Wind-induced loss assessment method and system for building envelope structures based on directionality and multiple openings

Abstract

The present invention discloses a method and system for assessing wind-induced damage to building envelope structures based on directionality and multiple openings. This method considers two types of wind-induced damage assessment: wind direction and multiple openings. Based on a simplified three-stage progressive damage process with potentially multiple openings, it uses first-order and multi-order MCS methods to assess envelope wind damage under various MRI conditions, separately estimating wind-induced damage to windows / glass doors and roof sheathing panels that consider directionality. This method overcomes the problem of the randomness of openings, which makes it difficult to assess from a directional perspective. Furthermore, the use of a high-order Monte Carlo method meets the requirements of simulating a double-layer cycle, achieving a double-layer cycle capable of characterizing the progressive damage of building structures. This method can quickly and accurately estimate wind-induced damage to the envelope components of low-rise buildings, thereby promoting damage mitigation strategies.

Description

Technical Field

[0001] The present invention relates to the technical field of wind disaster assessment for building structures, and in particular to a method and system for assessing wind-induced losses of building envelope structures based on directionality and multiple openings. Background Art

[0002] During extreme wind events, low-rise buildings' envelope components (e.g., windows and glass doors) are susceptible to severe damage, often caused by high wind loads or wind-borne debris (e.g., Yao et al. 2011; Kordi and Kopp 2011; Lan and Huang 2022). Due to the failure of these envelope components and the intrusion of rainwater into the building, the building interior and its contents are also susceptible to severe damage, resulting in significant economic losses (Abdelhady et al. 2020). Therefore, to facilitate risk assessment of low-rise buildings exposed to strong winds and effectively reduce wind-induced losses, a convenient and effective wind damage assessment method is needed.

[0003] In recent years, many researchers have focused on estimating wind-induced damage to building envelope components (e.g., Pinelli et al. 2011; Stewart et al. 2018; Smith et al. 2020). Lee and Rosowsky (2005) conducted a wind-induced vulnerability analysis of low-rise wood-frame envelope structures based on code-derived wind pressure loads. They found that the complementary lognormal cumulative distribution was a good fit for the complementary vulnerability. Furthermore, Li and Ellingwood (2006) conducted a probabilistic risk assessment of this type of building, emphasizing the use of uncertainty models. Rather than using code-derived wind loads directly, Huang et al. (2015) proposed a method for predicting wind damage to asphalt shingle roofs using wind tunnel data. This database-assisted approach was later validated by He et al. (2015) using field survey data on asphalt shingle roof damage on regional residences. Konthesingha et al. (2015) proposed a model for assessing wind-induced damage to metal envelope structures under extreme wind loads. Stewart et al. (2018) addressed the economic impact of wind-induced damage to building envelopes through risk analysis. However, these models do not consider wind direction effects, which have been shown to significantly impact wind damage estimates (Goyal and Datta 2013). Recently, Ji et al. (2018) proposed a method to account for directionality in wind damage estimates. This method involves Monte Carlo simulation (MCS) calculations, which are cumbersome and time-consuming. To overcome this shortcoming, Wu et al. (2023) developed an improved MCS method (first-order method) that accounts for directionality. Based on this method, they further proposed a new multi-order MCS method to account for the variability of wind pressure coefficients. However, these methods do not account for multiple openings in the windward wall (typically caused by wind loads or wind-borne debris). Although this method can provide wind-induced loss estimates at different return periods (MRIs) that account for directionality, it does not account for the internal pressure variations caused by multiple openings in the wall. Due to the random nature of the openings, simultaneously accounting for directionality and openings is challenging. Many post-disaster investigations have shown that these openings can cause a sharp increase in internal pressure, making roofs more susceptible to damage under strong winds (e.g., Qin and Stewart 2020; Estephan et al. 2021). To more accurately assess wind damage to building envelopes under different return intervals (MRIs), it is necessary to quickly and accurately estimate wind-induced damage to building envelope components (e.g., roof sheathing, windows, and glass doors) to promote the development of disaster prevention and mitigation strategies. A wind-induced loss assessment method for low-rise building envelopes that considers directionality and openings is needed. Summary of the Invention

[0004] In view of this, the purpose of the present invention is to provide a method and system for evaluating wind-induced losses of building envelopes based on directionality and multiple openings. This method effectively combines directionality and openings to evaluate wind-induced losses of building envelopes, improving the accuracy of wind-induced loss evaluation for low-rise building envelopes.

[0005] To achieve the above object, the present invention provides the following technical solutions:

[0006] The method for evaluating wind-induced losses of building envelopes based on directionality and multiple openings provided by the present invention includes the following steps:

[0007] Determine the building envelope and the probability model of wind-induced losses;

[0008] According to the joint probability density function (JPDF) of the annual average extreme wind speed in each direction and the JPDF of the extreme wind pressure coefficient received by the i-th window / glass door in the k-th direction, obtain the annual average extreme wind speed in the k-th direction and the extreme wind pressure coefficient received by the i-th window / glass door in the k-th direction;

[0009] According to the impact force of the debris momentum, calculate and judge the wind-induced loss evaluation of the i-th window / glass door in the k-th direction according to the relationship between capacity C and demand D;

[0010] According to the external pressure received by the window / glass door, calculate and judge the wind-induced loss evaluation of the i-th window / glass door in the k-th direction according to the relationship between capacity C and demand D;

[0011] Loop and repeat the windows / glass doors in all directions to obtain the damage ratio D W .

[0012] Furthermore, the calculation and judgment according to the relationship between capacity C and demand D are specifically as follows:

[0013] When the following conditions are met, judge whether the i-th window / glass door in the k-th direction is damaged: that is, C > D or C < D; where, C = capacity; D = demand.

[0014] Furthermore, it further includes the following steps:

[0015] Determine the opening condition I of the k-th direction according to whether the i-th window / glass door in the k-th direction is damaged W,k ; and according to the opening condition I of the k-th direction W,k , use the internal pressure coefficient C IN,k and the external pressure received by the roof covering panel in the k-th direction to obtain the net pressure in the k-th direction;

[0016] Obtain the JPDF of the multi-extreme net pressure on the roof covering panel according to the net pressure in the k-th direction;

[0017] The extreme wind pressure on the jth roof covering plate in the kth direction is obtained according to the JPDF of the multi-extreme net pressure;

[0018] The cycle is repeated for roof covering panels in all directions to obtain the extreme wind pressure on all roof covering panels;

[0019] The damage ratio D of the roof covering panels is calculated based on the relationship between capacity C and demand D according to the extreme wind pressure and random pressure on all roof covering panels. P .

[0020] Furthermore, the low-rise building enclosure structure adopts a three-stage progressive destruction process.

[0021] Furthermore, the wind damage assessment for the i-th window / glass door in the k-th direction is performed using a first-order Monte Carlo simulation method, and the specific steps are as follows:

[0022] Obtain annual extreme wind speed samples for windows / glass doors in various directions; the annual extreme wind speed samples in various directions include the external wind pressure coefficient and annual maximum wind speed of the enclosure structure components in various directions;

[0023] Calculate the estimated annual maximum wind speed in each direction

[0024] Calculate the wind loss ratio of wall opening conditions and windows / glass doors;

[0025] calculate Simulation sample

[0026] Calculate the annual extreme wind load vector for windows / glass doors in the kth direction

[0027] Get the pressure bearing capacity vector

[0028] Calculate the probability of damage to the i-th window / glass door caused by wind load in the k-th direction

[0029] Setting b ik , and judge according to the following conditions:

[0030] If b ik <p ik or Then the i-th window / glass door fails in the k-th direction, and D is set W,ik =1, otherwise D W,ik =0;

[0031] According to D W,ik Determine the opening conditions in each direction I W,k, calculate the wind loss ratio D of windows / glass doors W .

