# Determining the Optimal Scalar Intensity Measure of Floor Communication Towers

Authors: Bo Li; Qinghui Lai; Endong Guo; Chenxi Mao; Xiaofei Li
Journal: Shock and Vibration
 (2022)

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## Abstract

Various structural types and ground motion characteristics lead to distinct intensity measures of structural seismic performance. For the lattice high-rise steel structure of communication towers, determining the intensity measures to adjust ground motion is critical. Additionally, a crucial problem is whether the ground motion intensity parameters of pulse-like ground motion and ordinary ground motion are consistent. In this study, a standard floor four-leg angle steeled communication tower was considered the study object, and 50 pulse-like ground motions and 50 ordinary ground motions were identified to form a pulse-like ground motion set and ordinary ground motion set, respectively. For comparative analyses, 15 ground motion parameters, including amplitude, spectrum, duration, and energy parameters, were selected. The results revealed that for the lattice towers, such as communication tower, under the action of pulse-like ground motion or ordinary ground motion, efficiency, practicability, and sufficiency should be considered. Furthermore, the most suitable intensity measure was the spectral acceleration corresponding to the natural period of the tower. This study provides a basis for selecting the ground motion for dynamic time history analysis of the lattice steel tower.


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## Body

## 1. Introduction

With the continuous development of 5G communication technology and Internet, portable communication network services and applications, such as smartphone payment, online office and teaching, and webcast, have become an indispensable part of people's daily lives. As the main carrier of the communication antenna, the operation of communication towers is primarily associated with the smoothness of the communication system. Conventionally, the design of communication towers is considered for the perspective of its wind resistance performance [1–3]. However, China's Wenchuan earthquake, Yushu earthquake, and Japan’s ‘311’ earthquake and other earthquake damage investigations have revealed that in the event of an earthquake, damage to communication towers results in the suspension of communication with the outside world in some areas [4, 5]. In such scenarios, rescue operations cannot be performed effectively, causing considerable casualties and loss of property.Typically, dynamic time history analysis is used to analyse the seismic performance of structures. The results revealed that the ground motion parameters (intensity measures, IMi) suitable for the study of structural seismic performance differed with the type of structures and ground motion characteristics. For lattice towers, including transmission towers and communication towers, currently, the seismic intensity measures identified by dynamic time history analysis or amplitude modulated ground motion predominantly involve peak acceleration (PGA) [6, 7], peak velocity (PGV) [8], spectral acceleration Sa(T1) corresponding to the natural period of the structure [9, 10] and the ratio of peak velocity to peak acceleration (V/A) [11]. In theoretical research and engineering practice, ground motion intensity is typically quantitatively characterised by ground motion parameters, in which scalar parameters predominantly include amplitude parameters, spectrum parameters, duration parameters, and energy parameters [12–14]. The use of appropriate intensity measures to select and adjust natural ground motion and the selection of appropriate engineering demand parameters (EDP) to evaluate structural damage are conducive to reducing the discrete type of structural dynamic time history analysis results and improving calculation efficiency. Therefore, the selection of reliable intensity measures is critical for structural dynamic response analysis. Compared with ordinary ground motion, pulse-like earthquakes typically exhibit a wide response spectrum sensitive area. Because earthquakes produce high-energy input to the structure in a short time, this ground motion typically causes considerable damage to the engineering structure. However, for the lattice high-rise steel structure of the communication tower, determining the type of intensity measure that is the most effective to specify and adjust ground motion is critical. Currently, limited studies have been conducted to determine if the most effective parameters of pulse-like ground motion and ordinary ground motion are consistent.In this study, a standard floor four-leg angle steeled communication tower was considered the research object, 50 pulse-like ground motions and 50 ordinary ground motions were gathered from PEER ground motion data centre to form the pulse and ordinary ground motion sets, respectively. A total of 15 ground motion parameters, including amplitude parameters, spectrum parameters, duration parameters, and energy parameters, were selected for comparative analysis. Considering the uncertainty of the input ground motion, the optimal intensity measures under pulse-like ground motion and ordinary earthquake action were selected from the perspectives of efficiency, practicability, and sufficiency. This study provides a basis of selecting ground motion for dynamic time history analysis of lattice steel tower.


