

Author information

Authors and Affiliations



MR conceived and developed a novel idea, reviewed numerous papers, and summarized suitable ones. He also collected data, wrote, designed, and exported results from the NARX program in MATLAB.

Dr. HV analyzed and interpreted the data using the NARX method. His assistance in analyzing data played a significant role in writing the manuscript. All authors read and approved the final manuscript.

Corresponding author

Correspondence to Mostafa Rezvanifar.

Ethics declarations

Competing interests

The authors declare that they have no competing interests.

Additional information

Publisher’s Note

Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.

Rights and permissions

Open Access This article is licensed under a Creative Commons Attribution 4.0 International License, which permits use, sharing, adaptation, distribution and reproduction in any medium or format, as long as you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons licence, and indicate if changes were made. The images or other third party material in this article are included in the article's Creative Commons licence, unless indicated otherwise in a credit line to the material. If material is not included in the article's Creative Commons licence and your intended use is not permitted by statutory regulation or exceeds the permitted use, you will need to obtain permission directly from the copyright holder. To view a copy of this licence, visit The Creative Commons Public Domain Dedication waiver ( applies to the data made available in this article, unless otherwise stated in a credit line to the data.

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Rezvanifar, M., Vosoughifar, H. A modified NARX approach for evaluating the time history effect of climate change on load combination in designing façade structures. J. Eng. Appl. Sci. 70, 31 (2023).

Download citation

  • Received:

  • Accepted:

  • Published:

  • DOI: