integrating-collapse-simulation-of-building-structures-into-internship-experiences-for-community-college-students

Paper ID #27803 Integrating Collapse Simulation of Building Structures into Internship Experiences for Community College Students Dr Cheng Chen, San Francisco State University Dr Cheng Chen is currently an associate professor in the school of engineering at San Francisco State University His research interests include earthquake engineering, structural reliability and fire structural engineering Dr Wenshen Pong P.E., San Francisco State University Wenshen Pong received his Ph.D in Structural Engineering from the State University of New York at Buffalo He joined the School of Engineering at San Francisco State University in 1998 He teaches courses in Civil/Structural Engineering Dr Pong is a registered Professional Engineer in California He is a member of the American Society of Civil Engineers and the Structural Engineers Association of California He has published over fifty technical papers in the areas of Structural Control and Earthquake Engineering Dr Pong was the Director of the School of Engineering at SFSU with 20 full-time faculty and over 25 part-time faculty from 2009 to 2018 Dr Amelito G Enriquez, Canada College Amelito Enriquez is a professor of Engineering and Mathematics at Ca˜nada College in Redwood City, CA He received a BS in Geodetic Engineering from the University of the Philippines, his MS in Geodetic Science from the Ohio State University, and his PhD in Mechanical Engineering from the University of California, Irvine His research interests include technology-enhanced instruction and increasing the representation of female, minority and other underrepresented groups in mathematics, science and engineering Prof Nicholas Langhoff, Skyline College Nicholas Langhoff is an associate professor of engineering and computer science at Skyline College in San Bruno, California He received his M.S degree from San Francisco State University in embedded electrical engineering and computer systems His educational research interests include technology-enhanced instruction, online education, metacognitive teaching and learning strategies, reading apprenticeship in STEM, and the development of novel instructional equipment and curricula for enhancing academic success in science and engineering Dr Zhaoshuo Jiang P.E., San Francisco State University Zhaoshuo Jiang graduated from the University of Connecticut with a Ph.D degree in Civil Engineering Before joining San Francisco State University as an assistant professor, he worked as a structural engineering professional at Skidmore, Owings & Merrill (SOM) LLP As a licensed professional engineer in the states of Connecticut and California, Dr Jiang has been involved in the design of a variety of lowrise and high-rise projects His current research interests mainly focus on Smart Structures Technology, Structural Control and Health Monitoring and Innovative Engineering Education Prof Hamid Mahmoodi, San Francisco State University Hamid Mahmoodi received his Ph.D degree in electrical and computer engineering from Purdue University, West Lafayette, IN, in 2005 He is currently a professor of electrical and computer engineering in the School of Engineering at San Francisco State University His research interests include low-power, reliable, and high-performance circuit design in nano-electronic technologies He has published more than one hundred technical papers in journals and conferences and holds five U.S patents He was a co-recipient of the 2008 SRC Inventor Recognition Award, the 2006 IEEE Circuits and Systems Society VLSI Transactions Best Paper Award, 2005 SRC Technical Excellence Award, and the Best Paper Award c American Society for Engineering Education, 2019 Paper ID #27803 of the 2004 International Conference on Computer Design He has served on technical program committees of Custom Integrated Circuits Conference, International Symposium on Low Power