an overview of system identification methods and

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4th international conferenceon coasts, ports & marine structure,Nov 2000 Shahid Rajaee Port Complex, Bandar Abbass

AN OVERVIEW OF SYSTEM IDENTIFICATION METHODS AND APPLICATIONS PART I: METHODS OF SYSTEM IDENTIFICATION AND DYNAMIC TESTS Amin Ghafouripour Ph. D. Candidate - IAU Science & Research Campus, Associate Dean of Research IAU - Tehran Branch Engineering Faculty, Pars Padir Consulting Engineers. [email protected]

Ali Akbar Aghakouchak Associate Professor Tarbiat Modarres University Tehran-Iran.

[email protected] Hossein Kiamehr B. Sc. of Civil Engineering IAU - Tehran Branch, Project Engineer Pars Padir Consulting Engineers.

[email protected]

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Abstract: Methods of system identification (SI) for structural dynamic systems are reviewed in this paper. This paper discusses the scope and results of recently completed joint-industry research project in Iran. The project concluded the several parts in case of system identification. Herein presented the first part of this project. The methods considered, (relevant to stationary and non-stationary random processes) are parametric and nonparametric methods that are covered almost all existing methods. On the other part of this paper, types of dynamic tests and data acquisitions are described. At the end part of the paper, history and forecasting horizon of system identification are shown. Notice that, about 150 different papers & references were studied to implement these methods. For the purpose of effective applications, techniques of system identification need to be developed. So, the aim of the presented paper is to review the history, methods of system identification, type of tests and theories in the short summary for complete prospect of the system identification. This paper presented into two parts.

Keywords: System Identification, Random, Dynamic, Test, Damage, Model, Inspection, History, Parametric, Stationary, Structure.

1. Introduction: As a means towards, an understanding of structural dynamics, the dynamic response of a linear or non-linear systems, identification of system parameters, correction the mathematical models by experimental data and as the important results, damage detection and developing the methods for inspection of invisible parts of the structures such as micro-cracks in concrete structure, cracks in underwater parts of offshore and specially in aerospace structures are prospective of this science. The problem of system identification has become increasingly important in the area of structural engineering. The general subject of system identification originally began in the area of electrical engineering and later extended to the field of mechanical/control engineering. Various techniques have been developed, however methods available may not be readily or directly applicable to problems of structural/aerospace engineering systems. This means by: a) Structural systems are generally much larger in size and much more complex in behavior so that accurate mathematical idealization is not easy. b) Data recordings contaminated by noise. c) The behavior of systems in different type of loading may cause the non-linear effects.

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d) The availability of options for input-output observational data is usually limited. The presented paper describe the methods of system identification with their applications in different types of structures and also the history of this science relevant to the U.S. & European journals and including Chinese, Japanese and other eastern countries literatures, without Russian and Indian technical literatures.

2. The Aim of System Identification: The main idea of system identification is studying the behavior of existing structures by recording the output or input-output vibrations of structures in discrete time signals due to sources of vibrations. The input-output description of a discrete-time system consists of a mathematical expression which explicitly defines the relation between the input and output signals. The system is assumed to be a "black box" to the user. So this philosophy for identifying the specifications of system (structure) is system identification. On the other hand each system (structure) is the same as a filter to convert the input signals with the specific frequency and characteristics to the output signals with filtered frequencies due to system parameters. So the process of constructing models from experimental data is called system identification.