## 2. Ground Motion Records

In the process of dynamic time history analysis of earthquakes, accurate evaluation of ground motion is critical for determining whether the analysis results are effective. Pulse-like ground motion closely related to the relative position between site and seismic fault has attracted considerable attention in structural engineering. Because its main energy occurs in a concentrated time or frequency domain, pulse-like ground motion is generally recognised as the key factor causing severe damage to all engineering structures.By using the simplified and efficient method proposed by Zhai [15] for quantitatively identifying pulse-like ground motions, 50 pulse-like and 50 ordinary ground motions were obtained from the PEER ground motion database to form pulse-like and ordinary ground motion sets, and the cloud analysis method was employed to analyse the structure [16, 17]. The established ground motions are listed in Table 1.Table 1
Selected ground motions.
(a) Pulse-like ground motionsSeq.RSNEventYearStationMEpiD (km)177San fernando1971Pacoima dam6.6111.872184Imperial Valley-061979El centro6.5327.233250Mammoth Lakes-061980Long valley dam5.9414.044296Irpinia, Italy-021980Bagnoli irpinio6.222.295503Taiwan SMART1(40)1986SMART1 C006.3268.186506Taiwan SMART1(40)1986SMART1 I076.3267.987540N. Palm springs1986Whitewater6.064.248614Whittier Narrows-011987Downey—birchdale5.9915.299645Whittier Narrows-011987LB—orange ave5.9920.6810732Loma Prieta1989APEEL 26.9363.4911738Loma prieta1989Alameda naval air6.9390.7712764Loma prieta1989Gilroy6.9328.1113779Loma prieta1989LGPC6.9318.4614784Loma prieta1989Oakland—title6.9391.6815787Loma prieta1989Palo alto—SLAC lab6.9351.216802Loma prieta1989Saratoga—aloha ave6.9327.2317803Loma prieta1989Saratoga—W valley6.9327.0518805Loma prieta1989Stanford park. Garage6.9318.6019808Loma prieta1989Treasure island6.9397.4320821Erzican, Turkey1992Erzincan6.698.9721879Landers1992Lucerne7.2844.0222900Landers1992Yermo fire station7.2885.9923953Northridge-011994Beverly hills6.6913.3924960Northridge-011994Canyon country6.6926.4925963Northridge-011994Castaic6.6940.68261003Northridge-011994LA—saturn st6.6925.52271004Northridge-011994LA—sepulveda6.698.48281007Northridge-011994Los angeles6.6936.47291013Northridge-011994LA dam6.6911.79301045Northridge-011994Newhall6.6921.55311050Northridge-011994Pacoima Dam6.6920.36321054Northridge-011994Pardee—SCE6.6925.65331081Northridge-011994Stone canyon6.6921.75341084Northridge-011994Converter sta6.6913.11351085Northridge-011994Converter sta east6.6913.60361106Kobe, Japan1995KJMA6.9018.27371116Kobe, Japan1995Shin-osaka6.9045.97381119Kobe, Japan1995Takarazuka6.9038.60391120Kobe, Japan1995Takatori6.9013.12401148Kocaeli, Turkey1999Arcelik7.5153.68411170Kocaeli, Turkey1999Sakarya7.5190.66421176Kocaeli, Turkey1999Yarimca7.5119.30431182Chi-chi, Taiwan1999CHY0067.6240.47441197Chi-chi, Taiwan1999CHY0287.6232.67451198Chi-chi, Taiwan1999CHY0297.6239.70461231Chi-chi, Taiwan1999CHY0807.6231.65471244Chi-chi, Taiwan1999CHY1017.6231.96481504Chi-chi, Taiwan1999TCU0677.6228.70491550Chi-chi, Taiwan1999TCU1367.6248.75501602Duzce, Turkey1999Bolu7.1441.27(b) Ordinary ground motionsSeq.RSNEventYearStationMEpiD (km)1432Taiwan SMART1(25)1983SMART1 O016.50100.6421036Northridge-011994Mojave—hwys 146.69102.2431163Northridge-011994Rinaldi receiving sta7.51101.8641217Chi-chi, Taiwan1999CHY0607.6291.0851471Chi-chi, Taiwan1999TCU0157.62101.6261747Little skull mtn, NV1992Station #85.6599.6671789Hector mine1999Hesperia—4th and palm7.1398.5381929Anza-022001Corona4.92101.5691969Anza-022001Riverside4.92101.05101973Anza-022001Riverside Airport4.9299.31111995Gulf of California2001El Centro Array #115.7102.56122178Chi-chi, Taiwan-021999CHY0546.20100.24132833Chi-chi, Taiwan-021999KAU0786.20100.58142959Chi-chi, Taiwan-051999CHY0556.20102.15152961Chi-chi, Taiwan-051999CHY0576.20100.40162965Chi-chi, Taiwan-051999CHY0616.20100.17172966Chi-chi, Taiwan-051999CHY0626.20100.04182988Chi-chi, Taiwan-051999CHY1006.2099.39192990Chi-chi, Taiwan-051999CHY1076.2098.67203072Chi-chi, Taiwan-051999ILA0626.20102.97213073Chi-Chi, Taiwan-051999ILA0646.20102.68223074Chi-chi, Taiwan-051999ILA0666.2099.75233165Chi-chi, Taiwan-051999TCU0336.2099.89243194Chi-chi, Taiwan-051999TCU0856.20100.36253280Chi-chi, Taiwan-061999CHY0446.30101.89263286Chi-chi, Taiwan-061999CHY0556.30100.75273287Chi-chi, Taiwan-061999CHY0576.30100.89283291Chi-chi, Taiwan-061999CHY0616.30101.92293292Chi-chi, Taiwan-061999CHY0626.30101.03303316Chi-chi, Taiwan-061999CHY1006.3098.81313392Chi-Chi, Taiwan-061999ILA0666.30100.46323484Chi-chi, Taiwan-061999TCU0946.30100.17333531Chi-chi, Taiwan-061999TTN0246.30100.37343584Taiwan SMART1(25)1983SMART1 I106.5099.30353585Taiwan SMART1(25)1983SMART1 I116.5099.33363586Taiwan SMART1(25)1983SMART1 I126.5099.36373587Taiwan SMART1(25)1983SMART1 M026.5099.47383590Taiwan SMART1(25)1983SMART1 M056.5098.24393601Taiwan SMART1(25)1983SMART1 O096.5099.68403783Hector mine1999Beaumont7.1398.80413883Tottori, Japan2000HRS0176.61100.23423917Tottori, Japan2000OKY0146.61100.93433946Tottori, Japan2000SMN0186.61102.27443957Tottori, Japan2000SMNH136.6199.33454152Niigata, Japan2004FKS0216.6398.33464154Niigata, Japan2004FKS0236.6398.25474240Niigata, Japan2004TCG0096.63101.23484244Niigata, Japan2004TCGH096.63101.85495001Chuetsu-oki, Japan2007FKSH016.8099.92505060Chuetsu-oki, Japan2007GNM0016.80100.83


