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where, COV (.) represents the covariance calculation. Stochastic processes that consider project correlation typically use Cholesky decomposition matrices. This decom- position method has a prerequisite in that any given matrix must be positive definite or positive semi-definite. Suppose that A is any nxn positive definite matrix (covariance or correlation matrix) and satisfies X' AX>0 for all nonzero eigenvectors X, where X'AX denotes a 1*1 matrix, namely, a real number. Cholesky decomposition can be used when the matrix is positive definite to decompose the matrix into a lower triangular matrix C and an upper triangular matrix C’ (A=CC"). The coefficients (a,;) in matrix A can then be obtained by solving n equations via back substitution, as follows.

Figure 1 where, COV (.) represents the covariance calculation. Stochastic processes that consider project correlation typically use Cholesky decomposition matrices. This decom- position method has a prerequisite in that any given matrix must be positive definite or positive semi-definite. Suppose that A is any nxn positive definite matrix (covariance or correlation matrix) and satisfies X' AX>0 for all nonzero eigenvectors X, where X'AX denotes a 1*1 matrix, namely, a real number. Cholesky decomposition can be used when the matrix is positive definite to decompose the matrix into a lower triangular matrix C and an upper triangular matrix C’ (A=CC"). The coefficients (a,;) in matrix A can then be obtained by solving n equations via back substitution, as follows.

Related Figures (7)

Fig. 1. The proposed Monte Carlo simulation process.
Fig. 1. The proposed Monte Carlo simulation process.
* The reclaimed asphalt concrete materials can be recycled and is deductible from the cost. Average unit price of PWIs.
* The reclaimed asphalt concrete materials can be recycled and is deductible from the cost. Average unit price of PWIs.
Fig. 2. Experimental engineering cost simulation for TPC/TPCS.
Fig. 2. Experimental engineering cost simulation for TPC/TPCS.
The covariance, rank correlation matrices, and their Cholesky decomposition for PWI cost. Table 4
The covariance, rank correlation matrices, and their Cholesky decomposition for PWI cost. Table 4
Simulation results of the TPC and TPCS models. * MPE (mean percentage error)=absolute value (simulation mean—true mean)/true mean * 100%. > SDPE (standard deviation percentage error)=absolute value (estimate standard deviation—true standard deviation)/true standard deviation * 100%. © Mean absolute percentage error. Table 6
Simulation results of the TPC and TPCS models. * MPE (mean percentage error)=absolute value (simulation mean—true mean)/true mean * 100%. > SDPE (standard deviation percentage error)=absolute value (estimate standard deviation—true standard deviation)/true standard deviation * 100%. © Mean absolute percentage error. Table 6
The covariance, rank correlation matrices, and their Cholesky decomposition for PWI quantity. Table 5
The covariance, rank correlation matrices, and their Cholesky decomposition for PWI quantity. Table 5
Fig. 3. Cumulative distribution curves of actual value, T3, and S3.
Fig. 3. Cumulative distribution curves of actual value, T3, and S3.
Related topics:
Stochastic ProcessDecision MakingCost EstimationConstruction CostBit Error RateContinuous Simulation
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