**4.3. Reliability model of the generation units**

0 0 0 ì £ = í > î *d i i*

For the first hour, this model represents the expectation of the market for each delivery period. However, this expectation should change according to the values that the spot prices take in each sample and the information gathered by a *virtual* market taking place in each particular sample path. If perfect foresight is assumed, each virtual market could calculate without uncertainty the hourly forward price for its particular spot prices sample path simply as:

> ( ) , , 1 1 =

*i i j h FB S p p*

( ( )) ( ) , ,, 1 1

*d d i i w h w h w i ii*

*h h*

, ,

*d H W i w h w j*

*w h w j*

The equation (64) represents a model where any additional information that arrives as the spot price of the particular sample path is different form the forecasted in the first hour is dismissed by the virtual market. Thus, this model is representative of reality only for the first hour of simulation where no additional information could have been gathered by the virtual markets. On the other hand, the equation (66) represents a model where all the additional information is obtained beforehand for each Monte Carlo sample. Likewise, this model is suitable only for the last hour of simulation where all information is already known by the virtual market within each Monte Carlo sample. Finally, the two models can be combined, in order to simulate the forward price dynamics in correlation to the spot prices of each Monte Carlo sample path. In this work, it is assumed that the information gathered by each virtual market grows linearly,

*i*

*H*

*d i*

=

. Then, equations (64)2

*i*

=

*p H*

1 1

*d i i i*

×

*H H*

( )

*h*

+

each Monte Carlo sample path.

*H*

( ( ))

= ×

*H h*

*d H i w j*

( )

*h*

1

2 The prices for the first hour in a real market situation should consider the real market prices.

=

å

*i*

*i d i i i j h w*

*H WH h*

*p p*

*FC S*

*d i*

*i d*

*H if h H h*

*i*

*hif h H* (65)

*H h* (66)

and (66) are combined by a weighted average:

+

(67)

(68)

*B h F*

1

= =

*d i*

å å

*i*

*i*

*p H p*

1

( ( ))

1 1

,

1 The assumption that the information is linear with time could be replaced with a more complex information model, such as a function of the cumulated difference between the initial forecasted spot price and the particular spot prices of

*S j h*

*p*

*i*

where:

: delivery period for instrument *i*

augmenting for each hour1

: first hour of delivery period for instrument *i*

112 Dynamic Programming and Bayesian Inference, Concepts and Applications

*Hi*

*H* 0*i*

Other relevant source of uncertainty considered is the random failure of the generating units. The stochastic model of generator outages is built considering that the unit can reside in four mutually exclusive states: Operation (required), Reserve (not required), Unavailable (required) and Unavailable (not required), as shown in the diagram of space states in Figure 6 [11].

Figure 6. Four-state stochastic model of the generation units **Figure 6.** Four-state stochastic model of the generation units

particular hour.

the unit is generating or is in stand-by.

**4.4. Risk constraint formulation**

the objective function (56) becomes:

assumed linear with power output, i.e. marginal costs are constant.

This unit model accounts for the fact that peaking units exhibit higher availability rates. This result is explained by the fact the failure probability is typically very small when the unit is in the stand-by state. A generator is economically called online if its marginal cost of production is below the prevailing spot prices, following the decision model of equation (42). Variable costs of generation are This unit model accounts for the fact that peaking units exhibit higher availability rates. This result is explained by the fact the failure probability is typically very small when the unit is in the stand-by state. A generator is economically called online if its marginal cost of production

The operation-failure cycles of the generating unit are obtained from a chronological Markovian stochastic simulation. For each spot price sample, a time series of power output is synthesized for

1. Based on failure and repair rates defined by the state the unit resided in the previous hour, a random failure is simulated [12]. If a failure is in place, the output power is set to zero for this

2. The dispatch of the unit is simulated, taking into account the marginal cost of generation and the prevailing sample spot price at that time interval. Here perfect foresight of the spot price is

This chronological stochastic model reproduces with accuracy the dynamics involved in failure and repair cycles of generators, giving the possibility to select different failure rates depending on whether

As already mentioned before, the financial decision process can be modeled by means of a MDP. Naming profit *w B* for each sample the sum of income, cost and transaction cost over all instruments,

every generation unit. The hourly power output is simulated o following three steps:

assumed in order to decide the dispatch and fulfill the minimal generation times. 3. If dispatched, other unit's technical restrictions are fulfilled, e.g. ramping capabilities.

20

is below the prevailing spot prices, following the decision model of equation (42). Variable costs of generation are assumed linear with power output, i.e. marginal costs are constant.

( ) ( )

=

If *x* is independent of the Monte Carlo sample, the terms inside the summation over all future periods (*t* =2…*n*) are simply the expected profit for the period *t* after a decision *xt*−1→ *xt*. However, the model should take into account that future strategy decisions may be different for each Monte Carlo sample, accounting for adjustments the decision-maker almost certainly

future decision stages will depend on a set of variables *st*, which represent the variables considered by the decision maker in order to adapt the strategy to a particular situation and

( ) ( )

2

1

+ - - + ++ = + é ù ë û *t t tt t t tt t t tt t x*

The maximization can be solved by a set of recursive maximizations, each one solving only

With this model, the optimization can be decomposed in steps and the dynamic nature of a strategy can be accurately replicated. Despite the fact future trading decisions *xt*=2…*n* are considered and optimized, the practical product of this procedure is the new optimal reba‐ lanced state *xt*=1 starting from the previous trading position *xt*=0. The further trading positions are only optimal given the current information available and should be reconsidered later. Therefore, each new trading position (*xt*=2, *xt*=3, …, *xt*=*n*) should be the product of a similar optimization incorporating the additional market information available immediately before.

The value functions provide the expected continuation value within a state space defined by

solve the optimization problem, are unknown beforehand. It is here that the ADP approach is

3 There are several other decomposition methods, some of which exclude the decision as state space variable defining the value functions in a post-decision state space. These approaches make the step maximization sometimes harder but

3

present advantages such as a state space of fewer dimensions. See for example [2].

introduced to approximate the value and risk functions for the state space.

=

*V xx s B xx s V xx s* (74)

*B xx s B xx s* (73)

*V xx s* (75)

. However, the continuation functions, which are essential to

1 101 1

( ) ( ) ( )

max ( ) 1 , , - é ù ë û *t t tt t x*

1 1 1 11 ,, ,, max , ,

*t tt t x x t*

é ù ê ú + ë û *t* å *n*

max , , max , , = ¼

Risk-Constrained Forward Trading Optimization by Stochastic Approximate Dynamic Programming

E E *B x x B x x* (72)

¯ and the decision itself for

http://dx.doi.org/10.5772/57466

115

1 10 1 2

é ù ê ú éù é ù + ëû ë û ë û *t* å *n*

= ¼

1 2 n

would execute to face specific scenarios. Then, the expected profit *Bt*

1 2 n

Defining the continuation value functions *Vt* as:

the equation (72) becomes:

one decision stage:

the state variables, *xt*, *xt*−1 and *st*

max , max ,

*w wt tt x x t*

The operation-failure cycles of the generating unit are obtained from a chronological Marko‐ vian stochastic simulation. For each spot price sample, a time series of power output is synthesized for every generation unit. The hourly power output is simulated o following three steps:

This chronological stochastic model reproduces with accuracy the dynamics involved in failure and repair cycles of generators, giving the possibility to select different failure rates depending on whether the unit is generating or is in stand-by.