## 3. Intensity Measures

A reasonable intensity measure is a critical basis for evaluating the structural response and recoverable ability of the structural seismic function. This measure should reflect the structural seismic response index or damage indexes. The selection of intensity measures should be comprehensive and cover three elements of ground motion, namely amplitude parameters, spectrum parameters, and duration parameters, as well as energy parameters [12–14, 18]. The selection of intensity measures should specify representative ground motion parameters with clear physical meaning, wide application range, and high frequency in seismic engineering. The representative intensity measures discussed in this study are presented in Table 2. The intensity measures considered in this study did not include vector parameters.Table 2
IMs considered in this study.
ClassIMiExpressionNotationDefinition/referencesAmplitude parametersPGAPeak ground accelerationPGA=maxatPGVPeak ground velocityPGV=maxνtPGDPeak ground displacementPGD=maxdtV/ARatio of peak velocity to peak accelerationPGV/PGASpectrum parametersEPAEffective peak accelerationEPA=Sa/2.5EPVEffective peak velocityEPV=Sv/2.5SIHousner spectral intensitySIζ=∫0.12.5SVζ,TdtSa(T1)Spectral acceleration at the fundamental periodSaT1,ξDuration parametersUduConsistent durationUdu=∑itiSduDuration of strong ground motionS90=t95−t5Energy parametersCAVCumulative absolute velocityCAV=∫0tmaxatdtCAVSStandard cumulative absolute velocityCAVS=∑i∫titi+1WiatdtMIVMaximum incremental speedMIV=max∫0tmaxatdtMIDMaximum incremental displacementMID=max∫0tmaxvtdtAIArias intensityIA=π/2g∫0ta2tdt


## 4. Description of the Model

### 4.1. Overview of the Selected Tower and Finite Element Model

To analyse object representative, a 50 m high falling four-legged steel tower was selected as the structural prototype of the standard Atlas of communication tower formulated by China Tower Co. Ltd. General finite element software ABAQUS was used to construct the finite element model. Q345 and Q235 section steel was used for main material and inclined material, respectively, which were simulated by the beam element. The damping ratio is 2%. As a high-rise structure, the communication tower is highly influenced by the p-delta effect. Therefore, initial defects were introduced in the analysis process. Considering the influence of bending and shear deformation of members, the contribution to structural stiffness to natural vibration period and frequency was consistent with those in practice, and the geometric nonlinearity of the structure was considered. Because of the material nonlinearity of structural steel, pursuant to the ideal elastic-plastic assumption, von Mises criterion was implemented as the material yield criterion, and the double broken line constitutive model was adopted as the material constitutive model. The mechanical parameters are presented in Table3. The antenna platform at the top of the tower, lightning rod, bolts, and ladders at each section were applied as additional loads at the horizontal nodes of each section. The sketch of the prototype structure is displayed in Figure 1, and the components size and the additional mass of the tower are displayed in Table 4. The bottom of the tower was absolutely consolidated. According to the modal analysis, the mass participation ratios of the first three modes are 37.2%, 34.4%, and 20.5%, totally 92.1%. The first three mode shapes are shown in Figure 2.Table 3
Mechanical properties of Q345 and Q235.
MaterialYield stress (Pa)Strain-hardening ratioYoung’ modulus (Pa)Poisson’s ratioDensity (kg/m3)Q3453.45 E + 81.372.06 E + 110.37850Q2352.35 E + 82.06 E + 110.37850Figure 1
Sketch of the prototype Structure (unit: mm).Table 4
Components size.
Legs (unit: mm)Braces (unit: mm)Added mass (kg)L80 x 6L50 x 51003.3L100 x 8L56 x 5971.6L125 x 10L63 x 51126.7L140 x 12L63 x 51247.8L160 x 14L63 x 5273.4L180 x 16L70 x 5290.6L180 x 16L80 x 6270.3L200 x 16L90 x 7280.5L200 x 18L100 x 7295.6Figure 2
Mode shapes of (a) first order, (b) second order, and (c) third order.
(a)(b)(c)