Electronics Design, and International Symposium on Quality Electronics Design Dr Xiaorong Zhang, San Francisco State University Xiaorong Zhang received the B.S degree in computer science from Huazhong University of Science and Technology, China, in 2006, the M.S and the Ph.D degrees in computer engineering from University of Rhode Island, Kingston, in 2009 and 2013 respectively She is currently an Assistant Professor in the School of Engineering at San Francisco State University Her research interests include embedded systems, wearable technologies, neural-machine interface, and cyber-physical systems Mr Yifeng Xu, San Francisco State University Mr Alexander Carlson, ASPIRES Program Alexander Carlson developed an early interest in structural design and development After years of classroom practice, he was able to conduct research on the response of structural models under earthquake conditions Ms Julissa Rico Ruiz , ASPIRES Program Julissa Rico Ruiz is first generation student pursuing a Civil Engineering major, planning on specializing on Structural Engineering Having taken several foundational Engineering courses, she was able to integrate what she learned on this research Karina Reyna Mr Moises Arturo Vieyra, Canada College I am an undergraduate student at Canada College ready to transfer to a year University My future plan is to get my bachelors degree in civil engineering and work my way to creating my own company c American Society for Engineering Education, 2019 Integrating Collapse Simulation of Building Structures into Internship Experiences for Community College Students Alexander Carlson, Karina Reyna, Julissa Rico Ruiz, Moises Vieyra, Amelito G Enriquez and Nik Langhoff Cañada College, Redwood City, CA Yifeng Xu, Cheng Chen, Wenshen Pong, Hamid Shahnasser, Zhaoshuo Jiang, Hamid Mahmoodi, Hao Jiang, Kwok-Siong Teh and Xiaorong Zhang School of Engineering, San Francisco State University, San Francisco, CA 94132 E-mail: chcsfsu@sfsu.edu Abstract With the support from the US Department of Education through the Minority Science and Engineering Improvement Program (MSEIP), four community engineering students have participated in the “Accelerated STEM Pathways through Internships, Research, Engagement, and Support” (ASPIRES) at San Francisco State University in summer 2018 This paper presents the summer intern project findings on collapse simulation of a one-bay-one-story steel frame developed in the Open System for Earthquake Engineering Simulation (OpenSees) Interns conducted the research on the model identification and uncertainty quantification of the modified Ibarra-Medina-Krawinkler (IMK) model Through the Particle Swarm Optimization (PSO) and Markov Chain Monte Carlo (MCMC) analysis, the modified IMK model parameters are identified and their uncertainties are quantified This program provides mentorship for interns with the scientific research in earthquake engineering, and trains interns to integrate theory and practice to better prepare them for their transition to a four-year university Introduction Earthquakes are one of the most destructive natural disasters known to plague urban structures in seismically active regions Averagely 12,000 and 14,000 earthquakes occur annually worldwide ranging between magnitudes of less than 2.0, causing a glass to slightly shake on a table, and in excess of 8.0, causing structural damages and even complete collapse [1] The vast majority of annually recorded earthquakes are below 2.0 magnitude and the few making the news are of magnitudes surpassing 5.0 on the Richter-Scale While the low frequency of high magnitude earthquakes may lull the public into relative indifference to the importance of improving the understanding of structures and their individual components in reaction to earthquakes, the social upheaval associated with deaths and injuries along with economic costs associated with rebuilding and repairing should stand as great motivations for seismic hazard mitigation