3. Methods of Dynamic Tests: Data gathering system are based on dynamic tests and consists of the following methods. In all methods, discrete signals with selective interval time for each time series are recorded. The famous methods are described as follows and completely had been shown in Fig. 1. 3.1. Ambient Vibration Tests: Vibration of structures are recorded relevant to noises, traffic, vibrations, wind and light air excitation and so on that called ambient vibrations. For this type of tests input vibrations cannot be recorded. 3.2. Forced Vibration Tests: These types of tests are done by using the external sources of vibrations such as shakers. In this way there are 6 types of excitation: 3.2.1. Sine-Sweep excitation. 3.2.2. Steady-state sinusoidal excitation. 3.2.3. Man-excited vibrations. 3.2.4. Industrial equipment excitation. 3.2.5. Random excitations with hydraulic and electrodynamic vibrators (used for SATURN, APOLLO and SHUTTLE projects at NASA). 3

3.2.6. Active member test, the active member is made of piezoelectric material, which provides micron level displacements by varying its electric field. This used for large space structures erected in space to achieve their design configurations. Also suitable for continuous control of structures especially in space or underwater parts. 3.3. Shaking Table Tests: In this way only the scaled models of structures or small systems can be tested in laboratory. 3.4. Transient Vibration Test: The method of using the Gust effects, ship impact on offshore structures, hammer impact in aerospace structures or bridges, earthquake, Popper pressure on dams and explosion is called. It is similar to ambient vibration test with high energy of shaking, so it is possible to monitor the higher modes of structures and non-linear effects. 3.5. Microtremor Excitations: These types of tests are usually used for building structures, foundations or soil monitoring and interactions. Microtremor excitations and underground explosions are in this type of tests and earthquakes are sometimes recorded in this method. 3.6. Free Vibration Tests: One of the best methods for system identification is the free vibration method. In this way, pullback tests for buildings such as chimneys or using rocket propulsion and short gas blast from engine in aerospace structures can be used. Ram tests may use for bridges.

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Dynamic Tests Method Except Acoustic Emission And Piezoelectric Tests Ambient Vibration Tests

Forced Vibration Tests Sine-Sweep

Equipment Excitation

Human Excitation

Active Member

Random Excitation

Steady-State Sin. Vib.

Free Vibration Tests

Transient Vibration Tests

Rocket Propulsion

Pull-Back test

Earthquake Excitation

Ship Impact

Ram Tests

Gas Blast From Jet Engin

Hammer Impact

Poper Pressure

Gust Effects

Explosion Blast

Microtremor Tests Underground Explosion

Shaking Table Tests Microtremors

Seismic vibrations

Fig. 1. Methods of dynamic tests

4. Structural System and Mathematical Models: Structural/mechanical engineers deal with many types of structural dynamic systems and characteristics of these structures can be described by mathematical models. A variety of models have been developed for different purposes. A generic mathematical model suitable for most physical systems can be presented by the following equation: L[u(t)]=f(t) Where f(t) is inputs to the system that generates a corresponding output u(t) and L[ ] denoted the functional relationship between input and output models commonly used in structural and system engineering are shown in Fig. 2. 5

ODE: Ordinary differential equation to be written as: Md2y/dx2+Cdy/dx+Ky=LU

Mathematical Models for Describing the Dynamic Characteristics

Transfer function: The relations are represented as: Z(s)=G(s) . U(s) G(s)=[Ms2+Cs+K)-1 * L where Z(s) & U(s) are the Laplace transforms of Z(t) & U(t) and G(s) is the transfer function. SSM or state space model in continuous form can be derived for both linear and non-linear systems. State vector can be written as: X=[x1 x2]=[Z dZ] State equation is: [dx1 dx2]=[f(x1,x2,u)]+w={x2-M-1 *[Kx1+ Cx2-LU}+[0 M-1]z where w and z are system noises.

Ordinary Differential Equation (ODE)

Transfer Function Frequency Domain (TF)

State Space Model (SSM)

Auto-Regressive Moving Average (ARMA)

Auto-Regressive (AR)

Moving Average (MA)

Fig. 2. Mathematical models

ARMA model: When the system is controllable and observable the ARMAX model can be written as: y(i)=F1y(i-1)+F2y(i-2)+G1u(i-1)+G2(i-2)+e(i)+J1e(i-1)+J2e(i-2) And if the u(0) (input) is unmeasured the system called ARMA. For each model, there are many different algorithms of parameter estimation exist. These methods are called system identification methods, and based on the type of problem can be used. In part two of this paper all methods was described.