### 4.2. Model Verification

The rationality of the finite element model is directly relevant to the reliability of the analysis results. To verify the rationality of the aforementioned model, a 50-m four-legged steel tower was designed conforming to the standard Atlas of communication tower in Harbin, Heilongjiang Province, for the frequency test. A three-way acceleration sensor was placed on the top platform of the tower with a height of 48.2 m (Figure3). Pile foundations were used for the tower, and the soil was hard, which can be approximately equivalent to the fixed constraint at the bottom. According to the conversion relationship between the fundamental frequency and the first period, the natural periods in X and Y directions of the actual structure and finite element model were derived, as presented in Table 5. The natural period difference between the finite element model and the prototype structure of both directions was less than 15%, which revealed the finite element model of communication tower based on ABAQUS to be acceptable and reliable.Figure 3
Measured real (a) angle steel and (b) example of the installed three-directional acceleration transducers used for the measurements.
(a)(b)Table 5
Comparison of the natural periods between the model and the prototype structure.
XYF (Hz)T1 (s)f (Hz)T1 (s)Prototype tower1.510.661.500.67FE model1.740.571.740.57Difference-13.6%-14.9%


### 4.3. Structural Response

The function of the communication tower is to support the transmission antenna to receive and transmit signals in an area. The dynamic response to the tower under an earthquake is principally monitored by using the maximum roof drift (MRD) of the tower top relative to the tower bottom. Furthermore, as a lattice high-rise steel structure, the communication tower exhibits a large acceleration amplification effect at the top of the tower under the action of a horizontal earthquake, whereas the communication antenna and the tower top platform are mainly linked by bolts. The amplified acceleration at the top of the tower exhibits a large dynamic response to the connected bolts. Therefore, the acceleration amplification factor (AAF) at the top of the tower is a critical structural dynamic response demand parameter. Therefore, in this study, MRD and AAF were assigned as EDP. The structural response to the communication tower under the action of pulse-like ground motions and ordinary ground motions along theX direction is listed in Table 6.Table 6
Structural responses to pulse-like GMs and ordinary GMs.
Pulse-like GMsOrdinary GMsSequenceMRD (mm)AAFNo.MRD (mm)AAFPL1504.13OR1208.63PL2302.81OR 2209.47PL3784.89OR37013.71PL4434.65OR44015.87PL51107.80OR5608.71PL6725.71OR638.64PL72104.79OR7145.56PL81606.89OR815.88PL938010.14OR917.11PL101108.10OR1017.38PL112704.04OR11710.36PL121606.20OR1258.06PL131405.77OR13258.82PL141506.14OR143010.91PL15704.74OR152212.64PL161306.24OR16118.82PL1750014.32OR17307.68PL181607.79OR18209.13PL191708.19OR19108.16PL2027010.76OR2087.30PL21805.25OR211513.75PL221105.77OR22206.64PL232206.40OR2333.87PL241506.66OR242010.09PL251202.91OR25439.37PL263205.63OR2656.00PL272108.88OR27169.42PL281006.26OR28208.09PL291805.57OR294611.51PL303906.19OR301813.29PL311006.54OR311010.94PL321407.58OR3268.93PL33806.91OR331510.46PL342505.88OR34169.87PL351105.06OR351610.46PL36807.07OR362413.82PL371909.15OR371204.75PL382507.56OR382010.41PL392005.67OR3994.79PL40504.93OR40169.60PL4114012.22OR41229.02PL42705.58OR4245.57PL43807.45OR43168.50PL441507.94OR4435.21PL451306.81OR45206.14PL46404.13OR46237.53PL47905.91OR474012.10PL481507.65OR4856.81PL491007.05OR4924.75PL501408.99OR5084.30


## 4.1. Overview of the Selected Tower and Finite Element Model

To analyse object representative, a 50 m high falling four-legged steel tower was selected as the structural prototype of the standard Atlas of communication tower formulated by China Tower Co. Ltd. General finite element software ABAQUS was used to construct the finite element model. Q345 and Q235 section steel was used for main material and inclined material, respectively, which were simulated by the beam element. The damping ratio is 2%. As a high-rise structure, the communication tower is highly influenced by the p-delta effect. Therefore, initial defects were introduced in the analysis process. Considering the influence of bending and shear deformation of members, the contribution to structural stiffness to natural vibration period and frequency was consistent with those in practice, and the geometric nonlinearity of the structure was considered. Because of the material nonlinearity of structural steel, pursuant to the ideal elastic-plastic assumption, von Mises criterion was implemented as the material yield criterion, and the double broken line constitutive model was adopted as the material constitutive model. The mechanical parameters are presented in Table3. The antenna platform at the top of the tower, lightning rod, bolts, and ladders at each section were applied as additional loads at the horizontal nodes of each section. The sketch of the prototype structure is displayed in Figure 1, and the components size and the additional mass of the tower are displayed in Table 4. The bottom of the tower was absolutely consolidated. According to the modal analysis, the mass participation ratios of the first three modes are 37.2%, 34.4%, and 20.5%, totally 92.1%. The first three mode shapes are shown in Figure 2.Table 3
Mechanical properties of Q345 and Q235.
MaterialYield stress (Pa)Strain-hardening ratioYoung’ modulus (Pa)Poisson’s ratioDensity (kg/m3)Q3453.45 E + 81.372.06 E + 110.37850Q2352.35 E + 82.06 E + 110.37850Figure 1
Sketch of the prototype Structure (unit: mm).Table 4
Components size.
Legs (unit: mm)Braces (unit: mm)Added mass (kg)L80 x 6L50 x 51003.3L100 x 8L56 x 5971.6L125 x 10L63 x 51126.7L140 x 12L63 x 51247.8L160 x 14L63 x 5273.4L180 x 16L70 x 5290.6L180 x 16L80 x 6270.3L200 x 16L90 x 7280.5L200 x 18L100 x 7295.6Figure 2
Mode shapes of (a) first order, (b) second order, and (c) third order.
(a)(b)(c)