[0032] Furthermore, it also includes the roof covering damage ratio D P Calculate the roof covering board damage ratio D P Follow these steps to calculate:

[0033] According to the opening condition I in the kth direction W,k Calculate the net pressure coefficient C on the jth roof covering plate in this direction P,jk ;

[0034] According to the net pressure coefficient C P,jk The extreme value of get CDF, and vector The covariance matrix of

[0035] according to The sum and the covariance matrix of the kth direction Sample calculation of the annual maximum wind load vector for roof covering panels and the upward resistance vector

[0036] according to and Compare and determine D P,j , calculate the roof covering damage ratio D P .

[0037] The wind-induced loss assessment system for building envelope structures based on directionality and multiple openings provided by the present invention includes a memory, a processor, and a computer program stored in the memory and executable on the processor. The above method is implemented when the processor executes the program.

[0038] The beneficial effects of the present invention are:

[0039] The present invention provides a method and system for assessing wind-induced losses of building envelope structures based on directionality and multiple openings. The method can quickly and accurately estimate wind-induced damage to envelope structural components (e.g., roof sheathing panels, windows, and glass doors) of low-rise buildings to promote damage mitigation strategies. First-order and multi-order Monte Carlo simulation methods are used to evaluate wind damage while considering directionality and multiple openings on the wall. The proposed methods are compared through numerical examples to study the effects of the correlation of annual directional extreme wind speed and wind pressure coefficient on wind damage to multiple envelope structural components. The results show that the two methods may have different values for the damage rate of roof sheathing panels compared to the case where multiple openings are not considered, and the MRI is relatively large. In addition, the correlation related to wind pressure has a greater impact on the wind damage of roof sheathing panels, and the correlation related to wind speed may reduce the wind damage of roof sheathing panels with a larger MRI.

[0040] This paper provides two wind-induced loss assessment methods that consider wind direction and multiple openings. Based on a simplified three-stage progressive damage process with potentially multiple openings, first-order and multi-order MCS methods are used to assess envelope wind damage under various MRI conditions, respectively estimating wind-induced losses for directional windows / glass doors and roof sheathing. This method overcomes the difficulty of directional assessment due to the randomness of openings. Furthermore, the use of a high-order Monte Carlo method meets the requirements of simulating a double-layer cycle, achieving a double-layer cycle capable of characterizing the progressive damage of building structures.

[0041] Other advantages, objects, and features of the present invention will be described in part in the following description and, in part, will be apparent to those skilled in the art upon examination of the following description or may be learned from practice of the present invention. The objects and other advantages of the present invention may be realized and obtained through the following description. BRIEF DESCRIPTION OF THE DRAWINGS

[0042] In order to make the purpose, technical solutions and beneficial effects of the present invention more clear, the present invention provides the following drawings for illustration:

[0043] Figure 1 Simplified damage process for the building envelope. Figure 2 Framework for evaluating perimeter components for wind damage considering directionality and multiple openings (C = Capacity; D = Demand). Figure 3 is the PDF of the variables in Table 1. Figure 4 D W and D P The first-order CDF of . Figure 5 Figure 6 shows the comparison of window damage rate of the two proposed methods. P Figure 7 shows a low building envelope as an example. Figure 8is the probability distribution of annual extreme wind speed in the NW and E directions. Figure 9 is the probability distribution of the extreme external wind pressure coefficients of W1 and W7. Figure 10 is the window damage rate CDF. Figure 11 is the internal pressure coefficient (AOA=270°, I W =[1,1,0,0,0,0,0,0]). Figure 12 is the extreme value of the net wind pressure coefficient on the roof covering plate A. Figure 13 is the damage rate CDF of the roof covering. Figure 14 D W torque. Figure 15 for and DETAILED DESCRIPTION

[0044] The present invention will be further described below with reference to the accompanying drawings and specific embodiments so that those skilled in the art can better understand the present invention and implement it. However, the embodiments are not intended to limit the present invention.

[0045] Example 1

[0046] This method combines first-order and multi-order MCS methods that account for both wind direction effects and multiple openings. Using these two methods, we investigate the impact of two types of correlations on the first four moments of wind-induced losses. These correlations are: the correlation between the annual extreme wind speeds in each direction, and the correlation between the extreme wind pressure coefficients of multiple building envelope components (i.e., windows / glass doors and roof systems) in a given direction. For simplicity, this method uses "wind speed-related correlations" and "wind pressure-related correlations."

[0047] Firstly, based on a simplified progressive damage process, a novel first-order MCS method is used to evaluate the wind-induced losses of envelope components under different MRI conditions. This method simultaneously considers directionality and multiple openings in the wall. In order to incorporate the influence of the uncertainty of the extreme wind pressure coefficient into the assessment, a new multi-order MCS method is further adopted.

[0048] In strong winds, windows, glass doors, and roof sheathing are the most vulnerable components of the building envelope. The failure of these components is strongly coupled. For example, the failure of components on the windward wall (such as windows) can cause a sharp increase in internal pressure, making the roof sheathing more vulnerable to damage in strong winds. To account for this coupling effect, the method provided in this example uses a simplified three-stage progressive failure process (Wu et al. 2021) to describe the low-rise building envelope, as follows:

[0049] Phase 1: Enclosed building, first assumes that the building is enclosed and there is negative pressure (i.e. suction) inside;

[0050] Stage 2: Partially enclosed buildings. Due to high wind loads or wind-borne debris, some components on the windward wall (such as windows) are damaged, resulting in multiple openings in the wall, making the building a partially enclosed building. There is positive internal pressure. Due to the positive internal pressure, the net wind load on the roof increases, making the roof covering more susceptible to damage.

[0051] Stage 3: Loss of roof covering panels or component failure. Due to the large net wind pressure, some roof covering panels may be removed, resulting in multiple openings in the roof. Generally speaking, the appearance of these openings will reduce the internal pressure, and therefore the net pressure on the roof will also be reduced.

[0052] So far, assuming that the destruction process has been completed, the above three stages of destruction process are Figure 1 The letter symbols in the figure are as follows: C WE,ik represents the external wind pressure coefficient of the i-th window / glass door in the k-th direction; C PE,jk C represents the external wind pressure coefficient of the jth roof covering panel in the kth direction; IN,k represents the internal wind pressure coefficient in the kth direction; debris represents flying debris; wind represents wind; opening represents opening;

[0053] The wind damage to windows / glass doors in this example is estimated as follows:

[0054] Generally speaking, large wind pressure will cause windows / glass doors to be damaged. The limit state function of the i-th window / glass door in the k-th direction is as follows:

[0055] G W,ik =R W,i -Q W,ik (1)

[0056] Among them, G W,ik represents the limit state function; R W,i is the pressure bearing capacity of the i-th window / glass door; Q W,ik is the extreme wind pressure of the i-th window / glass door in the k-th direction,

[0057] It can be given by the following formula:

[0058]

[0059] Wherein, ρ is the air density; in this embodiment, ρ = 1.29 kg / m 3 ; V k is the average wind speed in the kth direction; C W,ik (V k) extreme value;

[0060] The estimation can be performed using the Gumbel transformation method (Cook and Mayne 1979) or methods based on the transformation process (e.g., Kown and Kareem 2011; Zhang et al. 2019);

[0061] Among them, C W,ik It represents the net wind pressure coefficient of the i-th window / glass door in the k-th direction, which is equal to the corresponding external wind pressure coefficient C WE,ik (V k ) and internal wind pressure coefficient C IN,k (V k ), the formula is as follows:

[0062] C W,ik (V k )=C WE,ik (V k )-C IN,k (V k );

[0063] Among them, C WE,ik (V k ) represents the external wind pressure coefficient; C IN,k (V k ) represents the internal wind pressure coefficient;

[0064] In the first stage of the simplified progressive failure process, it is assumed that C IN,k (V k )=0, so the formula is as follows:

[0065] C W,ik (V k )=C WE,ik (V k );

[0066] In addition to wind pressure, the impact of debris carried by the wind can also cause damage to windows / glass doors. Whether the window / glass door is damaged depends on wind conditions such as wind speed, wind direction, generation of debris, trajectory of debris and momentum of debris impact. This is a complex task. Currently, the "wind-borne debris risk model" proposed by Cope (2005) is widely used to analyze wind damage to low-rise buildings. This model assumes that the probability of damage to the i-th window / glass door due to debris carried by the wind in the k-th direction is It can be expressed as:

[0067]

[0068] Among them, n c is the total number of available missile objects;

[0069] c1=Φ[(Vk -60.75) / 6.75] is the proportion of potential missile objects in the air;

[0070] Φ(.) is the cumulative distribution function (CDF) of the standard normal variable;

[0071] c2=0.4 / 90×(V k -22.5) is the percentage of aerial missiles that hit houses;

[0072] c3 is the proportion of windows / glass doors in the impact wall;

[0073] c4=Φ[(V k -31.5) / 4.5] is the probability that the impact missile has momentum above the destruction threshold;

[0074] It should be noted that the c1, c2, and c3 given by Cope (2005) are mainly for the 3-second maximum gust wind speed. When the 10-minute average wind speed is used, these coefficient values should be adjusted.