on modern buildings Over the past several decades, as research institutions have gained better understanding of earthquake, the field of civil engineering has grown to encompass earthquake engineering This specialized subfield concentrates on limiting the seismic risk to the man-made environment in response to an array of disasters To encourage students to pursue the career in this field, internship opportunities are often offered to the next generation of engineers, introducing them to fundamentals of earthquake engineering that they will work on in the professional setting Community colleges such as Cañada College serve as the gateway to higher education for large numbers of students especially in California [2] However, for science and engineering fields, lower success and retention rates are observed at both community college and university levels resulting in underrepresentation of minority groups in these fields The Accelerated STEM Pathways through Internships, Research, Engagement, and Support (ASPIRES) program between San Francisco State University and Cañada College attempts to address some of these barriers to the successful transfer of community college engineering students to a four-year institution, including inadequate preparation for college-level courses, especially in mathematics, low success rates in foundational math courses, lack of practical context in the traditional engineering curriculum, and inadequate relevant internship opportunities for lower-division engineering students Four community college students participated in this program in 2018 and performed research in the earthquake-engineering field This study presents the scientific studies conducted by four community college civil engineering student interns in collapse simulation of building structures under earthquakes Project Statement Numerical simulation provides a cost and time effective approach for predicting structural response under earthquakes Physical and mathematical models are usually directly derived from theories [3] Empirical models, also known as phenomenological and data-driven models, are often derived from experimental data and observation The empirical model describes the relationship between observable properties with the assumption that the relationship extends from past observation [4] Well-known examples of empirical models include the Bouc-Wen model [7] [8] for nonlinear behavior, the Ibarra-Median-Krawinkler (IMK) [4] and modified IMK model [3] for modeling deterioration of structural components, and the nonparametric algebraic model for Magneto-rheological (MR) dampers [9] Parameters of these phenomenological models involve uncertainties due to measurements and optimization These uncertainties might be significant thus resulting in large variance in system response Computational simulations using models with deterministic parameters however could not account for the resulted uncertainties in system responses The application of Bayesian statistical framework takes the challenge of estimation on uncertainties in model parameters based on experiential results In this project, the modified IMK model [10] is applied to emulate the structural response close to collapses The objectives of this project are to apply modern optimization to the modified IMK model parameter calibration and to conduct corresponding uncertainty quantification, and to apply the associated uncertainties for computational simulation of building collapse Figure shows the model cyclic deterioration and associated definitions of the modified IMK model To define the hysteresis behavior, eight parameters 𝑀𝑀𝑐𝑐 namely 𝐾𝐾, 𝜃𝜃𝑝𝑝 , 𝜃𝜃𝑝𝑝𝑝𝑝 , Λ, 𝜃𝜃𝑢𝑢 , 𝑀𝑀𝑦𝑦 , , 𝑘𝑘𝑟𝑟𝑟𝑟𝑟𝑟 are used, where 𝐾𝐾 is the effective stiffness, 𝜃𝜃𝑝𝑝 is the pre𝑀𝑀𝑦𝑦 capping rotation, 𝜃𝜃𝑝𝑝𝑝𝑝 is the post-capping rotation, 𝜃𝜃𝑢𝑢 is the ultimate rotation, Λ is reference cumulative rotation capacity, 𝑀𝑀𝑦𝑦 is the effective yield moment, 𝑀𝑀𝑐𝑐 /𝑀𝑀𝑦𝑦 is the post yield ratio, and 𝑘𝑘𝑟𝑟𝑟𝑟𝑟𝑟 is the ratio