5. Methods of System Identification: In general, SI methods are classified as parametric and non-parametric. Parametric description or time domain method: Involves estimation of the system in terms of analytical representation that specifies the coefficients of the polynomials and the elements of the state-description matrices, which these are parameters of the model. System parameters are determined from observational recorded data of time series. Non-parametric identification or frequency domain method: Modal quantities as frequencies, damping ratios and mode shapes are identified from recorded data of time series. The transfer function of the model can be computed from frequency responses and there is no finite set of numbers that describes the system exactly.

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5.1. Parametric System Identification: Parametric identification has two main branches, which are stationary and non-stationary random processes. In Fig. 3 and Fig. 4, stationary and non-stationary random processes were shown. For non-stationary random processes the ARIMA method (Auto-regressive integrated moving average process) can be used. 5.1.1. Methods for non-stationary random processes: Non-stationary random processes are including the most of the phenomena but many of them are weakly stationary (not strong stationary) so sometimes, stationary methods are used. In addition there are some methods for decreasing the variance of the time series and transforming the non-stationary records to stationary types. This problem sometimes used for business and marketing with different average of data in duration of records and have seasonal variations. These are not used for dynamic measurements.

Fig. 3. Stationary Random Process

Fig. 4. Non-Stationary Random Process

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5.1.2. Methods for stationary random processes: The current "State of the art" in system identification for structural dynamics applications generally consists of three basic approaches: a) One-step algorithms that involve no iterations. It is based on a closed form minimization problem. These methods can be used as a preliminary step to locate areas of greatest error in the model; so the results may be used as a guide for selecting physical model parameters to be estimated using other methods. b) Iterative methods those are either deterministic or statistically based. The general class of iterative methods includes non-linear least square, Bayesian and Kalman filter techniques which pose the estimation problem in a statistical framework for both the model parameters and experimental data. These methods require the analyst to select the uncertain parameters a priori which sometimes very difficult. c) General mathematical programming and optimization techniques. These methods have not been extensively applied to system identification of structural models yet. In these studies there are "linear and non-linear" approaches can be derived and developed their algorithms. 5.1.3. Identification algorithms for linear systems: A number of current research efforts are aimed at reducing the computational requirements of the techniques and increasing the reliability of results. Also in the next few years one of the main important problems is damage detection that is derived from the results of this problem. The main basic algorithms were listed as follows, and in Fig. 5, Fig. 6 and Fig. 7 derived or developed techniques were shown. For more information about each model refer to references' papers. a) Extended Kalman Filter (EKF) b) Least square (LS) c) Best linear unbiased estimate (BLUE) d) Maximum likelihood estimate (MLE) e) Instrumental variables f) Neural networks g) Fuzzy systems h) Perturbation or optimization methods (error methods) i) Simulation and other mathematical methods (error methods) 5.1.4. Identification algorithms for non-linear systems: Many of the structures have non-linear behavior. For this reason, many of researchers were developed the methods that are shown in Fig. 8. 8

It was seen that structural systems have different Eigen values in different type of tests and this was related to non-linear behavior of structures. This means that results of forced vibration test and ambient vibration test sometimes have different values. In addition, many of system identification methods were developed for earthquake records in building structures. Parametric Time Domain Stationary Process Extended Kalman Filter (EKF) 32, 72, 80, 61

EKF for identification of Condensed Stiffness and Mass Matrices-72

Eigen Solution Regard to Stiffness-Senitive Analysis-110

Least Square Method (LSM) 28, 80, 81, 47, 52, 96

Substructuring Method with Weighted Force Iteration by EKF-61

Least Square (LS) 28

Least Mean Squares (LMS) 80, 81

Weighted LS (WLS) 52, 28, 47

Neural Network Methods 92, 48, 63

Maximun Likelihood Method 32, 39, 80

Best Linear Unbiased Estimate (BLUE)-32

Instrumental Variables 80, 32

Fuzzy Systems 110, 97

Perturbation Optimization 62, 49, 41, 36, 64, 53, 85, 84, 73, 35, 102, 99, 107, 58, 78, 105, 101