[0075] A widely used metric to capture the overall loss of a particular type of building envelope components (e.g., windows) is the damage ratio, which is defined as the ratio of the number of components that have been damaged to the total number of components (e.g., Zeng et al. 2020). Therefore, the damage ratio D of windows / glass doors in all directions is considered. W It can be given as follows:

[0076]

[0077] Where, M is the total number of windows / glass doors;

[0078] D W,ik represents the damaged or undamaged state of the i-th window / glass door in the k-th direction (k=1,2,…,K) (K is the total number of directions), which can be regarded as a Bernoulli random variable; the damaged (or undamaged) state of the i-th window / glass door in the k-th direction is recorded as D W,ik =1 or 0;

[0079] When G W,ik ≤0(ie R W,i ≤Q W,ik )or Time (b ik is a random variable uniformly distributed in the interval [0,1]), the i-th window / glass door is damaged in the k-th direction, D W,ik =1; otherwise, the i-th window / glass door is safe in the k-th direction, D W,ik =0;

[0080] Using D W,ikThe opening conditions of the building in the kth direction can be determined by using the index vector I W,k =[D W,1k ,D W,22 ,…,D W,Mk ]express;

[0081] Among them, D W,Mk Indicates the loss of the M-th space in the k-th direction;

[0082] The wind-induced loss of the roof covering in this embodiment is estimated as follows:

[0083] Whether the roof covering plate is damaged or not depends on the extreme suction wind load, the resistance of the roof covering plate and the gravity load. For buildings with light frame structures, the gravity load is usually low and offsets the wind suction response, so it is not considered in this embodiment.

[0084] The limit state function of the jth roof covering panel considering all directions can be expressed as:

[0085] G P,j =R P,j -Q P,j (5)

[0086] Among them, G P,j represents the limiting function of the j-th roof panel;

[0087] R P,j represents the resistance of the jth roof covering panel;

[0088] Q P,j represents the maximum extreme suction wind load of the jth roof covering panel in all directions and can be given by:

[0089] Q P,j =max(Q P,j1 ,Q P,j2 ,…,Q P,jK ) (6a)

[0090]

[0091] Among them, Q P,jk (k=1,2,…,K) is the extreme suction wind load of the jth roof covering panel in the kth direction;

[0092] C P,jk (V k ) can be estimated using the Gumbel transformation method or an estimation method based on the transformation process;

[0093] C P,jkrepresents the net wind pressure coefficient of the jth roof covering panel in the kth direction, which is equal to the corresponding external wind pressure coefficient C PE,jk (V k ) and internal wind pressure coefficient C IN,k (V k ) difference;

[0094] In the second stage of the simplified progressive failure process, the internal wind pressure coefficient C IN,k Usually greater than 0, so C P,jk (V k )=C PE,jk (V k )+C IN,k (V k );

[0095] C IN,k It can be derived from Bernoulli's equation;

[0096] C can be obtained based on the specific opening conditions in the kth direction. PI,k , we can calculate C P,jk (V k ) and subsequently

[0097] Similarly, let D P,j is a Bernoulli random variable representing whether the jth roof covering panel is damaged or not in all directions. When G P,j When ≤0, D P,j =1; when G P,j >0, D P,j =0; D P,j After that, the damage ratio D of the roof covering considering all directions can be determined using the following formula: P :

[0098]

[0099] Where N is the total number of roof covering panels; D P It represents the damage ratio of roof covering board;

[0100] like Figure 2 As shown, the method for assessing wind-induced damage to building envelope structures based on directionality and multiple openings provided in this embodiment includes the following steps:

[0101] Determine the low-rise building envelope and wind-induced loss probability model;

[0102] According to the JPDF of the annual average extreme wind speed in each direction and the JPDF of the extreme wind pressure coefficient on the i-th window / glass door in the k-th direction, the annual average extreme wind speed in the k-th direction and the extreme wind pressure coefficient on the i-th window / glass door in the k-th direction are obtained;

[0103] JPDF represents the joint probability density function;

[0104] According to the impact force of the debris momentum, calculate and judge the wind-induced loss assessment of the i-th window / glass door in the k-th direction according to the relationship between the capacity C and the demand D, and judge whether it is damaged;

[0105] According to the external pressure on the window / glass door, calculate and judge the wind-induced loss assessment of the i-th window / glass door in the k-th direction according to the relationship between the capacity C and the demand D, and judge whether it is damaged;

[0106] In this embodiment, when the following conditions are met, judge whether the i-th window / glass door in the k-th direction is damaged: that is, C > D or C < D; where, C = capacity; D = demand;

[0107] Repeat the windows / glass doors in all directions cyclically to obtain the damage ratio D W ;

[0108] Determine the opening condition I of the k-th direction according to whether the i-th window / glass door in the k-th direction is damaged W,k ; And according to the opening condition I in the k-th direction W,k , use the internal pressure coefficient C IN,k and the external pressure on the roof covering panel in the k-th direction to obtain the net pressure in the k-th direction;

[0109] Obtain the JPDF of the multi-extreme value net pressure on the roof covering panel according to the net pressure in the k-th direction;

[0110] Obtain the extreme wind pressure on the j-th roof covering panel in the k-th direction according to the JPDF of the multi-extreme value net pressure;

[0111] Repeat the roof covering panels in all directions cyclically to obtain the extreme wind pressures on all roof covering panels;

[0112] Calculate and judge according to the extreme wind pressures on all roof covering panels and the randomly generated pressures according to the relationship between the capacity C and the demand D to obtain the damage ratio D of the roof covering panel P .

[0113] This embodiment Figure 2 shows the use of the multi-order Monte Carlo simulation (MCS) method, incorporating all potential opening conditions into the wind damage assessment, and using the first-order Monte Carlo simulation (MCS) method for wind damage assessment. Due to the correlation between the wind loads of different enclosure structure components, in order to improve the accuracy of the analysis, the multi-order Monte Carlo simulation (MCS) method is also used. These two methods aim to estimate the wind damage degree of enclosure structure components under various different wind load body shapes, while considering the directionality and multiplicity of the openings on the wall.

[0114] Due to the randomness of openings in reality, it is difficult to determine when considering directionality. The method provided in this embodiment can simultaneously determine the wind-induced losses caused by the openings while considering directionality.

[0115] This embodiment adopts a three-stage progressive destruction process to describe the low building envelope structure, thereby setting up a double-layer loop that can characterize the progressive destruction of the building structure; meeting the needs of high-order Monte Carlo, which requires a double-layer loop for simulation.