## 4.2. Model Verification

The rationality of the finite element model is directly relevant to the reliability of the analysis results. To verify the rationality of the aforementioned model, a 50-m four-legged steel tower was designed conforming to the standard Atlas of communication tower in Harbin, Heilongjiang Province, for the frequency test. A three-way acceleration sensor was placed on the top platform of the tower with a height of 48.2 m (Figure3). Pile foundations were used for the tower, and the soil was hard, which can be approximately equivalent to the fixed constraint at the bottom. According to the conversion relationship between the fundamental frequency and the first period, the natural periods in X and Y directions of the actual structure and finite element model were derived, as presented in Table 5. The natural period difference between the finite element model and the prototype structure of both directions was less than 15%, which revealed the finite element model of communication tower based on ABAQUS to be acceptable and reliable.Figure 3
Measured real (a) angle steel and (b) example of the installed three-directional acceleration transducers used for the measurements.
(a)(b)Table 5
Comparison of the natural periods between the model and the prototype structure.
XYF (Hz)T1 (s)f (Hz)T1 (s)Prototype tower1.510.661.500.67FE model1.740.571.740.57Difference-13.6%-14.9%


## 4.3. Structural Response

The function of the communication tower is to support the transmission antenna to receive and transmit signals in an area. The dynamic response to the tower under an earthquake is principally monitored by using the maximum roof drift (MRD) of the tower top relative to the tower bottom. Furthermore, as a lattice high-rise steel structure, the communication tower exhibits a large acceleration amplification effect at the top of the tower under the action of a horizontal earthquake, whereas the communication antenna and the tower top platform are mainly linked by bolts. The amplified acceleration at the top of the tower exhibits a large dynamic response to the connected bolts. Therefore, the acceleration amplification factor (AAF) at the top of the tower is a critical structural dynamic response demand parameter. Therefore, in this study, MRD and AAF were assigned as EDP. The structural response to the communication tower under the action of pulse-like ground motions and ordinary ground motions along theX direction is listed in Table 6.Table 6
Structural responses to pulse-like GMs and ordinary GMs.
Pulse-like GMsOrdinary GMsSequenceMRD (mm)AAFNo.MRD (mm)AAFPL1504.13OR1208.63PL2302.81OR 2209.47PL3784.89OR37013.71PL4434.65OR44015.87PL51107.80OR5608.71PL6725.71OR638.64PL72104.79OR7145.56PL81606.89OR815.88PL938010.14OR917.11PL101108.10OR1017.38PL112704.04OR11710.36PL121606.20OR1258.06PL131405.77OR13258.82PL141506.14OR143010.91PL15704.74OR152212.64PL161306.24OR16118.82PL1750014.32OR17307.68PL181607.79OR18209.13PL191708.19OR19108.16PL2027010.76OR2087.30PL21805.25OR211513.75PL221105.77OR22206.64PL232206.40OR2333.87PL241506.66OR242010.09PL251202.91OR25439.37PL263205.63OR2656.00PL272108.88OR27169.42PL281006.26OR28208.09PL291805.57OR294611.51PL303906.19OR301813.29PL311006.54OR311010.94PL321407.58OR3268.93PL33806.91OR331510.46PL342505.88OR34169.87PL351105.06OR351610.46PL36807.07OR362413.82PL371909.15OR371204.75PL382507.56OR382010.41PL392005.67OR3994.79PL40504.93OR40169.60PL4114012.22OR41229.02PL42705.58OR4245.57PL43807.45OR43168.50PL441507.94OR4435.21PL451306.81OR45206.14PL46404.13OR46237.53PL47905.91OR474012.10PL481507.65OR4856.81PL491007.05OR4924.75PL501408.99OR5084.30