Using Probability Distribution for Parameters by User Choice-97

See Next Chart

Simulation Mathematical Methods 28, 60, 22, 108, 109, 83

See Next Chart

Fig. 5. Methods for estimation of parameters Perturbation Optimization Methods

Changes in Flexibility Matrix 62

Sensitivity Analysis with Weighted Values 49

Perturbation with Sensitivity Analysis 41, 36

Minimum Rank Update Theory 64

Complex Eigen Sensitivity 53

Best Achievable Eigen Vectors for Direct SI-58

Minimum Error Determination by Optimization for Base Isolating Structure-85

Sensitivity Analysis by Optimization & Residual Eigen Values-84

Damage Detection with Perturbation & Optimization for 2D Truss-105, 73

Darwinian Theory 101

Cost Function Minimization 98

Partial Eigen Structure Method 99, 107

Gradient Based Theory with Static & Dynamic Response-35

Fig. 6. Research papers in perturbation and optimization methods

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Fiber Optic Technique with Piezoelectric Sensors by LS 96

Statistical & Simulation Mathematical Methods Novel Approach for State Space Model with Kalman Filter Gain 149

ISSI, SSI 28

NSSI 28

Green Function for Plates-60

ASTRO / MOVE 28

Dynamic Residual for Simulation with Incomplete Measurments 108

MBCT-Multiple Boundry Condition 22

Mathematical Analysis for Piezoelectric Sensors 83

Gram-Schmidt & Fisher Methods for Sensor Placements 104

Cross Correlation by White Noise SI for Ambient Vibrations 109

Sequential Prediction Error-Using ARMA model 44

Movable Sensors with Input White Noise for Ambient Vibration-ARMA 34

State Space Model 32, 44

ARMA Model for Sensor Locations & Damage Detection 89

Fig. 7. Statistical and simulation methods Nonlinear Parametric System Identification 50 Equivalent Linear Models

Iterative Methods by Minimization of the Functional

Finding the NonLinear Analyse Model

Yasuda Truncation in Fourier Series Expansion of Input & Output Lead to Error

Weighted Global Iteration EKF 56

Kernel-Wiener Model-Orthogonal Series with White Gaussian Noise-50

NARMAX Non-Linear ARMA Model 44, 50

Chaotic Theory-Phase State Instead of Single Physical Strategy 78

Volterra Model for Non-Linear Models 50

ARMA Model with BOREL & Non-Parametric KERNEL Regressive Estimation

Gradient Base Theory Levenberg-Marquard Theory 102

Jacobi Series for Modeling the Non-Linear Structures 50

Modified BAYESIANused for F16 Airplane Analysis 72

Extended Kalman Filter using Taylor Series 50

Legendre Series for Modeling the Non-Linear Structures 50

Likeliohood Method for using the Earthquake Records 20, 40

Chebychev Series the Famous Model 50 Orthogonal Method-77

Non-Orthogonal Method-77

Fig. 8. Non-linear parametric identification methods

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5.2. Non-parametric System Identification: One of the important reasons that design by frequency methods is so widely used is that it is so often feasible to obtain the frequency response from experimental data. Furthermore, reliable experimental estimates to the frequency response can be obtained when noise is recent and when the system is weakly non-linear. The wide range of applications is used with this method so nonparametric methods had been shown in Fig. 9. The famous one frequency at a time algorithm is Fast Fourier Transform (FFT). Non-Parametric Methods Frequency Domain Fourier Transform 37, 38, 79, 54, 31, 31, 65, 76, 71, 74, 70, 69, 45, 100, 93, 59

State Space in Frequency Domain

Markov Parameters from SS-Domain Frequency 57, 148

Error Minimization Methods (Iteration)