[0116] In this embodiment, the wind damage assessment for the i-th window / glass door in the k-th direction adopts a first-order Monte Carlo simulation method. The specific steps are as follows:

[0117] Obtain annual extreme wind speed samples for windows / glass doors in various directions; the annual extreme wind speed samples in various directions include the external wind pressure coefficient and annual maximum wind speed of the enclosure structure components in various directions;

[0118] Calculate the estimated annual maximum wind speed in each direction

[0119] Calculate the wind loss ratio of wall opening conditions and windows / glass doors;

[0120] calculate Simulation sample

[0121] represents the extreme value of the net wind pressure coefficient vector associated with the window / glass door in the kth direction;

[0122] Calculate the annual extreme wind load vector for windows / glass doors in the kth direction

[0123] Get the pressure bearing capacity vector

[0124] Calculate the probability of damage to the i-th window / glass door caused by wind load in the k-th direction

[0125] Setting b ik , and judge according to the following conditions:

[0126] If b ik <p ik or Then the i-th window / glass door fails in the k-th direction, and D is set W,ik =1, otherwise D W,ik =0;

[0127] According to D W,ik Determine the opening conditions in each direction I W,k, calculate the wind loss ratio D of windows / glass doors W ;

[0128] Among them, D W,ik Indicates the damaged or undamaged state of the i-th window / glass door in the k-th direction;

[0129] I W,k represents the opening condition of the building in the kth direction;

[0130] The first-order MCS method provided in this embodiment is specifically as follows:

[0131] In the damage estimation of the enclosure structure components, it is necessary to use the WE,ik , C PE,jk ) External wind pressure coefficient and annual maximum wind speed of the enclosure structure components. The extreme value of the net wind pressure coefficient vector associated with the window / glass door in the kth direction is expressed as Its correlation matrix and marginal CDF are and The net wind pressure coefficient C of the i-th window / glass door in k directions can be directly obtained through the extreme net wind pressure coefficient data or the net wind pressure coefficient C of the i-th window / glass door in k directions. WE,ik The annual extreme mean wind speed vector is expressed as Its correlation matrix and marginal PDF are and Be prepared and C PE,jk Finally, the details of the first-order Monte Carlo simulation (MCS) method are as follows:

[0132] Randomly generate annual extreme wind speed samples in each direction, as follows:

[0133] Use the copula function (e.g. Wu et al. 2023) to convert non-Gaussian vectors have and Converted to a standard Gaussian vector Z cor , and its correlation matrix is when When it can be well described by Gumbel distribution, it can be easily obtained by formula (8)

[0134] According to the obtained Z can be simulated using the following equation cor Sample (Lu et al. 2020)

[0135]

[0136] Among them, Zcor Represents a vector of related standard Gaussian variables;

[0137] Z uncor is a standard Gaussian vector whose components are independent of each other;

[0138] H represents the lower triangular matrix;

[0139] Once you get Z cor The estimated values of the annual maximum wind speed in each direction can be obtained by using formula (16) and It can be well described by the extreme value Gumbel distribution;

[0140] in, represents the extreme wind speed in the Kth direction;

[0141] Determine the wind-induced loss ratio (i.e., damage ratio) for wall opening conditions and windows / glass doors as follows:

[0142] according to and related to the kth direction (k=1,2,…,K)

[0143] Execute the above steps Perform similar operations to obtain Simulation sample

[0144] in, Indicates the wind pressure coefficient on the Mth door and window in the kth direction;

[0145] According to formula (2), the annual extreme wind load vector of the window / glass door in the kth direction can also be obtained:

[0146] in, represents the wind load on the Mth door and window in the kth direction;

[0147] At the same time, a pressure bearing capacity vector is randomly generated and assuming that the resistances of windows / glass doors are independent of each other (e.g., Stewart et al., 2018);

[0148] in, Indicates the resistance of the Mth door and window;

[0149] Use the generated The probability of damage to the i-th window / glass door caused by wind load in the k-th direction can be determined Determined by formula (3), randomly generate bik , for i = 1, 2, ..., M and k = 1, 2, ..., K; b ik express;

[0150] If b ik <p ik or The i-th window / glass door fails in the k-th direction, so D W,ik =1, otherwise D W,ik =0; according to D W,ik (i=1,2,…,M), the opening condition I in each direction can be determined W,k (k=1,2,…,K), and use formula (4) to estimate the wind-induced loss ratio D of windows / glass doors W ;

[0151] in, represents the resistance of the i-th door and window; represents the wind load on the i-th door and window in the k-th direction;

[0152] The damage ratio D of the roof covering board considering the directionality and multiple openings in this embodiment is P , calculate as follows:

[0153] According to the opening condition I in the kth direction W,k Calculate the net pressure coefficient C on the jth roof covering plate in this direction P,jk ;

[0154] According to the net pressure coefficient C P,jk The extreme value of get CDF, and vector The covariance matrix of

[0155] according to The sum and the covariance matrix of the kth direction Sample calculation of the annual maximum wind load vector for roof covering panels and the upward resistance vector

[0156] according to and Compare and determine D P,j , calculate the roof covering damage ratio D P .

[0157] in, represents the cumulative probability distribution function of the wind pressure coefficient on the jth door and window in the kth direction; express The correlation matrix of DP,j represents the loss rate of roof panels in the jth simulation;

[0158] In this embodiment, the damage ratio D of the roof covering board is considered based on the directionality and multiple openings. P The calculation is as follows:

[0159] According to the opening condition I in the kth direction W,k , the corresponding internal pressure coefficient C is derived based on the Bernoulli equation IN,k ; Net pressure coefficient C on the jth roof covering plate in each direction P,jk (k=1,2,…,K) by C P,jk =C PE,jk +C IN,k .Calculated;

[0160] Record C P,jk The extreme value of (k=1,2,…,K) is Using the Gumbel transformation method (Cook and Mayne 1979) or methods based on transformation processes (e.g., Kown and Kareem 2011; Zhang et al. 2019), one can obtain CDF, and vector The covariance matrix of

[0161] according to and related to the kth direction (k=1,2,…,K)

[0162] Execute the above steps Perform similar operations to obtain A simulation sample:

[0163]

[0164] in, represents the wind pressure coefficient on the Nth plate in the kth direction;

[0165] The sample of the annual maximum wind load vector of the roof covering plate is obtained by calculation using equations (6a) and (6b):

[0166]

[0167] At the same time, an upward resistance vector is generated independently

[0168] in, represents the wind load on the Nth plate; represents the resistance of the Nth plate;

[0169] Will and Compare to determine D P,j , and then use formula (7) to calculate the roof covering plate damage ratio D P .

[0170] Repeat steps 1 to 3 N times s (For example, N s =10000) times to obtain N s Based on these samples, the damage ratio CDF of windows / glass doors can be developed and the damage ratio CDF of the roof covering Accordingly, through The damage rate of windows / glass doors in T years can be obtained by The T-year damage rate of the roof covering can be obtained, where and They are and The inverse function of .

[0171] in, represents the loss rate of doors and windows with a return period of T; represents the cumulative probability density function of the loss rate of doors and windows; represents the loss rate of roof panels with a return period of T; represents the cumulative probability density function of the roof panel loss rate; T represents time, in years;

[0172] This embodiment also provides a multi-order Monte Carlo simulation method for calculating the wind-induced loss of low-rise building envelope structures taking into account directionality and multiple openings, including the wind-induced loss ratio D of windows / glass doors. W and roof covering damage ratio D P The specific steps are as follows:

[0173] Get the higher order extreme mean wind speed in the kth direction The cumulative distribution function CDF, and described represents the cumulative probability distribution function of the extreme wind speed in the kth direction; express The cumulative probability distribution function of ; express The cumulative probability distribution function of ; is the high-order extreme wind speed vector, is the correlation matrix, is the marginal probability density function PDF, there is

[0174] When it is known and C PE,jk The process of the m-order (m>1) method with directionality and gap considerations is summarized as follows:

[0175] Get m extreme wind speed samples in each direction and calculate and the high-order extreme mean wind speed in the kth direction CDF of

[0176] pass and Get n Sample, get the maximum m values, expressed as

[0177] Determine the opening conditions and breakage rates of windows / glass doors;

[0178] pass and Simulate extreme wind pressure coefficients on m windows / glass doors in each direction

[0179] Get the annual extreme wind load vector sample for each window / glass door in the kth direction and the pressure bearing capacity vector

[0180] By generating calculate

[0181] By randomly generating b ik To determine D W,ik ; and according to D W,ik Determine each direction I W,k The opening conditions are estimated based on the opening conditions. W ;

[0182] The multi-order Monte Carlo simulation method provided in this embodiment is used to calculate the damage ratio D of the roof covering board. P ; The specific steps are as follows

[0183] Based on the opening condition I of the kth direction W,k , and the corresponding internal pressure coefficient C is obtained IN,k , and the net pressure coefficient C on the j roof covering panels in each direction P,jk ;

[0184] According to C by Gumbel transformation method P,jk estimate and

[0185] use and Calculate m extreme wind pressure coefficient samples

[0186] By comparing all Get the extreme wind load sample in the kth direction in the jth year

[0187] use Obtain annual extreme wind load vector samples considering wind directionality and the upward resistance vector Will and Compare and determine D P,j , and then calculate the roof covering board damage ratio D P .