## 5. Evaluation of IM

### 5.1. Results in Terms of Efficiency

The efficiency of intensity measures reveals that under a certain ground motion intensity condition, the discrete engineering structure requires small parameters. On the premise of not lowering the calculation accuracy, the estimated conditional probabilityPEDP|IM can be reduced, and the number of seismic records and dynamic time history analysis conditions required for analysis can be reduced to a certain extent. Typically, the validity of ground motion parameters is determined by conditional logarithmic standard deviation β to judge, and efficiency is the core index used to measure the superiority over an IMi [19].The relationship between the EDP and IMi approximately satisfies the logarithmic relationship, and its relationship formula is displayed as follows:(1)lnEDP=lna+b·lnIMi.The aforementioned formula satisfies the univariate linear regression model, and the least square principle can be used to perform regression analysis on the obtainedn scatter points (IMi, EDPi) to obtain the empirical regression lines of ln(IMi) and ln(EDP) and obtain the conditional logarithmic standard deviation, as follows.(2)βlnEDP|IMi=∑lnEDP−lna·IMib2n−2.For any intensity measureIMi, the smaller the conditional logarithmic standard deviation, βlnEDP|IMi, is the smaller the discrete type of seismic response to engineering structure is, indicating that the efficiency of the ground motion parameter IMi is higher, otherwise, the efficiency is lower.Under the action of pulse-like ground motions and ordinary ground motions, the conditional logarithmic standard deviation,βlnEDP|IMi, corresponding to the intensity measures to be analysed, and the structural dynamic response (MRD and AAF) was calculated by using the cloud analysis method, as displayed in Figure 4.(1)
For MRD and AAF, the conditional logarithmic standard deviationβlnEDP|IMi of spectrum parameters is the smallest, that is, among the four aforementioned four ground motion intensity parameters, spectrum parameters are the most effective.(2)
Figure4(a) reveals for the MRD, under the action of pulse-like ground motions and ordinary ground motions, with the exception that the conditional logarithmic standard deviation βlnEDP|IMi corresponding to Sa(T1) is basically equal, the values of other intensity measures corresponding to pulse-like ground motions are smaller. The MRD are predicted more efficiently with pulse-like ground motions than with ordinary motions, that is, regression models are better fitted to data from the pulse-like ground motion set than to that from ordinary sets.(3)
Figure4(b) reveals that for the AAF, βlnEDP|IMi corresponding to the duration parameters (Udu and Sdu) and CAV in the energy parameters under the action of pulse ground motion is significantly less than that under the action of ordinary ground motion, while the values of βlnEDP|IMi corresponding to other ground motion parameters are close under the action of pulse-like ground motions and ordinary ground motions.(4)
The aforementioned results revealed that for MRD and AAF, the discrete type of ground motion parameters considered in this study were less than that under ordinary ground motion. From the perspective of efficiency, the top-five most effective intensity measures are amplitude parameter PGA, spectrum parameters Sa (T1) and EPA, and energy parameters CAV and CAVs. The logarithmic standard deviation βlnEDP|IMi from duration parameter conditions is higher than 0.5, representing large discrete and unreliable intensity measures.Figure 4
Reveals the following: (a) MRD and (b) AAF, obtained from the cloud analysis subjected to pulse-like and ordinary ground motions.
(a)(b)


### 5.2. Results in Terms of Practicality

Practicality refers to whether a direct correlation exists between an IM and the engineering demand placed on the structure. For a specified intensity measure, the practicability is not strong, which indicates that the seismic response to the engineering structure is slightly influenced by the change in this parameter. The quantitative index of practicability can be assessed by using linear regression coefficientb given in (1). The larger the value of b is, the greater the influence of the change of intensity measures on the seismic response to engineering structures is, that is, the stronger the correlation is, the higher the practicability is; if the value of b is close to 0, the change in intensity measures does not affect the seismic response to engineering structures [20]. An example of the relative practicality of intensity measures is displayed in Figure 5.Figure 5
Example of the relative practicality of intensity measures.The regression coefficientb corresponding to various intensity measures can be derived by fitting the straight line of (1), as displayed in Figure 6. For intensity measures, the requirements of efficiency and practicability must be simultaneously met; therefore, only the practicability of the five most effective ground motion parameters evaluated in the previous step can be compared. The practicability of the selected intensity measures under the action of pulse-like ground motions is stronger than that under the action of ordinary ground motions. For the spectrum parameters EPA and Sa(T1), the regression coefficient b corresponding to Sa(T1) is larger. Thus, the practicability of Sa(T1) is stronger than EPA. This result reveals that Sa(T1) related to the vibration characteristics of the structure is more sensitive to the structural demand parameters than EPA. Furthermore, according to Figure 6(a) and 6(b), the regression coefficient b corresponding to CAVs under ordinary ground motion is close to 0, indicating poor practicability, that is, there is small or no dependence of the level of engineering demand on the CAV level. Typically, the amplitude parameter PGA, spectrum parameter Sa(T1), and energy parameter CAV are highly practical.Figure 6
Regression coefficient,b, corresponding to the engineering demanded parameters (a) MRD and (b) AAF, obtained from the cloud analysis subjected to pulse-like and ordinary ground motions.
(a)(b)