Frequency & Mode Shape with Ship or Hammer Impact 37, 38, 79, 54, 31, 32

Damage & Frequency Relations 65, 76

Root Mean Square Method 30

Viscoelastic Dampers Behavior 71

Wall Effects & False Ceiling Tests 74, 17

Chebychev Method Linear or Non-Linear 29

Base Isolator Investigation 70

Sensor Location Forced & Ambient 69

Ordinary-Classical Polinomials 29

Dam Tests with Popper, Ambient Force 93

Active Member Tests 45

Frequency Control in 21 Buildings 100

Offshore Identification with Spectral Density Function 19, 73, 10, 11, 12, 13, 14, 15, 16, 9

Chimney Test Ambient 19

Foundation-Soil Interaction 25, 27

Fig. 9. Non-parametric methods of system identification

6. Conclusion: In the study, methods of parametric and transfer function or non-parametric identifications are reviewed. In addition stationary and non-stationary random processes as the main important problems for using the identification models are studied. Also, the suitable methods for non-linear systems are reviewed. Methods of dynamic testing are noticed. By this means this paper shows the methods for each purpose and for further researches and for each type of methods the references for more information are specified.

7. Acknowledgments: The authors wish to thank the Prof. Ghafouri Ashtiyani the president of IIEES in Iran for his supports, Mr. Zanganeh minister of oil of Iran, Mr. Vakil, manager of production-national Iranian offshore oil company and his staff for their supports, Pars Padir consulting engineers, Islamic Azad University-Tehran branch and Vice research chancellor Dr. Ahmadnezhad for their supports. This work is the part of the well jointed-industry programs between IIEES, IAUTB, NIOOC and Pars Padir Co. Special thanks to Dr. M.T. Ahmadi for his consultants.

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AN OVERVIEW OF SYSTEM IDENTIFICATION METHODS AND APPLICATIONS PART II: THEORY, TYPE OF TESTED STRUCTURES, HISTORY AND PROSPECTIVE OF SYSTEM IDENTIFICATION

Ali Akbar Aghakouchak

Amin Ghafouripour

Associate Professor Tarbiat Modarres University Tehran-Iran.

Ph. D. Candidate - IAU Science & Research Campus, Associate Dean of Research IAU - Tehran Branch Engineering Faculty, Pars Padir Consulting Engineers.

[email protected] Hossein Kiamehr

[email protected]

B. Sc. of Civil Engineering IAU - Tehran Branch, Project Engineer Pars Padir Consulting Engineers.

[email protected]

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Abstract: The investigation reported in this paper looks into the number of system identification techniques. This paper discusses the scope and results of recently completed joint-industry research project in Iran. The project concluded the several parts in case of system identification. Herein presented the first part of this project. The methods considered, have been successful at identifying properties of linear systems in both parametric and nonparametric methods. For the purpose of effective application, techniques of system identification need to be developed based on existing methods. The aim of the presented paper is to review history, the main algorithms of system identification, type of tested structures and theories of system identification in the short summary for complete prospect of the system identification. This paper presented in two parts.

Keywords: System Identification, Random, Dynamic, Test, Damage, Model, Inspection, History, Parametric, Stationary, Structure.

1. Introduction: Modeling physical systems using different equations continue to have a very distinguished role in the process of scientific and engineering achievements. Linear or non-linear systems of structures caused the identification of system parameters have become developed in mathematical methods. The problem of system identification has become increasingly important in the area of structural engineering. The general subject of system identification originally began in the area of electrical engineering and later extended to the field of mechanical/control engineering. Various techniques have been developed, however available methods may not be readily or directly applicable to problems of structural/aerospace engineering systems. This means by: i) Structural systems are generally much larger in size and much more complex in behavior so that accurate mathematical idealization is not easy. ii) Data recordings contaminated by noise. iii) The behavior of systems in different type of loadings may cause the non-linear effects. iv) The availability of options for input-output observational data is usually limited. The input-output description of a discrete-time system consists of a mathematical expression which explicitly defines the relation between the input and output signals. The system is assumed to be a "black box" to the user. So this philosophy for identifying the specifications of system (structure) is

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system identification. On the other hand each system (structure) is the same as a filter to convert the input signals with the specific frequency and characteristics to the output signals with filtered frequencies due to system parameters. So the process of constructing models from experimental data is called system identification.