of residual moment [10] These parameters are selected for identification and uncertainty quantification In this project, Particle Swarm Optimization (PSO) [11] is applied for parameter identification and the Markov Chain Monte Carlo (MCMC) method [12] is used for uncertainty quantification Figure Modified IMK deterioration model There are wide ranges of simulation packages can be applied for numerical simulation In this study the Open System for Earthquake Engineering Simulation (OpenSees) [13], an objectoriented software framework where users can create finite element applications for simulating structural response under earthquakes, is selected for numerical simulation Two models are developed in this project as shown in Figure 2, where the first one is a one-bay-one-story steel frame for computational simulation of building under earthquakes and the second one is a single column model for PSO and MCMC analysis Figure Scheme of the one-bay-one-story model and single column model The one-bay-one-story model has the bay width of 150 inches, and story height of 100 inches with W36X150 section used for both beam and columns The material used in this model including elastic-beam-column material for beam and columns, and the modified IMK material at the bottom of the columns The modified IMK material is applied to the zero-length element with the concentrated plasticity selected in this study Also, the P-Delta effect is taken into account by using a column and a spring with negligible stiffness linked to the main frame through a truss element For the single column model, the modified IMK material at the bottom of the column is set as a zero-length element The column is modeled with elastic-beam-column material and it is defined to be rigid; therefore, the rotation at the IMK spring location can be control through the displacement control at top of the column The PSO method optimizes parameter sets by manipulating a population of candidate solutions in the search-space according to simple mathematical equations, guiding the particles to their best position within the search space and updated as better positions are found Overtime, this is expected to move the particle to the best solution as the particles converge to the global best position within the search-space, thus optimizing the solution set with respect to the actual data Best position means the position with smallest error Figure shows the flowchart of the PSO process and Figure presents the experimental results of moment and rotation 10 Moment -1 -2 -3 -0.03 -0.02 -0.01 0.01 0.02 0.03 0.04 Rotation Figure Flowchart of Particle Swarm Optimization Figure Experimental data of moment vs rotation The MCMC method is based on the Bayes theory which defines the posterior probability as: P(θ|y) = P(𝑦𝑦|θ)P(θ) P(𝑦𝑦) (1) where P(θ|y)is the posterior probability, P(𝑦𝑦|θ) represents the likelihood function, P(θ)is the past information given by the model and P(𝑦𝑦) is a single value that normalizes the likelihood times prior portion The posterior probability is the conditional probability of realizing θ for given 𝑦𝑦, and the likelihood is the probability of realizing 𝑦𝑦 giving θ For uncertainty quantification of the modified IMK model parameters, the probability of realizing θ the modified IMK parameter when given 𝑦𝑦 the experiment measurement can be taken as the posterior probability [14] In other words, through the application of MCMC simulation, the sets of modified IMK parameter can be sampled after the stationary distribution 𝜋𝜋 is reached In this project, the Metropolis-Hasting (MH) algorithm is applied for MCMC simulation The procedure of MH-type MCMC is as following [12]: (1) Start from the selection of initial value 𝜃𝜃 the modified IMK parameter set ( 𝜃𝜃 = 𝑀𝑀 𝑀𝑀 [𝐾𝐾, 𝜃𝜃𝑝𝑝 , 𝜃𝜃𝑝𝑝𝑝𝑝 , Λ, 𝜃𝜃𝑢𝑢 , 𝑀𝑀𝑦𝑦+ , 𝑀𝑀𝑦𝑦− , ( 𝑐𝑐 )− , ( 𝑐𝑐 )+ , 𝑘𝑘𝑟𝑟𝑟𝑟𝑟𝑟 ] ) and the prior distribution𝑞𝑞 𝑀𝑀𝑦𝑦 𝑀𝑀𝑦𝑦 (2) At step 𝑖𝑖, propose a new sample set 𝜃𝜃 ∗ from 𝑞𝑞(𝜃𝜃 𝑖𝑖−1 , ∙ ) (3) Accept 𝜃𝜃 ∗ if 𝜋𝜋(𝜃𝜃 ∗ )𝑞𝑞�𝜃𝜃 ∗ , 𝜃𝜃 𝑖𝑖 � > 𝜋𝜋�𝜃𝜃 𝑖𝑖−1 �𝑞𝑞(𝜃𝜃, 𝜃𝜃 ∗ ) (4) If the condition in step (3) is not satisfied, the 𝜃𝜃 ∗ is accept by probability 𝛼𝛼, which is defined as 𝛼𝛼(𝜃𝜃, 𝜃𝜃 ∗ ) = min{1, (5) If 𝜃𝜃 ∗ is rejected, 𝜃𝜃 𝑖𝑖 = 𝜃𝜃 𝑖𝑖−1 𝜋𝜋(𝜃𝜃∗ )𝑞𝑞�𝜃𝜃∗ ,𝜃𝜃𝑖𝑖 � 𝜋𝜋�𝜃𝜃𝑖𝑖−1 �𝑞𝑞(𝜃𝜃,𝜃𝜃∗ ) } (6) Repeat steps (2)-(6) until enough values are generated The likelihood function used in the MH type MCMC procedure is as follow: 𝑛𝑛 −1 𝑃𝑃(𝑦𝑦|𝜃𝜃, 𝜎𝜎 ) = (2𝜋𝜋)−2 𝜎𝜎 −𝑛𝑛 𝑒𝑒 2𝜎𝜎2 ∗(∑𝑛𝑛 𝑖𝑖=1(𝑦𝑦𝑖𝑖 −𝑓𝑓(𝑥𝑥𝑖𝑖 ;𝜃𝜃)) ) (2) where 𝜎𝜎2 represents the unknown variance and will be updated in the algorithm; n stands for the amount of independent observations In this study, a Matlab [15] based toolbox developed by Marko [10] is applied to perform MCMC simulation Student Findings In this project, the rotation and moment measurement from Zhang [16] downloaded from database [17] is used to perform PSO and MCMC Figure below shows the rotation versus moment curve from the experiment results The PSO analysis for model parameter identification is conducted first Given the experimental measurement, the PSO analysis is conducted with 40 particles through 50 iterations to minimize the error between the experimental measurement and the OpenSees output Table below shows the model parameters pre- and post-PSO analysis Table 1: IMK model parameters pre- and post-PSO Recommended Values PSO Results (𝑀𝑀𝑐𝑐 /𝑀𝑀𝑦𝑦 )+ 1.15 (𝑀𝑀𝑐𝑐 /𝑀𝑀𝑦𝑦 )− 1.05 𝑀𝑀𝑦𝑦+ (𝑘𝑘𝑘𝑘𝑘𝑘 − 𝑖𝑖𝑖𝑖) 30350 𝑀𝑀𝑦𝑦− (𝑘𝑘𝑘𝑘𝑘𝑘 − 𝑖𝑖𝑖𝑖) -30350 𝐾𝐾(𝑘𝑘𝑘𝑘𝑘𝑘 − 𝑖𝑖𝑖𝑖/𝑟𝑟𝑟𝑟𝑟𝑟) 𝜃𝜃𝑝𝑝 (𝑟𝑟𝑟𝑟𝑟𝑟) 𝜃𝜃𝑝𝑝𝑝𝑝 (𝑟𝑟𝑟𝑟𝑟𝑟) 1.28 1.28 23377 -23377 3227360 0.022 4000000 0.025 0.25 Λ 10 𝑘𝑘𝑟𝑟𝑟𝑟𝑟𝑟 𝜃𝜃𝑢𝑢 (𝑟𝑟𝑟𝑟𝑟𝑟) 0.27 1.2 0.5 0.4 0.4 0.4 Figure compares the rotation and moment plot between experiment measurement and OpenSees analysis It can be observed that using the parameter identified by PSO, the OpenSees analysis results fit much better the experiment measurement 10 4 (a) 4 (b) 2 1 Moment Moment 10 -1 -1 -2 -2 -3 -4 -0.03 -0.02 -0.01 0.01 0.02 0.03 -3 -0.03 0.04 -0.02 -0.01 0.01 0.02 0.03 0.04 Rotation Rotation Figure Comparison between experiment and OpenSees output, (a) pre- and (b) post-PSO analysis The PSO results are taken as the initial parameter set of MCMC, and the total simulation number is selected to be 10000 Figure present the probability density of all parameters given the observation of the experiment measurements It can be overserved that parameters like 𝐾𝐾 and 𝑀𝑀𝑦𝑦+ and 𝑀𝑀𝑦𝑦− have smaller variance when compared with the rest parameters such as 𝜃𝜃𝑝𝑝 , 𝜃𝜃𝑝𝑝𝑝𝑝 , 𝜃𝜃𝑢𝑢 , 𝑘𝑘𝑟𝑟𝑟𝑟𝑟𝑟 , (𝑀𝑀𝑐𝑐 /𝑀𝑀𝑦𝑦 )+ and (𝑀𝑀𝑐𝑐 /𝑀𝑀𝑦𝑦 )− K 0.9 p 1.1 1.2 10 0.04 0.042 0.044 0.16 0.18 0.2 0.25 M M + c 1.1 k -10000 -9000 c 1.3 M -8000 0.3 M M y 1.2 0.2 0.22 0.24 u c p 1.4 0.7 0.8 0.9 0.35 0.4 0.2 0.3 - res 0.4 0.5 0.6 9000 10000 M + y y 1.1 6000 7000 8000 y -7000 -6000 -5000 Figure PDF of parameters from MCMC results After the MCMC simulation, the parameter sets from MCMC chain are selected for computational simulation of a single-story-single-bay frame for uncertainty quantification of the structural response under recorded ground motions from the Northridge and the Chi-Chi earthquakes [18] Figure shows the time histories of two ground motions used for analysis (a) 0.5 (b) 0.3 0.2 Accel(g) Accel(g) 0.1 -0.5 -0.1 -0.2 -1 10 15 20 25 -0.3 50 100 150 Time(s) Time(s) Figure Time history of (a) Northridge earthquake and (b) Chi-Chi earthquake The parameter sets are applied to the one-bay-one-frame model to perform the dynamic analysis, and the maximum story drift are recorded Figure below shows the histogram of 10000 dynamic analysis results From Figure 8, it can be observed that the uncertainty of maximum story drift ratio can be evaluated (a) 6000 5000 5000 4000 4000 3000 3000 2000 2000 1000 1000 6.9 6.95 7.05 Drift Ration (%) (b) 6000 7.1 7.15 7.2 1.74 1.75 1.76 1.77 1.78 1.79 1.8 Drift Ration (%) Figure Max drift ratio of the steel frame (a) Northridge earthquake (b) Chi-Chi earthquake Project Assessment This program trained the interns with project and time management, teamwork