### 5.3. Results in Terms of Sufficiency

Sufficiency is a crucial index to assess the independence of the ground motion parameter and indicates the correlation between the ground motion parameter (IMi) and ground motion information parameter (magnitude M or source-to-site distance R). A sufficient ground motion parameter should be statistically independent of the ground motion information parameter. If the demand residuals and seismic information parameters are not statistically independent of each other, the p value of regression analysis would be less than the given significance level, indicating that the sufficiency of IMi is poor. The p value of 0.05 was considered the cutoff for an insufficient IMi. If the p value value is larger, the sufficiency of IM would be stronger [21]. Because of the limitations on the length of the article, only the scatter and fitting line expressions of the required residual of AAF and magnitude M when PGA is a ground motion parameter are presented in Figure 7.Figure 7
Testing the sufficiency of PGA with respect to M for predicting AAF.Thep values derived from the three highly practical intensity measures PGA, Sa(T1), and CAV for the seismic magnitude and source-to-site distance F-text are displayed in Figure 8. The results reveal that under the action of ordinary ground motions, the p value among PGA, CAV, and magnitude M is equal to 0, indicating a complete linear correlation and sufficiency is 0. If PGA or CAV is taken as IM to select the ground motions for the dynamic time history analysis of the floor four-leg angle steeled communication tower, the results are strongly related to the magnitude of the earthquake event. Under the action of pulse-like ground motions, the p value between PGA and source-to-site distance R is equal to 0, demonstrating complete linear correlation. Only the correlation coefficient p value between the spectrum parameter Sa(T1) and the magnitude M or source-to-site distance R is greater than the given significance level of 0.05 under the action of pulse-like ground motions or ordinary ground motions, that is, it satisfies the sufficiency requirements.Figure 8
Medianp values obtained from investigating the sufficiency of typical IMi with respect to (a) magnitude and (b) source-to-site distance.
(a)(b)Briefly, for the lattice tower such as the communication tower, irrespective of whether under the action of pulse-like and ordinary ground motions, the most suitable intensity measure is the spectral acceleration Sa(T1) corresponding to the natural period of the structure from the three aspects of efficiency, practicability, and sufficiency.


## 5.1. Results in Terms of Efficiency

The efficiency of intensity measures reveals that under a certain ground motion intensity condition, the discrete engineering structure requires small parameters. On the premise of not lowering the calculation accuracy, the estimated conditional probabilityPEDP|IM can be reduced, and the number of seismic records and dynamic time history analysis conditions required for analysis can be reduced to a certain extent. Typically, the validity of ground motion parameters is determined by conditional logarithmic standard deviation β to judge, and efficiency is the core index used to measure the superiority over an IMi [19].The relationship between the EDP and IMi approximately satisfies the logarithmic relationship, and its relationship formula is displayed as follows:(1)lnEDP=lna+b·lnIMi.The aforementioned formula satisfies the univariate linear regression model, and the least square principle can be used to perform regression analysis on the obtainedn scatter points (IMi, EDPi) to obtain the empirical regression lines of ln(IMi) and ln(EDP) and obtain the conditional logarithmic standard deviation, as follows.(2)βlnEDP|IMi=∑lnEDP−lna·IMib2n−2.For any intensity measureIMi, the smaller the conditional logarithmic standard deviation, βlnEDP|IMi, is the smaller the discrete type of seismic response to engineering structure is, indicating that the efficiency of the ground motion parameter IMi is higher, otherwise, the efficiency is lower.Under the action of pulse-like ground motions and ordinary ground motions, the conditional logarithmic standard deviation,βlnEDP|IMi, corresponding to the intensity measures to be analysed, and the structural dynamic response (MRD and AAF) was calculated by using the cloud analysis method, as displayed in Figure 4.(1)
For MRD and AAF, the conditional logarithmic standard deviationβlnEDP|IMi of spectrum parameters is the smallest, that is, among the four aforementioned four ground motion intensity parameters, spectrum parameters are the most effective.(2)
Figure4(a) reveals for the MRD, under the action of pulse-like ground motions and ordinary ground motions, with the exception that the conditional logarithmic standard deviation βlnEDP|IMi corresponding to Sa(T1) is basically equal, the values of other intensity measures corresponding to pulse-like ground motions are smaller. The MRD are predicted more efficiently with pulse-like ground motions than with ordinary motions, that is, regression models are better fitted to data from the pulse-like ground motion set than to that from ordinary sets.(3)
Figure4(b) reveals that for the AAF, βlnEDP|IMi corresponding to the duration parameters (Udu and Sdu) and CAV in the energy parameters under the action of pulse ground motion is significantly less than that under the action of ordinary ground motion, while the values of βlnEDP|IMi corresponding to other ground motion parameters are close under the action of pulse-like ground motions and ordinary ground motions.(4)
The aforementioned results revealed that for MRD and AAF, the discrete type of ground motion parameters considered in this study were less than that under ordinary ground motion. From the perspective of efficiency, the top-five most effective intensity measures are amplitude parameter PGA, spectrum parameters Sa (T1) and EPA, and energy parameters CAV and CAVs. The logarithmic standard deviation βlnEDP|IMi from duration parameter conditions is higher than 0.5, representing large discrete and unreliable intensity measures.Figure 4
Reveals the following: (a) MRD and (b) AAF, obtained from the cloud analysis subjected to pulse-like and ordinary ground motions.
(a)(b)