[0188] in, express Cumulative probability distribution function; express Correlation matrix; represents the wind load on the jth plate in the kth direction; D P,j represents the loss rate of the roof panel in the jth simulation;

[0189] The multi-level MCS method provided in this embodiment is specifically as follows:

[0190] Assuming that the extreme response of a year always comes from the strongest (first) wind in a year, this method ignores the influence of the second, third and other higher-order wind speeds. In order to consider these effects in wind damage assessment, it is necessary to give the higher-order extreme average wind speed in the kth direction. The cumulative distribution function (CDF) of (k=1,2,…,K) is given by (Wu et al. 2023) as follows:

[0191]

[0192] Where n = 100,

[0193] when and Both are described by the Gumbel distribution according to the formula given by (Gumley and Wood 1982), namely:

[0194]

[0195]

[0196]

[0197] in, (or or )and (or or ) are the mode and dispersion parameters; represents the cumulative probability distribution function of the extreme wind speed in the kth direction; express The cumulative probability distribution function of ; express The cumulative probability distribution function of ; express The location parameter follows the extreme value type I distribution; express The location parameter follows the extreme value type I distribution; express The location parameter follows the extreme value type I distribution; express The scale parameter follows the extreme value type I distribution; express The scale parameter follows the extreme value type I distribution; express The scale parameter follows the extreme value type I distribution;

[0198] will be recorded as is the high-order extreme wind speed vector, denoted as and are their correlation matrix and marginal probability density function (PDF), respectively. According to the study (Zhang 2015),

[0199] Considering that most existing wind-borne debris risk models are only applicable to uniform wind fields, and the impact of wind turbulence on the trajectory of wind-borne debris is not yet fully understood (Zhao et al. 2021), only the wind turbulence model is considered here. The effect on wind pressure, when known and C PE,jk The process of the m-order (m>1) method with directionality and gap considerations is summarized as follows:

[0200] Generate m extreme wind speed samples in each direction as follows:

[0201] Through formula (9) and use and Evaluate

[0202] As in the above steps The generation process is similar, using and Get n Sample, record the largest m values, expressed as

[0203] in, Indicates the mth maximum wind speed sample value in the kth direction;

[0204] Determine the opening conditions and breakage rates of windows / glass doors as follows:

[0205] based on and Use the same steps as above The same simulation process simulates the extreme wind pressure coefficients on m windows / glass doors in each direction:

[0206]

[0207] in, express The lth sample of

[0208] Get the annual extreme wind load vector sample for each window / glass door in the kth direction:

[0209]

[0210] in, It can be estimated by the following formula:

[0211]

[0212] At the same time, a pressure bearing capacity vector is also generated independently

[0213] Use the generated It can be calculated according to formula (3)

[0214] Randomly generate b ik , where i = 1, 2, ..., M and k = 1, 2, ..., K to determine D W,ik ;

[0215] Based on D W,ik , we can determine each direction I W,k (k=1,2,…,K) and estimate D according to formula (4) W ;

[0216] Among them, b ik represents the i-th random number in the k-th direction; p ik represents the failure probability of the i-th door or window in the k-th direction; represents the resistance of the i-th door and window; represents the wind load of the i-th door and window in the k-th direction;

[0217] This embodiment also provides a roof covering sheet damage rate that takes into account directionality and multiple openings, as follows:

[0218] Based on the opening condition I of the kth direction W,k According to the Bernoulli equation, the corresponding internal pressure coefficient C is obtained IN,k ; Net pressure coefficient C on j roof covering panels in each direction P,jk (k=1,2,…,K) The calculation formula is:

[0219] C P,jk =C PE,jk +C IN,k ;

[0220] From C P,jk estimate and

[0221] Generate through the above steps method, using (j=1,2,…,N) and m extreme wind pressure coefficient samples can be obtained in, Indicates the lth sample;

[0222] pass The extreme wind load sample of the kth direction in the jth year can be obtained

[0223] use can be Obtain annual extreme wind load vector samples considering wind directionality At the same time, the upward resistance vector is generated independently

[0224] Will and Compare to determine D P,j , and then use formula (7) to estimate D P .

[0225] Similar to the above steps, repeat steps 1 to 3 N times. s times, you can get and

[0226] In summary, both proposed methods take into account the directional effect and multiple openings in the wall. The fundamental difference between the two methods is that the multi-order method considers the influence of high-order extreme wind speeds on wind pressure.

[0227] Example 2

[0228] This embodiment provides multiple numerical examples to study the wind loss when considering multiple openings in a wall and the difference between the wind losses of the two methods.

[0229] When estimating wind-induced losses of low-rise building envelope components, a probabilistic model for variables such as extreme wind speeds is required. Referring to the numerical case of Wu et al. (2023), Table 1 summarizes the (denoted as V I , V II and V III ), (denoted as C PI 、C PII and C PIII )and (denoted as C WI , C WII and C WIII ), assuming that these models follow a Gumbel distribution (e.g., Wu et al. 2023).

[0230] Figure 3 (a) shows V I 、V II and V III The probability density functions (PDFs) of the two groups show that there are significant differences between them. Figure 3 (b) and Figure 3 (c) in the figure shows the C PI , C PII and C PIII and C WI , C WII and C WIII The probability density function of .

[0231] Figure 3 The wind speed in it means wind speed;

[0232] Extreme wind pressure coeffcient represents the extreme wind pressure coefficient;

[0233] Obviously, for most roof sheathing and windows / glass doors, the maximum extreme wind pressure coefficient is C PIII and C WIII .

[0234] Table 1 Probability model of variables involved in this study

[0235]

[0236] In this embodiment, the comparison of wind-induced losses with and without considering multiple openings is as follows:

[0237] In order to consider the effect of openings on the wind-induced loss of wall and roof covering panels, two numerical examples are analyzed. The details of these two examples are summarized in Table 2. Each example has two mutually perpendicular directions and two windows in each direction, so M = 4. For each example, the probability model of the variables includes and These models are also summarized in Table 2. In addition, it is also necessary to estimate the wind pressure bearing capacity R of the i-th window W,i and the wind pressure bearing capacity R of the jth roof panel P,j .

[0238] Assume R W,i and R P,j All obey the normal distribution, R W,i The mean and standard deviation are 0.2 kN and 0.04, respectively. P,j The mean and standard deviation are 1.0 kN and 0.15 respectively. Other parameters are set as follows: N = 100, N s =40000, n c =200, c3 = 0.4. Considering that directions 1 and 2 are perpendicular to each other, it is assumed that windows numbered 1 and 2 fail only in direction 1, and windows numbered 3 and 4 fail only in direction 2.

