2.1. Parameter recognition considered as inverse problem

In a classical mechanical analysis of civil engineering problems, we determinate displacements and/or stresses of a structure with known engineering constants, such as the Young's modulus, E (with the unit GPa), and the Poisson's ratio, ν, which had been identified from laboratory or in-site experiments. This kind of problems can be termed forward problems, that is, we evaluate the unknown dependent variables (physical quantities) from prescribed parameters and dimensions analytically if there exist some closed-form relationships, or numerically using computational schemes (such as the finite element methods, FEMs) if the domain and/or boundary conditions are complicated.

On the other hand, an inverse problem in this case is to identify the engineering constants of a structure through evaluated or measured displacements and/or stresses. For a simple problem which can be analyzed and the results can be expressed in closed-form mathematical relationship, the inverse problem can be easily obtained from mathematical operation. However, for a practical huge structure of complicated shape, closed-form relationship cannot be obtained. Recently, a lot of schemes had been developed for parameter recognition (classification and regression) in the


Table 1. Comparison of forward problem and inverse problem.

CLSM can be defined as a kind of self-compacting cementitious material that is in a flowable state at the initial period of placement and has specified compressive strength of 1200 psi (8.27 MPa) (or less at 28 days) or is defined as excavatable if the compressive strength is 300 psi (2.07 MPa) (or less at 28 days) [1]. Recent studies have reported that the maximum CLSM strength of approximately up to 1.4 MPa is suitable for most of backfilling applications when re-excavation is required [2, 3] It is also recommended that depending upon the availability and project requirements, any recycle material would be acceptable in the production of CLSM with prior tests its feasibility before uses [4]. The special features of CLSM can be summarized as follows: durable, excavatable, erosion-resistant, self-leveling, rapid curing, flowable around confined spacing, wasting material usage, elimination of compaction labors

There are several studies on the engineering properties of CLSMs by laboratory experiments [5–10], and numerical analyses of applications of CLSM to civil engineering, such as excavation and backfill after retaining walls [11–13], bridge abutments [14–17], pipeline and trench ducts [18], pavement bases [19–24], and so on. All these studies reflect requirement of the identification of mechanical constants of the CLSMs. Though it is known that the Young's modulus of CLSMs lies between soil and commonly used concrete, precise determination of engineering material properties of CLSMs (even for soil and concretes) is a questionable and difficult problem. For example, modulus of elasticity is evaluated by experiments using secant modulus of stress-strain curve or estimated from empirical formula of Young's modulus with

Besides, artificial neural networks had been widely applied to various engineering [25], especially to civil and construction engineering [26, 27]. Alternately, several studies were conducted on the application of inverse problems in structural and geotechnical problems [28–32].

In a classical mechanical analysis of civil engineering problems, we determinate displacements and/or stresses of a structure with known engineering constants, such as the Young's modulus, E (with the unit GPa), and the Poisson's ratio, ν, which had been identified from laboratory or in-site experiments. This kind of problems can be termed forward problems, that is, we evaluate the unknown dependent variables (physical quantities) from prescribed parameters and dimensions analytically if there exist some closed-form relationships, or numerically using computational schemes (such as the finite element methods, FEMs) if the domain and/or

On the other hand, an inverse problem in this case is to identify the engineering constants of a structure through evaluated or measured displacements and/or stresses. For a simple problem which can be analyzed and the results can be expressed in closed-form mathematical relationship, the inverse problem can be easily obtained from mathematical operation. However, for a practical huge structure of complicated shape, closed-form relationship cannot be obtained. Recently, a lot of schemes had been developed for parameter recognition (classification and regression) in the

and equipment, and so on.

98 Advanced Applications for Artificial Neural Networks

28-day compressive strength or weight of concrete.

2. Problem definition and data preparation

boundary conditions are complicated.

2.1. Parameter recognition considered as inverse problem

field of machine learning and artificial intelligence, among which neural networks such as backpropagation artificial neural network (BPANN) and radial basis function neural network (RBFNN) are proven to be powerful and efficient if well designed, trained, and tested.

The two problems are compared and illustrated in Table 1, where problems with and without closed-form relationship between parameters and physical quantities are shown, respectively. In Table 1, a well-known example in civil engineering, displacement at the end of a cantilevered beam subjected to a concentrated load is shown, in which Δ, P, L, E,I denotes the end displacement, loading, length, Young's modulus, and moment of inertia, respectively.

This research study aims to consider the identification of engineering constant of a typical CLSM-backfilled region as an inverse problem. The processes employed are as follows: (1) preparation of training data, and testing data through numerical analysis (using ANSYS); (2) preparation of verification data (from experiments on CLSMs); (3) normalization of training data, testing data, and verification data; (4) conducting prediction using neural networks of BPANN and RBFNN along with comparison study of parameters involved in the networks; and (5) selection of a useful network topology for parameter recognition.

In the following sections, the procedures are explained with numerical results.
