Packaging Process Optimization in MultiheadWeighers with Double-Layered Upright and Diagonal Systems

[EN] In multihead weighers, packaging processes seek to find the best combination of passage hoppers whose product content provides a total package weight as close as possible to its (nominal) label weight. The weighing hoppers arranged in these machines dispense the product quantity that each package contains through computer algorithms designed and executed for this purpose. For its part, in the packaging process for double-layered multihead weighers, all hoppers are arranged in two levels. The first layer comprises a group of weighing hoppers, and the second comprises a set of booster hoppers placed uprightly or diagonally to each weighing hopper based on design of the machine. In both processes, the initial machine configuration is the same; however, the hopper selection algorithm works differently. This paper proposes a new packaging process optimization algorithm for double-layer upright and diagonal machines, wherein the hopper subset combined has previously been defined, and the packaging weight is expressed as actual values. As part of its validation, product filling strategies were implemented for weighing hoppers to assess the algorithm in different scenarios. Results from the process performance metrics prove that the new algorithm improves processes by reducing variability. In addition, results reveal that some machine configurations were also able to improve their operation.We express our gratitude for the support from Universidad Simon Bolivar, and Universitat Politecnica de Valencia.Garcia-Jimenez, R.; García-Díaz, JC.; Pulido-Rojano, ADJ. (2021). Packaging Process Optimization in MultiheadWeighers with Double-Layered Upright and Diagonal Systems. Mathematics. 9(9):1-20. https://doi.org/10.3390/math9091039S1209

Bicriteria food packaging process optimization in double-layered upright and diagonal multihead weighers

[EN] Double-layered multihead weighing machines contain twice the number of hoppers as present in a simple machine with the same number of heads, which enables additional objective optimization possibilities considering the increased number of combinations among hoppers. This research study deals with bicriteria optimization for double-layered upright and diagonal machines using brute force as the optimization criteria. One of the optimization objectives is related to the target weight; the target weight must be at least and as close as possible to the weight to pack. Furthermore, this study also aims to minimize the time for which a certain portion of a product remains in the hopper while waiting to be selected for package formation. This time is known as priority and is measured based on the number of iterations or the number of packages produced by the machine while the hopper waits to be discharged. For these purposes, Different strategies were tested for both machines, which simultaneously optimize the target weight and the priority of the hoppers, showing the reduction of the extraction of the process in addition to reducing the costs of excess product and its reprocessing.We express our gratitude for the support from Universidad Simon Bolivar, Colombia, and Universitat Politecnica de Valencia.Garcia-Jimenez, R.; García-Díaz, JC.; Pulido-Rojano, AD. (2023). Bicriteria food packaging process optimization in double-layered upright and diagonal multihead weighers. Journal of Computational and Applied Mathematics. 428:1-10. https://doi.org/10.1016/j.cam.2023.11516811042

Logic and the Challenge of Computer Science

https://deepblue.lib.umich.edu/bitstream/2027.42/154161/1/39015099114889.pd

Bi-objective optimization of a multihead weighing process

[EN] A multihead weighing process is a packaging technology that can be of strategic importance to a company, as it can be a key to competitive advantage in the modern food industry. The improvement in the process quality and sensory quality of food packaged in a multihead weighing process investigated in this paper is relevant to industrial engineering. A bi-objective ad hoc algorithm based on explicit enumeration for the packaging processes in multihead weighers with an unequal supply of the product to the weighing hoppers is developed. The algorithm uses an a priori strategy to generate Pareto-optimal solutions and select a subset of hoppers from the set of available ones in each packing operation. The relative importance of both aforementioned objectives is dynamically managed and adjusted. The numerical experiments are provided to illustrate the performance of the proposed algorithm and find the optimum operational conditions for the process.García-Díaz, JC.; Pulido-Rojano, A.; Giner-Bosch, V. (2017). Bi-objective optimization of a multihead weighing process. European J of Industrial Engineering. 11(3):403-423. doi:10.1504/EJIE.2017.084882S40342311

Transitive Closure Logic and Multihead Automata with Nested Pebbles

Several extensions of first-order logic are studied in descriptive complexity theory. These extensions include transitive closure logic and deterministic transitive closure logic, which extend first-order logic with transitive closure operators. It is known that deterministic transitive closure logic captures the complexity class of the languages that are decidable by some deterministic Turing machine using a logarithmic amount of memory space. An analogous result holds for transitive closure logic and nondeterministic Turing machines. This thesis concerns the k-ary fragments of these two logics. In each k-ary fragment, the arities of transitive closure operators appearing in formulas are restricted to a nonzero natural number k. The expressivity of these fragments can be studied in terms of multihead finite automata. The type of automaton that we consider in this thesis is a two-way multihead automaton with nested pebbles. We look at the expressive power of multihead automata and the k-ary fragments of transitive closure logics in the class of finite structures called word models. We show that deterministic twoway k-head automata with nested pebbles have the same expressive power as first-order logic with k-ary deterministic transitive closure. For a corresponding result in the case of nondeterministic automata, we restrict to the positive fragment of k-ary transitive closure logic. The two theorems and their proofs are based on the article ’Automata with nested pebbles capture first-order logic with transitive closure’ by Joost Engelfriet and Hendrik Jan Hoogeboom. In the article, the results are proved in the case of trees. Since word models can be viewed as a special type of trees, the theorems considered in this thesis are a special case of a more general result

Spectral analysis of multi-spindle machining heads

Vibration analysis can be extremely useful in predictive/ preventative maintenance. In this investigation, multi-spindle machining heads were analyzed using equipment from Technology for Energy Corporation. A spectral analysis program was also written in order to better understand black box results provided by commercial software. Three case studies indicate that gear mesh frequencies, bearing noise, and the natural frequencies of spindles and shafts represent the majority of the peaks found in the frequency spectrum for multi-spindle heads. These frequencies were calculated analytically and then identified in each frequency spectrum. The results show that in many cases the gear mesh frequencies are too close to the natural frequencies of the spindles and shafts. This causes the spindles to be excited at their natural frequency and can lead to premature failure of the spindle bearings