Heuristic approach for prediction of behavioral data

Y.E. Toshev

Institute of Mechanics and Biomechanics, Bulgarian Academy of Sciences, Sofia, Bulgaria

Introduction

The aim of the study is to propose a new heuristic approach for the prediction of the behavior of living systems and to prove that the method is valid in the case of human locomotion.

The heuristic approach

The Volterra-Wiener representation makes it possible to obtain the input/output relation in case of two input parameters x₁, x₂ and one output parameter y, using the homogeneous polynom given by Eq. 1.

(1)

Unfortunately in case of 10 input parameters the number of coefficients in Eq.1 is 200000. It is not possible to carry out such a large number of experiments. The proposed heuristic method is very similar to the mass animal selection which involves: (a) selection of one male and one female animal group (analogous to establish hypotheses); (b) breeding and receiving the first propagation (analogous to obtaining the first generation of solutions); (c) selection of the "best" newborn animals (analogous to select the best solutions); (d) next breeding and receiving the next new propagation (analogous to obtain the second generation of solutions) up to the moment when the properties of the newborn animals begin to degenerate (analogous to stop the computing).

(2)

(3)

Suppose y is given by Eq. 2 named "global description" and the experimental values form the data matrix A. We replace Eq. 2 with a series of "partial descriptions" given by the Eqs. 3. For each Eq. 3 we generate the mean value (l=1,2,...m) using only Eq. 1. Using the statistical criterion F-test we compare with the known mean value and we select the best solutions that form the first generation of solutions. Using the same algorithm we generate the next "partial description" and we obtain the second generation of solutions. Generation by generation the criterion F-test decreases. The procedure stops when the F-test value begins to increase.

Results of the prediction of human locomotion

The biomechanical goal is to predict the vertical components of the ground reactions, both for the right and the left leg, using only a set of 9 selected individual body parameters: x1-body height; x2-ground-iliospinale; x3-ground-tibiale; x4-tibiale-sphyrion; x5-distancia cristarum; x6-conjugata externa; x7-hip circumference; x8-knee circumference; x9-body weight. Using force-plates the ground reactions of 25 individuals are registered, the first 7 harmonics are calculated and the 9 body parameters are measured. Every harmonic for every person is obtained using the heuristic approach. Finally, using the inverse Fourier transformation we obtain the predicted ground reactions for every person as functions of the time.

Conclusion

Five generations of solutions are enough to obtain with good convergence a sufficiently small F-test value. The proposed new heuristic approach constitutes a valid outline for diagnostic purposes and gives predicted results that are in very good agreement with the experimental data.

References

1. Toshev, Y.; Monchaud, S. (1997). Une approche heuristique appliquee en biomecaniquee. Comptes Rendus de l’Academie des Sciences, France, 325 (2b), 135-142.