In order to deal with the issue of huge computational cost very well in direct numerical simulation, the traditional response surface method (RS M as a classical regression algorithm is used to approximate a functional relationship between the state variable and basic variables in reliability design.
This was not straight-forward to explain, and calls for a more comprehensive analysis of the relationship between the state variable PC NP and the input parameter v dPCN.
Namely, the estimation algorithms use the observation matrix, the system matrix for the state variable and the crossvariance function between the state variable and the signal.
Contrary to Hu et al. (2013) approach, this field of uniform random numbers, termed a probability field, displays spatial patterns related to the conductivity spatial patterns, and, therefore, the correlation between probabilities and state variable is as strong as the correlation between conductivities and state variable could be.
The results indicated that SMI could help establish a statistical relationship between state variables and composting microbial characteristics, where discrete and nonlinear complexities exist.
We now describe the typical interactions between the state variables, starting from a low level of Ca (i.e., close to Ca bas ) and a pair ( x, y ) such that ( x, y, Ca ) lies just below F −.
In all cases, (x1, x2, x3, x4), are the state variables of the system, T1,2 are the effectors' main time constants while k1,2 introduce a time scale separation between the state variables of each effector's phase flow.
Every arc in a DBN representing an action is from the layer X to X ′ and represents the dependencies between state variables under an action a.
Furthermore, there is not a clear one-to-one mapping between the state variables of the original and reduced models as in the case of proper lumping [ 27].
The result is a visual representation of the inter-relationships between the state variables whose output can be made completely equivalent to the code-based solution.