ability, technical writing and presentation, as well as knowledge in earthquake engineering Surveys were conducted anonymously to give a quantitative assessment of this program and serves as reference on future improvement of this program Interns were asked to mark questions with values from to 5, where stands for strongly disagree/least satisfied and stands for strongly agree/most satisfied Tables below show the anonymous surveying results from students after the summer internship Question: As a result of your participation in the program, how much did you learn about each of the following? Purpose of internship gain hands-on experience in research solidify my choice of major gain skills needed to successfully complete a BS degree clarify whether graduate school would be a good choice for me clarify whether I wanted to pursue a STEM research career work more closely with a particular faculty member get good letters of recommendation have a good intellectual challenge read and understand a scientific report write a scientific report ask good questions related to the scientific process set up a scientific experiment work with others to plan and conduct scientific experiments talk to professors about science think like a scientist Average rating 4.28 3.92 4.12 4.08 4.08 4.00 3.80 4.28 4.24 4.00 4.20 4.16 3.96 4.04 4.12 It can be observed that internes have positive response on this internship improving their ability on scientific related tasks such as writing a scientific report and setting up a scientific experiment Also, their team work capability was trained through working with others to plan and conduct scientific experiments Question: Tell us how much you agree with each of the following statements Please indicate your level of agreement with the following statements I was able to conduct the scientific research that is part of my summer internship I am confident I will transfer to a four-year institution I am confident I will complete a BS in a STEM field I can imagine myself continuing after my BS to pursue a Master’s Degree in a STEM field I have a clear career path I have skill in interpreting results I have tolerance for obstacles faced in the research process I am ready for more demanding research I understand how knowledge is constructed I understand the research process in my field I have the ability to integrate theory and practice I understand how scientists work on real problems I understand that scientific assertions require supporting evidence I have the ability to analyze data and other information I understand science I have learned about ethical conduct in my field I have learned laboratory techniques Average rating 4.48 4.76 4.64 4.32 4.28 4.28 4.40 4.28 4.32 4.28 4.20 4.40 4.52 4.40 4.36 3.96 4.32 I have an ability to read and understand primary literature I have skill in how to give an effective oral presentation I have skill in science writing I have self-confidence I understand how scientists think I have the ability to work independently I am part of a learning community I have a clear understanding of the career opportunities in science 4.40 4.40 4.08 4.32 4.24 4.64 4.16 4.24 These specific feedbacks from interns more convincingly prove that the ten-week internship benefits the interns by not only better understanding their future career but also engaging them in a collaborative environment Summary and Conclusion This paper presents the findings from ASPIRES interns on the model parameter identification and uncertainty quantification on modified IMK model Two OpenSees models are developed for analysis The model parameters are identified using PSO under the given rotation and moment measurement from the experiment Good agreement can be observed between the rotation and moment relationship from experiment measurement and OpenSees output using the parameters identified by PSO MCMC technique is then applied for uncertainty quantification on model parameters, and the effect from uncertainty of model