[0239] Table 2 Two numerical examples used to study the effect of openings on wind-induced losses of roof coverings

[0240]

[0241] After knowing these parameters, the probability distribution of wind-induced damage to windows can be obtained by following the above steps. The probability distribution is as follows: Figure 4 (a) in the equation is D W For simplicity, only the results for the first wind speed are presented here. It should be noted that this assumes that the annual extreme wind speeds in the two directions are independent of each other. It can be seen that for example A2, the window damage probability under different MRI conditions is much greater than that for example A1. This is primarily due to the higher extreme wind speed in the dominant wind direction in example A2. Clearly, the window damage probability under different MRI conditions in both numerical examples is less than 0.5, which is primarily related to the window failure assumption mentioned above.

[0242] Figure 4 (b) in the equation is D P, the wind-induced loss probability distributions of the roof covering panels of numerical examples A1 and A2 at the first-level wind speed were compared with and without wall openings considered. It should be noted that the internal wind pressure coefficient under specific opening conditions is approximately equal to the average value of the external wind pressure coefficient at the opening. As expected, when multiple wall openings are considered, the damage probability of the roof covering panel under a given MRI is greater than that without considering wall openings. Through comparison, it can be found that for a relatively small MRI, such as A2, the damage probability of its roof covering panel is much greater than that of, for example, A1, mainly because the extreme wind speed in the dominant wind direction of numerical example A2 is larger. However, for a relatively large MRI, the damage probability of the roof sheathing related to A1 is much smaller than that related to A2. This is because when multiple openings appear in the wall, the internal wind pressure in A2 decreases slightly.

[0243] Figure 4 In the abscissa -ln(-ln(P(Dw)<d))), the number corresponding to the return period is represented; A1(without openins) represents the result of numerical case A1 without considering openings; A1(with openings) represents the result of numerical case A1 considering openings; A2(without openings) represents the result of numerical case A2 without considering openings; A2(with openings) represents the result of numerical case A2 considering openings;

[0244] The comparative analysis of the first-order and multi-order MCS simulation methods in this embodiment is as follows:

[0245] To address the influence of openings in the wall on the wind damage of the roof covering panel, two examples were used, and their details are summarized in Table 2. Each example has 2 mutually perpendicular directions, and 2 windows in each direction, so M = 4. For each example, the probability models of the variables including and are also summarized in Table 2. The damage estimation also requires the wind pressure capacity of the i-th window R W,i and the j-th roof covering panel R P,j . It is assumed that both R W,i and R P,j follow a normal distribution. The mean value and standard deviation of R W,i are 0.2 kN and 0.04 respectively, and the mean deviation and standard deviation of R P,j are 1.0 kN and 0.15 respectively. Other parameter settings are as follows: N = 100, N s = 40000, n c = 200, c3 = 0.4. Considering that directions 1 and 2 are perpendicular to each other, the windows numbered 1 and 2 are assumed to fail only in direction 1, and the windows numbered 3 and 4 are assumed to fail only in direction 2.

[0246] Table 3 Seven numerical cases comparing the two methods

[0247]

[0248] Notice:

[0249]

[0250] in, Indicates measurement Parameters of variability; express The location parameter follows the extreme value type I distribution; express The scale parameter follows the extreme value type I distribution; Indicates measurement Parameters of variability; express The location parameter follows the extreme value type I distribution;

[0251] express The scale parameter follows the extreme value type I distribution; Indicates measurement Parameters of variability; express The location parameter follows the extreme value type I distribution; express The scale parameter of the extreme value type I distribution; V I Indicates the Class I wind speed of the case setting; V II Indicates the Class II wind speed of the case setting; V ITI Indicates the Class III wind speed of the case setting; C PI Indicates the Class I roof wind pressure coefficient of the case setting; C PII Indicates the Class II roof wind pressure coefficient of the case setting; C PIII Indicates the Class III roof wind pressure coefficient of the case setting; C WI Indicates the wind pressure coefficient of Class I windows in the case setting; C WII Indicates the wind pressure coefficient of Class II windows in the case setting; C WIII Indicates the wind pressure coefficient of the Class III windows in the case setting;

[0252] Based on these probability models, the window damage rate can be easily obtained by following the above method. As shown in Table 3, the window damage rate in numerical examples B3, B6 and B7 is and The probability models for are the same as those in numerical examples B1, B4, and B5, respectively, so Figure 5Only B1, B2, B4 and B5 are shown in the figure, where the and multiple components in each direction (or The results of independent (indicated by "Inde") and fully correlated (indicated by "Full-cor") analysis were combined. The window damage ratios of the larger MRI obtained by the two methods were very close, which is consistent with the results of Wu et al. (2023). For the window damage ratios of the smaller MRI, the two methods were Figure 5 The estimation results in (a), (b) and (c) are also very close, while the multi-order method is Figure 5 The estimated result in (d) is much larger than that of the first-order method, which leads to a conclusion: for relatively large and smaller The window damage ratios derived from both methods can be significant.

[0253] Figure 5 The vertical axis d represents the loss rate; First-order method (Inde) represents the result of the first-order method when variables are independent; Multi-order method (Inde) represents the result of the multi-order method when variables are independent; First-order method (Full corr) represents the result of the first-order method when variables are fully correlated; Multi-order method (Full corr) represents the result of the first-order method when variables are independent; Numerical example B1 (or B3) represents the result of numerical case B1 or B3; Numerical example B2 represents the result of numerical case B2; Numerical example B4 (or B6) represents the result of numerical case B4 or B6; Numerical example represents a numerical case;

[0254] Figure 6 compares the damage ratio D of the roof covering panels calculated by the two methods for Examples B1 to B7 in Table 4. P . Ratio of window damage to D W Similarly, the D of the larger MRI value calculated by the two methods P Very close. and are very small, and Figure 6 (a) shows the D of the smaller MRI value calculated by the two methods. P Also very close. Increase or This does not change the trend of small differences between the two methods, as shown in (b) and (c) in Figure 6. However, in the dominant direction The increase of widens the difference between the two methods, as shown in (d), (e), (f), and (g) in Figure 6. This leads to a conclusion that Relatively large and (or ) is relatively small, the D estimated by the two methods P There may be significant differences between Relatively large, and and When both are relatively small, as in the case of (g) in Figure 6 , the difference may also be large.

[0255] The First-order method (inde&inde) in Figure 6 shows the results of the first-order method when both wind speed and wind pressure coefficients are considered independent;

[0256] Multi-order method (inde&inde) represents the result of multi-order method considering that wind speed and wind pressure coefficients are independent;

[0257] First-order method (fcorr&fcorr) represents the result of the first-order method when both wind speed and wind pressure coefficients are fully correlated;

[0258] Example 3

[0259] In this embodiment, an actual roof system building is constructed to illustrate the proposed method. A low building with a timber frame and a roof slope of 1:12 is used, as shown in FIG7 . Then, an experiment is conducted to obtain data and perform analysis.

[0260] To account for the effects of wall openings, eight windows (labeled W1 to W8 in Figure 7) were symmetrically distributed across all walls, with a width of 1.83 meters and a height of 1.07 meters. Furthermore, 80 wooden panels (indicated by the dashed lines in Figure 7) were distributed across the roof system, with a length of 1.22 meters and a width of 2.44 meters. Based on the research of Lee and Rosowsky (2005), the wind load resistance of the panels was assumed to follow a normal distribution with a mean of 1.2 kN / m² and a coefficient of variation (COV) of 0.15.

[0261] In FIG7 , A represents plate A;

[0262] The wind tunnel test of the building has been carried out to obtain the dataset of wind pressure coefficients on the building exterior wall (Ho et al. 2005). The wind pressure coefficient data obtained from the wind tunnel test is publicly available. In the wind tunnel test, the model scale is set to 1:100, the sampling frequency is 500 Hz, and the duration is 100 seconds. At a height of 10 meters, the average wind speed within 10 minutes is 13.7 m / s, and at the roof height of 3.66 meters, it is 6.1 m / s. The pressure joints (see the red “+” in Figure 7) include 335 joints on the roof and 11 joints on the wall. Each joint has wind pressure coefficient data at wind angles of 0° - 90° and 270° - 360°, with an interval of 5°.