Oxysaver: A High Conservation Demand Oxygen Delivery System with Increased Throughput

## **Association of Environmental Pollutants and the Prevalence of Intellectual Disability in Caribbean Countries from 2006 to 2016**

**Demian Arturo Herrera Morban1 and Ana Carolina Escarraman Martinez2**

1Research Coordinator, Centro de Investigación Dr. Hugo Mendoza, Hospital Pediátrico, Santo Domingo, República Dominicana Master in Early Care and Child Development 2Associate Researcher, Centro de Investigación Dr. Hugo Mendoza, Hospital Pediátrico, Santo Domingo, República Dominicana

Environmental pollutants are considered risk factors for developing intellectual disability when exposure occurs during pregnancy and the first years of life. This has been poorly studied in Caribbean countries. Our main objective is to investigate this association. This is a descriptive-exploratory study based on data obtained from the "Our World in Data" platform (https://ourworldindata.org/) in Microsoft Excel format that included the desired variables. Only the countries that reported all the variables of interest were included.

Multivariable regression analyses and linear regression analyses were performed with the SPSS version 20 programs and the Microsoft Excel spreadsheet. Multivariable regression analysis, including all the variables, demonstrated a significant correlation (r= 0.99, p = 0.049) between the incidence of intellectual disability and the environmental pollutants measured. Household air pollution (r = 0.95, pandlt;0.001) and the prevalence of anemia among pregnant women (r =0.94, pandlt;0.001) demonstrated the strongest correlation with the prevalence of intellectual disability. Our hypothesis for the association of environmental pollutants and the incidence of intellectual disability is likely. We demonstrated that environmental pollutants are strongly associated with the incidence of intellectual disabilities in Caribbean countries. Other factors not included in our study, including the socioeconomic level, could also influence the different variables and the presence of intellectual disability.

#### Introduction

Environmental pollutants are considered risk factors for the development of intellectual disability when exposure occurs during pregnancy and the first years of life. This has been poorly studied in Caribbean countries, so our main objective is to investigate this association.

#### Methodology

A descriptive-exploratory study based on data obtained from the "Our World in Data" platform (https:// ourworldindata.org/) in Microsoft Excel format that included the desired variables. Only the countries that reported all the variables of interest were included. Multivariable regression analyses and linear regression analyses were performed using SPSS version 20 programs and the Microsoft Excel spreadsheet.

*Table 1. Regression analysis.*

#### Results and Discussion

The multivariable regression analysis including all the variables demonstrated a significant correlation (r= 0.99, p = 0.049) between the incidence of intellectual disability and the environmental pollutants measured. After performing a linear regression with each variable,

household air pollution (r = 0.95, p<0.001) and the prevalence of anemia among pregnant women (r =0.94, p<0.001) demonstrated a strong correlation with the prevalence of intellectual disability. Outdoor air pollutants (r = 0.71, p<0.001) and annual CO2 emissions (r=0.53, p<0.001) demonstrated a weaker but still statistically significant correlation.

The results found in the analysis for this study suggest that our hypothesis for the association of environmental pollutants and the incidence of intellectual disability is likely. This can be supported by the results found in Emerson et al., where children with intellectual disabilities were more likely to live close to areas with high exposure to outdoor air pollution, in comparison with children without intellectual disabilities (1). Figure 1. Correlation Scatter Plots of statistically significant variables.

During our analysis, there was a strong correlation between anemia in pregnancy and the presence of intellectual disability. A previous study by Wiegersma et al. found that ASD and intellectual disability prevalence was higher in children of mothers with anemia during pregnancy (2). While we found a strong correlation between household air pollution and intellectual disability, we could not find studies that supported these results.

#### Conclusion

We demonstrated that environmental pollutants are strongly associated with the incidence of intellectual disabilities in Caribbean countries. These results coincide with previous studies that have identified the presence of environmental pollutants as risk factors for the development of intellectual disabilities. Other factors not included in our study, including the socioeconomic level, could also influence the different variables and the presence of intellectual disability. References

#### Authors

Demian Arturo Herrera Morban1 and Ana Carolina Escarraman Marinez2

1 Research Coordinator, Centro de Investigación Dr. Hugo Mendoza, Hospital Pediátrico, Santo Domingo, República Dominicana Master in Early Care and Child Development

2 Associate Researcher, Centro de Investigación Dr. Hugo Mendoza, Hospital Pediátrico, Santo Domingo, República Dominicana

1


**Plastic Adaptation: A Neuronal Imperative Capable of Confounding the Goals of Stem Cell Replacement Therapy for either Huntington's or Parkinson's Disease of Confounding the Goals of Stem Cell Replacement Therapy for either Huntington's or Parkinson's Disease**

**Plastic Adaptation: A Neuronal Imperative Capable**

DOI: 10.5772/intechopen.71790

Michael I. Sandstrom, Kevin A. Anderson, Naveen Jayaprakash, Parnit K. Bhupal and Gary L. Dunbar Naveen Jayaprakash, Parnit K. Bhupal and Gary L. Dunbar Additional information is available at the end of the chapter

Michael I. Sandstrom, Kevin A. Anderson,

Additional information is available at the end of the chapter

http://dx.doi.org/10.5772/intechopen.71790

#### **Abstract**

**References**

6 Neuroplasticity - Insights of Neural Reorganization

2010;**21**:457-471

2005;**81**(1):31-37

[1] Chaban V, editor. Irritable Bowel Syndrome-Novel Concepts for Research and Treatment.

[2] Chaban V. Unraveling the Enigma of Visceral Pain. New York: Nova Publishers; 2016. 77 p. ISBN: 978-63489-430-8. Library of U.S. Congress Control Number:<PHONE_NUMBER> [3] Schaible HS. Peripheral and central mechanisms of pain generation. In: Stein C, editor.

[4] Sommer C. Serotonin in pain and pain control. Handbook of Behavioral Neuroscience.

[5] Brierley S, Linden D. Neuroplasticity and dysfunction after gastrointestinal inflamma-

[6] Brumovsky P, Gebhart G. Visceral organ cross-sensitization—An integrated perspec-

[7] Chaban V. Visceral pain modulation in female primary afferent sensory neurons. Current

[8] Chaban V, Li J, McDonald J, Rapkin A, Micevych P. Estradiol attenuates ATP-induced increase of intracellular calcium through group II metabotropic glutamate B receptors in

[9] Li J, McDonald J, Rapkin A, Micevych P, Chaban V. Inflammation in the uterus induces pERK and substance P activation in DRG neurons innervating both uterus and colon in

[10] Chaban V, Mayer E, Ennes H, Micevych P. Estradiol inhibits ATP-induced [Ca2+]i

[11] Chaban V, Micevych P. Estrogen receptor-α mediates estradiol attenuation of ATPinduced Ca2+ signaling in dorsal root ganglion neurons. Journal of Neuroscience Research.

[12] Chaban V. Estrogen modulation of visceral nociception. In: Ritzner, Weizman, editors. Neuroactive Steroids in Brain Function, and Mental Health: New Perspectives for

[13] Patrone C, Anderson S, Korhonen L, Lindholm D. Estrogen receptor-dependent regulation of sensory neuron survival in developing dorsal root ganglion. Proceeding National