parameters to the maximum drift of a one-bay-one-story steel frame is analyzed A survey is conducted on feedback of the ASPIRES program It can be observed from the survey that students have positive response on this program The ASPIRES program is successful in mentoring interns on scientific research in engineering, and help students gain hands on experience on integrate theory and practice After the program, student responses to the survey questions indicate better understanding in their subjects and their desire to continue perusing degree after bachelor’s degree Acknowledgements This summer research internship was supported by the US Department of Education through the Minority Science and Engineering Improvement Program (MSEIP), “Accelerated STEM Pathways through Internships, Research, Engagement, and Support” (ASPIRES), Grant No P120A150014 References: [1] [2] [3] Incorporated Research Institutions for Seismology, https://www.iris.edu/hq/inclass/factsheet/how_often_do_earthquakes_occur California Community Colleges Student Success Task Force (CCCSSTF) (2012) Advancing student success in California community colleges Retrieved from http://www.californiacommunitycolleges.cccco.edu/Portals/0/StudentSuccessTaskForce/SSTF_Fina lReport_Web_010312.pdf McMullin, E (1968), “What Do Physical Models Tell Us?” in B van Rootselaar and J F Staal (eds.), Logic, Methodology and Science III Amsterdam: North Holland, 385–396 [4] Frigg, Roman and Hartmann, Stephan, "Models in Science", The Stanford Encyclopedia of Philosophy (Summer 2018 Edition), Edward N Zalta (ed.), forthcoming URL = [5] Lignos, D.G., and Krawinkler, H (2011) “Deterioration modeling of steel components in support of collapse prediction of steel moment frames under earthquake loading”, Journal of Structural Engineering, ASCE, Vol 137 (11), 1291-1302 [6] Ibarra, L.F., Medina, R.A and Krawinkler, H.(2005).“Hysteretic models that incorporate strength and stiffness deterioration.” Earthquake Engineering Structural Dynamics, 34(12), 1489–1511 [7] Spencer, B F., Dyke, S J., Sain, M K., and Carlson, J D (1997) “Phenomenological model for magnetorheological dampers.” Journal of Engineering Mechanics, 10.1061/(ASCE)07339399(1997)123:3(230), 230–238 [8] Yang, G., Spencer, B., Carlson, J., and Sain, M (2002) “Large-scale MR fluid dampers: Modeling and dynamic performance considerations.” Engineering Structures, 24(3), 309–323 [9] Song, X., Aimadian, M., and Southward, S C (2005) “Modeling magnetorheological dampers with application of nonparametric approach.” Intelligent Material, System and Structures, 16(5), 421–432 Beck, J L (1989) ‘‘Statistical system identification of structures.’’ Proceedings of 5th International Conference Structural Safety and Reliability, ASCE, New York, 1395–1402 [10] Lignos, D.G., and Krawinkler, H (2011) Deterioration modeling of steel components in support of collapse prediction of steel moment frames under earthquake loading, Journal of Structural Engineering, ASCE, Vol 137 (11), 1291-1302 [11] Brownlee, J (2015) Particle Swarm Optimization Retrieved from http://www.cleveralgorithms.com/nature-inspired/swarm/pso.html [12] Marko, L (2008) Adaptive MCMC Methods with Applications in Environmental Geophysical Models [13] Pacific Earthquake Engineering and Research Center OpenSees: The Open System for Earthquake Engineering Simulation, 2004 [14] Caicedo, J.M., Jiang, Z., and Baxter, S.C (2017) Including Uncertainty in Modeling the Dynamic Response of a Large-Scale 200 kN Magneto-Rheological Damper ASCE-ASME Journal of Risk and Uncertainty in Engineering Systems, Part A: Civil Engineering, 3(2) [15] MATLAB, The MathWorks, Inc., Natick, Massachusetts, United States [16] Zhang, X (2004) Seismic Performance of Wide Flange Beam to Deep-Column Moment Connections Ph.D dissertation, Lehigh University [17] Lignos, D.G Retrieved from http://dimitrios-lignos.research.mcgill.ca/databases/steel/ [18] PEER Ground Motion Database Retrieved from PEER Ground Motion Database