[0263] The assessment of wind-induced losses of the roof covering in this embodiment is as follows:

[0264] In addition to the wind pressure coefficient data, wind hazard estimation also requires extreme wind speed data. In this embodiment, the wind speed data used in Wu et al. (2023) is used to develop the probability distribution of the annual extreme wind speed in each direction (denoted by N, NE, E, SE, S, SW, W, and NW respectively), as well as the correlation coefficient matrix of the directional annual extreme wind speed. For simplicity, only the marginal probability distributions of the annual extreme wind speeds in the NW and E directions are presented, as Figure 8 shown. For comparison, the Gumbel distribution obtained by data fitting is also plotted. It is observed that the annual extreme wind speed well conforms to the Gumbel distribution.

[0265] Figure 8 In, the abscissa -ln(-ln(Vk<v))) represents the value corresponding to the return period; the ordinate v represents the wind speed value; Observed represents the observed value; Gumbel distribution represents the Type-I extreme value distribution;

[0266] According to the wind disaster damage estimation procedure, first, the opening conditions need to be determined. To determine whether the windows fail, it is necessary to calculate the marginal probability distribution and the correlation coefficient matrix of the extreme external wind pressure coefficients on multiple windows within 10 minutes; as done by Wu et al. (2023), it is developed using the transformation process method based on HPM and obtained using the formula developed by Ji et al. (2018). For brevity, only the probability distributions related to the extreme pressure coefficients on W1 and W7 are presented in Figure 9 . Similar to the annual extreme wind speed, the extreme pressure coefficients well follow the Gumbel distribution.

[0267] Figure 9The horizontal axis Extreme external wind pressure coefficient represents the extreme external wind pressure coefficient; the vertical axis Probability of exceedance represents the exceedance probability; Empirical represents the empirical value; Gumbel represents the extreme value type I distribution; Observed represents the observed value; AOA represents the wind angle of attack;

[0268] Based on the normal distribution assumption, the wind pressure bearing capacity of each window is 1.5kN / m2 with a coefficient of variation of 0.2. Based on the extreme wind pressure coefficient and extreme wind speed obtained, the wind-borne debris risk model is used to calculate the wind pressure bearing capacity of each window. s =40000, m=10 and n c = 200, the above method can be used to obtain the failure state of each window in each direction in each simulation, ultimately taking into account the window damage ratio with respect to directionality. For comparison, the following analysis will discuss the five results in Table 4. These results characterize the degree of correlation between extreme wind speeds in various directions (referred to as speed-related correlations) and the degree of correlation between multiple extreme values of the external wind pressure coefficient in each direction (referred to as pressure-related correlations). For example, "fcorr&fcorr&inde" indicates a result with complete pressure correlation (i.e., complete correlation) and no speed-related correlation (mutual independence).

[0269] Figure 10 (a) compares the window damage ratio D obtained by the two methods. W . It was observed that the D under different MRI conditions obtained by the two methods W is very close, which can be attributed to the fact that in this numerical example, and For the sake of brevity, only Figure 11 (b) shows D in a first-order way. W The probability distribution of the five cases is similar to the damage ratio of roof covering panels without considering multiple openings in Wu et al. (2023). Compared with “fcorr&fcorr&fcorr” or “inde&inde&fcorr”, “fcorr&fcorr&inde” or “inde&inde&inde” reduces D W , with relatively low MRI but increased D W , with relatively larger MRI. This suggests that the estimates of window damage proportion by “fcorr&fcorr&fcorr” (or “inde&inde&inde”) and “inde&inde&fcorr” (or “fcorr&fcorr&inde”) are not sensitive to the pressure-related correlation.

[0270] Figure 10 Where “fcorr&fcorr&inde” represents the results with wind pressure coefficient (i.e., complete correlation) and speed (mutually independent); “fcorr&fcorr&fcorr” represents the results with complete correlation of wind pressure coefficient and complete correlation of speed; “inde&inde&inde” represents the results with complete independence of wind pressure coefficient and speed; “inde&inde&fcorr” represents the results with complete independence of wind pressure coefficient and wind speed; First-order method (real) represents the results of first-order method considering actual correlation; Multi-order method (real) represents the results of multi-order method considering actual correlation; First-and multi-order methods represent the first-order and full-order methods; First-order methods for five cases represents the first-order method for the five results in Table 4; real represents the results considering actual correlation;

[0271] Table 4 Five results related to speed and pressure

[0272]

[0273] If the fault state of the i-th window in each direction is determined in each simulation, the opening condition of the building in the k-th direction can be determined. w,k Through the Bernoulli equation, we can simulate I w,k The internal pressure coefficient under .

[0274] For the sake of brevity, only the I W =[1,1,0,0,0,0,0,0], the time history and power spectral density (PSD) of the internal pressure coefficient, as shown in Figure 11 As shown. The figure also shows the time frequency information of the external pressure coefficient at the opening for comparison. It can be seen that the internal pressure coefficient is almost between the external pressure coefficients of the openings W1 and W2. Obviously, Figure 11 The PSD of the internal pressure in (b) has a peak at the Helmholtz frequency of 4.84 Hz.

[0275] Figure 11The vertical axis Wind pressure coeficient represents the wind pressure coefficient; the horizontal axis Frequency represents the frequency; External pressure coeficient (W1) represents the external wind pressure coefficient near window W1; External pressure coeficient (W2) represents the external wind pressure coefficient near window W2; Internal pressure coefiient represents the internal pressure coefficient; Time histories represents the time history; PSDs represents the power spectrum; PSD represents the cumulative probability density function;

[0276] Based on the internal pressure coefficient under the simulated specific opening state, the extreme value of the net wind pressure coefficient on the roof system can be determined. Figure 12 (a) and (b) in the figure show the probability distribution of the extreme net wind pressure coefficient of the roof wind-resistant board A (as shown in Figure 7) under different opening conditions and wind direction angles of 270 degrees and 360 degrees respectively. The results show that the Gumbel distribution can well describe the extreme net wind pressure coefficient. At the same time, it is observed that I W =[1,1,0,0,0,0,0,0] and I W =[0,0,0,0,0,0,1,0], the maximum net wind pressure coefficient is at AOA=2700 and AOA=3600 respectively. This is because once the components on the downwind side and side wall are damaged, the internal pressure will decrease.

[0277] According to the extreme value of the net wind pressure coefficient obtained, the damage ratio of the roof covering in year T can be estimated. Figure 13 (a) shows the Similar to the window damage ratio, the different T values obtained by the two methods is very close, which can be attributed to the fact that in this numerical example and For the sake of brevity, Figure 13 (b) in Table 5 shows only the first-order method for the five cases listed in Table 5. As T increases, the value of the equation changes from “fcorr&fcorr&fcorr” (or “inde&inde&inde”) to “inde&inde&fcorr” (or “fcorr&fcorr&inde”). The difference increases first and then decreases. For example, for T = 10, 30 and 100 years, the difference is calculated by "inde&inde&inde" and "fcorr&fcorr&inde". The differences are 0.01%, 20.4% and -2.3% respectively. This is mainly because the damage ratios in different cases have the same mean, but other high-order moments (such as standard deviation, skewness and kurtosis) are different. At the same time, it can be seen that in T <T p = 60 years, "inde&inde&inde" To be less than "fcorr&fcorr&fcorr". Figure 10 Compared with the window case in (b), the T p / T up Larger, among which T up represents the payoff period where the corresponding damage ratio is equal to 1. This is because the standard deviation of the damage ratio of roof coverings for "fcorr&fcorr&fcorr" is smaller than that for "inde&inde&inde", but the standard deviation of the damage ratio of windows is larger.

[0278] Figure 13 Proposed two methods means the two methods proposed in this patent;

[0279] First-order methods for five correlation cases represent the first-order methods for the five correlation cases in Table 4;

[0280] Based on the first four moments of the damage ratio, these moments have been shown to be functions of the damage state (Wu et al. 2023). Figure 10 (b) and Figure 13 The damage ratio is shown in (b).