[14] Micevych P, Christensen A. Membrane-initiated estradiol actions mediate structural plasticity and reproduction. Frontiers in Neuroendocrinology. 2012;**33**(4):331-341 [15] Kim Y, Anderson M, Park K, Zheng Q, Agarwal A, Gong C, Young L, Shaoqiu, LaVinka P, Zhou F, Bergles D, Hanani M, Guan Y, Spray D, Dong X. Coupled activation of primary

sensory neurons contributes to chronic pain. Neuron. 2016;**91**(5):1085-1096

rat DRG neurons. Journal of Neuroscience Research. 2011;**89**(11):1707-1710

tion. Nature Review: Gastroenterology and Hepatology. 2014;**11**(10):611-627

Rijeka: InTech; 2017. 85 p. ISBN 978-953-51-2827-4

Analgesia. Heidelberg: Springer; 2007. pp. 435-463

tive. Autonomic Neuroscience. 2010;**153**(1-2):106

rats. Journal of Neuroscience Research. 2008;**86**:2746-2752

increase in DRG neurons. Neuroscience. 2003;**118**(6):941-948

Research and Treatment. Berlin: Springer; 2008. pp. 89-102

Academy of Sciences USA. 1999;**96**:10905-10910

Trends in Neurology. 2015;**9**:111-114

Although stem cell transplant therapy offers considerable promise for deteriorative diseases, the efficacy of its application may be mitigated by endogenous compensatory mechanisms in the host brain. Plastic compensation follows neurodegeneration, beginning at its very onset and minimizing early symptom expression. As researchers attempt to correlate symptom remission with the ability of transplanted cells to adopt specific cell phenotypes, they need to be vigilant of the possibility that competing, local compensatory effects may be altering the outcome. Clearly plastic compensatory mechanisms could confound desired transplant-derived improvements by supplanting the beneficial contributions of the transplants. As circuit-level adaptations occur, more explicit explorations of their relevance to neuronal transplantation success are needed. Conceptual models of undirected transplanted cells adopting preconceived appropriate roles require revision. The notion that newly transplanted neuronal precursors will incorporate themselves into host circuitry with mutual cooperation across both parties (i.e., transplant and host) without some symbiosis-promoting mechanism is naïve. Undirected local circuits could react to newly transplanted additions as intruders. We advocate that appropriate signaling from transplanted cells to the host environment is required to optimize the therapeutic relevance of transplantation. This review surveys critical signaling mechanisms that might promote symbiotic interdependence between the host and new transplants.

**Keywords:** stem cells, transplantation, Parkinson's disease, Huntington's disease, adaptive plasticity, development

© 2016 The Author(s). Licensee InTech. This chapter is distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/3.0), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. © 2018 The Author(s). Licensee IntechOpen. This chapter is distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/3.0), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

#### **1. Introduction**

For several years now, efforts have been underway to examine and refine technology associated with promoting the incorporation of pluripotent stem cells from various origins following transplantation into the brains of patients suffering from various deteriorative diseases [1–3], or to test the viability of such treatments using experimental animal models [4–6]. The typical pattern of findings associated with clinical efforts is initial moderate symptom improvement, followed by either resumption of symptoms over time or highly variable therapeutic outcomes [7–9]. Common arguments raised for the mechanism underlying inconsistent effectiveness are that either the transplanted cells are not merging sufficiently with the host brain due to a timely competition-related synaptogenesis process, that transplanted cells are not surviving in the harsh environment of the host due to immune-system/inflammatory host responses, or both [8–11] (also see the extensive review by cell type [12]). While evidence for these arguments certainly exists, it remains unclear whether those arguments cover all the relevant possibilities that threaten the longevity of the transplanted stem cells' utility. One potential threat to the long-term efficacy of this treatment, or to stem cell transplant therapies in general, which is frequently overlooked, would be *plastic adaptation*. Briefly, plastic adaptation represents a multitude of cellular responses that occur with the apparent role of maintaining cellular homeostasis, yet within the nervous system also supports the maintenance of a sort of dynamic status quo in which compensatory changes adjust the actions or response capacities of local healthy neurons in support of a superseding circuit-associated need. Plastic adaptation also occurs within the physiologically healthy brain in order to adjust for novel needs, supporting changes such as long-term memory, habit formation, and other sorts of behavioral adaptation of organisms to new surroundings and demands (for examples see [13, 14]). A surge of inquiry into what are now known as epigenetic mechanisms supports the notion of a clear capacity of cells to respond to environmental stimuli by generating enduring changes in their genetic expression [15–18]. This, combined with numerous demonstrations of more transient receptor plasticity [19–22], defines neuronal cells as versatile in both shortand long-term periods in adjusting to their neurochemical and electrophysiological circumstances at their membranes and within their nuclei, respectively. Following transplantation, it is likely that plastic adaptation responses could occur in both populations of neuronal cells of concern, either the transplanted cells or the surrounding host cells that likely interact with the transplanted cells.

might contribute to the developing circuit [35, 36]. As needs are met, postsynaptic neurons decrease their encouragement of subsequent equivalent connections by adapting their signaling [37–40]. How new afferents drive or control action potentials contributes significantly to circuit behavior, depending on factors as subtle as the proximity of synapses to a target neuron's trigger zone, while on the postsynaptic side the development of the trigger zone may modify when and how action potentials arise [41–46]. Incorporation into circuits relates to both identity and survival as neurons develop. As the neuronal phenotype is established, developing cells become increasingly dependent upon both afferent and efferent connections to other neurons. Neuronal fate seems to result from aspects of stimulation in the context of neurotrophic factors such as brain-derived neurotrophic factor (BDNF). Excitatory postsynaptic potentials known to increase intracellular calcium seem to participate in driving developmental determinations. This was shown by a series of experiments performed on precursor cells *in vitro* where calcium chelation blocked the establishment of neuronal phenotypes normally induced by either electrical or NMDA-glutamate stimulation in conjunction with BDNF [47–49]. Thus, precursors that receive insufficient controlling input to engage their activity likely adopt non-neuronal, glial, or support cell status, modifying or diminishing their contribution to circuits. When growing neurons establish connections to other neuronal populations, this provides them with target-derived trophic support that staves off programmed cell death that is likely to occur in its absence [50–53]. Surviving long enough to establish contributions is of course also important for transplanted populations, but evidence indicates that this is easier in the more forgiving context of development. A very useful series of explorations documenting how transplantation faces diminished success as the host ages was thoroughly documented in a mini-review by Sally Temple [54]. In addition, often the younger and less "experienced" or "committed" precursor cells are shown to more easily adapt into their transplanted roles than similar, yet older, populations [55–57]. In other contexts, such as the ability to properly generate blood cells following bone marrow transplants, younger donors seem to yield more successful results than older donors, indicating this age-dependency is not limited to neuronal populations [58, 59]. The similar goals of establishing appropriate cell populations to fill various niches following transplantation suggest if the environment were less competitive or more accommodating, and cells were guided by the more overt signals available during development, the process of incorporation would be more straightforward. In the adult brain, the mechanisms of plasticity engage to maintain the continuity of established function with mechanisms to prevent deviation from working systems; otherwise all nervous systems would constantly deteriorate into chaos. Thus, while similar concerns are present with transplantation, (i.e., coaxing the new cells to make useful and appropriate contributions to established circuitry), we cannot expect that new additions will naturally get swept into correct and working interactions the way they do

Plastic Adaptation: A Neuronal Imperative Capable of Confounding the Goals of Stem Cell…

http://dx.doi.org/10.5772/intechopen.71790

9

To tease out the contributions of plastic adaptation to the success or longevity of stem cell transplantation therapy, it seems there is a need to expand inquiry further than whether transplanted cells develop into neurons, survive, or form mutually integrative connections with endogenous neurons. It appears equally important to determine how the cell populations influence each other and how each population adapts to this influence over time. There may be important clues

during development.

