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Human posture prediction can often be formulated as a nonlinear multiobjective optimization (MOO) problem. The joint displacement function is considered as a benchmark of human performance measures. When the joint displacement function is used as the objective function, posture prediction is a MOO problem. The weighted-sum method is commonly used to find a Pareto solution of this MOO problem. Within the joint displacement function, the relative value of the weights associated with each joint represents the relative importance of that joint. Usually, weights are determined by trial and error approaches. This paper presents a systematic approach via an inverse optimization approach to determine the weights for the joint displacement function in posture prediction. This inverse optimization problem can be formulated as a bi-level optimization problem. The design variables are joint angles and weights. The cost function is the summation of the differences between two set of joint angles (the design variables and the realistic posture). Constraints include (1) normalized weights within limits and (2) an inner optimization problem to solve for joint angles (predicted posture). Additional constraints such as weight limits and weight linear equality constraints, obtained through observations, are also implemented in the formulation to test the method. A 24 degree of freedom human upper body model is used to study the formulation and visualize the prediction. An in-house motion capture system is used to obtain the realistic posture. Four different percentiles of subjects are selected to run the experiment. The set of weights for the general seated posture prediction is obtained by averaging all weights for all subjects and all tasks. On the basis of obtained set of weights, the predicted postures match the experimental results well.

Errors in separating diffuse scattering resulting from local order from that from static and dynamic displacements have been examined; the Borie-Sparks symmetry procedure was employed, which includes second-order terms in the displacements. The largest source of error when X-rays are employed is the variation in the ratio of scattering factors across the volume measured in reciprocal space. Large errors in the Warren local-order parameters result for clustering systems with displacement terms of the same order as the local-order parameters (or larger), but not if the size terms are smaller. For systems with local order the errors in these parameters are small. Uncertainties in the size terms are always appreciable. Other errors that were considered are: higher-order terms, extrapolation under Bragg peaks, errors in Compton scattering, background and surface roughness, and uncertainties in composition or polarization resulting from a monochromator.

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The human posture prediction model is one of the most important and fundamental components in digital human models. The direct optimization-based method has recently gained more attention due to its ability to give greater insights, compared to other approaches, as how and why humans assume a certain pose. However, one longstanding problem of this method is how to determine the cost function weights in the optimization formulation. This paper presents an alternative formulation based on our previous inverse optimization approach. The cost function contains two components. The first is the weighted summation of the difference between experimental joint angles and neutral posture, and the second is the weighted summation of the difference between predicted joint angles and the neutral posture. The final objective function is then the difference of these two components. Constraints include (1) normalized weights within limits; (2) an inner optimization problem to solve for the joint angles, where joint displacement is the objective function; (3) the end-effector reaches the target point; and (4) the joint angles are within their limits. Furthermore, weight limits and linear weight constraints determined through observation are implemented. A 24 degree of freedom (DOF) human upper body model is used to study the formulation. An in-house motion capture system is used to obtain the realistic posture. Four different percentiles of subjects are selected and a total of 18 target points are designed for this experiment. The results show that using the new objective function in this alternative formulation can greatly improve the accuracy of the predicted posture.