2. Identification Algorithms: The mathematical models of structures and methods of system identification were described in the first part of the paper. Herein the basic mathematical algorithm of each method is shown. A variety of models have been developed for different purposes. A mathematical model for most structures can be presented by the following equation: L[u(t)]=f(t) Where: f(t): Input to the system, L[ ]: Relationship between input and output of system and u(t):output of system. 2.1. Types of Stationary Models: For each model many of different algorithms of parameter estimation exist. Models have been used in a wide range of engineering applications such as structural engineering. It is important to use a model to implement the real behavior of structures. 2.1.1. Moving Average model (MA): For analysis of a series of time output signal Zt can be written as a series of input random variables (yj) with parameter estimators ar. Also m is the average value of output. Hence: Zt= m+at+y1at-1+y2at-2+ ......= m+Syj at-j :j= 0,....., h 2.1.2. Moving Average model with different grades (MA(q)): This model is full random with zero mean value as: cZ=at -Q1at-1 ...... -Qq at-q Where Q=y 2.1.3. Auto Regressive model (AR): One of the suitable models is AR model for returned the Z value to the last values plus random impact and noted as follows: Zt -f1Zt-1 - . . . . . - fpZt-p=at 2.1.4. Auto Regressive Moving Average model (ARMA): For a stationary process there are a relation between MA & AR models. At the time the value of yi is a linear function of its arguments, the auto regressive moving average or ARMA model is obtained depending on which coefficients in the model are zero. ARMA model used when the measurable input is missing and this model used for different purposes. For the identification of modal quantities, the transfer function has been widely employed. 2.1.5. State Space model (SS): The State Space model in continuous form can be derived for linear and non-linear systems. By defining the state vector as:

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x=[x1 x2]= [z z’] The below equation: Mz” + Cz’ + Kz = Lu Can be transformed into a state equation as: [x’1 x’2]={ f(x1, x2, u) } + w Which w is system noises that account for the un-measurable input disturbances and errors in modeling. 2.1.6. Transfer function: In the case of linear structural systems, the equation of motion can also be represented by using the transfer function as: Z(s) = G(s) U(s) and G(s) = (Ms2 + Cs + K)-1 L Where Z(s) and U(s) are the Laplace transforms of z(t) and u(t), and G(s) is the transfer function of the system. 2.2. Methods for Parameter Estimation: Here a brief introduction about the parametric methods presented. 2.2.1. Extended Kalman Filter method (EKF): The EKF algorithm is derived from the state-space form of the differential equation of motion. Starting from an initial guess, this extended state space is recursively updated as new observations are made available. The update is based on Kalman filter formalism. 2.2.2. Maximum Likelihood method (ML): The Maximum likelihood technique consists of evaluating those parameters that maximize the probability of observing the measured data. This probability is referred to as the likelihood function of the measurements. 2.2.3. Least Squares method (LS): The recursive least squares method consists of updating a least squares fit to the available data as more data is made available. 2.2.4. Best Linear Unbiased Estimate method (BLUE): The least squares estimation of a constant in noise is not only unbiased but also consistent. So with insist on the estimate be both a linear function of the data and unbiased, we could show that the BLUE is a weighted least squares. 2.2.5. Neural networks method: In Neural networks method, the basic strategy is to train a neural network to recognize the behavior of the undamaged structure as well as the behavior of the structure with various possible damage states. When the trained network is subjected to the measurement of the structural response, it should be able to detect any existing damage. 2.2.6. Fuzzy method: In Fuzzy theory, the imprecision is interpreted as the designer’s choice to use a particular value for the uncertain parameter. In another word, if the uncertain parameter is described as a random variable following a specified probability distribution, the probabilistic approach can be used.