During nervous system development, the mechanisms that guide the distributions of cells and their connectivity offer a far more forgiving flexibility when compared to the harsher, more demanding adult environment we face when attempting to correct deterioration with transplants [23–26]. Growth distances for neurites are shorter given the smaller neuropil, and more overt chemical gradients support pathfinding [27–29]. A developmental neurogenesis surge supports self-repair in the event of cell destruction because phenotype commitment is guided by a progressive fulfillment of niches and feedback signals once niches are filled [30–34]. Differential neuronal responsibilities within developing circuits are coaxed into existence in the context of an enhanced adaptive plasticity on either side of synaptic clefts, where each contributes to phenotype adoption of the other while it is determined what they might contribute to the developing circuit [35, 36]. As needs are met, postsynaptic neurons decrease their encouragement of subsequent equivalent connections by adapting their signaling [37–40]. How new afferents drive or control action potentials contributes significantly to circuit behavior, depending on factors as subtle as the proximity of synapses to a target neuron's trigger zone, while on the postsynaptic side the development of the trigger zone may modify when and how action potentials arise [41–46]. Incorporation into circuits relates to both identity and survival as neurons develop. As the neuronal phenotype is established, developing cells become increasingly dependent upon both afferent and efferent connections to other neurons. Neuronal fate seems to result from aspects of stimulation in the context of neurotrophic factors such as brain-derived neurotrophic factor (BDNF). Excitatory postsynaptic potentials known to increase intracellular calcium seem to participate in driving developmental determinations. This was shown by a series of experiments performed on precursor cells *in vitro* where calcium chelation blocked the establishment of neuronal phenotypes normally induced by either electrical or NMDA-glutamate stimulation in conjunction with BDNF [47–49]. Thus, precursors that receive insufficient controlling input to engage their activity likely adopt non-neuronal, glial, or support cell status, modifying or diminishing their contribution to circuits. When growing neurons establish connections to other neuronal populations, this provides them with target-derived trophic support that staves off programmed cell death that is likely to occur in its absence [50–53]. Surviving long enough to establish contributions is of course also important for transplanted populations, but evidence indicates that this is easier in the more forgiving context of development. A very useful series of explorations documenting how transplantation faces diminished success as the host ages was thoroughly documented in a mini-review by Sally Temple [54]. In addition, often the younger and less "experienced" or "committed" precursor cells are shown to more easily adapt into their transplanted roles than similar, yet older, populations [55–57]. In other contexts, such as the ability to properly generate blood cells following bone marrow transplants, younger donors seem to yield more successful results than older donors, indicating this age-dependency is not limited to neuronal populations [58, 59]. The similar goals of establishing appropriate cell populations to fill various niches following transplantation suggest if the environment were less competitive or more accommodating, and cells were guided by the more overt signals available during development, the process of incorporation would be more straightforward. In the adult brain, the mechanisms of plasticity engage to maintain the continuity of established function with mechanisms to prevent deviation from working systems; otherwise all nervous systems would constantly deteriorate into chaos. Thus, while similar concerns are present with transplantation, (i.e., coaxing the new cells to make useful and appropriate contributions to established circuitry), we cannot expect that new additions will naturally get swept into correct and working interactions the way they do during development.

**1. Introduction**

8 Neuroplasticity - Insights of Neural Reorganization

the transplanted cells.

For several years now, efforts have been underway to examine and refine technology associated with promoting the incorporation of pluripotent stem cells from various origins following transplantation into the brains of patients suffering from various deteriorative diseases [1–3], or to test the viability of such treatments using experimental animal models [4–6]. The typical pattern of findings associated with clinical efforts is initial moderate symptom improvement, followed by either resumption of symptoms over time or highly variable therapeutic outcomes [7–9]. Common arguments raised for the mechanism underlying inconsistent effectiveness are that either the transplanted cells are not merging sufficiently with the host brain due to a timely competition-related synaptogenesis process, that transplanted cells are not surviving in the harsh environment of the host due to immune-system/inflammatory host responses, or both [8–11] (also see the extensive review by cell type [12]). While evidence for these arguments certainly exists, it remains unclear whether those arguments cover all the relevant possibilities that threaten the longevity of the transplanted stem cells' utility. One potential threat to the long-term efficacy of this treatment, or to stem cell transplant therapies in general, which is frequently overlooked, would be *plastic adaptation*. Briefly, plastic adaptation represents a multitude of cellular responses that occur with the apparent role of maintaining cellular homeostasis, yet within the nervous system also supports the maintenance of a sort of dynamic status quo in which compensatory changes adjust the actions or response capacities of local healthy neurons in support of a superseding circuit-associated need. Plastic adaptation also occurs within the physiologically healthy brain in order to adjust for novel needs, supporting changes such as long-term memory, habit formation, and other sorts of behavioral adaptation of organisms to new surroundings and demands (for examples see [13, 14]). A surge of inquiry into what are now known as epigenetic mechanisms supports the notion of a clear capacity of cells to respond to environmental stimuli by generating enduring changes in their genetic expression [15–18]. This, combined with numerous demonstrations of more transient receptor plasticity [19–22], defines neuronal cells as versatile in both shortand long-term periods in adjusting to their neurochemical and electrophysiological circumstances at their membranes and within their nuclei, respectively. Following transplantation, it is likely that plastic adaptation responses could occur in both populations of neuronal cells of concern, either the transplanted cells or the surrounding host cells that likely interact with

During nervous system development, the mechanisms that guide the distributions of cells and their connectivity offer a far more forgiving flexibility when compared to the harsher, more demanding adult environment we face when attempting to correct deterioration with transplants [23–26]. Growth distances for neurites are shorter given the smaller neuropil, and more overt chemical gradients support pathfinding [27–29]. A developmental neurogenesis surge supports self-repair in the event of cell destruction because phenotype commitment is guided by a progressive fulfillment of niches and feedback signals once niches are filled [30–34]. Differential neuronal responsibilities within developing circuits are coaxed into existence in the context of an enhanced adaptive plasticity on either side of synaptic clefts, where each contributes to phenotype adoption of the other while it is determined what they

To tease out the contributions of plastic adaptation to the success or longevity of stem cell transplantation therapy, it seems there is a need to expand inquiry further than whether transplanted cells develop into neurons, survive, or form mutually integrative connections with endogenous neurons. It appears equally important to determine how the cell populations influence each other and how each population adapts to this influence over time. There may be important clues to the mysteries surrounding the impermanence of replacement therapy in how these populations adjust to the presence of the *other*. This chapter was written to consider current knowledge about plastic adaptation as it pertains to the act of incorporating transplanted neuronal cells or precursors into a damaged host brain. In addition, this review represents a general call for more direct inquiry into this subject in future efforts to explore and hone such a promising therapeutic technology. If plastic changes compromise the capacity to maintain symptom-suppressing benefits of these transplants, solutions to this will likely require more than tracking the quality and longevity of behavioral benefit or the anatomical persistence of the transplants over extended periods. Success may be enhanced by recognizing the ongoing patterns of plasticity with which transplanted neuronal cells must cooperate to earn the opportunity to contribute. Given that the age of both the cells transplanted and the host into which they have been transplanted are relevant to their incorporation and therapeutic efficacy, it appears that the capacity to adapt into the new environment depends on factors or signals from both elements that need to be understood to support moving forward intelligently with this therapeutic endeavor. The remainder of this review will address concerns regarding the host adaptive responses to the transplant as well as the transplant's adaptive response to the host that ought to be considered in this regard, focusing largely on efforts with Huntington's and Parkinson's disease.

this does not happen, we appear surprised that transplantation efforts impede healthy behavior restoration over time, or show diminished effectiveness over time—but we should not be. While beyond the scope of this chapter, we nonetheless feel it is important to also acknowledge the prominence of neuronal circuit dependence on both use and the ongoing local actions of the immune system. It is likely that a repetitive drive on the circuit due to the person or animal engaging in systemic practice to recapture the skill they once had also supports circuit-level adaptation. This is likely why Parkinson's patients who regularly move and push themselves to actively engage compromised limbs rather than remaining sedentary reap clinical benefits from those actions [62, 63]. It is intriguing to consider these effects in the context of their ultimate therapeutic mechanisms which promote restoration or strengthening of key circuits with positive contributions to adaptation efforts, as well as the fact that once a part of a circuit, transplant-derived neurons may require practice to become proficient in their established roles. Of course, immune rejection and the broader context of inflammation also enter into this equation, given the common desire to utilize transplants in the context of deteriorative diseases or trauma-related damage. While it is arguable that convincing the immune system not to overreact has been extensively studied as a factor in this context (e.g., [64]), the inflammatory response certainly has the capacity to tailor the very adaptation mechanisms we will discuss (e.g., [65]). For extensive reviews of the reciprocal interactions between neural systems and inflammatory systems relevant to plasticity see Di Filipo and colleagues [66], or