## 5.2. Results in Terms of Practicality

Practicality refers to whether a direct correlation exists between an IM and the engineering demand placed on the structure. For a specified intensity measure, the practicability is not strong, which indicates that the seismic response to the engineering structure is slightly influenced by the change in this parameter. The quantitative index of practicability can be assessed by using linear regression coefficientb given in (1). The larger the value of b is, the greater the influence of the change of intensity measures on the seismic response to engineering structures is, that is, the stronger the correlation is, the higher the practicability is; if the value of b is close to 0, the change in intensity measures does not affect the seismic response to engineering structures [20]. An example of the relative practicality of intensity measures is displayed in Figure 5.Figure 5
Example of the relative practicality of intensity measures.The regression coefficientb corresponding to various intensity measures can be derived by fitting the straight line of (1), as displayed in Figure 6. For intensity measures, the requirements of efficiency and practicability must be simultaneously met; therefore, only the practicability of the five most effective ground motion parameters evaluated in the previous step can be compared. The practicability of the selected intensity measures under the action of pulse-like ground motions is stronger than that under the action of ordinary ground motions. For the spectrum parameters EPA and Sa(T1), the regression coefficient b corresponding to Sa(T1) is larger. Thus, the practicability of Sa(T1) is stronger than EPA. This result reveals that Sa(T1) related to the vibration characteristics of the structure is more sensitive to the structural demand parameters than EPA. Furthermore, according to Figure 6(a) and 6(b), the regression coefficient b corresponding to CAVs under ordinary ground motion is close to 0, indicating poor practicability, that is, there is small or no dependence of the level of engineering demand on the CAV level. Typically, the amplitude parameter PGA, spectrum parameter Sa(T1), and energy parameter CAV are highly practical.Figure 6
Regression coefficient,b, corresponding to the engineering demanded parameters (a) MRD and (b) AAF, obtained from the cloud analysis subjected to pulse-like and ordinary ground motions.
(a)(b)


## 5.3. Results in Terms of Sufficiency

Sufficiency is a crucial index to assess the independence of the ground motion parameter and indicates the correlation between the ground motion parameter (IMi) and ground motion information parameter (magnitude M or source-to-site distance R). A sufficient ground motion parameter should be statistically independent of the ground motion information parameter. If the demand residuals and seismic information parameters are not statistically independent of each other, the p value of regression analysis would be less than the given significance level, indicating that the sufficiency of IMi is poor. The p value of 0.05 was considered the cutoff for an insufficient IMi. If the p value value is larger, the sufficiency of IM would be stronger [21]. Because of the limitations on the length of the article, only the scatter and fitting line expressions of the required residual of AAF and magnitude M when PGA is a ground motion parameter are presented in Figure 7.Figure 7
Testing the sufficiency of PGA with respect to M for predicting AAF.Thep values derived from the three highly practical intensity measures PGA, Sa(T1), and CAV for the seismic magnitude and source-to-site distance F-text are displayed in Figure 8. The results reveal that under the action of ordinary ground motions, the p value among PGA, CAV, and magnitude M is equal to 0, indicating a complete linear correlation and sufficiency is 0. If PGA or CAV is taken as IM to select the ground motions for the dynamic time history analysis of the floor four-leg angle steeled communication tower, the results are strongly related to the magnitude of the earthquake event. Under the action of pulse-like ground motions, the p value between PGA and source-to-site distance R is equal to 0, demonstrating complete linear correlation. Only the correlation coefficient p value between the spectrum parameter Sa(T1) and the magnitude M or source-to-site distance R is greater than the given significance level of 0.05 under the action of pulse-like ground motions or ordinary ground motions, that is, it satisfies the sufficiency requirements.Figure 8
Medianp values obtained from investigating the sufficiency of typical IMi with respect to (a) magnitude and (b) source-to-site distance.
(a)(b)Briefly, for the lattice tower such as the communication tower, irrespective of whether under the action of pulse-like and ordinary ground motions, the most suitable intensity measure is the spectral acceleration Sa(T1) corresponding to the natural period of the structure from the three aspects of efficiency, practicability, and sufficiency.


## 6. Conclusions

In this study, a standard floor four-leg angle steel communication tower was considered. Based on the cloud analysis method, a linear logarithmic regression fitting method of intensity measures, considering the uncertainty of input ground motion, the optimal intensity measures under pulse-like ground motions, and ordinary ground motions, was determined from the perspectives of efficiency, practicability, and sufficiency.(1)
For MRD and AAF, the discrete type of ground motion parameters considered in this study is less than that under the action of impulse ground motion. From the perspective of efficiency, the top-five most effective intensity measures are amplitude parameter PGA, spectrum parameter Sa(T1) and EPA, and energy parameter CAV and CAVs. The duration parameters are discrete and noneffective intensity measures.(2)
Under the action of pulse ground motion, the practicability of the selected intensity measures is stronger than that of ordinary ground motion. For the spectrum parameters EPA and Sa(T1), Sa(T1) is more practical than EPA. Furthermore, the regression coefficient b corresponding to CAVs under ordinary ground motion is close to 0, indicating that the practicability is considerably poor. Typically, the amplitude parameter PGA, spectrum parameter Sa(T1), and energy parameter CAV are highly practical.(3)
For the lattice tower, such as the communication tower, irrespective of whether the measure is under the action of pulse-like ground motion or ordinary ground motion, considering from the three aspects of efficiency, practicability, and sufficiency, the most suitable intensity measure is the spectral acceleration Sa(T1) corresponding to the natural period of the structure.The scalar intensity measures are considered in this study. In a subsequent study, the vector intensity measures can be elaborated.



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