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2.3. Methods for Non-Parametric System Identification: One of the important reasons that design by frequency response methods is so widely used is that it is so often feasible to obtain the frequency response from experimental data. Furthermore, reliable experimental estimates of the frequency response can be obtained when noise is present and when the system is weakly non-linear. Models based on such frequency response data can then be used effectively in control system design. The presence of non-linearity leads to the concept of the “describing function”. With considering the case of linear, constant and stable models including the possibility of unmeasured noise inputs to the system, the situation will be described with below transform function: Y(z) = G(z) U(z) + H(z) W(z) Which in the equation Y is the plant output, U is the known plant control input, and W is the unmeasured noise. Note that unmeasured noise might be or might not be random. G is thus the plant transfer function and H is the unknown but stable transfer function from the noise to the system output. The frequency response of this system is the evaluation of G(z) for z on the unit circle.

3. Type of Tested Structures: In the recent years many different types of structures were tested by different methods of dynamic tests. The paper shows the summary of different type of tested structures. Bridge: Steel bridge, concrete bridge, box girder bridge, cable stayed and cable suspended bridge, prestressed box girder bridge, arch bridge, box culvert, voided slab deck bridge. Industrial & Equipment: Power station equipment, turbines, antenna structure. Foundation: Pile group, soil, foundation-soil interaction, soil-structure interaction. Building: Steel and concrete buildings with frame, shear wall, bracing, eccentric bracing, masonry building, nuclear power station building. Offshore structure: Jacket type platform, risers in tension leg platform, monopod platform. Liquid storage tank: Circular types were tested. Dam: Concrete dam, earth dam. Aerospace structure: Apollo, Saturn I to V, shuttle, airplane structure, space truss, helicopter and rotating part structure, landings mechanism of airplane (F16 jet) and many types of airplanes. Partitions in building: Internal wall effects on structure, false ceiling effects and behavior. Chimney. Base isolated buildings or added dampers: Base isolator, viscoelastic damper, semi-active hydraulic damper. Concrete Silo.

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4. History of System Identification: In this reviewed history of system identification, there are two types of approaches can be shown that used by scientists: Type 1: Experimental approaches. Type 2: Mathematical approaches. Experimental approaches which have been started since 1958 by testing the golden gate bridge for the first time and in 1954 the random theory and correlation method was proposed. From 1960 to 1980 most of the methods were non-parametric and from 1980 to 1990 parametric and non-parametric approaches were developed. From 1990 to 2000 the theoretical approaches with developing the new methods were established and forced vibration tests are very popular. Since 1960 to 1980 ambient vibration tests have been popular and most of researchers like to use these type of tests but because the new technology of forced vibrations, low errors, measurable input data and high signal to noise ratio, it has became popular for different type of structures. Finally, from 1998, new approaches for ambient vibrations have been published and because of the low cost of this type of tests it seems to be recommended for several cases such as offshore or aerospace structures. In next figures the history of development of system identification is shown.

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5. Conclusion: In the study, classical theory of parametric and non-parametric identification methods are reviewed and type of tested structures are described for further researches. Finally, the history of system identification for better further studies is shown and the prospect of the system identification was studied. By this means this paper shows the methods for each purpose of system identification. The history shows the rate of development, type of works, type of theoretical and experimental researches.

6. Acknowledgments: The authors wish to thank the Prof. Ghafouri Ashtiyani the president of IIEES in Iran for his supports, Mr. Zanganeh minister of oil of Iran, Mr. Vakil, manager of production-national Iranian offshore oil company and his staff for their supports, Pars Padir consulting engineers, Islamic Azad University-Tehran branch and Vice research chancellor Dr. Ahmadnezhad for their supports. This work is the part of the well jointed-industry programs between IIEES, IAUTB, NIOOC and Pars Padir Co. Special thanks to Dr. M.T. Ahmadi for his consultants.

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