Plastic Adaptation: A Neuronal Imperative Capable of Confounding the Goals of Stem Cell…

http://dx.doi.org/10.5772/intechopen.71790

11

Do the new additions engage with the existing circuits in positive adaptation-enhancing ways? Along the way it appears that there are adaptations on both sides that might enhance or diminish this relationship. If the adaptations diminish this circuit-supporting relationship, then the ability of the new transplanted cells to continue their presence and effectively support positive behavioral improvements will likely be lost and the clinical efforts of transplantation will likely be considered insufficient or transient. Alternatively, if the adaptations that occur enhance the circuit-supporting relationship while avoiding interfering with ongoing adaptive efforts, the success may extend further than the initial witnessed improvements into continuous ongoing improvements, rather than plateauing at some yet incomplete recovery. In this chapter we will divide our appreciation of transplantationrelated plasticity as new cells establish roles contributing to existing yet compromised circuits first into whether the endogenous circuit adopts the newcomers as team players, and second whether the transplanted cells adopt the roles required of them to contribute to the

**3. Adaptation of endogenous host tissue to neural transplantation**

Although adult neurogenesis was overlooked in the past and neuroscientists were convinced that new neurons were not produced beyond the early stages of development, it has now been demonstrated conclusively that there are select regions in the brain that regularly accept new neurons into established circuits that are derived from precursor neuroblasts that retain mitotic capacity throughout our lives, and divide asymmetrically to produce new neurons as

Xanthos and Sandkuhler [67].

circuit or not.

#### **2. Achievements of "successful" transplantations**

Therapeutic support derived from neural transplantation likely necessitates circuit-level reconstruction so that certain missing neurobehavioral actions are restored. However, it is important to acknowledge that circuits can be supported by either the addition of new neuronal contributions that might restore disconnected components or by bolstering the inherent capacity of compromised circuits to adjust or compensate. The brain's inherent capacity to compensate for damage/disruption or "repair itself" is considerable and likely the reason why physical or occupational therapies support function restoration. Trophic support and other general support of persisting residual circuit components, receptor sensitivity adjustments, sprouting, and several other inherent mechanisms contribute to reparation (for an extensive review of these mechanisms see [60]). These trophic or supportive contributions can be accomplished by nonneural cells or glia that likely contribute mostly indirectly to neuronal circuit actions. In fact, Blurton-Jones and colleagues [61] demonstrated that transplant-derived BDNF was eventually responsible for supporting cognitive improvements in a rodent Alzheimer's model by promoting enhanced synaptic density in the hippocampus between preexisting neurons. Thus, it appears that either the transplanted cells become active contributors to the circuit or they support the existing circuit that itself seems to engage compensatory mechanisms supporting at least partial function. Therefore, it appears beneficial to respect that plastic adaptation persists as an ongoing process, regularly promoting positive improvements in functional circuits, and that a *successful* contribution of transplanted stem cells to existing neural circuitry necessitates a recognizable supportive contribution to this endeavor. It is our overarching concern that transplant efforts do not typically respect this context, usually holding a more direct circuit reconstruction as paramount with the presumption that the host brain will somehow also recognize our clinical perspective and modify ongoing adaptive mechanisms accordingly. When this does not happen, we appear surprised that transplantation efforts impede healthy behavior restoration over time, or show diminished effectiveness over time—but we should not be.

to the mysteries surrounding the impermanence of replacement therapy in how these populations adjust to the presence of the *other*. This chapter was written to consider current knowledge about plastic adaptation as it pertains to the act of incorporating transplanted neuronal cells or precursors into a damaged host brain. In addition, this review represents a general call for more direct inquiry into this subject in future efforts to explore and hone such a promising therapeutic technology. If plastic changes compromise the capacity to maintain symptom-suppressing benefits of these transplants, solutions to this will likely require more than tracking the quality and longevity of behavioral benefit or the anatomical persistence of the transplants over extended periods. Success may be enhanced by recognizing the ongoing patterns of plasticity with which transplanted neuronal cells must cooperate to earn the opportunity to contribute. Given that the age of both the cells transplanted and the host into which they have been transplanted are relevant to their incorporation and therapeutic efficacy, it appears that the capacity to adapt into the new environment depends on factors or signals from both elements that need to be understood to support moving forward intelligently with this therapeutic endeavor. The remainder of this review will address concerns regarding the host adaptive responses to the transplant as well as the transplant's adaptive response to the host that ought to be considered

in this regard, focusing largely on efforts with Huntington's and Parkinson's disease.

Therapeutic support derived from neural transplantation likely necessitates circuit-level reconstruction so that certain missing neurobehavioral actions are restored. However, it is important to acknowledge that circuits can be supported by either the addition of new neuronal contributions that might restore disconnected components or by bolstering the inherent capacity of compromised circuits to adjust or compensate. The brain's inherent capacity to compensate for damage/disruption or "repair itself" is considerable and likely the reason why physical or occupational therapies support function restoration. Trophic support and other general support of persisting residual circuit components, receptor sensitivity adjustments, sprouting, and several other inherent mechanisms contribute to reparation (for an extensive review of these mechanisms see [60]). These trophic or supportive contributions can be accomplished by nonneural cells or glia that likely contribute mostly indirectly to neuronal circuit actions. In fact, Blurton-Jones and colleagues [61] demonstrated that transplant-derived BDNF was eventually responsible for supporting cognitive improvements in a rodent Alzheimer's model by promoting enhanced synaptic density in the hippocampus between preexisting neurons. Thus, it appears that either the transplanted cells become active contributors to the circuit or they support the existing circuit that itself seems to engage compensatory mechanisms supporting at least partial function. Therefore, it appears beneficial to respect that plastic adaptation persists as an ongoing process, regularly promoting positive improvements in functional circuits, and that a *successful* contribution of transplanted stem cells to existing neural circuitry necessitates a recognizable supportive contribution to this endeavor. It is our overarching concern that transplant efforts do not typically respect this context, usually holding a more direct circuit reconstruction as paramount with the presumption that the host brain will somehow also recognize our clinical perspective and modify ongoing adaptive mechanisms accordingly. When

**2. Achievements of "successful" transplantations**

10 Neuroplasticity - Insights of Neural Reorganization

While beyond the scope of this chapter, we nonetheless feel it is important to also acknowledge the prominence of neuronal circuit dependence on both use and the ongoing local actions of the immune system. It is likely that a repetitive drive on the circuit due to the person or animal engaging in systemic practice to recapture the skill they once had also supports circuit-level adaptation. This is likely why Parkinson's patients who regularly move and push themselves to actively engage compromised limbs rather than remaining sedentary reap clinical benefits from those actions [62, 63]. It is intriguing to consider these effects in the context of their ultimate therapeutic mechanisms which promote restoration or strengthening of key circuits with positive contributions to adaptation efforts, as well as the fact that once a part of a circuit, transplant-derived neurons may require practice to become proficient in their established roles. Of course, immune rejection and the broader context of inflammation also enter into this equation, given the common desire to utilize transplants in the context of deteriorative diseases or trauma-related damage. While it is arguable that convincing the immune system not to overreact has been extensively studied as a factor in this context (e.g., [64]), the inflammatory response certainly has the capacity to tailor the very adaptation mechanisms we will discuss (e.g., [65]). For extensive reviews of the reciprocal interactions between neural systems and inflammatory systems relevant to plasticity see Di Filipo and colleagues [66], or Xanthos and Sandkuhler [67].

