Proyecto de aula

There are various optimization methods available in MATLAB™, including Genetic Algorithm (GA), global search, multistart, patternsearch, simulated annealbnd (SA), and gamultiobj. According to the MATLAB™ help, for the “single global solution” option only GA, SA and pattern search are recommended. Considering the fact that pattern search method is slower than the other two optimization techniques, GA and SA are selected for optimization purposes. In this section, a brief overview of the two common global optimization tools is given and the objective function used in the optimization process is introduced. This is then followed by the results of the two optimization techniques which are used to determine an optimal placement of the inertia sensors on the arm.

3.2.1

Simulated Annealing Overview

Simulated annealing (SA) is a method for solving unconstrained nonlinear optimization problems. Annealing is a thermal process for obtaining low energy states of a solid in a heat bath. The method models the objective function as a physical process of heating a material and then slowly lowering the temperature to decrease defects, thus minimizing the system energy. The key feature of SA is that it provides a means to escape local minimums by allowing so called “hill-climbing moves” in hopes of finding a global minimum. The search is started with a randomized state. The fitness of the individual population is evaluated during each iteration and is carried out a stochastic selection to constitute the next generation and consequently the new point. The distance of the new generated point from the current point is based on a probability distribution with a scale proportional to the temperature. The algorithm not only accepts all new points that lower the objective function, but also with a certain probability points that raise the objective

function. By accepting points that raise the objective, the algorithm avoids being trapped in local minimums in early iterations and is able to explore globally for better solutions.

3.2.2

Genetic Algorithm Overview

GA is a population based stochastic optimization method which mimics Darwin’s principle of natural selection and genetic inheritance. The fundamental concepts of GAs were introduced by Holland [111]. In GA, a sequence of populations of candidate solutions to the optimization problem is generated by using a set of genetically inspired stochastic solution transition operators to transform each population of candidate solutions into a generation population. These operations include selection, crossover and mutation. Every solution is assigned a fitness value based on the initial guess, bound limitation and other constraints. Then the selection operator is applied to choose comparatively ‘fit’ chromosomes to be a part of propagation process. In generation step new individuals are formed through crossover and mutation operators. Crossover operator combines the genetic information between chromosomes to explore the search space, whereas mutation operator is used to maintain adequate diversity in the population of chromosomes to avoid premature convergence. By doing so, it is guaranteed that the technique finds global minimum rather than local minimum.

3.2.3

Objective Function

It can be seen from Eqs. (‎3-13) to (‎3-15) that parameters , , , and govern the noise level in the three angular acceleration components. In order to get an equivalent measure that incorporates the three variance components an expression which makes use of equal weighting is formulated as

. ‎3-16

2

Eq. (‎3-16) forms the basis for calculating the propagation of uncertainty which later is used as the objective function for noise minimization in the proposed optimization problem. For the space available on the arm, the parameters , , , and are replaced with , , and respectively, where the fractions have been introduced to represent the sensor locations on the arm. Hence the variables

are constrained in the range of [0, 1] while denote, respectively, arm lengths in x and z directions. It may be noted that Eq. (‎3-16) is a function of four variables (three independent variables and one dependent variable) and is highly nonlinear.

3.2.4

Results

Considering the nonlinear objective function given in Eq. (‎3-16) and the associated constraints, routines within the MATLAB™ global optimization toolbox have been employed to find the minimum noise and eventually optimal sensor placements. For this purpose, the GA from the global optimization toolbox is used and the results are compared with those obtained via the SA available within the same toolbox. It may be noted that in order to guarantee that the resultant minimum produced by the algorithm represents the global minimum, the tolerance parameter is reduced from the default value to a sufficiently low value of 1e-300. Table ‎3-1 gives a comparison of the two methods as well as the predicted locations of the sensors which yield the minimum noise in calculating the angular acceleration.

Table ‎3-1: Optimal Sensor Placement Predictions

GA SA

Iterations 195 4982

Stopping Criteria Generations: 10000 - l 0.508 0.508 m 1 1 n 1 1 Function Value 0.01192458 0.01192458

It is proposed that the predicted locations will be considered when implementing a typical sensor cluster for epileptic patient monitoring. To apply optimization result to the

experimental set up, five Motion Node™ unit sensors are considered to be employed, out of which three will be placed on the proposed locations on right arm while other two will be placed on head and the chest to add further useful insight for distinguishing between daily typical normal activity and seizure condition.