進行可靠度評估前，需要分析極限狀態函數中各不確定性的機率特性。影響建築物耐風可靠度之不確定性可能源於風載重或結構特性，包括強風平均風速、表面風壓分布及建築物的自然頻率和阻尼比等；其中，表面風壓為空間和時間的函數。由於風載重的不確定性較顯著，因此，本研究的重點是探討如何以隨機域模擬表面風壓隨空間和時間的變化及以隱藏式馬可夫鏈（Hidden Markov Chain；HMC）模型模擬每日最大風速隨時間的變化，並以前述兩機率模型量化風載重的不確定性，應用於建築物耐風可靠度評估。
由於每日最大風速具非穩態特性，本文發展隱藏式馬可夫鏈模型來分析和模擬之；隱藏式馬可夫鏈模是由非穩態自迴歸模型和馬可夫鏈所構成。先將資料進行正規化和常態轉換，再根據貝氏分析演算法估計模型參數，其中每個參數在不同時間均為隨機變數。以實測平時風風速資料為例來驗證所提模型之準確性，數值模擬結果顯示人造資料與實測資料有近似的統計特性，所檢核的統計特性包括超越機率和非穩態行為。再以HMC模型為基礎，模擬產生長時間人造平時風風速資料，作為後續估計強風平均風速不確定性的基礎。
由於表面風壓隨時間和空間之變異具隨機性，可用隨機域來模擬之。以風洞試驗中一高寬比為6的方形建築模型的橫風向合成風壓資料為例來建立隨機域。橫風向合成風壓資料是合成兩側風面表面風壓資料，其具近似常態、空間非同質（nonhomogeneous）-時間弱穩態（weakly stationary）的特性。將橫風向合成風壓視為其標準偏差隨空間變化函數與模擬為正規化風壓的空間弱同質-時間弱穩態隨機域相乘。根據橫風向合成風壓資料建立其空間-時間交頻譜密度函數，並估計函數中的待定參數。若建築物模擬為連續系統，可直接使用所得隨機域作後續分析；若建築物模擬為離散多自由度系統，則需將所得隨機域離散化。本文採用局部空間平均法來離散隨幾域，推導離散後各區域風壓之交頻譜密度函數解析式。
說明建立隨機域的必要性，用隨機域量化表面風壓的不確定性後，以一垂直懸臂梁為例，推導由橫風向合成風壓所造成橫風向自由端加速度在強風作用延時內大於門檻值的機率解析式。
用前述兩機率模型分別量化強風平均風速和表面風壓的不確定性後，以一方形高層建築在承受 年強風平均風速作用下為例，估計由橫風向合成風壓所造成橫風向層間變位角在強風作用延時內大於門檻值的機率。以離散化多自由度線性系統作為結構分析模式，其阻尼比和自然頻率角頻率以隨機變數模擬之。由於橫風向合成風壓為時間的函數，使用快速積分法將極限狀態函數表示為條件超越機率的函數。配合蒙地卡羅模擬來估計層間變位角超越機率，得知在假設僅橫風向合成風壓具有不確定性，強風平均風速、阻尼比和自然頻率角頻率為平均值時，高模態廣義橫風向風力頻譜，要達到與低模態相同準確性，所需之離散區域須較小；較高門檻值下第1模態條件超越機率要達到與較低門檻值相同準確性，所需之離散區域須較小；條件超越機率若要達到與廣義橫風向風力頻譜相同準確性，所需的離散區域要更小。此案例分析結果顯示，若忽略強風平均風速的不確定性，在門檻值為 ，會大於未忽略時下超越機率的平均值，在門檻值 ，會小於未忽略時下超越機率的平均值。

The probability information on uncertain parameters in the limit-state function is required before reliability is evaluated. Uncertainties that are considered in evaluating structural reliability under wind loading could rise from wind loading or structure properties such as, surface pressure, strongly mean wind speed, natural frequency and damping ratio, in which surface pressure varies randomly with space and time. Due to the pronounced uncertainty of wind loading, developing a Hidden Markov Chain (HMC) model and random field model to characterize the variation in wind speed with time and that in surface pressure with space and time respectively is main part. The uncertainties of wind loading are quantified by using the previous two models, and then are used in evaluating structural reliability.

Wind speed time series are generally non-stationary, this research proposes a HMC to analyze field wind speed data and to simulate synthetic wind speed data. The recorded wind speed data is used to demonstrate the implementation of the proposed approach. It is shown that the statistical properties of the simulated data are very similar to those of the field data. Long-term synthetic wind speed data is generated based on HMC, and then is used to estimate the uncertainty of strongly mean wind speed.

Variation in surface pressure with space and time is random, this research proposes a random field model to simulate the uncertainty of surface pressure. The recorded surface pressure data is used to establish an analytical random filed model for across-wind integration pressure data. Across-wind integration pressure is characterized by a Gaussian, space nonhomogeneous and time weakly stationary random field. A function form of space-time cross-spectral density function of the random field is determined by analyzing integration pressure data, and the parameters in the function are estimated by fitting integration pressure data. If a building is modeled as a MDOF system, the random filed is discretized. Local average method is used to discretize the random field, and cross-spectral density analytical function of spatial averages is derived.

To show that developing random field is necessary, an analytical solution for the reliability of top acceleration of a cantilever beam which is represented by a linear continuous system subjected to across-wind integration pressure which is modeled as a random field is derived.

To show the previous two models’ application in reliability analyses, the reliability of interstory drift ratio of a building which is represented by a MDOF system subjected to across-wind integration pressure which is modeled as a random field is estimated considering uncertainties of parameters in the wind loading and structure properties. Because the across-wind integration pressure is the function of time, the limit-state function can be described by a function of conditional probability using fast integration method. The overall probability is estimated by using Monte-Carlo simulations. The numerical results are as follows:
1. If across-wind integration pressure is uncertain and strongly mean wind speed, natural frequency and damping ratio are equal to their mean values, the size of segment for high mode generalized across-wind force spectra is smaller than that of segment for low mode generalized across-wind force spectra to have the same accuracy for high mode and low mode generalized across-wind force spectra.
2. If across-wind integration pressure is uncertain and strongly mean wind speed, natural frequency and damping ratio are equal to their mean values, the size of segment for conditional probability in high threshold is smaller than that of segment for conditional probability in low threshold to have the same accuracy for high and low threshold.
3. For this example, the probability with negligence of the uncertainty of the strongly mean wind speed is larger than that with consideration of parameter uncertainties for thresholds of 0.005, 0.006 and 0.007; the probability with negligence of the uncertainty of the strongly mean wind speed is smaller than that with consideration of parameter uncertainties for a threshold of 0.008.

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