Do the new additions engage with the existing circuits in positive adaptation-enhancing ways? Along the way it appears that there are adaptations on both sides that might enhance or diminish this relationship. If the adaptations diminish this circuit-supporting relationship, then the ability of the new transplanted cells to continue their presence and effectively support positive behavioral improvements will likely be lost and the clinical efforts of transplantation will likely be considered insufficient or transient. Alternatively, if the adaptations that occur enhance the circuit-supporting relationship while avoiding interfering with ongoing adaptive efforts, the success may extend further than the initial witnessed improvements into continuous ongoing improvements, rather than plateauing at some yet incomplete recovery. In this chapter we will divide our appreciation of transplantationrelated plasticity as new cells establish roles contributing to existing yet compromised circuits first into whether the endogenous circuit adopts the newcomers as team players, and second whether the transplanted cells adopt the roles required of them to contribute to the circuit or not.


**Analysis and Research on the Comprehensive Performance of Vehicle Magnetorheological Regenerative Suspension**

### **Jinhui Huang, Enrong Wang and Hailong Zhang \***

Vibration Control Lab, School of Electrical and Automation Engineering, Nanjing Normal University, Nanjing 210097, China<EMAIL_ADDRESS>(J.H<EMAIL_ADDRESS>(E.W.)

**\*** Correspondence<EMAIL_ADDRESS>
Received: 17 September 2020; Accepted: 13 October 2020; Published: 22 October 2020

**Abstract:** Magnetorheological (MR) regenerative suspension system can not only achieve excellent comprehensive suspension performance but also effectively recover and utilize vibration potential energy, which has been a research hotspot in the field of vehicle engineering. In this paper, for the 1/4 vehicle's MR regenerative suspension system parallel with a tubular permanent magnet linear motor (TPMLM), the dynamic model of the MR semi-active suspension system and the TPMLM finite element model are established separately to form a joint simulation platform. The simulation analysis of the comprehensive suspension performance and regeneration performance under different road excitations is performed. The results show that installing TPMLM does not change the natural resonance frequency of the suspension system, which ensures good driving comfort and handling stability. At the same time, it has considerable regeneration power. This research can provide a reference for the stability analysis and popularization of the vehicle's MR regenerative suspension system.

**Keywords:** magnetorheological suspension; regenerative energy; joint simulation; suspension performance

### **1. Introduction**

The suspension is an important assembly and functional part of the vehicle. Magnetorheological (MR) semi-active suspension system has become a research hotspot in the field of vehicle suspension due to its simple structure, low energy consumption, and adaptability to various road conditions. In addition, with the increasingly prominent worldwide energy problems, energy conservation and utilization have become another important topic in the field of vehicle engineering. Research shows that in the daily use of cars, 14–26% of the fuel energy is used to overcome road friction and air resistance to drive the car [1]. The main way is to dissipate the heat energy through suspension damping damper. This part of the energy has not been fully utilized yet and has considerable recovery value.

Karnopp [2] and Browne [3] et al. carried out the researches on the recovery and utilization of vibration energy of vehicle suspension for the first time in the 1980s, indicating that suspension vibration energy has a great potential utilization value. Huang et al. [4] established a vehicle regenerative suspension model for the electrodynamic active regenerative suspension of permanent magnet direct current brushless motor combined with a ball screw structure and analyzed its mechanical properties and regenerative characteristics. The conclusion that its ride comfort needs to be improved was found. Yu et al. [5] reviewed and summarized the researches on regenerative suspension in recent years. By comparing the mechanical regenerative suspension with the electromagnetic regenerative suspension, it was found that the electromagnetic regenerative suspension is convenient for energy conversion and convenient for storage and reuse. Dong et al. [6] used a ball screw combined with a

rotating motor as the power generation device and analyzed the corresponding relationship between the performance of regenerative generation and the external excitation of the two working modes of power generation device and magnetorheological damper (MRD) connected in series and parallel. The idea that vibration generation storage and suspension vibration reduction completed at the same time was proposed. Kou et al. [7] proposed a parallel ball screw semi-active suspension actuator structure, which is transformed into a unidirectional rotation power generation of a direct current brushless motor through a ball screw mechanism and a parallel gearbox structure. Zhu et al. [8] carried out research on a vehicle suspension regenerative power generation device integrated with tubular permanent magnet linear motor (TPMLM) and MRD, to directly supply power to the MRD through vibration power generation, without additional driving power. Kou et al. [9] designed a novel regenerative suspension power generation device integrating TPMLM and MRD, using skyhook semi-active control. This research showed that the suspension could realize energy self-supply. Lv et al. [10] made a comprehensive analysis of the hydraulic regenerative suspension system and analyzed the shock-absorbing and regenerative characteristics of the system, but the authors did not make a comprehensive analysis of the MR regenerative suspension in parallel with TPMLM.

The above work shows that the vibration energy of vehicle suspension has considerable recycling value. On the one hand, it can supply power for MRD, and on the other hand, it can recover and store energy to increase the cruising range of electric vehicles. However, the addition of the regenerative device may cause the suspension resonance point to shift, thus changing the inherent suspension characteristics of the vehicle, which has not been effectively improved. To solve this problem, based on the joint simulation, this paper establishes the MR regenerative suspension system simulation model in parallel with TPMLM, to analyze the system's comprehensive suspension performance and regenerative characteristics by observing the inherent suspension characteristics under different road excitations.

### **2. 1**/**4 MR Regenerative Suspension System**

Figure 1 shows the structure diagram of the 1/4 MR regenerative suspension system, mainly composed of carriage, suspension spring, MRD, regenerative motor, and wheels. Wherein, *ms* is the sprung mass, *mu* is the unsprung mass. *Ks* is the stiffness coefficient of the suspension spring. *Fd* is the output damping force of the damper. *Fm* is the electromagnetic force of the linear motor. *Kt* is the equivalent stiffness coefficient of the tire. *Ct* is the tire equivalent damping coefficient. *xi* , *xs* , and *xu* are the displacement of the road, the vertical relative displacement of the carriage, and the vertical relative displacement of the chassis, respectively.

**Figure 1.** The structure of the 1/4 magnetorheological (MR) regenerative suspension system. The explanations of *ms*, *mu*, *Ks* ,*Kt* , *Fd* , *Fm*, *Ct* , *xi*, *xu*, *xs* are listed in the main-text.

### *2.1. MR Semi-Active Vehicle Suspension*

Assuming that the sprung mass and the unsprung mass are rigid bodies, the motion is only perpendicular to the ground direction. The suspension system has a linear stiffness coefficient and the damping coefficient. The effective stroke of the damper and the linear motor is not exceeded in the process of motion. Furthermore, the dynamic model of the regenerative suspension system shown in Equation (1) is established.

$$\begin{aligned} \mathbf{m}\_{\rm s} \ddot{\mathbf{x}}\_{\rm s} &= -\mathbf{K}\_{\rm s} (\mathbf{x}\_{\rm s} - \mathbf{x}\_{\rm u}) - (\mathbf{F}\_{\rm d} + \mathbf{F}\_{\rm m}) \\ \mathbf{m}\_{\rm u} \ddot{\mathbf{x}}\_{\rm u} &= \mathbf{K}\_{\rm s} (\mathbf{x}\_{\rm s} - \mathbf{x}\_{\rm u}) + \mathbf{F}\_{\rm d} + \mathbf{F}\_{\rm m} \\ &- \mathbf{K}\_{\rm t} (\mathbf{x}\_{\rm u} - \mathbf{x}\_{\rm i}) - \mathbf{c}\_{\rm t} (\dot{\mathbf{x}}\_{\rm u} - \dot{\mathbf{x}}\_{\rm i}) \end{aligned} \tag{1}$$

The output damping force of MRD selects the modified Bouc–Wen phenomenon model [11], of which driving current modulation is separated from the hysteresis operator.

$$F\_d(\mathbf{i}\_d, \mathbf{x}\_r) = c(\mathbf{i}\_d) F\_h(\mathbf{x}\_r) \tag{2}$$

$$c(i\_d) = 1 + \frac{k\_2}{1 + e^{-a\_0(i\_d + I\_0)}} - \frac{k\_2}{1 + e^{-a\_0 I\_0}} \tag{3}$$

$$F\_h(\mathbf{x}\_r) = c\_1 \dot{\mathbf{y}} + k\_1(\mathbf{x}\_r - \mathbf{x}\_0) \tag{4}$$

$$\begin{array}{c} \dot{y} = \frac{1}{c\_0 + c\_1} \left[ \alpha z + c\_0 \dot{x}\_r + k\_0 (\mathbf{x}\_r - \mathbf{y}) \right] \\ \dot{z} = -\gamma \left| \dot{x}\_r - \dot{y} \right| z |z|^{n-1} - \\ (\beta |z|^n - A) \left( \dot{x}\_r - \dot{y} \right) \end{array} \tag{5}$$

where *id* is the drive current. *c*(*id* ) is the drive current modulation function. *Fh* (*xr*) is the Bouc–Wen hysteresis operator. *y* is the internal piston displacement of the Bouc–Wen model. *I*0 is the current saturation adjustment parameter, and *x*0 is the initial displacement. *z* is a unitless progressive variable, and *k*1, *k*2, *a*0, *c*0, *c*1, α, β, γ, *A* are constants of model parameters.

