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It is very im 】 )ortant to estima 重e 重he cumula 童ive damage of bui 】 dings by a strong ground mo1 沁 】 l quanti 重atively ， becavse i重 is necessary to judge whether they are ableIo be ロ sed ot not in future ， Even af 量er 量hey are judged 10 be ab 】 e to bc used ， jl is a 】 so ne じessary lQ judge the amount or method of reinfoTcing thじm ． ln this paper ， the estimation of cumulative damage of buildillg wilh hys 重eretic restoring force by using wavelet analysis ｛ o strong response mot 沁 n is proposed ． Firs 日y ， j重 was assumed that the abm )rmal signa ［ s might be contained in t血¢ obsefved accelera 重ion records 、 ． which shou 】d be prDduced auhe poin 重 changing from elastlc Ij皿 it to plastic 且 imit and migh 重 be detected by wave 】 et ana 】 ysis ． ThrQugh 重he nllmerical evalua1io 旧 using the mod 巳 】 ， it is proved lha 目 his assump 重ioll is じ orrcct and it is cenfirmed thatrthe wave ］ et analysis will be llsed 重o estinla 電e tlle cumu 】 ativc damagc Df bui 且dings by eur 瑠hquake ， effe じ tively ．

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This paper dea】 s with the active control of respo 皿se of structures such as bui］ dings and towers using a 加 11ed mass damperwith pendulum and lever mechanism (LP − TMD) ． During a s 重 rong earlhquake ， a stru〔 加 re shows the no 】 11inear respoIlse due to hystereticres10ring force alld the 1he changes in stiffness and damping occur ． Theref()re ， tlle colltrol system shou 工 d have the robustness ． 111 this paper ， a sliding mode co 皿 tro工methodwitll strong robustlless is iltroduced to control the response of I】onlinear s重 ructure ． The active control system of TMD with pelldulum and lever based on the sliding mode co 皿trol method is applied to the f()ur − degree − of − freedom

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