[0281] From the above analysis, it can be seen that the damage state of the facade of a low-rise building is significantly affected by the wind pressure resistance of the windows. For the sake of simplicity, the damage to the windows caused by flying debris is ignored. The first four moments of the damage ratio of windows and roof coverings are used as the function of the wind pressure resistance of the windows. The wind pressure resistance of the windows is assumed to conform to the normal distribution with a mean of The standard deviation is

[0282] As required, 40,000 samples of window damage ratios were obtained using the first-order method and the and Figure 14 Shows and As The first four moments of the function. As expected, in each case As it increases, it decreases. However, The increase makes all cases From negative to positive. At the same time, it is observed that It is almost unaffected by pressure dependence, but changes when considering velocity dependence. The velocity dependence coefficient can be increased by Especially for and for Higher order moments (i.e. and ).for In this rare case, the correlation coefficient will decrease Based on these observations, it can be predicted that the velocity correlation coefficient will reduce the damage ratio estimate for structures with relatively low MRI but increase the damage ratio estimate for structures with relatively large MRI. These observations are consistent with the results obtained by Wu et al. (2023) without considering roof sheathing with multiple openings on the wall.

[0283] Figure 14 Mean means mean; Standard deviation means standard deviation; Skewness means skewness; Kurtosis means kurtosis; represents the mean window loss rate; represents the standard deviation of window loss rate; represents the skewness of the window loss rate; represents the kurtosis of the window loss rate; represents the mean resistance of the window;

[0284] Similarly, 40,000 samples of damage ratios of roof covering panels can be obtained. The first four moments (using and Indicates) Figure 15 The following are the detailed observations:

[0285] in, represents the mean roof loss rate; represents the standard deviation of roof loss rate; represents the skewness of roof loss rate; represents the kurtosis of roof loss rate;

[0286] With each case and In comparison, with They first increase and then decrease, mainly because once the windows on the side and lee walls are damaged, the internal pressure decreases significantly. (Right now ), which means that almost all windows on the wall are inoperable. and remains almost unchanged. In particular, in each case along with The increase and decrease of the and along with It decreases and increases from 0.4kN / m2 to 0.75kN / m2 and from 0.75kN / m2 to 2.0kN / m2.

[0287] Overall, nor were they affected by stress-related correlations that and For example, from "fcorr&fcorr&inde" and "inde&inde&inde" to and The mean absolute differences were 3.3%, 4.8%, 5.1% and 9.8% respectively. and The maximum absolute differences are 6.0%, 13.7%, 16.7%, and 26.5%, respectively. It is important to note that these differences are mainly due to the wind pressure coefficients associated with the windows rather than the roof sheathing.

[0288] Apart from In addition, the other three moments (i.e. and ) is greatly affected by speed dependence. For example, and The mean absolute differences between “inde&&inde&fcorr” and “inde&inde&inde” are 23.3%, 3.5%, 12.9% and 19.2% respectively. It is important to note that this correlation reduces the and of and almost all of and

[0289] Compared to the study by Wu et al. (2023), which did not consider multiple windows or roof sheathing openings in the wall, the extent and manner in which the pressure-velocity correlations affect the damage fraction of the roof sheathing are somewhat different when the wall openings are considered. These changes are primarily due to the internal pressures caused by the different opening conditions in the wall.

[0290] The above embodiments are merely preferred embodiments for the purpose of fully illustrating the present invention, and the scope of protection of the present invention is not limited thereto. Equivalent substitutions or modifications made by those skilled in the art based on the present invention are within the scope of protection of the present invention. The scope of protection of the present invention shall be subject to the claims.

Claims

1. A wind-induced loss assessment method for building envelope structures based on directionality and multiple openings, characterized by: It includes the following steps: Determine the building envelope and the probability model of wind-induced losses; Based on the joint probability density function (JPDF) of the annual average extreme wind speeds in each direction and the JPDF of the extreme wind pressure coefficients on the i-th window / glass door in the k-th direction, obtain the annual average extreme wind speed in the k-th direction and the extreme wind pressure coefficients on the i-th window / glass door in the k-th direction; Calculate and determine the wind-induced loss assessment of the i-th window / glass door in the k-th direction according to the impact force of the debris momentum in accordance with the relationship between capacity C and demand D; Calculate and determine the wind-induced loss assessment of the i-th window / glass door in the k-th direction according to the external pressure on the window / glass door in accordance with the relationship between capacity C and demand D; Repeat the cycle for all windows / glass doors in all directions to get the damage ratio D W ; The wind-induced loss assessment of the i-th window / glass door in the k-th direction adopts the first-order Monte Carlo simulation method, and the specific steps are as follows: Obtain the annual extreme wind speed samples of the windows / glass doors in each direction; the annual extreme wind speed samples in each direction include the external wind pressure coefficients of the envelope components in each direction and the annual maximum wind speed; Calculate the estimated annual maximum wind speed in each direction Calculate the wall opening conditions and the wind-induced loss ratio of the windows / glass doors; calculate Simulation sample Calculate the annual extreme wind load vector for windows / glass doors in the kth direction Get the pressure bearing capacity vector Calculate the probability of damage to the i-th window / glass door caused by wind load in the k-th direction Setting b ik , and judge according to the following conditions: If b ik <p ik or Then the i-th window / glass door fails in the k-th direction, and D is set W,ik =1, otherwise D W,ik =0; According to D W,ik Determine the opening conditions in each direction I W,k , calculate the wind loss ratio D of windows / glass doors W .

2. The method for assessing wind-induced damage to building envelope structures based on directionality and multiple openings according to claim 1, wherein: The calculation and determination in accordance with the relationship between capacity C and demand D are specifically as follows: Judge whether the i-th window / glass door in the k-th direction is damaged when the following conditions are met: that is, C > D or C < D; where, C = capacity; D = demand.

3. The method for assessing wind damage to building envelope structures based on directionality and multiple openings according to claim 1, wherein: It further includes the following steps: Determine the opening condition I in the kth direction based on whether the i-th window / glass door in the k-th direction is damaged W,k ; and according to the opening condition I in the kth direction W,k , using the internal pressure coefficient C IN,k The net pressure in the kth direction is obtained by summing the external pressure on the roof covering plate in the kth direction; Based on the net pressure in the k-th direction, obtain the JPDF of the multi-extreme net pressure on the roof covering panel; Based on the JPDF of the multi-extreme net pressure, obtain the extreme wind pressure on the j-th roof covering panel in the k-th direction; Loop and repeat the roof covering panels in all directions to obtain the extreme wind pressures on all roof covering panels; The damage ratio D of the roof covering panels is calculated based on the relationship between capacity C and demand D according to the extreme wind pressure and random pressure on all roof covering panels. P .

4. The method for assessing wind damage to building envelope structures based on directionality and multiple openings according to claim 1, wherein: The building envelope adopts a low-rise building envelope with a three-stage progressive failure process.

5. The method for assessing wind damage to building envelope structures based on directionality and multiple openings according to claim 1, wherein: Also includes the roof covering damage ratio D P Calculate the roof covering board damage ratio D P Follow these steps to calculate: According to the opening condition I in the kth direction W,k Calculate the net pressure coefficient C on the jth roof covering plate in this direction P,jk ; According to the net pressure coefficient C P,jk The extreme value of get CDF, and vector The covariance matrix of according to The sum and the covariance matrix of the kth direction Sample calculation of the annual maximum wind load vector for roof covering panels and the upward resistance vector according to and Compare and determine D P,j , calculate the roof covering damage ratio D P .

6. A system for assessing wind damage to building envelope structures based on directionality and multiple openings, comprising a memory, a processor, and a computer program stored in the memory and executable on the processor, characterized in that: When the processor executes the program, it implements the method described in any one of claims 1 to 5 above.

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