.

The improved skyhook semi-active controller is applied. Namely, when the acceleration of vehicle sprung mass is inconsistent with the relative velocity of damper, the MRD output damping force is increased. On the contrary, the MRD output damping force is reduced to suppress the resonance amplitude of sprung mass. The MRD semi-active control current *id* is as follows.

$$\begin{cases} \left| k\_{sky} \right| \dot{\mathbf{x}}\_s \Big|^2, \dot{\mathbf{x}}\_s \Big( \dot{\mathbf{x}}\_s - \dot{\mathbf{x}}\_\mu \Big) \ge 0 \\ \mathbf{0}, \dot{\mathbf{x}}\_s \Big( \dot{\mathbf{x}}\_s - \dot{\mathbf{x}}\_\mu \Big) < 0 \end{cases} \tag{6}$$

where *ksky* is the ceiling control coefficient.

### *2.2. Design of Regenerative TPMLM*

Moving-coil type TPMLM is selected in this paper. Compared with the same size moving-magnetic one, it has a higher energy density, the smaller mass of moving magnetic parts, and higher electromechanical conversion efficiency. The structure diagram is shown in Figure 2, which is divided into I-V according to the material medium. The five areas are core area, winding area, air gap area, permanent magnet area, and back iron area. The magnetic tile adopts the Halbach magnetization arrangement method. This method has the highest average magnetic field energy density. The axial magnetic field distribution accounts for a high proportion of the fundamental wave component, thus reducing the electromagnetic conversion output harmonic content [12].

The regenerative suspension mainly uses TPMLM to recover electric energy. The power can be stored or used directly after conversion. The side effect can be ignored in the analysis. The principle and equation of the rotating motor are directly applied to calculate and design the linear motor and perform park transformation. Turn the motor model from *a* − *b* − *c* stationary coordinate system to a rotating *d* − *q* − *o* coordinate system.

**Figure 2.** Structure of moving-coil tubular permanent magnet linear motor (TPMLM).

In *d* − *q* coordinate system, the induced electromotive force is as follows.

$$\begin{aligned} \mu\_{\rm sd} &= \frac{d\psi\_{\rm sd}}{\frac{d\mathbf{t}}{dt}} - \omega\psi\_{\rm sq} + R\_{\rm s}i\_{\rm sd} \\ \mu\_{\rm sq} &= \frac{d\psi\_{\rm sq}}{dt} + \omega\psi\_{\rm sd} - R\_{\rm s}i\_{\rm sq} \end{aligned} \tag{7}$$

where *usd* and *usq* are the components of stator *d* and *q* coordinate axis. *isd* and *isq* are the *d* and *q* coordinate axis components of stator current. *Rs* is stator resistance. ψ*sd* and ψ*sq* are stator flux linkage.

The flux linkage equation in the *d* − *q* coordinate system is as follows.

$$\begin{aligned} \psi\_{sd} &= \mathcal{L}\_s \mathcal{i}\_{sd} + \psi\_f \\ \psi\_{sq} &= \mathcal{L}\_s \mathcal{i}\_{sq} \end{aligned} \tag{8}$$

where *Ls* is the stator inductance, ψ*f* is the flux linkage of the permanent magnet poles.

The motion equation of the mover is as follows.

$$m\_d \frac{d\_v}{d\_t} = F\_p - F\_{\text{gen}} - B \cdot v \tag{9}$$

where *md* is the mass of the mover. *Fgen* is the electromagnetic force on the mover. *Fp* is the suspension pressure of the vehicle on the mover, and *B* is the mechanical damping coefficient.

The expression of *Fgen* is as follows.

$$F\_{\rm gen} = \frac{\Im \pi}{2\pi} p(\psi\_{\rm sd} i\_{\rm sq} - \psi\_{\rm sq} i\_{\rm sd}) = \frac{\Im \pi}{2\pi} p \psi\_f i\_{\rm sq} \tag{10}$$

where *p* is the number of pole pairs.

### **3. Establishment of a Joint Simulation Platform**

The TPMLM finite element model is established in Ansys/Maxwell, and the vehicle MR semi-active suspension system dynamics model is established in Matlab/Simulink to build the joint operation on the Simplorer platform. Figure 3 is the schematic diagram of the simulation platform.

In Maxwell 2D simulation, the solving domain boundary conditions are set as balloon boundary. The left boundary of the iron core and the right boundary of back iron are set as vector potential boundaries. A winding is set, and six coils are added to it. The moving type in motion setup is set to the positive z-axis direction. The simulation time is from 0 to 1 s, and the time step size is 1 ms. The permanent magnet material uses NdFeB30.

out based on the data obtained by the joint simulation.

*Vehicles* **2020**, *2*, FOR PEER REVIEW 5

**Figure 3.** Schematic diagram of the MR regenerative suspension system simulation platform. (**a**) A finite element simulation model, (**b**) Suspension dynamics simulation model, (**c**) Joint simulation model.

By running the MR suspension dynamic model in Matlab/Simulink under different road conditions *xi* , a displacement *xposition* is obtained, which is the output of the position interface in Figure 3c. Meanwhile, *xposition* is input to excite the finite element model of the TPMLM through the Simplorer (here named S\_TRB1) module. Then, the joint simulation is implanted. After that, the comprehensive performance analysis of the vehicle MR regenerative suspension system is carried out based on the data obtained by the joint simulation.

The TPMLM structure parameters used in the simulation are shown in Table 1. *R*0,*RI* ,*RII*, *RIII*, *RIV*, *RV* are the radius of the cross-sectional circle of each area of the motor model from the inside to the outside. µ*rI*, µ*rII*, µ*rIII*, µ*rIV*, µ*rV* are the relative permeability of the material in area I-V, and τ*p* is the permanent magnet pole pitch. *Brem* is the permanent magnet remanence. *mN* is the number of winding slots. *Nw* is the number of winding turns. *Kc* is the winding full-slot ratio. *Rdc* is the winding direct current resistance. ρ*c* is the winding wire conductivity. *Sw* is the winding single-slot cut area. MRD is the actual identification parameter; *k*0 = 185.954, *k*1 = 2750.7, *k*2 = 9.991, *a*0 = 7.601, *I*0 = 0.0683, α = 19970, β = 179900, γ = 8901.5, *c*0 = 1367.4, *c*1 = 6204.1, *n* = 2, *A* = 24.518, *x*0 = −0.004.

**Table 1.** Data parameters of 1/4 magnetorheological (MR) regenerative suspension [13].

### **4. Comprehensive Performance Analysis of Regenerative Suspension**

### *4.1. Suspension Performance*

Firstly, the frequency response of the MR regenerative suspension system is analyzed. For nonlinear systems, constant amplitude harmonic excitation will cause a large acceleration excitation signal at high frequencies and saturation of suspension components. Therefore, the segmented harmonic excitation signal shown in Equation (11) is used to meet the requirement of limiting the amplitude of the displacement harmonic signal at high frequencies.

$$\begin{aligned} a\_m \sin(2\pi ft) \; f &\le f\_T \\ a\_m \left(\frac{f\pi}{f}\right) \sin(2\pi ft) \; f &> f\_T \end{aligned} \tag{11}$$

where *am* is the single-frequency harmonic amplitude. *fT* is the turning frequency. The natural frequency band of the car body and wheels is covered, setting *am* = 2 cm, *fT* = 2.1 Hz.

Using the system frequency domain response about sprung mass acceleration transmission rate *T*as, unsprung mass acceleration transmission rate *T*au, suspension dynamic travel transmission rate *T*dr, and tire's dynamic load coefficient (DLC), the overall suspension performance of vehicle suspension ride comfort and operational stability is evaluated, including resonance suppression, vibration isolation, suspension travel limit, and tire grip [11]. It can be seen from Figure 4 that the first resonance point of *T*as is 1.5 Hz, which meets the requirements of passenger car stability. *T*au is slightly distorted due to simulation reasons. Both *T*dr and DLC show that the TPMLM does not significantly change the handling performance of MR suspension.

**Figure 4.** The frequency response of MR regenerative suspension. (**a**) Transmission rate of the sprung mass acceleration, (**b**) Transmission rate of the unsprung mass acceleration, (**c**) Transmission rate of the suspension dynamic travel, (**d**) Dynamic load coefficient of the tire.

*Vehicles* **2020**, *2*

Vehicles often encounter various impact roads during driving, which is a short time and high intensity. The smooth pulse signal excitation shown in Equation (12) is used [14].

$$\alpha\_l = 0.25 a\_m e^2 (\mu \omega\_0 t)^2 e^{-\mu \omega\_0 t}; \mu = 1, 2, 3 \tag{12}$$

In the equation, *am* is the amplitude of the smooth pulse signal, ω0 is the fundamental frequency, and µ is the pulse stiffness coefficient. A larger µ value will cause the excitation to produce larger shock and acceleration signals.

Figure 5 shows the time-domain transient response of *as* , *au*, *xr* , and *Ft* under smooth pulse excitation. The stabilization time of each response adjustment of the system is within 1 s. Due to the addition of TPMLM, small-scale oscillations appear in the initial stage of impulsive excitation, especially the sprung mass acceleration *as* , but the response amplitude does not increase significantly.

**Figure 5.** Dynamic characteristics under smooth pulse excitation. (**a**) Sprung mass acceleration under smooth pulse, (**b**) Free spring-mass acceleration under smooth pulse, (**c**) Suspension dynamic travel under smooth pulse, (**d**) Tire dynamic force under smooth pulse.

The random road is established based on the filtered white noise method, which is used to simulate the wheel excitation input when the vehicle is running on the actual road and gives a general analysis of the performance of the suspension system. The differential equation of road roughness is

*Vehicles* **2020**, *2*

$$
\dot{q}(t) + 2\pi n\_{00} uq(t) = 2\pi n\_0 \sqrt{\mathcal{G}\_q(n\_0)\mu \mathcal{W}(t)}\tag{13}
$$

where *q*(*t*) is the function of road roughness. *W*(*t*) is the Gaussian white noise signal with power spectral density (PSD) of 1. *n*00 is the cutoff frequency of the road spatial frequency, *n*00 = 0.011 m−1 , *n*0 is the reference spatial frequency of the road. *n*0 = 0.1 m−1 . *Gq*(*n*0) is the PSD of the road under the reference spatial frequency *n*0, related to pavement classification and speed *u* in steady-state. This experiment selects *u* = 20 m/s, *Gq*(*n*0) = 64 × 10−6 m3 .

Figure 6 shows *au*, *xr* , and *Ft* under random road excitation. It can be seen that the first resonance point of the MR regenerative suspension system is 1.5 Hz, and the second resonance point is about 9.5 Hz, which is consistent with the transmission rate under the above variable amplitude harmonic excitation. It is also indicated that the addition of TPMLM does not significantly change the system stability.

**Figure 6.** Power spectral density (PSD) under random road excitation. (**a**) PSD of the sprung mass acceleration, (**b**) PSD of the unsprung mass acceleration, (**c**) PSD of the suspension dynamic stroke, (**d**) PSD of the tire dynamic force.

### *4.2. Regenerative Characteristics*

Under the single-frequency harmonic road excitation in Equation (14), above smooth road excitation, and random road excitation, the output regeneration characteristics are observed. The average output power *Pm* and the effective power value *P* are employed as the evaluation indicators, as shown in Equations (15) and (16).

$$\mathbf{x}\_i = a\_m \sin(2\pi ft) \tag{14}$$

where *am* is excitation amplitude, *f* is frequency. The typical frequencies observed here are 1.5 Hz near the resonant frequency of the sprung mass, 6 Hz at the intermediate frequency, and 15 Hz near the resonant frequency of the unsprung mass.

The average output power of the regenerative motor

$$\overline{P}\_m = \frac{1}{T} \int\_0^T u(t)i(t)dt\tag{15}$$

Power effective value

$$P = \sqrt[2]{\frac{\sum\_{0}^{T} P\_{m} ^{2}}{T}} \tag{16}$$

The instantaneous output power is shown in Figures 7–9. Table 2 lists the corresponding average output power and power effective value. It can be seen that the effective value of the output power at 1.5 Hz under harmonic excitation reaches about 500 W. As the frequency is increased, the regenerated power is greatly increased. On the impact road, the regenerative time is very short, but the effective value of output power is also about 50 W. On a general road, the recovered power is only 1.5 W on a flat A-class road. With the increase of road unevenness, the output power increases observably, which reaches about 46 W on a C-class road. The above results show that under the excitation of typical frequency harmonics, the MR regenerative suspension has a considerable performance of power regeneration.

**Figure 7.** *Cont.*

**Figure 7.** The instantaneous output power of regenerative motor under sinusoidal excitation. (**a**) Output power at 1.5 Hz, (**b**) Output power at 6 Hz, (**c**) Output power at 10 Hz.

**Figure 8.** The instantaneous output power of regenerative motor under a smooth pulse.

**Figure 9.** *Cont.*

**Figure 9.** The instantaneous output power of regenerative motor under the random road. (**a**) Output power under A-class road, (**b**) Output power under B-class road, (**c**) Output power under C-class road.

**Table 2.** The average and effective output power of the regenerative motor.

### **5. Conclusions**

(1) For the MR regenerative suspension system in parallel with TPMLM, a stability analysis method based on the comprehensive suspension performance under different road excitation is proposed, especially observing whether the resonance point shifts after installing TPMLM;

(2) Dynamic model of the MR suspension system and a finite element model of TPMLM are established, respectively. Matlab/Simulink and Ansys software are used for joint simulation to obtain the comprehensive suspension performance and regenerative characteristics under the road excitation of harmonic, impact, and random pavement.

(3) The simulation results show that the MR regenerative suspension system with improved skyhook control meets the requirements of the natural resonance frequency of the vehicle suspension and effectively improves the driving comfort. At the same time, it has considerable regeneration power.

**Author Contributions:** Conceptualization, J.H. and H.Z.; methodology, J.H. and E.W.; software, J.H.; formal analysis, J.H. and H.Z.; writing—original draft preparation, J.H.; writing—review and editing, E.W. and H.Z.; All authors have read and agreed to the published version of the manuscript.

**Funding:** This research received no external funding.

**Conflicts of Interest:** The authors declare no conflict of interest.

### **References**

**Publisher's Note:** MDPI stays neutral with regard to jurisdictional claims in published maps and institutional affiliations.

© 2020 by the authors. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (http://creativecommons.org/licenses/by/4.0/).